The predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.
To predict the sales in Glover's Golf Emporium's eleventh business year, we can use the concept of linear growth. We have two data points: sales in the second year ($160,000) and sales in the seventh year ($335,000).
Let's first find the annual increase in sales:
Increase in sales = Sales in the seventh year - Sales in the second year
Increase in sales = $335,000 - $160,000
Increase in sales = $175,000
Next, we need to determine the rate of increase per year. Since we have a linear growth pattern, we can calculate the average annual increase by dividing the total increase in sales by the number of years:
Average annual increase = Increase in sales / Number of years
Average annual increase = $175,000 / (7 - 2) years
Average annual increase = $175,000 / 5 years
Average annual increase = $35,000 per year
Now, we can predict the sales in the eleventh business year by adding the average annual increase to the sales in the seventh year:
Predicted sales in the eleventh year = Sales in the seventh year + (Average annual increase * Number of additional years)
Predicted sales in the eleventh year = $335,000 + ($35,000 * (11 - 7))
Predicted sales in the eleventh year = $335,000 + ($35,000 * 4)
Predicted sales in the eleventh year = $335,000 + $140,000
Predicted sales in the eleventh year = $475,000
Therefore, the predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.
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Arc BC on circle A has a length of 115,
- inches. What is the radius of the circle?
115/6 pi
138°
The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
The length of an arc with a central angle Ф with circle radius (r) is given by:
Length of arc = (Ф/360) * 2πr
Given the length of arc as 115π/6 in and angle of 138°, hence:
Length of arc = (Ф/360) * 2πr
Substituting:
115π/6 = (138/360) * 2πr
r = 25 inches
The radius of the circle is 25 inches.
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Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.
For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).
Applying this transformation to each vertex of triangle NMO, we get:
N' = (2(-1) - (-5), 2) = (5, 2)
M' = (2(-1) - (-2), 1) = (2, 1)
O' = (2(-1) - (-3), 3) = (3, 3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
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2) Looking at your average from question 1, with an expected weight of 4 ounces, what is the % error in actual weights? (Assume you think the answer is 10%. Find 10% of 4 ounces to check to see if that answer is reasonable!) Do not round!
A) 17.5%
B) .128%
C) 10%
D) 0.175%
The calculated percentage error with the assumed answer of 10%
To find the percentage error in actual weights, we can use the formula:
Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%
In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:
Measured Value = Expected Value + (10% of Expected Value)
= 4 ounces + (10/100) * 4 ounces
= 4 ounces + 0.4 ounces
= 4.4 ounces
Now we can calculate the percentage error:
Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%
= [(0.4 ounces) / 4 ounces] * 100%
= (0.4/4) * 100%
= 0.1 * 100%
= 10%
Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.
The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%
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Select the correct answer.
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir bracelets, which are $3.25 each. All prices include taxes.
Which inequality can be used to solve for how many bracelets Omar can buy?
A.
3.25x + 13.50 ≤ 40
B.
3.25x + 13.50 ≥ 40
C.
13.50x + 3.25 ≤ 40
D.
13.50x + 3.25 ≥ 40
Answer:
A.
3.25x + 13.50 ≤ 40
Step-by-step explanation:
Help, please !!!!
A scatter plot is shown on the coordinate plane.
scatter plot with points at 1 comma 9, 2 comma 7, 3 comma 5, 3 comma 9, 4 comma 3, 5 comma 7, 6 comma 5, and 9 comma 5
Which two points would a line of fit go through to best fit the data?
(1, 9) and (9, 5)
(1, 9) and (5, 7)
(2, 7) and (4, 3)
(2, 7) and (6, 5)
Answer:
(2,7) and (6,5)
Step-by-step explanation:
The line of best fit would be approximately:
y = -.4x + 8
(1,9)
9 = -.4(1) + 8
9 = 7.6
(9,5)
y = -.4x + 8
5 = -.4(9) + 8
5 = 4.4
(5,7)
y = -.4x + 8
7 = -.4(5) + 8
7 = 6
(2,7)
y = -.4x + 8
7 = -.4(2) + 8
7 = 7.2
(4,3)
y = -.4x + 8
3 = -.4(4) + 8
3 = 6.4
(6,5)
y = -.4x + 8
5 = -.4(6) + 8
5 = 5.6
0.059 and 0.01 which is greater?
Is this relation a function yes or no?
Answer:
Yes
Step-by-step explanation:
Yes, it is a function. If you perform the vertical-line test, the line only touches a point once.
The Graph shows the velocity of a train
a) use four strips of equal width to estimate the distance the train travelled in the first 20 seconds
b) is your answer to part a) an understimate or an overestimate?
Answer:
To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:
a) Calculate the average velocity for each strip by finding the average height of each strip.
b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.
c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.
Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.
Without seeing the graph, it's difficult to provide a definitive answer.
Find y" by implicit differentiation.
cos(y) + sin(x) = 1
y" = cos(y) * dy/dx - sin(x) + sin(y) by implicit differentiation.
To find the second derivative (y") by implicit differentiation, we will differentiate the equation with respect to x twice.
Equation: cos(y) + sin(x) = 1
Differentiating once with respect to x using the chain rule:
-sin(y) * dy/dx + cos(x) = 0
Now, differentiating again with respect to x:
Differentiating the first term:
-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2
Differentiating the second term:
-d/dx(cos(x)) = -(-sin(x)) = sin(x)
The equation becomes:
-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2 + sin(x) = 0
Now, let's isolate the second derivative, d^2y/dx^2:
-d^2y/dx^2 = d/dx(sin(y)) * dy/dx - sin(x) + sin(y)
Substituting the previously obtained expression for d/dx(sin(y)) = cos(y):
-d^2y/dx^2 = cos(y) * dy/dx - sin(x) + sin(y)
Thus, the second derivative (y") by the equation:
y" = cos(y) * dy/dx - sin(x) + sin(y)
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Is the expression quadratic 3x+5y-2
No, the expression 3x + 5y - 2200 is not a quadratic expression.
A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.
It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.
"3x + 5y - 2" is a linear expression, not a quadratic expression.
In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.
The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.
It is a first-degree polynomial, meaning that the highest power of the variable is 1.
Linear expressions often have a graph that is a straight line.
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No. The expression, 3x + 5y - 2, is not quadratic.
What are quadratic expressions?The expression "3x+5y-2" is a linear expression, not quadratic.
Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.
The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.
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In the following figure, assume that a, b, and c = 5, e = 12, and d = 13. What is the area of this complex figure? Note that the bottom triangle is a right triangle. The height of the equilateral triangle is 4.33 units.
Answer:
The area of the complex figure is approximately 210.92 square units.
Step-by-step explanation:
Let's calculate the area of the complex figure with the given information.
We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.
1. Equilateral Triangle:
The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:
Area of Equilateral Triangle = (base^2 * √3) / 4
In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.
Area of Equilateral Triangle = (13^2 * √3) / 4
Area of Equilateral Triangle ≈ 42.42 square units
2. Right Triangle:
The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).
Area of Right Triangle = (base * height) / 2
In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).
Area of Right Triangle = (5 * 5) / 2
Area of Right Triangle = 12.5 square units
3. Rectangle:
The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).
Area of Rectangle = length * width
Area of Rectangle = 13 * 12
Area of Rectangle = 156 square units
Now, to get the total area of the complex figure, we add the areas of each component:
Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle
Total Area = 42.42 + 12.5 + 156
Total Area ≈ 210.92 square units
Therefore, the area of the complex figure is approximately 210.92 square units.
Natalie is selling fruit at the Saturday market. She has a
otal of 48 pears that she wants to sell. She makes bags of
pears and sells them for $5 per bag. In which equation
oes b represent the number of bags of pears?
If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:
b = total_number_of_pears / pears_per_bag
In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.
Given that Natalie has a total of 48 pears, we can substitute the value into the equation:
b = 48 / pears_per_bag
Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.
Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:
b = 48 / 4
Simplifying the equation gives:
b = 12
So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.
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Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
9x2 − y2 + 3z2 = 0
(Write an equation for the cross section at
z = 0
using x and y.)
(Write an equation for the cross section at
y = −9
using x and z.)
(Write an equation for the cross section at
y = 9
using x and z.)
(Write an equation for the cross section at
x = 0
using y and z.)
Answer:
Step-by-step explanation:
To sketch the surface represented by the equation 9x² - y² + 3z² = 0 and find the equations for the cross sections, we can start by isolating each variable and considering different values for the fixed variables.
(1) - Cross section at z = 0:
Substituting z = 0 into the equation, we get 9x² - y² = 0 . Rearranging this equation, we have:
9x² = y²
Taking the square root of both sides, we get:
y = ±3x
So the equation for the cross section at z = 0 is y = ±3x and our trace is a line in the xy-plane.
(2) - Cross section at y = -9:
Substituting y = -9 into the equation, we get 9x² - (-9)² + 3z² = 0. Simplifying this equation, we have:
9x² - 81 + 3z² = 0
Rearranging, we obtain:
9x² + 3z² = 81
Dividing by 3, we get:
3x² + z² = 27
So the equation for the cross section at y = -9 is 3x² + z² = 27 and our trace is an ellipse in the xz-plane.
(3) - Cross section at y = 9:
Substituting y = 9 into the equation, we get 9x² - (9)² + 3z² = 0. Simplifying this equation, we have:
9x² - 81 + 3z² = 0
Rearranging, we obtain:
9x² + 3z² = 81
Dividing by 3, we get:
3x² + z² = 27
So the equation for the cross section at y = -9 is 3x² + z² = 27 and our trace is an ellipse in the xz-plane.
(4) - Cross section at x = 0:
Substituting x = 0 into the equation, we get - y² + 3z² = 0. Rearranging this equation, we have:
y² = 3z²
Taking the square root of both sides, we get:
y = ±√3z
So the equation for the cross section at x = 0 is y = ±√3z and our trace is a parabola in the yz-plane.
In simplest radical form, what are the solutions to the quadratic equation 0 =-3x² - 4x + 5?
-b± √b²-4ac
2a
Quadratic formula: x =
O x= -2±√19
3
Ox=-
2+2√19
3
0 x= 2+√15
3
0 x = 2+2√/19
3
Answer:
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula:x = (-b ± √(b² - 4ac)) / (2a)In this case, a = -3, b = -4, and c = 5. Plugging these values into the formula, we get:x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))Simplifying further:x = (4 ± √(16 + 60)) / (-6) x = (4 ± √76) / (-6) x = (4 ± 2√19) / (-6)We can simplify the expression further:x = -2/3 ± (√19 / 3)Therefore, the solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are:x = (-2 ± √19) / 3The solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are x = (-2 + √19) / 3 and x = (-2 - √19) / 3.
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Comparing the equation to the standard quadratic form ax² + bx + c = 0, we have a = -3, b = -4, and c = 5.
Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))
= (4 ± √(16 + 60)) / (-6)
= (4 ± √76) / (-6)
= (4 ± 2√19) / (-6)
= -2/3 ± (1/3)√19
Therefore, the solutions to the quadratic equation are:
x = -2/3 + (1/3)√19 and x = -2/3 - (1/3)√19
In simplest radical form, the solutions are:
x = (-2 + √19) / 3 and x = (-2 - √19) / 3.
These expressions cannot be further simplified since the square root of 19 is not a perfect square.
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2(x+5)-5 x 12 example pls
When x = 3, the expression 2x - 50 evaluates to -44.
To demonstrate an example using the expression 2(x + 5) - 5 × 12, let's simplify it step by step:
Start with the given expression.
2(x + 5) - 5 × 12
Apply the distributive property.
2x + 2(5) - 5 × 12
Simplify within parentheses and perform multiplication.
2x + 10 - 60
Combine like terms.
2x - 50
The simplified form of the expression 2(x + 5) - 5 × 12 is 2x - 50.
Let's consider an example for substituting a value for the variable x:
Suppose we want to evaluate the expression when x = 3. We substitute x = 3 into the simplified expression:
2(3) - 50
Now, perform the calculations:
6 - 50
The result is -44.
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Question
evaluate the expression 2(x+5)-5 x 12.
PLEASE HELP. The value of "y" varies directly with "x".
If y 6, then x = 2.
Find "y" if x = 5.
k = 3
y = [?]
Answer:
y=15
Step-by-step explanation:
y varies directly as x so:
y=k(x)
y = kx
if y is 6 and x is 2;
input the values
y=kx
6=k(2)
[tex] \frac{6}{2} = \frac{2k}{2} [/tex]
k = 3
then find y if x=5
use the previous formula
y=kx so:
y=3(5)
therefore y=15
Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Answer:
In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.
Explanationn:
The two cyclists are 54 miles apart and heading toward each other.
One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.
They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.
Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.
In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.
We need to find the speed of cyclist A in miles per hour.
Speed = Distance / Time
So the speed of cyclist A is:
36 miles / 2 hours = 18 miles per hour
Therefore, the speed of the faster cyclist is 18 mi/h.
Ram borrowed Rs. 250000 from sit a at the rate of 21%: per annum. At the end of monts, how much should he pay compounde à half yearly ?
The end of 6 months, Ram should pay Rs. 276250 compounded half-yearly.
Ram borrowed Rs. 250000 from Sit at an interest rate of 21% per annum. To calculate the compound interest, we need to know the compounding period. In this case, the interest is compounded half-yearly, which means it is calculated twice a year.
To find out how much Ram should pay at the end of 6 months, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount to be paid at the end of the time period
P = the principal amount (the initial amount borrowed) = Rs. 250000
r = the interest rate per period (in decimal form) = 21% = 0.21
n = the number of compounding periods per year = 2 (since it's compounded half-yearly)
t = the number of years = 6 months = 6/12 = 0.5 years
Plugging in these values into the formula, we get:
A = 250000(1 + 0.21/2)^(2*0.5)
Simplifying the equation:
A = 250000(1 + 0.105)^(1)
A = 250000(1.105)
A = Rs. 276250
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Given the following rectangles, identify all combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping. You can't cut any of the rectangles but you may use some of them multiple times. More than one answer may be correct; mark all that apply.
Rectangles you are given:
answer options:
two C rectangles, two D rectangles, and two B rectangles
one each of rectangles A, B, C, and D
one A rectangle and four B rectangles
three E rectangles and two B rectangles
one E rectangle, one C, one D, and three B rectangles
The combinations of assembling these rectangles for which it is possible to create a rectangle with the length of 15 and the width 11 with no gaps or overlapping are:
One each of rectangles A, B, C, and D.One A rectangle and four B rectangles.What is a rectangle?A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides.
Required
Which group forms a rectangle of
[tex]\text{Length}=15[/tex]
[tex]\text{Width}=11[/tex]
First, calculate the area of the big rectangle
[tex]\text{Area}=\text{Length}\times\text{Width}[/tex]
[tex]\text{A}_{\text{Big}}=15\times11[/tex]
[tex]\text{A}_{\text{Big}}=165[/tex]
Next, calculate the area of each rectangle A to E.
[tex]\text{A}_{\text{A}}=11\times7[/tex]
[tex]\text{A}_{\text{A}}=77[/tex]
[tex]\text{A}_{\text{B}}=2\times11[/tex]
[tex]\text{A}_{\text{B}}=22[/tex]
[tex]\text{A}_{\text{C}}=6\times6[/tex]
[tex]\text{A}_{\text{C}}=36[/tex]
[tex]\text{A}_{\text{D}}=6\times5[/tex]
[tex]\text{A}_{\text{D}}=30[/tex]
[tex]\text{A}_{\text{E}}=13\times4[/tex]
[tex]\text{A}_{\text{E}}=52[/tex]
Then consider each option.
(a) 2C + 2D + 2B
[tex]2\text{C}+2\text{D}+2\text{B}=(2\times36)+(2\times30)+(2\times22)[/tex]
[tex]2\text{C}+2\text{D}+2\text{B}=72+60+44[/tex]
[tex]2\text{C}+2\text{D}+2\text{B}=176[/tex]
(b) A + B + C + D
[tex]\text{A}+\text{B}+\text{C}+\text{D}=77+22+36+30[/tex]
[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]
(c) A + 4B
[tex]\text{A} + 4\text{B}=77+(4\times22)[/tex]
[tex]\text{A} + 4\text{B}=77+88[/tex]
[tex]\text{A} + 4\text{B}=165[/tex]
(d) 3E + 2B
[tex]3\text{E}+2\text{B}=(3\times52)+(2\times22)[/tex]
[tex]3\text{E}+2\text{B}=156+44[/tex]
[tex]3\text{E}+2\text{B}=200[/tex]
(e) E + C + D + 3B
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+(3\times22)[/tex]
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=52+36+30+66[/tex]
[tex]\text{E} + \text{C} + \text{D} + 3\text{B}=184[/tex]
Recall that:
[tex]\text{A}_{\text{Big}}=165[/tex]
Only options (b) and (c) match this value.
[tex]\text{A}+\text{B}+\text{C}+\text{D}=165[/tex]
[tex]\text{A} + 4\text{B}=165[/tex]
Hence, options (b) and (c) are correct.
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A ____ is just another way of saying what we want to count by on our graph.
Answer:
A scale is just another way of saying what we want to count by on our graph.
Step-by-step explanation:
A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.
Which linear equation shows a proportional relationship?
y equals negative one sixth times x
y equals one sixth times x minus 8
y = −6x + 1
y = 6
Answer:
y = (-1/6)x represents a proportional relationship.
The value v of a tractor purchased for $13,000 and depreciated linearly at the rate of $1,300 per year is given by v= -1,300t+13,000, where t represents the number of years since the
purchase. Find the value of the tractor after (a) two years and (b) six years. When will the tractor have no value?
a) the value of the tractor after two years is $10,400.
b) the value of the tractor after six years is $5,200.
To find the value of the tractor after a certain number of years, we can substitute the value of t into the equation v = -1,300t + 13,000.
a) After two years:
Substituting t = 2 into the equation, we get:
v = -1,300(2) + 13,000
v = -2,600 + 13,000
v = 10,400
Therefore, the value of the tractor after two years is $10,400.
b) After six years:
Substituting t = 6 into the equation, we get:
v = -1,300(6) + 13,000
v = -7,800 + 13,000
v = 5,200
Therefore, the value of the tractor after six years is $5,200.
To find when the tractor will have no value, we need to find the value of t when v = 0. We can set the equation v = -1,300t + 13,000 equal to 0 and solve for t:
-1,300t + 13,000 = 0
-1,300t = -13,000
t = -13,000 / -1,300
t = 10
Therefore, the tractor will have no value after 10 years.
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Jade decided to rent movies for a movie marathon over the weekend. The function g(x) represents the amount of money spent in dollars, where x is the number of movies. Does a possible solution of (6.5, $17.50) make sense for this function? Explain your answer.
Yes. The input and output are both feasible.
No. The input is not feasible.
No. The output is not feasible.
No. Neither the input nor output is feasible.
The output value is feasible. The input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.
Jade decided to rent movies for a movie marathon over the weekend.
The function g(x) represents the amount of money spent in dollars, where x is the number of movies.
The given function is g(x) which represents the amount of money spent in dollars, where x is the number of movies.
The solution given is (6.5, $17.50).
We need to find whether the solution makes sense for the given function or not.
The input is given as 6.5 and the output is given as $17.50.
This means that Jade rented 6.5 movies and spent $17.50 on renting those movies.
To check whether the solution makes sense or not, we need to see if the input and output values are feasible or not.
The input value 6.5 is not a feasible value because it is not possible to rent half a movie.
Jade can rent 6 movies or 7 movies but not 6.5 movies.
Therefore, the input value is not feasible.
On the other hand, the output value $17.50 is a feasible value because it is possible for Jade to spend $17.50 on renting 6 movies.
The output value is feasible.
Since the input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.
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A rocket is launched from 168 feet above the ground at the time t=0. The function that model thsi situation is given by h =-16t^2+96t+168 where t is the time in seconds and h is the height of the position of the rocket above the ground level in feet. what is the reasonable domain restriction for t in this context?
The domain for the time in this context is (0, 7.4)
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
Let h represent the height of the ball after spending t seconds. A ball is thrown straight up from the top of a building that is 168 ft high with an initial velocity of 96 ft/s.
Given the equation:
h(t) = -16t² + 96t + 168
The reasonable domain restriction for t, is when the height of the rocket is above the ground. Hence the domain for the time in this context is (0, 7.4)
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Find a polynomial with real coefficients that has the given zeros. 5+2i, 5-2i, -1 One such polynomial P(x) can be defined as P(x) = x³ - 9x² + x + 29.
The polynomial with real coefficients from the zeros is P(x) = 2x³ - 18x² + 2x + 58
Find a polynomial with real coefficients from the zeros.From the question, we have the following parameters that can be used in our computation:
zeros = 5+2i, 5-2i, -1
One such polynomial P(x) can be defined as
P(x) = x³ - 9x² + x + 29.
When this polynomial is multiplied by a costant, the roots and zeros remain the same
Let the constant be 2
So, we have
New P(x) = 2(x³ - 9x² + x + 29)
Evaluate
New P(x) = 2x³ - 18x² + 2x + 58
Hence, the function is P(x) = 2x³ - 18x² + 2x + 58
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What is the volume of the triangular prism?
3 in.
15 in.
13 in.
Please show the graph with correct points in x and y. Please specify if it’s a hollow dot or solid dot for each point. I’ll give good rating! Thank you!
The graph of the solution to the inequality is attached as image to this answer.
Understanding Piece-Wise FunctionThe piece-wise defined function h(x) represents different values of y (the output) depending on the value of x (the input). Each interval of x has a different value assigned to it.
In this particular case, the inequality statements define the intervals for x and their corresponding output values.
Let's break it down:
- For values of x that are greater than -3 and less than or equal to -2, h(x) is assigned the value of -1.
- For values of x that are greater than -2 and less than or equal to -1, h(x) is assigned the value of 0.
- For values of x that are greater than -1 and less than or equal to 0, h(x) is assigned the value of 1.
- For values of x that are greater than 0 and less than or equal to 1, h(x) is assigned the value of 2.
Any values of x outside of these intervals are not defined in this piece-wise function and are typically represented as "not a number" (NaN).
For example, if you were to evaluate h(-2.5), it falls within the first interval (-3 < x ≤ -2), so h(-2.5) would be equal to -1. Similarly, if you were to evaluate h(0.5), it falls within the fourth interval (0 < x ≤ 1), so h(0.5) would be equal to 2.
The graph of the piece-wise function h(x) consists of horizontal line segments connecting the specified values of y for each interval, resulting in a step-like pattern.
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A gaming system costs $600 and is on sale for 15% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
Answer$535.50
Step-by-step explanation:
15% is equal to .15
So, multiply 600.00x .15=90
600.00 - 90.0=510.
510. 00x .05=25.50
510.00+25.50=535.50
Your answer is $535.5
Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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See picture dfown below for refgerecnce
The value of the quadratic function y = x² - 4x + 3 is determined by substituting the given value of x into the equation and performing the necessary calculations.
1. Start with the quadratic function: y = x² - 4x + 3.
2. Determine the value of x for which you want to find the value of y.
3. Substitute the given value of x into the equation.
4. Perform the necessary calculations to simplify the expression.
5. Evaluate the expression to find the value of y.
For example, let's find the value of y when x = 2:
1. Start with the quadratic function: y = x² - 4x + 3.
2. We want to find the value of y when x = 2.
3. Substitute x = 2 into the equation: y = (2)² - 4(2) + 3.
4. Simplify the expression: y = 4 - 8 + 3.
5. Perform the necessary calculations: y = -1.
6. Therefore, when x = 2, the value of the quadratic function y = x² - 4x + 3 is -1.
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