Answer:
x + y = 11
2x - y = 19
--------------
3x = 30
x = 10, so y = 1
I NEED HELP ON THIS ASAP!! PLEASE IT'S DUE TODAY!
The exponential function to represent the number of new participants of the challenge as a function of the day number, is f(x) = 12 × 4ˣ.
How to find the exponential function ?Let f(x) be the number of new participants on day x.
On day 0 (today), Aliyah, Kim, and Reese are the only participants. They each send selfies to 4 friends, so there will be 3 x 4 = 12 new participants on day 1.
From day 1 onwards, each new participant will send selfies to 4 friends. Therefore, the number of new participants will quadruple each day. This gives us an exponential growth function:
f(x) = 12 × 4ˣ
where f(x) represents the number of new participants on day x.
Find out more on exponential functions at https://brainly.com/question/30257335
#SPJ1
Find the number of permutations with of the letters in each word
The trigonometry functions when calculated are sin(A) = 18/34 and cos(A) = 30/34
Calculating the trigonometry functionsFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where we have
Opposite = 18Adjacent = 30Hypotenuse = 34Using the above as a guide, we have the following:
sin(A) = 18/34
cos(A) = 30/34
Hence, the values are sin(A) = 18/34 and cos(A) = 30/34
Read more about right triangles at
https://brainly.com/question/2437195
#SPJ1
Complete the table using the information given.
Using the above information, we can calculate the missing figures in the table and this is shown on the table attached.
What is the table about?For the "Shorts" row: It's given that 42 people were wearing shorts.
Since it's mentioned that twice as many people were wearing closed-toed shoes as open-toed shoes, and 30 people were wearing open-toed shoes, we can deduce that 30 people were also wearing closed-toed shoes.So, the total number of people wearing closed-toed shoes is 30, and the total number of people wearing shorts is also 42, since they are the same group of people.Therefore, the "Close-Toed Shoes" column in the "Shorts" row is also 42, and the "Total" column is the sum of open-toed and closed-toed shoes, which is 84.
To know more about table here:
https://brainly.com/question/12151322
#SPJ1
See text below
30 people surveyed were wearing open-toed shoes.
1/3 of the people with open-toed shoes were wearing
pants.
• 42 people were wearing shorts.
Twice as many people were wearing closed-toed shoes
than open-toed shoes.
Complete the table using the information given.
Open-Toed Shoes Close-Toed Shoes Total
Shorts ------- ------ --------
Pants ------ ---------- ------
Total ------ ---------- ---------
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.
learn more about the central limit theorem
brainly.com/question/18403552
#SPJ4
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.
learn more about period here
brainly.com/question/3649898
#SPJ4
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)
2㏒_[6](2)+3㏒_[6](3)+㏒_[6](12)
Answer: 4
Step-by-step explanation:
Given:
[tex]2log_62+3log_63+log_612[/tex]
Rewrite using the power property:
[tex]log_62^2+log_63^3+log_612[/tex]
Rewrite by adding the logarithms together (multiplying) since they all have a common base of 6:
[tex]log_6(2^2*3^3*12)[/tex]
Simplify by multiplying:
[tex]log_6(4*27*12)[/tex]
[tex]log_6(1,296)[/tex]
Evaluate the logarithm:
[tex]log_6(1,296)[/tex]
4
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
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
Timmy is building a model of a building in his town that is 180 meters. He is using a scale of 1.5 cm. = 3.5 meters. How tall will his model be?
Answer: 77
Step-by-step explanation: You could set up a proportion for this question. 1.5 centimeters = 3.5 meters x centimeters = 180 meters 1.5 x 180 / 3.5 Rounded to the nearest whole number, the answer is 77.
the table shows several packages of assorted spools of thread available at a store. what is the price per spool of each kind of thread?
I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.
However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.
To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).
You can use this method to find the price per spool for each type of thread in the table you are looking at.
For more questions like Spool visit the link below:
https://brainly.com/question
#SPJ11
Given a circle has a center at (-6, 14) and a diameter of 30, write the equation of the circle
Answer:
The center of the circle is at (-6, 14), and the radius is 15, so we have this equation:
[tex] {(x + 6)}^{2} + {(y - 14)}^{2} = 225 [/tex]
the ricardo household used w cubic feet of water during a summer month express the number of ccf of water they used algebraically
Ricardo used w/100 Ccf of water.
Given that, Ricardo household used w cubic feet of water in a month of summers,
we need to express the number of ccf of water they used algebraically,
Ccf = A CCF is a unit of measurement of volume.
The CCF is used to measure gas consumption, used in the billing of natural gas and water delivered to households.
1 CCF = 100 cubic feet
CCF means Centum Cubic Feet.
1 cubic feet = 0.01 Ccf
Therefore,
w cubic feet = 0.01 × w Ccf
= w / 100
Hence, Ricardo used w/100 Ccf of water.
Learn more about unit conversion, click;
https://brainly.com/question/19420601
#SPJ1
What is the equation of the line 2x+3y+1=0 after it has been reflected across y=-1 and rotated about o(2,3) by 180
The equation of the line 2x + 3y + 1 = 0 after it has been reflected across y = -1 and rotated about O(2,3) by 180 degrees is -2x + y = 15.
To reflect the line 2x + 3y + 1 = 0 across the line y = -1, we need to subtract twice the y-coordinate of each point on the line from the equation of the line.
This is because the reflection of a point across a line is obtained by reflecting it across the line's perpendicular bisector, which is also the line with the same x-coordinates and twice the distance from the point to the line.
Subtracting twice the y-coordinate, we get:
2x + 3(-2y - 1) + 1 = 0
Simplifying the equation, we get:
2x - 6y - 5 = 0
Now, to rotate the line about the point O(2,3) by 180 degrees, we can use the rotation formula:
x' = 2a - x
y' = 2b - y
where (x,y) are the coordinates of a point on the original line, and (x',y') are the coordinates of the same point after rotation about the point (a,b).
Substituting the coordinates of two points on the line, we get:
(0,-1) → x' = 2(2) - 0 = 4, y' = 2(3) - (-1) = 7
(-1/2,0) → x' = 2(2) - (-1/2) = 4 1/2, y' = 2(3) - 0 = 6
Now, we can use the two points (4,7) and (4 1/2,6) to find the equation of the rotated line using point-slope form:
slope = (6-7) / (4 1/2 - 4) = -2
y - 7 = -2(x - 4)
y = -2x + 15
To learn more about reflection click on,
https://brainly.com/question/29108540
#SPJ4
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%.
Learn more about probability:
https://brainly.com/question/24756209
#SPJ11
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.
Learn more about proportions here:
https://brainly.com/question/29861166
#SPJ1
The complete question is:
A researcher wants to determine whether there is a linear relationship between number of rom-com movies and engagements. The table displays a partial computer printout of the regression analysis and is based on a sample of eight subjects.
Predictor Coeff St. Dev t Ratio p-Value
Constant 4.35744984 2.385747738 5.7382918 0.00375268
Rom-com movies 1.34457321 0.526645738
What is the value of the t-test statistic for H0: β = 0
The value of test statistic is 2.553089.
What is a test statistic?A test statistic is a numerical summary of a sample that is used to make inferences about the population from which the sample was drawn. It is often used in hypothesis testing to determine whether a null hypothesis should be rejected or not.
The test statistic is calculated from the sample data and is compared to a distribution of the test statistic under the null hypothesis. If the test statistic falls in a region of the distribution that is unlikely to occur by chance, then the null hypothesis is rejected in favor of an alternative hypothesis.
Value of test Statistic = 1.34457321/0.526645738
= 2.553089
So, value of test statistic is 2.553089
Learn more about test statistic on
https://brainly.com/question/4621112
#SPJ1
James fills the rectangular prism 80 percent with sand. How many cubic inches of sand are in the rectangular prism.
The volume of sand in the rectangular prism is 80 percent of the total volume, which can be written as:
0.8 x V = 0.8(L x W x H) cubic inches
What is rectangular prism?A three-dimensional object with six faces, including two at the top and bottom and four lateral faces, called a rectangular prism. The prism's faces are all rectangular in shape. There are three sets of identical faces as a result.
We need to know the dimensions of the rectangular prism to solve the problem. Let's assume the dimensions are length = L inches, width = W inches, and height = H inches.
The volume of the rectangular prism is given by V = L x W x H cubic inches.
If the rectangular prism is filled 80 percent with sand, then 20 percent of the volume is empty space. So, the volume of sand in the rectangular prism is 80 percent of the total volume, which can be written as:
0.8 x V = 0.8(L x W x H) cubic inches
Therefore, we need to know the dimensions of the rectangular prism to find the volume of sand.
Learn more about volume of rectangular prism on:
https://brainly.com/question/23717073
#SPJ1
The complete question is:
James fills the rectangular prism 80 percent with sand. How many cubic inches of sand are in the rectangular prism?
A 30 pack of copy paper cost $48.30 a 32 pack cost $49.60 which is the better buy (help me explain it)
Answer:
Step-by-step explanation:
the 32 pack because it costs just slightly more
Frank and Joey ordered a large pizza. Frank ate 20% of rye pizza and Joey at 4/5 of the pizza. What percentage of the pizza did they eat in all
The percentage of the large pizza they ate is 100%
To calculate the percentage of pizza they both ate we have to add and then covert the fractions to percentage.
Given from the question
Frank ate 20% of the large pizza and Joey ate 4/5 portion of the large pizza
Converting 4/5 into percentage
For converting into percentage we have to multiply 100 to the fraction
= 4/5 x 100
= 80%
Now, let us proceed by adding the collected two percentages to find out the total percentage of pizza consumed by Frank and Joey
20% + 80%
= 100%
The percentage of the large pizza they ate is 100%.
To learn more about fractions,
https://brainly.com/question/30154928
#SPJ4
Send total home runs during the baseball season for over five other home runs during the first half of the season what is the fraction of home run hit through and a half of the season as a decimal
Terrell hit 0.8 of his home runs during the first half of the baseball season, which is the decimal equivalent of the fraction (4)/(5).
A fraction is a way of representing a part of a whole, where a whole is divided into equal parts and the fraction represents the number of those equal parts that are being considered.
A decimal number is a number expressed in the base-ten positional system, where each digit can take one of ten possible values and the value of each digit is determined by its position relative to the decimal point.
To write a fraction as a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). In this case, the fraction is (4)/(5), which means Terrell hit 4 out of 5 home runs during the first half of the season
(4)/(5) = 0.8
Learn more about fraction here
brainly.com/question/548650
#SPJ4
The given question is incomplete, the complete question is:
Terrell hit a total of 10 home runs during the baseball season. He hit (4)/(5) of the home runs during the first half of the season. Write the fraction of home runs hit during the first half of the season as a decimal.
4. A fish tank is in the shape of a cuboid. It
has a base of width 80cm and length of 1.2 m.
Water is put into the tank to a depth of 70cm.
There are 700 000 small fish in the tank. Each
one of them needs a litre of water.
Is there enough water for the fish in the tank?
The volume of water in the tank won't be enough for the fish.
What is volume of a cuboid?A cuboid is a solid shape or a three-dimensional shape. The volume of a cuboid is expressed as;
V = l×w× h
where l is the length, w is the width and h is the height.
The volume of water needed by the fish is 700,000× 1litre = 700,000 litres.
The volume of water the tank can occupy is
V = l× b× h
V = 80× 1200× 70
V = 6,720,000cm³
in litres ;
V = 6,720,000/1000
V = 6720litres
therefore the volume water in the tank is not enough for the fish
learn more about volume of cuboid from
https://brainly.com/question/46030
#SPJ1
HELP ME PLEASE!!!!!!!
Answer:
Step-by-step explanation:
Graph # Matching equation
1 |-3x|
2 |-x|
3 -|2x|
You can tell which one matches by finding the slope and whether the V points up or down
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]
a cube has edge length 4 inches. a. find the surface area and volume of the cube. surface area square inches volume cubic inches b. the cube is dilated by a scale factor of 0.25. find the surface area and volume of the image. surface area square inches volume cubic inches
The surface area and volume of a cube with different edge length are
When a cube with edge length 4inches ,
Surface area = 96 square inches and Volume =64 cubic inches.
Cube dilated by scale factor 0.25 ,
Surface area = 6 square inches and Volume =1 cubic inches.
The surface area of a cube is = 6 times the area of one face.
Each face of this cube has an area equals to
= (4 inches) x (4 inches)
= 16 square inches,
So the total surface area is,
Surface area
= 6 x 16 square inches
= 96 square inches
The volume of a cube = length of one edge cubed.
Here, the edge length is 4 inches,
Volume
= (4 inches)^3
= 64 cubic inches
When a cube is dilated by a scale factor of 0.25, all of its edges are multiplied by 0.25.
This implies,
The edge length of the image cube is
0.25 x 4 inches = 1 inch.
Surface area of the image cube = 6 times the area of one face.
Each face of the image cube has an area of
= (1 inch) x (1 inch)
= 1 square inch,
So the total surface area is,
Surface area
= 6 x 1 square inch
= 6 square inches
Volume of the image cube = length of one edge cubed.
Here, the edge length is 1 inch,
Volume
= (1 inch)^3
= 1 cubic inch
Therefore, the surface area and volume for the given dimensions are
For edge length 4inches , Surface area = 96 square inches and Volume =64 cubic inches.
For scale factor 0.25 , Surface area = 6 square inches and Volume =1 cubic inches.
Learn more about volume here
brainly.com/question/30594221
#SPJ4
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.
For more information about Speed, visit:
https://brainly.com/question/30461913
#SPJ4
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?
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:
Ms. Yamato's gross pay is $2644. Her deductions total $548.30.
What percent of her gross pay is take-home pay?
A. 84%
B. 79%
C. 21%
D. 18%
Thus, the correct Percent response is B) 79%.
what is a percent?Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".
If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.
We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:
$2644 - $548.30 = $2095.702.
By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:
($2095.70 / $2644) * 100% = 79%
Thus, the correct response is B) 79%.
To know more about percent visit:
brainly.com/question/28670903
#SPJ1
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
To know more about surface area , here
brainly.com/question/29298005
#SPJ4
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]
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!