A town’s population increases at a constant rate. In 2010 the population was 56,000 . By 2012 the population had increased to 81,000 . If this trend continues, predict the population in 2016. The population will be Number in 2016.
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Given: A town's population increases at a constant rate. In 2010 the population was 56,000. By 2012 the population had increased to 81,000.
Required: To predict the population in 2016.
Explanation: The population is increasing at a constant rate. In 2 years, the increase in population is-
[tex]81000-56000=25000[/tex]Thus the slope (or rate of change of population per year) is-
[tex]\frac{25000}{2}=12500[/tex]Thus, in 2016 after 6 years, the increase in population will be-
[tex]12500\times6=75000[/tex]Hence, the population in 2016 will be-
[tex]56000+75000=131000[/tex]Final Answer: The population will be 131,000 in 2016.
Related Questions
For the polynomial function ƒ(x) = .5x3 + .25x2 + .125x + .0625, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.x = .5, touchx = −.5, touchx = .5, crossx = −.5, cross
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Given:
The polynomial is
[tex]f(x)=.5x^3+.25x^2+.125x+0.0625[/tex]Required:
Find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.
Explanation:
The zeros of polynomial are
[tex]\begin{gathered} x\approx0.5 \\ x=\pm0.5i \end{gathered}[/tex]Now,
So, graph is crossing at -0.5
Answer:
Hence, fourth option is correct.
Recall that we can compare the vertical distance between any two points on the same vertical line to measure verticalchange. In the same way, the horizontal distance between any two points on the same horizontal line will measurehorizontal change.Suppose the linear function y = ax + b undergoes a horizontal change of 5 units. This is equivalent to what verticalchange?A) a vertical change of 5 + b unitsB)a vertical change of 5a + b unitsC)a vertical change of 5 unitsD)a vertical change of 5/a unitsE)a vertical change of 5a units
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Given the linear function:
y = ax + b
And it undergoes a horizontal shift of 5 units
Let the original line be f(x) and the new line be g(x)
g(x) = f(x - 5)
The vertical change will be the horizontal change times a, using the definition of slope.
Thus, since the horizontal change here is 5 units, the vertical change is 5a units
ANSWER:
E) a vertical change of 5a units
Which expressions are equivalent to the one below? Check all that apply.log3 3+ log3 27A. log3 81B. log3 (3^4)C. 4D. log 10
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The given expression is
[tex]log_33+log_327[/tex]We will use the rule
[tex]log_ba+log_bc=log_b(ac)[/tex][tex]\begin{gathered} log_33+log_327=log_3(3\times27) \\ \\ log_3(3\times27)=log_3(81) \end{gathered}[/tex]Since 81 = 3 x 3 x 3 x 3, then
[tex]\begin{gathered} 81=3^4 \\ log_3(81)=log_3(3^4) \end{gathered}[/tex]We will use the rule
[tex]log_b(a^n)=nlog_b(a)[/tex][tex]undefined[/tex]Solve for h: A = (1/2)*b*h*O h = 2*A*bO h = A *(b/2)O h = (2*A)/b0 h = (2+b)/A
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list the first 5 multiples of the denominator and each fraction in order of least to greatest
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The fraction given is 2/6.
The first five multiples of the denominator are as follows;
[tex]\begin{gathered} \frac{2}{6}, \\ 6,12,18,24,30 \end{gathered}[/tex]The other fraction is 7/10.
The first five multiples of the denominator are as follows;
[tex]\begin{gathered} \frac{7}{10}, \\ 10,20,30,40,50 \end{gathered}[/tex]Basically, you simply multiply the denominator by any series of numbers, in this case from 1 to 5. Therefore you'll have
6 x 1 = 6, 6 x 2 = 12, and so on. The same principle applies to the other denominator, that is 10.
Find the area of the shaded region assume all angles are right angles
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The given figure is of a rectangle which is enclosed in the large rectangle.
Area of rectangle = Length x Width
Dimension of large rectangle, 10 and 20.
Area of larger rectangle = 10 x 20
Area of larger rectangle = 200
Dimension of the small rectangle, 14 and 6.
Area of small rectangle = 14 x 6
Area of small rectangle = 84
Area of shaded region = Area of large rectangle - Area of small rectangle
Area of shaded region = 200 - 84
Area of shaded region = 116
Area of shaded region is 116 unit²
For the data set 1,7,7,7,8, the mean is 6. What is the mean absolutedeviation?O A. The mean absolute deviation is 10.O B. The mean absolute deviation is 6.O c. The mean absolute deviation is 2.O D. The mean absolute deviation is 5.
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The mean absolute deviation is given by:
[tex]\frac{\sum ^{}_{}\lvert x_i-\bar{x}\rvert}{n}[/tex]where xi represent each data, x bar the mean and n the number of data we have. Then:
[tex]\begin{gathered} \frac{\lvert1-6\rvert+\lvert7-6\rvert+\lvert7-6\rvert+\lvert7-6\rvert+\lvert8-6\rvert}{5} \\ =\frac{\lvert-5\rvert+\lvert1\rvert+\lvert1\rvert+\lvert1\rvert+\lvert2\rvert}{5} \\ =\frac{5+1+1+1+2}{5} \\ =\frac{10}{5} \\ =2 \end{gathered}[/tex]Therefore the mean absolute value is 2 and the answer is C.
Consider the function f(x) = 5 - 4x ^ 2, - 5 <= x <= 1 .
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Given: A function-
[tex]f(x)=5-4x^2,\text{ }-5\leq x\leq1[/tex]Required: To determine the absolute maxima and minima of the function.
Explanation: The given function is-
[tex]f(x)=5-4x^2[/tex]Differentiating the function,
[tex]f^{\prime}(x)=-8x[/tex]Setting f'(x)=0 gives-
[tex]\begin{gathered} -8x=0 \\ \Rightarrow x=0 \end{gathered}[/tex]So we have to check the function at the boundary points of the interval [-5,1] and x=0 as follows-
Hence, the absolute maximum is 5 at x=o, and the minimum is -95 at x=-5.
Final Answer: The absolute maximum value is 5, and this occurs at x=0.
The absolute minimum value is -95, and this occurs at x=-5.
Refer to the figure below to answer the following questions: (a) When placed in Quadrant ), name the coordinates of point T that forms parallelogram QTRS. (b) When placed in Quadrant II, name the coordinates of point T that forms parallelogram QRST. (c) When placed in Quadrant IV, name the coordinates of point T. that forms parallelogram QRTS. Given Points Q(-1,3), R(3.0), and S(-2,-1) Q T. S
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A parallelogram is a quadilateral that has two pairs of parallel sides. The opposite sides of a parallelogram are equal.
Given the points:
Q(-1,3), R(3,0), and S(-2,-1)
a) When placed in quadrant I, let's find the point T that forms a parallellogram.
Here the distance QS and RT must be equal.
Use the distance formula:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]The point of T that forms a parallellogram when placed in quadrant I is:
T(4, 4)
From point R
b) When placed in Quadrant II, let's find the point T that forms a parallellogram.
We have:
T(-6, 2)
From point Q, make a movement 5 units left and 1 unit down
The point of T that forms a parallellogram when placed in quadrant II is:
T(-6, 2)
c) When placed in quadrant IV, let's find the point T that forms a parallelogram.
We have:
T(2, -4)
From point R, make a movement of down 4 units and left 1 unit.
The point of T, that forms a parallelogram when placed in quadrant IV is:
T(2, -4)
ANSWER:
a) (4, 4)
b) (-6, 2)
c) (2, -4)
Find the distance between the points. Round to the nearest tenth if necessary. (3, 7), (-5, -7) Distance?
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To find the distance between both points you have to apply pythagoras theorem.
First draw both points and form a rigth triangle with the distance between them as the hypothenuse:
The length of the base of the triangle "a" is determined by the difference between the x-coordinates of both points:
[tex]a=x_2-x_1=3-(-5)=3+5=8[/tex]The heigth of the triangle "b" is determined by the difference between the y-coordinates of both points:
[tex]b=y_2-y_1=7-(-7)=7+7=14[/tex]Now using phytagoras theorem you can calculate the length of the hypotenuse as:
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8)^2+(14)^2=c^2 \\ c^2=260 \\ c=\sqrt[]{260} \\ c=2\sqrt[]{65}=16.12 \end{gathered}[/tex]The distance between points (3,7) and (-5,-7) is 2√65
The Nut Shack sells hazelnuts for $6.80 per pound and peanuts nuts for $4.80 per pound. How much of each type should be used to make a 44 pound mixture that sells for $5.94 per pound?
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18.92 pounds of peanut and 25.08 pounds of nut shack should be used to make the mixture
Explanation:the cost per pound for the nut shack = $6.80
let the amount of pounds of nut shack used in the mixture = n
the cost per pound for the peanuts = $4.80
let the amount of pounds for the peanuts used in the mixture = p
We want to obtain 44 pounds of mixture which sells for $5.94 per pound
sum of pounds mixture = 44
amount of pounds of nut shack used in the mixture + amount of pounds for the peanuts used in the mixture = 44
[tex]n+p=44\text{ }....\mleft(1\mright)[/tex]cost per pound for the nut shack (amount used) + cost per pound for the peanuts (amount used) = cost per pound of the mixture (amount of mixture)
6.80(n) + 4.80(p) = 5.94(44)
[tex]6.8n+4.8p=261.36\text{ }\ldots\mleft(2\mright)[/tex]using substitution method:
from equation 1, we can make n the subject of formula
n = 44 - p
substitute for n in equation (2):
[tex]\begin{gathered} 6.8(44\text{ - p) + 4.8p = 261.36} \\ 299.2\text{ - 6.8p + 4.8p = 261.3}6 \\ 299.2\text{ - 2p = 261.3}6 \end{gathered}[/tex][tex]\begin{gathered} collect\text{ like terms:} \\ 299.2\text{ - 261.36 - 2p = 0} \\ \text{add 2p to both sides:} \\ 37.84\text{ = 2p} \\ \text{divide both sides by 2:} \\ \frac{37.84}{2}\text{ = p} \\ p\text{ = 18.9}2 \end{gathered}[/tex]substitute for p in equation 1:
[tex]\begin{gathered} n\text{ + 18.92 = 44} \\ n\text{ = 44 - 18.9}2 \\ n\text{ = 25.0}8 \end{gathered}[/tex]18.92 pounds of peanut and 25.08 pounds of nut shack should be used to make the mixture
I need help with this work question 10Find the area of each regularpolygon. Leave your answer insimplest form.
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Given:
Number of sides in octagon = 8
Length of apothem = 14.1
Side length = 11.7
Required: Area
Explanation:
The area of a regular polygon is one-half the product of its apothem and its perimeter.
Here, the area of the regular octagon is
[tex]\begin{gathered} A=\frac{1}{2}ap \\ =\frac{1}{2}\times14.1\times8\times11.7 \\ =659.88 \end{gathered}[/tex]Final Answer: Area of the regular octagon is 659.88 square units.
Factor 4a²x - 4ax - 8x.
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Answer:
4x(a+1)(a-2)
Explanation:
Given the polynomial:
[tex]4a^2x-4ax-8x[/tex]First, factor out 4x in all the terms:
[tex]=4x(a^2-a-2)[/tex]Next, factor the expression in the parenthesis:
[tex]\begin{gathered} =4x(a^2-a-2) \\ =4x(a^2-2a+a-2) \\ =4x[a(a-2)+1(a-2)] \\ =4x(a+1)(a-2) \end{gathered}[/tex]The factored form of the polynomial is 4x(a+1)(a-2).
the area of a trapezium is 1680 sq cm. One of the parallel sides is 64 cm and the perpendicular distance between the parallel sides is 28 cm. find the length of the other parallel side.
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Answer:
The missing side length is 56
Step-by-step explanation:
1680 = 1/2 · (64 + x) · 28
1680 · 2 = 28 · (64 + x)
3360 = 1792 + 28x
28x = 3360 - 1792
28x = 1568
x = 1568 ÷ 28
x = 56
Hope this helps.
Your team has carefully researched and selected two possible painting companies. Pro Painters charge $200 per hour plus $6000 in material fees. Illusion Ltd charges $150 per hour plus $8000 in material fees.Create a graph of the cost for both companies using the grid below. Circle the point of intersection. Be sure your lines are properly identified.
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Given:
• Pro Painters:
Charge per hour = $200
Material fees = $6000
• Illusion Ltd:
Charge per hour = $150
Material fees = $8000
Let's create a graph of the cost for both companies.
Represent each situation using the slope-intercept form:
y = mx + b
In this case, y represents the total charge, m is the charge per hour, x represents the number of hours, and b represents the material fees.
We have the following:
• Equation for Pro Painters:
y = 200x + 6000
• Equation for Illsion Ltd:
y = 150x + 8000
To graph let's create two points on each equation.
We have:
• Pro painters:
y = 200x + 6000
When x = 1: y = 200(10) + 6000 = 8000
When x = 3: y = 200(30) + 6000 = 12000
We have the points:
(x, y) ==> (10, 8000), (30, 12000)
Plot the points and connect them using a straight line.
• Illusion Ltd:
y = 150x + 8000
When x = 2: y = 150(20) + 8000 = 11000
When x = 4: y = 150(40) + 8000 = 14000
We have the points:
(x, y) ==> (20, 11000), (40, 14000)
Plot the points and connect them using a straight line.
We have the graph below:
The green line represents the cost for Pro Painters
The blue line represents the cost for Illusion Ltd.
From the graph, the point of intersection is (40, 14000).
This means at 40 hours, the cost for both companies will be the same ($14,000)
ANSWER:
• Equation for Pro painters: , y = 200x + 6000
,• Equation for Illusion Ltd: , y = 150x + 8000
,• Point of intersection: (40, 14000)
2x<=-3y+9. graph solution set for this inequality
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We have to graph the solution set for the inequality:
[tex]2x\le-3y+9[/tex]The first step is to graph the function that divides the solution region from the other region. This line correspond to the equality within this inequality:
[tex]2x=-3y+9[/tex]If we rearrange it we can find two points to graph it:
[tex]\begin{gathered} 2x=-3y+9 \\ 2x+3y=9 \end{gathered}[/tex]When x=0, then y is:
[tex]\begin{gathered} 2\cdot0+3y=9 \\ y=\frac{9}{3} \\ y=3 \end{gathered}[/tex]Then, the y-intercept is at y=3.
When y=0, then x is:
[tex]\begin{gathered} 2x+3\cdot0=9 \\ x=\frac{9}{2} \end{gathered}[/tex]Now we now that the x-intercept is at x=9/2.
We have two points from the line, so we can graph it as:
Now, we know the line that limits the solution region.
As the inequality includes the equal sign, we know that this limit is included in the solution region.
The only thing left is to find is if the solution region is above this line or if it is below.
One easy way to test it is to select a point from one of the regions and replace (x,y) in the inequality: if the inequality stands true, then this point is in the solution region and we then now on which side the solution region is.
In this case, we can test with point (0,0) to make it easier:
[tex]\begin{gathered} (x,y)=(0,0)\Rightarrow2\cdot0\le-3\cdot0+9 \\ 0\le-0+9 \\ 0\le9\to\text{True} \end{gathered}[/tex]As the inequality is true for this point, we know that the solution region includes (0,0).
Then, we know that the solution region is below the line.
We then can graph it as:
Sally's wallet contains:5 quarters3 dimes• 8 nickels• 4 penniesA coin is drawn from the purse and replaced 240 times. How many times can you predict that a nickle or apenny will be drawn?
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The total number of coins in the wallet, is:
[tex]5+3+8+4=20[/tex]Since there are 8 nickels and 4 pennies, there are 12 coins which are either nickels or pennies. Then, the probability of picking a nicle or a penny, is:
[tex]\frac{12}{20}=\frac{3}{5}[/tex]Multiply 3/5 by 240 to find the expected amount of times that a nicke or penny will be drawn:
[tex]\frac{3}{5}\times240=144[/tex]Simplify the expression.
9. (x^-3)^-5x^6
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Answer: x to the power of 21
Step-by-step explanation:
Can you explain.Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given.f(x) = -6x^4+5x^2+4;-2 and -1
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SOLUTION:
We are to show that the given polynomial function has a real zero between the numbers given.
[tex]f(x)=-6x^4+5x^2\text{ + 4}[/tex]At x = -2, we substitute -2 for x in the given function;
[tex]\begin{gathered} f(-2)=-6(-2)^4+5(-2)^2\text{ + 4} \\ f(-2)\text{ = -6(16) + 5(4) + 4} \\ f(-2_{})\text{ = -96 + 20 + 4} \\ f(-2)\text{ = -72} \end{gathered}[/tex]At x = -1, we substitute -1 for x in the given function;
[tex]\begin{gathered} f(-1)=-6(-1)^4+5(-1)^2\text{ + 4} \\ f(-1)\text{ = -6(1) + 5(1) + 4} \\ f(-1)\text{ = -6 + 5 + 4} \\ f(-1)\text{ = 3} \end{gathered}[/tex]CONCLUSION:
Since the function f went from -72 to +3 over the interval of -2 to -1, that means it must have passed through zero.
We consider the sets D = {m, n, p, q} E = {3,6,8} and the relation from D to E.R = {(m, 3), (m, 8), (n, 6), (n, 8) (p, 3), (q, 3), (q, 6)a) List the pairs of D × Eb)R is it a proper subset of D × E? Why ?c)Represent the relation R using a Cartesian network
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D= {m, n, p, q}
E= {3,6,8}
a) D x E = { (m, 3), (m, 6), (m, 8), (n, 3), (n,6), (n,8), (p, 3), (p, 6), (p, 8), (q, 3), (q, 6),
(q, 8) }
b) We need to know what a proper subset is.
Proper subset
A proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.
From the above definition, we can say R is a proper subset of D x E because there are element in D x E that is NOT in R.
six fifths, eight ninths, 0.5, forty percent?
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Answer:
I'm assuming this is a greatest to least, but in case it was not, I put least to greatest, too.
Step-by-step explanation:
Greatest to least:
6/5, 8/9, 0.5, 40%
Least to greatest:
40%, 0.5, 8/9, 6/5
Hope this helps!
Hi , can you help me to solve this problem please.
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The polynomials are classified as shown in the image below
Calculate the density of the cube.240 grams4 cm3 cm5 cm
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Answer:
4 g / cm^2
Explanation:
The density is defined is
[tex]p=\frac{M}{V}[/tex]where m is the mass of the object and V is its volume.
Now in our case, we see that the cube weighs M = 240 g and has a volume of
[tex]V=3\operatorname{cm}\times5\operatorname{cm}\times4\operatorname{cm}=60\operatorname{cm}^3[/tex]With the value of M and V in hand, we now calculate the density
[tex]p=\frac{240g}{60\operatorname{cm}^3}[/tex][tex]p=\frac{40g}{\operatorname{cm}^3}[/tex]which is our answer!
What is the value of x in the solution to the system of equations below?2x+3y=112x+y=1
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Answer:
x=-2
Explanation:
Given the system of equations:
[tex]\begin{gathered} 2x+y=1 \\ 2x+3y=11 \end{gathered}[/tex]We use the method of elimination by subtracting.
This gives us:
[tex]\begin{gathered} -2y=-10 \\ y=\frac{-10}{-2} \\ y=5 \end{gathered}[/tex]We then substitute y=5 into any of the equations to solve for x.
[tex]\begin{gathered} 2x+y=1 \\ 2x+5=1 \\ 2x=1-5 \\ 2x=-4 \\ x=-\frac{4}{2} \\ x=-2 \end{gathered}[/tex]Therefore, the value of x in the solution to the system of equations is -2.
Hello. I am trying to help my 9th grade daughter with text corrections. It has been over 20 yrs since I had Algebra 1 and Im a bit rusty. She gets easily frustrated especially in math so Im trying to do some of the leg work before going over how to do it with her. I appreciate your help in advance.
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The half-life of a radioactive substance is given 3 hours.
Given the initial amount of substance is 800 grams. After 3 hours, the substance becomes half that is 400 grams. Then again after 3 more hours, the substance becomes half again that is 200 grams. Again after three hours, the substance becomes half that is 100 grams.
Thus, the amount of radioactive material after 9 hours is 100 grams.
If AABC is similar to ARST, find the value of x.
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Given that
[tex]\begin{gathered} \Delta ABC\text{ is similar to }\Delta RST \\ \text{Therefore, the ratio of the corresponding sides is equal.} \\ \text{That is,} \\ \frac{AB}{RS}=\frac{BC}{ST}=\frac{AC}{RT} \end{gathered}[/tex]Given that AB = 12, BC =18, AC =24 and RS =16, RT=x
We now use the ratio of the corresponding sides to find side RT( the value of x).
Hence,
[tex]\begin{gathered} \frac{AB}{RS}=\frac{AC}{RT} \\ \frac{12}{16}=\frac{24}{x} \\ x=\frac{24\times16}{12} \\ x=32 \end{gathered}[/tex]Therefore, the value of x (RT) is 32
Write 7.916 x 10-7 in decimal form.
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In order to convert the number to decimal form, we need to look at the exponent of the number 10 multiplying the number 7.916.
The exponent is equal to -7, which means we will need to add 7 times the number 0 to the left of the number 7.916. Also, the decimal point will be moved 7 positions to the left.
So we have:
[tex]7.916\cdot10^{-7}=0.0000007916[/tex]A sofa and a love seat together costs $600. The sofa costs $75 less than double the love seat. How much do they each cost The equation
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To solve this problem we need to create an equation, where the unkown variable, x, represents the cost for the love seat. We know that the sofa costs $75 less than the love seat, therefore we have:
[tex]y=x-75[/tex]The cost for both pieces of furniture together is equal to $600. So if we add them we have:
[tex]x+y=600[/tex]We can swap the expression for y on the second equation.
[tex]\begin{gathered} x+(x-75)=600 \\ x+x-75=600 \\ 2x-75=600 \\ 2x=675 \\ x=\frac{675}{2}=337.5 \end{gathered}[/tex]Now we know that the love seat costs $337.5. We will use the first equation to find the cost of the sofa.
[tex]y=337.5-75=262.5[/tex]The sofa costs $262.5.
Joe goes running in the park. He runs 3 miles and does it in 42 minutes. How many minutes doe it take him to run a mile? This topic is distance = rate x time
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You must use this formula:
[tex]d=rt[/tex]Where "d" is the distance, "r" is the rate and "t" is time.
If you solve for "r":
[tex]r=\frac{d}{t}[/tex]If you solve for "t":
[tex]t=\frac{d}{r}[/tex]Knowing that Joe runs 3 mile in 42 minutes, you can find "r". Notice that:
[tex]\begin{gathered} d=3mi \\ t=42\min \end{gathered}[/tex]Then:
[tex]r=\frac{3mi}{42\min}=0.0714\frac{mi}{\min}[/tex]Knowing the rate, you can set up the following in order to find the time in minutes it takes Joe to run a mile:
[tex]\begin{gathered} d=1mi \\ r=0.071\frac{mi}{\min} \end{gathered}[/tex]Substituting values into the formula for calculate the time, you get:
[tex]t=\frac{1\min}{0.0714\frac{mi}{\min}}=14\min [/tex]The answer is: It takes him 14 minutes to run a mile.
Hi I need help with this math problem, i’m in high school calculus 1
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Step 1:
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.
Step 2
Parent function y = f(x)
In general, a vertical stretch is given by the equation
y=bf(x). If b>1, the graph stretches with respect to the y-axis, or vertically. If b<1, the graph shrinks with respect to the y-axis.
The function becomes y = 1.4f(x) when trainsform vertically
The function is shifted 3 units to the left and it becomes y = 1.4f(x + 3)
Final answer
y = 1.4f(x + 3)