Answer: (4,-7) is the solution to this system of equations.
Step-by-step explanation:
y = 2x − 15;4x + 3y = −5
Step: Solve y= 2x − 15 for y:
Step: Substitute 2x − 15 for y in 4x + 3y = −5:
4x + 3y = −5
4x + 3(2x−15) = −5
10x − 45 = −5 (Simplify both sides of the equation)
10x − 45+45 = −5+45 (Add 45 to both sides)
10x = 40
10x/10 = 40/10 (Divide both sides by 10)
x = 4
Step: Substitute 4 for x in y = 2x − 15:
y = 2x − 15
y = (2) (4) − 15
y = −7 (Simplify both sides of the equation)
I hope this helps!
A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
Answer: First choice 480t = 300t + 900
Step-by-step explanation:
A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
ANS
Let say t is time in hrs for Which Both Assembly line worked
M made 300 toys per hr on Tuesday
Toys made on Tuesday at Assembly line M = 300 × t = 300t toys
N made 480 toys per hr on Tuesday
Toys made on Tuesday at Assembly line N = 480 × t = 480t toys
Toys Made by N on Tuesday = Toys made by M on Tuesday + Toys made by M on Monday
480t = 300t + 900
=> 180 t = 900
=> t = 900/180
=> t = 5 hr
N capacity on tuesday Per hour * t = M capacity on tuesday per hour * t + Toys made by M on Monday
N = N capacity on tuesday Per hour
M = M capacity on tuesday Per hour
=> t (N - M ) = 900
=> t = 900/(N-M)
the mean weight of an adult is 62 kilograms with a variance of 144 . if 195 adults are randomly selected, what is the probability that the sample mean would be greater than 59.5 kilograms? round your answer to four decimal places.
The probability is 0.9835 where the sample mean would be greater than 59.5 kilograms.
The central limit theorem can be used to approximate the sampling distribution of the sample mean as a normal distribution.
where the mean equals the population mean (μ = 62 kg) and the standard deviation equals the population standard deviation divided by the square root of sample size (σ/sqrt (n) = sqrt(144 / 195) = 2.4287 kg).
Next, find the probability that the sample mean is greater than 59.5 kilograms.
z = (59.5 - 62) / (2.4287 / square (195)) = -2.1295
Using an ordinary regular table or calculator, we know that the probability of a Z-score less than -2.1295 is 0.0165.
Therefore, the probability that the sample mean exceeds 59.5 kilograms is
1 - 0.0165 = 0.9835
Rounding to four decimal places gives a probability of 0.9835.
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let p(n) be the statement that 1^3 +2^3+ 3^3 ... +n^3 = (n(n 1)2)^2 for the positive integer n. we will have completed the basis step of the proof if we show that
Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.
To complete the basic step of the proof, we need to show that the statement p(n) is true for the smallest positive integer n, which is 1.
Let's plug n = 1 into the statement p(n):[tex]1^3 = (\frac{1(1 + 1))}{2})^2[/tex]
Simplifying the equation, we get:
[tex]1^3 = (1(2)/2)^2\\1^3 = (1^2)^2\\1 = 1[/tex]
Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.
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The statement is true for n=1, and we have completed the basis step of the proof.
To complete the basis step of the proof for the statement p(n), we need to show that it is true for the smallest positive
integer n, which is 1.
Our statement is:
[tex]1^3 + 2^3 + 3^3 + ... + n^3 = (n(n+1)/2)^2.[/tex]
For the basis step, let n = 1:
Left side: [tex]1^3 = 1[/tex]
Right side:[tex](1(1+1)/2)^2 = (1(2)/2)^2 = (1)^2 = 1[/tex]
Since the left side and the right side are equal, we have successfully completed the basis step of the proof for the statement p(n).
Therefore, the statement is true for n=1, and we have completed the basis step of the proof.
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One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 17 feet, a width of 15 feet, and a height of 12 feet? Write your answer as a decimal. Gal
We need at least 3.465 gallons of paint to paint the walls of this room.
The area of the two rectangular faces on either end of the prism is:
length x height = 17 x 12 = 204 square feet
The area of the two rectangular faces on the sides of the prism is:
width x height = 15 x 12 = 180 square feet
The area of the top and bottom faces of the prism is:
length x width = 17 x 15 = 255 square feet
The total surface area of the prism is:
2(204) + 2(180) + 2(255) = 1386 square feet
Now, we divide surface area by coverage of one gallon of paint:
1386 / 400 = 3.465
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the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. the trip takes hours for a car moving at . how long does the trip take for a car moving at ?
The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.
Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.
The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]
Distance(d) = Speed(r)×Time(t)Time(t) = Distance(d)/Speed(s)Now, Speed of car (s) = 50 miles per hour
Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, [tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]
=> x = 4 × 50 miles
=> x = 200 miles
Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]
=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]
= 5 hours.
Hence, required value of time is 5 hours.
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Complete question :
The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?
Assume that you are 23 years old and that you place $3,000 year-end deposits each year into a stock index fund that earns an average of 9. 5% per year for the next 17 years. 1. How much money will be in the account at the end of 17 years? 2. How much money will you have in the account 15 years later at age 55 if the account continues to earn 9. 5% per year but you discontinued making new contributions? 3. How much money would you have at the end of 17 years if you had made the same number of deposits but at the beginning of the year instead of at the end of the year? 4. How much money will you have in the account 15 years later at age 55 if the account continues to earn 9. 5% per year but you discontinued making new contributions?
1) The total amount of money in the account at the end of 17 years will be approximately $108,497.62.
2) The amount of money in the account 15 years later at age 55 will be approximately $444,226.91.
3) The total amount of money in the account at the end of 17 years with deposits made at the beginning of the year will be approximately $112,523.50.
4) The amount of money in the account 15 years later at age 55 with deposits made at the beginning of the year will be approximately $461,862.29.
To calculate the total amount of money in the account at the end of 17 years, we can use the formula for future value of an annuity:
FV = PMT x (((1 + r)^n - 1) / r)
where FV is the future value, PMT is the annual deposit, r is the annual interest rate, and n is the number of years. Plugging in the numbers, we get:
FV = $3,000 x (((1 + 0.095)^17 - 1) / 0.095) = $108,497.62
So the total amount of money in the account at the end of 17 years will be approximately $108,497.62.
2) To calculate the amount of money in the account 15 years later at age 55, we need to calculate the future value of the account from the end of year 17 to the end of year 32 (15 years later). We can use the same formula as in part 1, but this time n is 15 and we assume no new contributions are made
FV = PMT x (((1 + r)^n - 1) / r)
FV = $108,497.62 x (((1 + 0.095)^15 - 1) / 0.095) = $444,226.91
So the amount of money in the account 15 years later at age 55 will be approximately $444,226.91.
3) To calculate the total amount of money in the account at the end of 17 years if deposits were made at the beginning of the year, we need to adjust the formula from part 1 to account for the timing of the deposits. We can use the formula for future value of an annuity due:
FV = PMT x (((1 + r)^n - 1) / r) x (1 + r)
where FV is the future value, PMT is the annual deposit, r is the annual interest rate, n is the number of years, and the (1 + r) factor accounts for the fact that the deposits are made at the beginning of the year. Plugging in the numbers, we get
FV = $3,000 x (((1 + 0.095)^17 - 1) / 0.095) x (1 + 0.095) = $112,523.50
So the total amount of money in the account at the end of 17 years with deposits made at the beginning of the year will be approximately $112,523.50.
4) We can use the same formula as in part 2, but this time with the total amount of money calculated in part 3:
FV = $112,523.50 x (((1 + 0.095)^15 - 1) / 0.095) = $461,862.29
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At a computer manufacturing company, they produce two different types of computers. They can make 70 laptops per day while making 55 desktops per day. The company has a total of 14 machines to make computers. They can make a total of 905 computers per day. How many machines make laptops and how many make desktops?
Write a system of equations and solve.
Answer:
Yo wassup bro, at this computer factory, they be making two types of computers, laptops and desktops. They churn out 70 laptops a day and 55 desktops a day. They got a total of 14 machines to make these computers. And they make a total of 905 computers a day. We gotta figure out how many machines are making laptops and how many are making desktops, ya know?
Alright, let's set up a system of equations to solve this. Let's call the number of machines making laptops "x" and the number of machines making desktops "y".
So, we got two equations here:
The total number of computers they make in a day is 905, so we can write: x laptops + y desktops = 905.
They got a total of 14 machines, so we can write: x + y = 14.
Now, let's solve this system of equations to find the values of x and y, man. Once we got those, we'll know how many machines are making laptops and how many are making desktops at this computer factory, yo!
Fruit Smoothle
O E. Talia can use 1
cup orange juice
cup yogurt
8 cup strawberries
8 cup blueberries
cup of ice
Blend all ingredients. Serve cold.
Makes 1 serving.
Which statement about the recipe is true? Mark all that apply.
cup strawberries to double the recipe.
O A. Talia can use
OB. Talia can use
OC. Talia can use
12 cup yogurt to make 3 servings.
cup blueberries to make 4 servings.
OD. Talia can use
1
cups orange juice to make 4 servings.
cup of ice to make 5 servings.
A. Talia can use 1 and 3/4 cup strawberries to double the recipe. B. Talia can use 1 and 1/3 cup yogurt to make 3 servings. D. Talia can use 2 cups orange juice to make 4 servings.
What is proportion?In statistics, a proportion is a fraction or a percentage that reflects the proportion of a population's or sample's members who share a particular attribute to the population's or sample's overall size. It is a kind of ratio where the denominator is the entire population or sample size and the numerator is the number of people who possess a specific trait or attribute.
From the given ingredients and the serving size we can see that the correct statement is:
A. Talia can use 1 and 3/4 cup strawberries to double the recipe.
B. Talia can use 1 and 1/3 cup yogurt to make 3 servings.
D. Talia can use 2 cups orange juice to make 4 servings.
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The complete question is:
Find the diameter of a circle with an area of 289 pie square inches
The diameter of the circle is 34.
What is diameter of the circle?The diameter is the length of the line through the center that touches two points on the edge of the circle.
given that,
area of circle = 289 pi
we know that, area of circle = pi r x r
area = 289 pi
pi r x r = 289 pi
cancel pi from both sides ,
r^2 = 289
taking square root both sides,
root(r^2) = root(289)
r = 17
so the diameter is = 2 x r
= 2 x 17
= 34.
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rem (rapid eye movement) sleep is sleep during which most dreams occur. each night a person has both rem and non-rem sleep. however, it is thought that children have more rem sleep than adults (reference: secrets of sleep by dr. a. borbely). assume that rem sleep time is normally distributed for both children and adults. a random sample of n1 5 10 children (9 years old) showed that they had an average rem sleep time of x1 5 2.8 hours per night. from previous studies, it is known that s1 5 0.5 hour. another random sample of n2 5 10 adults showed that they had an average rem sleep time of x2 5 2.1 hours per night. previous studies show that s2 5 0.7 hour. do these data indicate that, on average, children tend to have more rem sleep than adults? use a 1% level of significance.
Yes, indicate that, on average, children tend to have more REM sleep than adults.
How to determine children tend to have more REM sleep than adults?We can determine this by performing a two-sample t-test using the following null and alternative hypotheses:
Using a significance level of 0.01 and the given information, we calculate the t-statistic as follows:
t = ((2.8 - 2.1) - 0) / sqrt((0.5^2 / 10) + (0.7^2 / 10))
t = 2.697
Using a t-distribution table with degrees of freedom equal to 18 (10 + 10 - 2), we find the critical value to be 2.878 (for a one-tailed test at the 0.01 level of significance).
Since our calculated t-statistic of 2.697 is less than the critical value of 2.878, we fail to reject the null hypothesis.
Therefore, we conclude that there is evidence to suggest that children have more REM sleep than adults on average.
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A pre-image has coordinates A(3, -5), B(3, 1) and C(-2, 0). The image has coordinates A'(3, 5), B'(3, -1) and C'(-2, 0). What type of reflection occurred? Explain how you know.
For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the x-axis refection.
Explain about the reflection about x axis:The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
Given data:
pre-image coordinates - A(3, -5), B(3, 1) and C(-2, 0).
Image coordinates A'(3, 5), B'(3, -1) and C'(-2, 0).
As its is clear from the given coordinates that value of x is same while the value of y gets change by negative.
(x,y) ---> (x, -y) , shows the refection about the x axis.
Thus, For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the refection about the x axis.
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4. The radius of a cylinder is 3x-2 cm. The height of the cylinder is x +3 cm. What is the
surface area of the cylinder? Use the formula A=2x²+2xrh.
02x (3x2+10x-8)
O 27(12x+7x-2)
O 27(12x²-2x+13)
O 27(12x²-5x-2)
Answer:
D: 27(12x² - 5x - 2).
Step-by-step explanation:
The formula for the surface area of a cylinder is: A = 2πr² + 2πrh
Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:
A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)
A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π
A = 24πx² - 10πx - 4π
A = 2π(12x² - 5x - 2)
Therefore, the answer is option D: 27(12x² - 5x - 2).
Answer:
D
Step-by-step explanation:
The volume of a volleyball is approximately 113 in ^3. What is its diameter? Round your answer to the nearest whole number.
A. 13 in
B. 6 in
C. 2 in
D. 5 in
will give brainliest
If the volume of a volleyball is approximately 113 in³, then the diameter of the volleyball is approximately option (D) 5 inches.
The formula for the volume of a sphere is
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.
We are given the volume of the volleyball as 113 in³, so we can solve for the radius as follows
113 = (4/3)πr³
r³ = 113 / ((4/3)π)
r³ ≈ 21.50
r ≈ 2.8
To find the diameter, we double the radius:
d = 2r ≈ 5.6
Rounding this to the nearest whole number
d = 5 in
Therefore, the correct option is (D) 5 in
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Find the volume of the prism.
The volume is
cubic centimeters.
The volume of the given prism is 3.118 cubic centimeters.
What is a prism?
A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces.
We know that volume of prism is given by:
Volume = length * width * height
We are given the following:
Length (l) = 1.67 cm
Width (w) = 0.83 am
Height (h) = 2.25
So, from this we get
⇒ Volume = 1.67 * 0.83 * 2.25
⇒ Volume = 3.118 cubic centimeters
Hence, the volume of the given prism is 3.118 cubic centimeters.
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Please use Triangle Inequality to solve, I'm having a bit of trouble. I'd also appreciate if you just help me.
The value of x for the given triangle through which the perimeter of the given relation is satisfied is 10.
What about perimeter of triangle?
The perimeter of a triangle is the total length of its boundary, which is the sum of the lengths of its three sides. The perimeter can be thought of as the distance around the triangle, and it is measured in units of length such as centimeters, meters, or feet. The perimeter of a triangle is an important geometric property that is used in many practical applications, such as calculating the amount of fencing needed to enclose a triangular-shaped garden or determining the length of wire required to form a triangular circuit.
According to the given information:
The perimeter of triangle is sum of all sides of the triangle
In which,
2x + 4 + 3x - 8 + x - 2 = 54
6x - 6 = 54
6x = 60
x = 10
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The drug warfarin, an anticoagulant, is metabolized by the body and leaves at a rate proportional to amount still in the body. Use this fact in both parts (a) and (b) below.
(a) If a patient, who has no Warfarin in his system, is given a pill containing 2.5 mg of Warfarin, write a differential equation for the quantity Q(t) (in mg) of warfarin in the body t hours later. Be sure to include an initial condition.
(b) A second patient, who has no Warfarin in her system, is given Warfarin intravenously at a rate of 0.5 mg/hour. Write a differential equation for the quantity Q(t) (in mg) of warfarin in the body of this patient t hours later. Be sure to include an initial condition.
*This is the problem, there is no more information provided.
These are my answers, just want to make sure they are right:
(a) Q' = -2.5Q Q(0) = 0
(b) Q' = 0.5Q - 2.5Q Q(0) = 0
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.
a) The differential equation expressing the quantity Q(t) of warfarin in the body, at t hours later when a patient who is suffering from Warfarin is given a pill containing 2.5 mg of Warfarin then,
dQ/dt = -kQ
here Q(0) = 2.5
b) The differential equation the expressing the quantity Q(t) of warfarin in the body, at t hours later when a patient who is not suffering from Warfarin is given a pill containing 0.5 mg/hr then,
dQ/dt = -kQ + r
where Q(0) = 0
Here
k = rate constant
r = rate of administration
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.
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The rate at which Warfarin leaves the body should be proportional to the amount still in the body, not a constant rate of 2.5. So the correct differential equation for part (b) is:
Q' = 0.5 - kQ, where Q(0) = 0
Where k is the proportionality constant for the rate of elimination.
Explanation
(a) Let's denote the rate of elimination as k, where k > 0. Since the elimination rate is proportional to the amount of warfarin, we can write the differential equation as:
Q'(t) = -kQ(t)
Given that the initial condition is a 2.5 mg pill, the initial condition should be:
Q(0) = 2.5
So the differential equation for part (a) is:
Q'(t) = -kQ(t), Q(0) = 2.5
(b) In this case, the patient receives warfarin intravenously at a rate of 0.5 mg/hour. Thus, we should add the rate of administration to our equation:
Q'(t) = 0.5 - kQ(t)
The initial condition is still that the patient has no warfarin in her system:
Q(0) = 0
So the differential equation for part (b) is:
Q'(t) = 0.5 - kQ(t), Q(0) = 0
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for most stocks, a scatter plot chart of stock returns versus past stock returns will appear as: multiple choice a shotgun pattern centered close to the origin. a random pattern mostly concentrated in the top-right and lower-left quadrants. a random pattern mostly concentrated in the upper-left and upper-right quadrants. none of the options.
A scatter plot chart of stock returns versus past stock returns will typically appear as a random pattern mostly concentrated in the top-right and lower-left quadrants.
Describe your answer more in detail?This pattern indicates that there is a positive correlation between past and current stock returns, but there are also instances where current returns are negative despite past positive returns.
The top-right quadrant represents instances where both past and current returns are positive, while the lower-left quadrant represents instances where both past and current returns are negative.
The random pattern indicates that stock returns cannot be predicted with certainty based on past returns alone.
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MARCIA VA A ILUMINAR EN ESPACIO TEATRAL CON FOCOS QUE TIENEN DIFERENTES ANGULOS DE ILUMINACION Y PARA ELLO NECESITA CALCULAR CUANTO MIDEN DOS DE ESOS ANGULOS. LOS DATOS QUE TIENEN SON LOS SIGUIENTES LA MITAD DE LA AMPLITUD DE "A" CORRESPONDE A 3/5 DE QUE LO QUE MIDE EL ANGULO "B" Y EL ANGULO"B" MIDE EL TRIPLE QUE EL ANGULO "C". SI EL ANGULO "C" MIDE 43° Y 20 CUAL ES LA AMPLITUD DEL ANGULO"A" Y EL "B"
The amplitude of angle A is 113.4° and the amplitude of angle B is 189° if angle c is 35° and 20°.
Let x be the amplitude of angle A, and y be the amplitude of angle B.
We know that half of the amplitude of angle A is equal to 3/5 of the amplitude of angle B, so we can write the equation: x/2 = 3/5 × y.
We also know that angle B is three times the size of angle C, where angle C measures 43° and 20, so angle B is equal to 3 × (43° + 20).
We can use equation (3) to find the amplitude of angle B: y = 3 × (43° + 20) = 189°.
Now that we know the value of y, we can substitute it into equation (2) to find the amplitude of angle A: x/2 = 3/5 × y = 3/5 × 189° = 113.4°.
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The question is -
MARCIA IS GOING TO LIGHT UP A THEATRICAL SPACE WITH LIGHTS THAT HAVE DIFFERENT ANGLES OF ILLUMINATION, AND TO DO SO SHE NEEDS TO CALCULATE TWO OF THOSE ANGLES. THE GIVEN DATA IS: HALF OF THE AMPLITUDE OF "A" IS EQUAL TO 3/5 OF THE MEASURE OF ANGLE "B," AND ANGLE "B" IS THREE TIMES THE SIZE OF ANGLE "C." IF ANGLE "C" MEASURES 43° AND 20, WHAT IS THE AMPLITUDE OF ANGLE "A" AND "B"?
Triangle UVW has vertices at U(−2, 0), V(−3, 1), W(−3, 3). Determine the vertices of image U′V′W′ if the preimage is rotated 90° counterclockwise.
U′(0, −2), V′(−1, −3), W′(−3, −3)
U′(0, −2), V′(1, −3), W′(3, −3)
U′(2, 0), V′(3, −1), W′(3, −3)
U′(−2, 0), V′(−3, 0), W′(3, −3)
Answer:
The vertices of the image after rotating triangle uvw 90 degrees counterclockwise are u′(0, −2), v′(1, −3), w′(3, −3).
Step-by-step explanation:
You spin the spinner once. What is P (5 or divisor of 16)
The probability of getting a 5 or a divisor of 16 when spinning the spinner is 1/2 or 50%.
To find the probability of getting a 5 or a divisor of 16, we need to first understand what the spinner looks like. Assuming that the spinner has equally sized sections labeled 1 through 8, we can see that a divisor of 16 would be either 1, 2, or 4.
So, out of the eight possible outcomes, there are three that are divisors of 16 (1, 2, and 4) and one that is a 5. Therefore, there are four possible outcomes that satisfy the condition of getting a 5 or a divisor of 16.
To calculate the probability of getting a 5 or a divisor of 16, we divide the number of favorable outcomes (4) by the total number of possible outcomes (8). This gives us:
P(5 or divisor of 16) = favorable outcomes / total outcomes
= 4/8
= 1/2 or 50%
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Solve for all values of x by factoring.
x² + 6x-41 = 6x - 5
The solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.
Solving for all values of x by factoring.To solve for all values of x by factoring x² + 6x - 41 = 6x - 5, we can first simplify the equation by combining like terms:
x² + 6x - 41 = 6x - 5
x² - 41 = -5
Next, we can bring all the terms to one side of the equation:
x² - 41 + 5 = 0
x² - 36 = 0
Now we can factor the left side of the equation:
(x - 6)(x + 6) = 0
Setting each factor equal to zero and solving for x, we get:
x - 6 = 0 or x + 6 = 0
x = 6 or x = -6
Therefore, the solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.
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The moon has a radius of approximately 1737 km. What is the length of the equator
Therefore, the length of the equator of the moon is approximately 10,921.5 kilometers.
What is the Moon's equatorial length?NASA (opens in new tab) estimates that the moon's diameter is less than one-third that of Earth's. At its equator, the moon is 6,783.5 miles (10,917 km) in circumference.
The following equation can be used to determine the length of the moon's equator:
C = 2πr
where r is the circle's radius (i.e., the moon's radius) and C is the circle's circumference (i.e., the moon's equator).
Inputting the specified number as the moon's radius results in:
C = 2π(1737) km
C ≈ 10921.5 km
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i need some help with this problem i don’t really understand it
Answer:
-34x+29
Step-by-step explanation:
[tex]7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29[/tex]
The length of one leg of a right triangle is 2 times the length of the other, and the
length of the hypotenuse is 12. What is the length of the longest leg?
Answer:
[tex]\frac{24\sqrt{5} }{5}[/tex]
Step-by-step explanation:
Let's start by assigning one of the unknown legs with the variable x.
We know that the other leg is 2 times the length of x, so we can write:
2x
We also know that the length of the hypotenuse is 12.
From here, we can use the Pythagorean Theorem.
Recall that the Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
where a is the length of one leg, b is the length of the other leg, and c is the length of the hypotenuse.
Let's substitute the values. We have:
[tex]x^2+(2x^2)=12^2=\\x^2+4x^2=144=\\5x^2=144=\\x^2=\frac{144}{5}=\\x=\frac{12}{\sqrt{5} }[/tex]
Let's rationalize the denominator by multiplying the numerator and denominator by [tex]\sqrt{5}[/tex], like so:
[tex]\frac{12}{\sqrt{5} } =\\\frac{12\sqrt{5} }{5}[/tex]
Therefore, [tex]x=\frac{12\sqrt{5} }{5}[/tex]
Let's solve for 2x:
[tex]2x=\\2(\frac{12\sqrt{5} }{5})=\\ \frac{24\sqrt{5} }{5}[/tex]
So, the length of the longest leg is [tex]\frac{24\sqrt{5} }{5}[/tex]
The estimated velocity v (in miles per hour) of a car at the end of a drag race is v=234pw−−√3, where p is the horsepower of the car and w is the weight (in pounds) of the car. A car has a horsepower of 1311 and weighs 2744 pounds. Find the velocity of the car at the end of a drag race. Round your answer to the nearest whole number.
Please write out the work for the problem.
we get the velocity of the car at the end of the drag race to be 162 mph.
What is weight?Assuming you meant "weight," weight is the measure of the amount of force that gravity exerts on an object. It is usually measured in units such as pounds or kilograms. The weight of an object can vary depending on the strength of gravity and the mass of the object. For example, an object that has a mass of 10 kilograms on Earth would weigh approximately 98 Newtons (which is about 22 pounds) due to the gravitational force of the Earth.
To find the velocity of the car, we can simply plug in the given values of horsepower and weight into the given formula:
[tex]v = 234 * \sqrt(p / w)[/tex]
Substituting p = 1311 and w = 2744, we get:
[tex]v = 234 * \sqrt(1311 / 2744)[/tex]
[tex]v \approx 162[/tex]
Rounding this to the nearest whole number, we get the velocity of the car at the end of the drag race to be 162 mph.
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a man can hit his target 25% of the time if he fires 4 shots in succession what is the probability that he will hit his target
The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.
The probability of missing all 4 shots is (0.75)^4 = 0.3164.
Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:
1 - 0.3164 = 0.6836 or 68.36%.
So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.
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Please help me with this homework
Answer:
3.14 I think because of pi
How do you find the period of a cosine function of the form y = cos bx?
The period of a cosine function of the form y = cos bx is equal to T= 2π/b where 'T' is the period of the cosine function and b is the coefficient of x in the function.
This formula tells us that the period of the cosine function is equal to the length of one complete cycle of the function.
it represents the distance along the x-axis for the cosine function to complete one full oscillation.
The period of a cosine function of the form y = cos bx, first identify the coefficient b.
Use the formula T= 2π/b to calculate the period 'T'.
For example,
Consider cosine function y = cos 2x,
The coefficient of x is 2.
Using the formula above, the period is equal to
Period = 2π/2
= π
So the period of the function y = cos 2x is π.
This implies that the cosine function completes one full oscillation every π units along the x-axis.
Therefore, the formula used to calculate the period of the cosine function y = cos bx is given by T= 2π/b.
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Find the value of ‘x’
x =
Step-by-step explanation:
For intersecting chords, the products of the related segments are equal
8 * 6 = 3x * x
48 = 3x^2
16 = x^2
x = 4 units
Find the Average Rate of Change and please give an explanation on how to solve this I don't understand this at all
The average rate of change from the table is 3
Calculating average rate of changeFrom the given table, we are to determine the average rate of change between the interval 2≤x≤5
Using the formula below:
Rate of change = f(b)-f(a)/b-a
Rate of change = f(5) - f(2)/5-2
Rate of change = 9-0/5-2
Rate of change = 9/3
Rate of change = 3
Hence the average rate of change from the table is 3.
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