For the given system of linear equations, x=2 and y=-6.
System of EquationsA system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
The given equations are:
3x+y=0 (1)
4x+y=2 (2)
First, you should multiply one of equations for -1. For solving this exercise, the equation 1 will be multiplied for -1. Then,
-3x-y=0 (1)
4x+y=2 (2)
Thus, you can apply the addition method because you can eliminate the variable y when you sum the equations 1 and 2. See below.
-3x-y+4x+y=2
x=2
Like x=2 from equation 2, you can find y.
4x+y=2, for x=2 you have
4*2+y=2
8+y=2
y=2-8
y=-6
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red. Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow. Determine the theoretical probability of the spinner not landing on red, P. 0.125 0.250 0.675 0.875
The theoretical probability of the spinner not landing on red is 0.875.
How to determine the theoretical probability of the spinner not landing on redThe total number of sections on the spinner is 8, out of which only one section is red. Therefore, the probability of the spinner landing on red is:
P(Red) = 1/8
The probability of the spinner not landing on red would be the probability of landing on any other section, which is:
P(Not Red) = 1 - P(Red) = 1 - 1/8 = 7/8
Therefore, the theoretical probability of the spinner not landing on red is 7/8 or 0.875 in decimal form.
So, the correct answer is: 0.875.
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Answer:
D
Step-by-step explanation:
Which statement is true? Please help
The statement that is equivalent to each other would be =
2×(4+2)-6 = 14÷(3.5×2)+4. That is option A.
What is equivalent equations?An equivalent equation is the type of equation that appears different but has the same answer when simplified or solved.
The first part;
=2×(4+2)-6
= 2×(6)-6
= 12-6 = 6
The second part;
= 14÷(3.5×2)+4
= 14÷7+4
= 2+4
= 6
Therefore, 2×(4+2)-6 = 14÷(3.5×2)+4. is a true statement.
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Mary needs $9000 in 9 years. What amount can she deposit in a sinking fund at the end of each quarter at 4% interest compounded quarterly so she will have her $9000?
Please serious answers only
Mary needs to deposit $282.44 at the end of each quarter into a sinking fund that earns 4% interest compounded quarterly in order to have $9,000 in 9 years.
what is deposit ?
In the context of finance, a "deposit" refers to the act of placing money or funds into a bank account, investment account, or other financial account. A deposit can also refer to the initial payment made to secure or initiate a purchase
In the given question,
To calculate the sinking fund payment that Mary needs to make at the end of each quarter, we can use the formula for the future value of an annuity:
FV = PMT x [(1 + r/n)ⁿᵇ - 1]/(r/n)
Where:
FV = future value (the amount Mary needs to accumulate, which is $9,000 in this case)
PMT = payment per period (what Mary needs to find)
r = annual interest rate (4% in this case)
n = number of compounding periods per year (4, since interest is compounded quarterly)
t = number of years (9 in this case)
Substituting these values into the formula, we get:
$9,000 = PMT x [(1 + 0.04/4)³⁶ - 1]/(0.04/4)
Simplifying and solving for PMT, we get:
PMT = $9,000 / [(1.01³⁶ - 1)/0.01]
PMT = $9,000 / 31.8422
PMT = $282.44 (rounded to the nearest cent)
Therefore, Mary needs to deposit $282.44 at the end of each quarter into a sinking fund that earns 4% interest compounded quarterly in order to have $9,000 in 9 years.
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PLEASE HELP DUE TODAY
Answer:
y=-1/12x+61/12
Step-by-step explanation:
y=-1/12x+61/12
a region is bounded by two concentric circles, as shown by the shaded region in the figure above. the radius of the outer circle, r , is increasing at a constant rate of 2 inches per second. the radius of the inner circle, r , is decreasing at a constant rate of 1 inch per second. what is the rate of change, in square inches per second, of the area of the region at the instant when r is 4 inches and r is 3 inches? responses
The rate of change of the area is 20π square inches per second.
How to calculate area of the shaded region?The area of the shaded region can be calculated as the difference between the areas of the outer circle and the inner circle:
A = πr^2 - πr'^2
where r is the radius of the outer circle, r' is the radius of the inner circle, and π is the constant pi.
To find the rate of change of the area, we can take the derivative of both sides of the equation with respect to time t:
dA/dt = d/dt (πr^2) - d/dt (πr'^2)
Using the chain rule, we can express the derivatives in terms of the rates of change of the radii:
dA/dt = 2πr (dr/dt) - 2πr' (dr'/dt)
Substituting the given values at the instant when r=4 inches and r'=3 inches, we have:
dA/dt = 2π(4)(2) - 2π(3)(-1) = 20π
Therefore, the rate of change of the area is 20π square inches per second.
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Question 8 of 10
f(x) = x2. What is g(x)?
g(x)
5
f(x)
D. g(x)-
(2, 1):
5
A g(x) = 4x²
OB. g(x)=x²
O C. g(x)-1x²
Thus, the new function g(x) on the graph is the result of dilation with the scale factor of 2. g(x) = 4x².
Explain about the dilation of function:When a function is drawn closer to or farther away from an axis, it is said to have "dilated."
The connection between the two functions shown in the above graph can be explained in two different ways. Either:To create the dashed line, the solid line has either been "dilated vertically by a factor of 2" or the solid line has been "dilated vertically by the a factor of 0.5".Given data:
Parent function f(x) = x²
New function g(x) = ?
From the given graph, consider the point (2,1) on the graph of g(x) function.
For the same value of y = 1 unit, x = 1 on the graph of f(x)
Thus, x ---> 2x (dilation by the scale factor of 2)
Now function:
g(x) = (2x)²
g(x) = 4x²
Thus, the new function g(x) on the graph is the result of dilation with the scale factor of 2. g(x) = 4x².
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In art class students are mixing blue and red paint to make purple paint. Hawa mixes 1 cup of blue paint and 5 cups of red paint. Jacob mixes 4 cups of blue paint and 13 cups of red paint. Use Hawa and Jacob’s percent of red paint to determine whose purple paint will be redder.
Hawa percent of red paint (to nearest whole number) =
%
Jacob percent of red paint (to nearest whole number) =
%
Hawa ’s purple paint will be redder.
Jacob’s purple paint will be redder.
The two purple paints will be equally red.
attempt 1 out of 2
Miracle Jackson
Which is more? (Percent Comparison)
Apr 10, 6:51:14 PM
Watch help video
In art class students are mixing blue and red paint to make purple paint. Hawa mixes 1 cup of blue paint and 5 cups of red paint. Jacob mixes 4 cups of blue paint and 13 cups of red paint. Use Hawa and Jacob’s percent of red paint to determine whose purple paint will be redder.
Answer:
Step-by-step explanation:
cara computes the mean and variance for the set 87, 46, 90, 78, and 89. she finds the mean to be 78. her steps for finding the variance are shown below. what is the first error cara made in computing the variance?
If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.
As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.
However, the formula for calculating the variance is:
Variance = (sum of the squared differences from the mean) / (number of observations)
The first error Cara may have made is in calculating the sum of the squared differences from the mean.
The correct steps to find the variance are:
Find the mean:
Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78
Calculate the differences from the mean for each observation:
87 - 78 = 9
46 - 78 = -32
90 - 78 = 12
78 - 78 = 0
89 - 78 = 11
Square each difference:
[tex]9^2 = 81[/tex]
[tex](-32)^2 = 1024[/tex]
[tex]12^2 = 144[/tex]
[tex]0^2 = 0[/tex]
[tex]11^2 = 121[/tex]
Find the sum of the squared differences:
81 + 1024 + 144 + 0 + 121 = 1370
Divide the sum of squared differences by the number of observations:
Variance = 1370 / 5 = 274.
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Mr rivera is making a healthy dessert
Apple crisp has 10 grams of sugar per serving.
Greek frozen yogurt has 5 grams of sugar per serving.
What is the unit rate?In Mathematics, the unit rate is sometimes referred to as unit price or unit ratio and it can be defined as the price that is being charged by a seller for the sale of a single unit of product or quantity.
How to complete the statements with the unit rate?In order to complete the statements with the unit rate, we would have to divide the amount of grams of sugar by the number of servings for each product or recipe as follows;
Apple crisp = 80 grams/8 servings = 10 grams of sugar per serving.
Greek frozen yogurt = 60 grams/12 servings = 5 grams of sugar per serving.
In conclusion, we can reasonably infer and logically deduce that the recipe that has the least amount of sugar per serving is the Greek frozen yogurt because 5 grams is less than 10 grams.
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Complete Question:
Mr. Rivera is making a healthy dessert for his nephew who has diabetes. He wants to choose the recipe with the least amount of sugar per serving. Apple crisp has 8 servings and contains 80 grams of sugar. Greek frozen yogurt has 12 servings and contains 60 grams of sugar.
How much sugar per serving does each dessert have? Complete the statements with the unit rate.
Apple crisp has _____ grams of sugar per serving. Greek frozen yogurt has _____ grams of sugar per serving.
In ΔHIJ, the measure of ∠J=90°, HI = 6. 7 feet, and JH = 4. 8 feet. Find the measure of ∠I to the nearest degree
The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.
In the triangle HIJ,
The measure of angle J is equal to 90 degrees.
This implies ,
HI is the hypotenuse.
JH is the opposite side to angle I.
In triangle HIJ,
Using trigonometric ratio we get,
sin ∠I = Opposite side / Hypotenuse
Substitute the values we have,
⇒ sin ∠I = 4.8 / 6.7
⇒ sin ∠I = 0.72
Now , take sin⁻¹ both the side of the equation we get,
⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )
Here sin⁻¹(sin ∠I) = ∠I
⇒∠I = sin⁻¹( 0.72 )
⇒∠I = 46.05 degrees
Therefore, the measure of angle I is equal to 46.05 degrees.
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Factor.
z squared+18z–19
(z - or + ?)(z- or + ?)
Answer:
(z - 1) (z + 19)
Step-by-step explanation:
z² + 18z - 19
Consider the form x² + bx + c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is −19 and whose sum is 18.
-1, 19
Write the factored form using these integers.
(z - 1) (z + 19)
Steven read that the actual distance between Memphis and Chicago is about 525 miles. On a map, the distance between the two cities is about 10 inches. Which is most likely the scale used to make the map?
Answer:About 1,012 Inches
Step-by-step explanation:
The Olympic record for the men's 50-meter freestyle is 21.91 seconds. Express this speed in meters per second
Answer:
50 meters/21.91 seconds = 2.282 m/sec
2. Which sequence of transformations takes the graph of y = k(x) to the graph of
y=-k(x + 1)?
A. Translate 1 to the right, reflect over the x-axis, then scale vertically by a factor of 1/2
B. Translate 1 to the left, scale vertically by 1/2 , then reflect over the y-axis.
C. Translate left by 1/2, then translate up 1.
D. Scale vertically by 1/2, reflect over the x-axis, then translate up 1.
The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.
What does term "transformation of a graph" means?The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.
Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.
For the given problem, Transformation to get the desired result can be carried out as:
Translate '1' to the left: The transformation "x + 1" in "-k(x + 1)" shifts the graph horizontally to the left by 1 unit.Scale vertically by '1/2' : The 1/2 factor in "-k(x + 1)" vertically scales the graph, compressing it vertically.Reflect over the y-axis: The minus sign before "k" in "-k(x + 1)" reflects the graph over the y-axis, flipping it horizontally.Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.
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A rug is 1/2 yard by 2 5/6 yards.
Keith solves 1/2 times 2 5/6 to find the area of the rug in square yards.
Enter numbers to complete Keith's calculation for the area of the rug
The area of the rugs in square yards with given dimensions 1/2 yard by 2 5/6 yards is equal to 1 5 /12 square yards.
Dimensions of the rug are,
1/2 yard by 2 5/6 yards
Area of the rug in square yards solved by Keith is equal to
= 1/2 times 2 5/6
= ( 1/ 2 ) × ( 2 5/6 )
Convert mixed fraction into proper fraction we get,
2 5/6 = ( 6 × 2 + 5 ) / 6
⇒ 2 5/6 = 17 / 6
⇒ Area of the rug in square yards solved by Keith = ( 1 / 2 ) × ( 17 / 6 )
⇒ Area of the rug in square yards solved by Keith = ( 17 / 12 )
⇒ Area of the rug in square yards solved by Keith = 1 5 /12 square yards.
Therefore, the area of the rugs is equal to 1 5 /12 square yards.
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what is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 44 centimeters, a width of 9 99 centimeters, and a height of 10 1010 centimeters?
Step-by-step explanation:
Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3
Select each expression that is equivalent to 3(n + 6).
Answer:
3(n + 6) = 2(n + 6) + (n + 6)
3(n + 6) = 3n + 18
Could anyone help? I genuinely don't understand what the question is asking. All I need. is for you to set up the equations for me. An answer isn't necessary unless you'd like to be marked brainliest.
Answer:
9) Keep the denominators the same, and subtract the numerators. Then simplify if necessary.
[tex] \frac{3x + 2}{x + 5} - \frac{2x - 3}{x + 5} [/tex]
[tex] = \frac{3x + 2 - (2x - 3)}{x + 5} [/tex]
[tex] = \frac{3x + 2 - 2x + 3}{x + 5} [/tex]
[tex] \frac{x + 5}{x + 5} = 1[/tex]
10) Find the LCD. Rewrite each rational expression as an equivalent expression with the LCD as the denominator. Add the numerators and write the sum over the LCD. Then simplify if necessary.
[tex] \frac{4x}{x - 2} + \frac{x - 4}{x - 5} [/tex]
[tex] = \frac{4x(x - 5) + (x - 4)(x - 2)}{(x - 2)(x - 5)} [/tex]
[tex] = \frac{4 {x}^{2} - 20x + {x}^{2} - 6x + 8 }{(x - 2)(x - 5)} [/tex]
[tex] = \frac{5 {x}^{2} - 26x + 8}{(x - 2)(x - 5)} [/tex]
[tex] = \frac{5 {x}^{2} - 26x + 8 }{ {x}^{2} - 7x + 10} [/tex]
0.000309 in scientific
Answer:
0.000309 in scientific notation is 3.09 x 10^(-4)
Answer:
0.309x10 to the -4 power
Step-by-step explanation:
just move the decimal place back till its a whole number and do that number to the power of ten if that makes sense
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one more than the reciprocal of a particular number is $\frac{7}{3}$. what is the original number expressed as a common fraction?
Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.
1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).
Step 1: Set up the equation using the given information.
One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:
Reciprocal of the original number + 1 = $\frac{7}{3}$
Step 2: Solve for the reciprocal of the original number.
Reciprocal of the original number = $\frac{7}{3}$ - 1
Step 3: Simplify the equation.
Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$
Reciprocal of the original number = $\frac{4}{3}$
Step 4: Find the original number.
Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:
Original number = $\frac{1}{(\frac{4}{3})}$
Step 5: Simplify the expression.
Original number = $\frac{1}{1} \times \frac{3}{4}$
Original number = $\frac{3}{4}$
The original number expressed as a common fraction is $\frac{3}{4}$.
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PLEASE HELP ILL MARK U AS BRAINLIEST!!
Answer: 64 sqaure centimetres.
Step-by-step explanation:
- Surface area means the area of all exterior sides of a 3D dimensional shape. This means we'll have to find the area of every face and then add them all together.
Top and Bottom
4 x 4 = 16
16 x 2 = 32
Both faces are the same so once we find the area of one, we can just double it.
North, South, East and West Side
4 x 2 = 8
8 x 4 = 32
All four remaining faces had the same dimensions, meaning that once you found one, you just had to multiply that answer by 4.
To find the overall surface area add all the areas you have.
32 + 32 = 64
or
16 +_16 + 8 + 8 + 8 + 8 = 64
Solve for x. -7.6 -1.2 + X 0.5
What is the Y-intercept of boundary line of y < c + 5 ?
Answer: The given inequality is:
y < c + 5
We can rewrite this inequality in slope-intercept form, y = mx + b, by isolating y:
y < c + 5
y - 5 < c
c > y - 5
In slope-intercept form, this is:
y = 1x + (-5)
The y-intercept of this boundary line is -5.
Step-by-step explanation:
Phil is baking a pie with cranberries and apples. Apples cost $0.60/cup and cranberries cost $0.40/cup. Phil wants to spend no more than $4.20 on the fruit for his pie.
Question
What is an inequality that represents the combinations he can use?
Given this snippet of code, what is the value of x after executing the last statement? int x = 10, *y; y = &x; y = y + 1; *y = 100;
The value of x after executing the last statement is still 10.
After executing the last statement, the value of x is still 10. The snippet of code declares an integer variable x and a pointer variable y that points to the address of x. Then, y is incremented by 1 (which means it now points to the next memory location after x). Finally, the value 100 is assigned to the memory location pointed to by y, which is actually beyond the memory allocated for variable x. This can lead to unexpected behavior, but since the value of x is never modified directly, its value remains unchanged at 10.
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what is the summation notation for 8+4+2+1+1/2
Answer:
15 1/2
Step-by-step explanation:
hope this helped
One hundred grams of radium are stored in a container. The amount RR (in grams) of radium present after tt years can be modeled by R=100e−0. 00043tR=100e−0. 00043t. After how many years will only 5 grams of radium be present? Round your answer to the nearest whole year
It will take approximately 368.6 years for the amount of radium to decay to 5 grams.
We are given the model for the amount of radium present after t years:
R = 100e^(-0.00043t)
We are also told to find the time when only 5 grams of radium will be present, here we have to use exponential decay. In other words, we need to find the value of t when R = 5.
Substituting R = 5 into the model, we get
5 = 100e^(-0.00043t)
Dividing both sides by 100, we get
0.05 = e^(-0.00043t)
Taking the natural logarithm of both sides, we get
ln(0.05) = -0.00043t
Solving for t, we get
t = -ln(0.05)/0.00043
Using a calculator, we get
t ≈ 368.6 years
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survey of small businesses with websites found that the average amount spent on a site was $11,000 per year with a standard deviation of $3,000. given a sample of 40 businesses, what is the margin of error if you are to assume a 95% confidence level? (round your answer to two decimal places.)
The margin of error for the 95% confidence level is approximately $873.15.
To calculate the error bars for the 95% confidence level, we need to find the critical value of the z-score from the standard normal distribution table.
Accepting a 95% certainty level, the importance level (α) is 0.05, which implies the certainty level is 1-α = 0.95.
On the off chance that we see the z-score at the 95% certainty level on the standard typical conveyance table, we get an esteem of 1.96.
Then you can use the formula for Tolerance (E).
error bar (E) = z * (standard deviation / sqrt(n))
where:
z = critical value in the standard normal distribution table
standard deviation = $3,000
n=40
Substitute the obtained value.
Error Bar (E) = 1.96 * ($3,000 / sqrt(40))
≈ $873.15
Therefore, the margin of error for the 95% confidence level is approximately $873.15.
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A grab-bag contains 30 packages worth $. 65 each, 10 packages $. 60 cents each, and 15 packages worth $. 30 each. How much should the game owner charge to make it a fair game?
$0. 55
$0. 40
$0. 60
$0. 30
The game owner should charge option (a) $0.55 to make it a fair game
To determine how much the game owner should charge to make it a fair game, we need to calculate the average value of each package. We can do this by finding the total value of all the packages and dividing it by the total number of packages.
The total value of the 30 packages worth $.65 each is:
30 x $.65 = $19.50
The total value of the 10 packages worth $.60 each is:
10 x $.60 = $6.00
The total value of the 15 packages worth $.30 each is:
15 x $.30 = $4.50
The total value of all the packages is
$19.50 + $6.00 + $4.50 = $30.00
The total number of packages is
30 + 10 + 15 = 55
The average value of each package is
$30.00 / 55 = $0.55
Therefore, the correct option is (a) $0.55
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Subtract the sum of -52 and - 638 from the sum of - 29 and 303 the value is
The solution of the expression is 964.
To start solving this problem, let's find the sum of -29 and 303. The sum of two numbers is the result when you add them together. So,
-29 + 303 = 274
The sum of -29 and 303 is 274.
Now, let's find the sum of -52 and -638. To add two negative numbers, you just add their absolute values and put a negative sign in front of the result. So,
-52 + (-638) = -690
The sum of -52 and -638 is -690.
Finally, the problem asks us to subtract the sum of -52 and -638 from the sum of -29 and 303. To subtract one sum from another, we just subtract the second sum from the first. So,
( -29 + 303 ) - ( -52 + -638 )
We can simplify the expression by rearranging the terms:
274 - (-690)
When we subtract a negative number, it's the same as adding its absolute value. So,
274 + 690 = 964
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