Answer:
7 years
Step-by-step explanation:
Let x be number of years the populations be equal
City A's population of 1115000 is decreasing at a rate of 15000 per year.
The population is decreasing at a constant rate so we use equation
y= mx + b
where m is the slope(rate), b is the initial population
m= -15000 (decreasing) , b= 1115000
y= -15000 x + 1115000
City B's population of 698000 is increasing at a rate of 45000 per year.
m= 45000 (increasing) , b= 698000
y= 45000 x + 698000
Now we set the equations equal and solve for x
45000 x + 698000 = -15000 x + 1115000
Add 15000 on both sides
60000 x + 698000 = 1115000
Subtract 689000 on both sides
60000 x = 417000
Divide by 60000 on both sides
x= 6.95
So after 7 years the population will be equal.
Final answer:
To find the number of years until the populations are equal, set up an equation based on the population change per year for both cities. Solve for the variable representing years, and round to the nearest whole number. The populations of City A and City B will be equal in approximately 7 years.
Explanation:
To solve for the number of years until the populations of City A and City B are equal, let's set up an equation. Begin with the populations at the starting point: City A has 1,115,000 residents and is losing 15,000 per year, while City B has 698,000 residents and is gaining 45,000 per year. Let x represent the number of years after which the populations will be equal.
For City A, the population after x years will be 1,115,000 - 15,000x. For City B, the population after x years will be 698,000 + 45,000x. Therefore, we can set up the following equation to find when they are equal:
1,115,000 - 15,000x = 698,000 + 45,000x
To solve for x, combine like terms and get all the x terms on one side:
1,115,000 - 698,000 = 45,000x + 15,000x
417,000 = 60,000x
Divide both sides by 60,000 to solve for x:
x = 417,000 / 60,000
x ≈ 6.95
Since we round to the nearest whole number, the populations will be equal in approximately 7 years.
Convert 846 km/h to miles per hour. (Recall: 1 mi ≈ 1.61 km) a. 770 mi/h c. 525 mi/h b. 684 mi/h d. 465 mi/h
Answer:
answer is 525.
Hopefully I could Help :)
Quadrilateral MATH is dilated by a scale factor of 2.5 centered at (1, 1) to create quadrilateral M’ A’T” H’
M' A'T" H' is (1,1) and (2.5) equals 3.6 to form a quadrilateral. A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.
What is meant by scale factor of quadrilateral?The scale factor is the ratio of one figure's side length to the other figure's corresponding side length.The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger. The scale factor is the ratio of one figure's side length to the other figure's corresponding side length. A scale factor is the amount by which an object is multiplied to produce a second object of different size but with the same appearance. Just a larger or smaller version of the original is created, not an exact copy.Let the scale factor of quadrilateral is center at 2.5 at (1, 1) then
(1,1) and (2.5) equals 3.6
(1,1) + (2.5) = 3.6
Therefore, the statement exists true about the dilation is
B. [tex]$\overline{A^{\prime} T^{\prime}}$[/tex] will overlap [tex]$\overline{A T}$[/tex]
C.[tex]$\overline{M^{\prime} A^{\prime}}$[/tex] will overlap [tex]$\overline{M A}$[/tex]
D. The slope of [tex]$\overline{H T}$[/tex] is equal to the slope of [tex]$\overline{\bar{H}^{\prime} T^{\prime}}$[/tex]
The complete question is :
Show the graph below
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Final Answer:
The dilated quadrilateral MATH with a scale factor of 2.5 centered at (1, 1) transforms into the quadrilateral M’A’T’H’.
Explanation:
Quadrilateral MATH is dilated by a scale factor of 2.5 centered at (1, 1). The dilation process involves multiplying the coordinates of each vertex (M, A, T, H) by the scale factor. Let's denote the original coordinates as (x, y), and the new coordinates as (x', y').
1. For point M (x_M, y_M):
- x'_M = 2.5 * (x_M - 1) + 1
- y'_M = 2.5 * (y_M - 1) + 1
2. Similarly, for points A, T, and H:
- x'_A = 2.5 * (x_A - 1) + 1
- y'_A = 2.5 * (y_A - 1) + 1
- x'_T = 2.5 * (x_T - 1) + 1
- y'_T = 2.5 * (y_T - 1) + 1
- x'_H = 2.5 * (x_H - 1) + 1
- y'_H = 2.5 * (y_H - 1) + 1
These formulas calculate the new coordinates for each point after the dilation. The resulting coordinates (x', y') form the vertices of the dilated quadrilateral M’A’T’H’. The center of dilation, (1, 1), is crucial in determining how each point is transformed. The scale factor of 2.5 indicates that the new coordinates are 2.5 times the distance from the center for each point. The final quadrilateral M’A’T’H’ is an enlarged version of the original MATH, maintaining the same shape but with all dimensions multiplied by the scale factor.
For points A(−4, 8) and B(6, −14), what is the y-coordinate of the midpoint of line segment AB?
Answer:
The y coordinate is -3
Step-by-step explanation:
To find the midpoint, we use
midpoint = (x1+x2)/2, (y1+y2)/2
You only ask for the y coordinate.
y midpoint = (y1+y2)/2
y midpoint = (8+-14)/2
= -6/2
= -3
Answer:
-3
Step-by-step explanation:
usatestprep answer
Pierce wishes to purchase a municipal bond with a par value of $500 from Chattahoochee County, and he is trying to decide which broker he should employ to purchase the bond. Broker A charges a 3.1% commission on the market value of each bond sold. Broker B charges a flat $24 for each bond sold. If the bond has a market rate of 88.754, which broker will give Pierce the better deal, and by how much? a. Broker B’s commission will be $9.75 less than Broker A’s. b. Broker B’s commission will be $3.51 less than Broker A’s. c. Broker A’s commission will be $13.76 less than Broker B’s. d. Broker A’s commission will be $10.24 less than Broker B’s.
Answer:
(d)
Step-by-step explanation:
Bond's par value = $500
market value of the bond = 88.754% * 500
= 443.77
Commission rate charged by broker A = 3.1%
Commission of broker A = [tex]\frac{3.1}{100}[/tex]*443.77
= $13.75687
Commission of broker B = $24
Difference between the commission of broker A and broker B = 24-13.756
= $10.24
Hence, (d) Broker A's commission will be $10.24 less then Broker B's.
Answer:He should take the option one of sales commission of 3.1% on
each bond. If he takes the 2nd option, he is required to pay 24$ per
bond. But if he takes the ist option, he is required to pay 15.5$ per bond.
88.754 is the market rate. Total investment is of 500$. Multiply the commission
rate with the amount and you get 15.5 $. There is a difference of 8.5 dollars
between the two options.
The answer is D
Graph the image of this figure after a dilation with a scale factor of 1/2 centered at the point (-3,0)
Answer:
See image for answer
Step-by-step explanation:
I drew lines connecting the center of dilation and the points. Then, I divided the x-coordinate and the y-coordinate by 2 and I got the point. I did the same thing for the rest of the points and then connected them into a triangle.
which statement is true about f(x)=-2/3 x+4 -6
The graph of f(x) has a vertex of (–4, 6).
The graph of f(x) is horizontally stretched.
The graph of f(x) opens upward.
The graph of f(x) has a domain of x -6
Answer:
The correct answer is The graph of f(x) is horizontally stretched.
Step-by-step explanation:
We can tell it is horizontally stretched by the fact that there is a coefficient of less than 1 in the front.
We know that (-4, 6) isn't a vertex, because it is in vertex form. The vertex is the opposite of the number being added to x and the y value is the constant. Since the constant is -6, it is not a vertex.
The negative coefficient in the front makes it open down, so it doesn't open up.
The domain should be all real numbers as there is no number that cannot be put into the equation.
Evaluate (ab)^2 for a=3 and b=4
Answer:
144 is the answer
Answer:
144
Step-by-step explanation:
Steps:
a times b = 3 times 4. That equals 12.
Then you put 12^2. 12 times 12 equals 144.
Given g(x)=5x+1, find g(2)
g(2) This means that x is 2, so you can plug in 2 for "x" in the equation
g(x) = 5x + 1
g(2) = 5(2) + 1
g(2) = 10 + 1
g(2) = 11
To find the value of the function 'g(x) = 5x + 1' at x = 2, we substitute x with 2. Multiply 5 by 2 to get 10, then add 1 to get 11, so g(2) = 11.
Explanation:In the given function g(x) = 5x + 1, we are asked to find the value of g(2).
This involves replacing x in the function with 2. So, g(2) = 5(2) + 1. Multiply 5 by 2 to get 10, then add 1. This results in g(2) = 11.Learn more about Function Evaluation here:https://brainly.com/question/35863537
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A coin is thrown at random into the rectangle below.

What is the likelihood that the coin will land in the green region?
It is certain.
It is impossible.
It is likely.
It is unlikely
Answer:
The answer is c hope it helps.
Step-by-step explanation:
Hence, option (C) is correct.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.
The analysis of events governed by probability is called statistics.
As per the given information it would be option (C) i.e., it is likely
Hence, option (C) is correct.
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Solve the system of equations by substitution.
6 = −4x + y −5x − y = 21
Answer:
Solve the system by the elimination method.
2x + y = 20 6x – 5y = 12
Answer:
First, we solved the system of equations by substitution and found x = -3, y = -6. Then, by employing the elimination method, we determined the solution to the second system as x = 7, y = 6.
Explanation:To solve the system of equations by substitution and elimination, let's start with the substitution method.
Solve the system by substitution:
Given equations: 6 = −4x + y and −5x − y = 21.
Step 1: From the first equation, isolate y: y = 4x + 6.
Step 2: Substitute y in the second equation: -5x - (4x + 6) = 21.
Step 3: Solve for x: -9x = 27, so x = -3.
Step 4: Substitute x back into the equation for y: y = 4(-3) + 6 = -6.
Solution: x = -3, y = -6.
Solve the system by the elimination method:
Given equations: 2x + y = 20 and 6x − 5y = 12.
Step 1: Multiply the first equation by 5, and the second by 1, to align coefficients of y.
Step 2: Add the modified equations to eliminate y: 10x + 5y + 6x - 5y = 100 + 12.
Step 3: Combine like terms and solve for x: 16x = 112, so x = 7.
Step 4: Substitute x back into one of the original equations to solve for y: 2(7) + y = 20, so y = 6.
Solution: x = 7, y = 6.
Can some other help me it says In four games the basketball team scored 47,52,
63,and 66 points what is the meaning of the scores? what is the range of the scores? can someone please help me
Answer:
Mean: 57; Range: 19
Step-by-step explanation:
132, 217, 217, 120, 173, 261, 133, 150, 163, 241, 121, 153. I need it smallest to biggest.
Smallest to Largest-
120, 121, 132, 133, 150, 153, 163, 173, 217, 241, 261.
Hope this helps you!
Least Greatest
120, 121, 132, 133, 150, 163, 173, 217, 217, 241, 261
Hope helps!-Aparri
How do you find unit rate from a proportional relationship shown in a table
Answer:
To find the unit rate, you have reduce the fraction until you get 1 in the denominator.
Step-by-step explanation:
ex: 16/4 = 4/1 = 4 this is the unit rate.
unit means 1.
PLEASE HELP whats the rate of change per year?
Answer:
The rate of change per year equals: (125.000-180000)/ 5= -11000
That means that the business loses 11000 $ each year
Step-by-step explanation:
Help Pre-Calc
Fill in the blank question :
Calculate the average rate of change f(x) over the interval (-4,-1) using the formula ___________. The value of f(-1) is ____. The value of f(-4) is ____. The average rate of change of f(x) over the interval (-4,-1) is ____.
Answer:
Average rate of change = 2
Step-by-step explanation:
We need to find the average rate of change of f(x) over the interval [-4,-1], so first we need to find the end points at x=-4 and x=-1.
From graph we see that y=-3 when x=-4, So the point is (-4,-3)
From graph we see that y=3 when x=-1, So the point is (-1,3)
Now we can plug these points into average rate of change formula:
[tex]Average\ rate=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]
where (a,f(a)) and (b,f(b)) are the given points.
[tex]Average\ rate=\frac{-3-3}{-4-\left(-1\right)}[/tex]
[tex]Average\ rate=\frac{-3-3}{-4+1}[/tex]
[tex]Average\ rate=\frac{-6}{-3}[/tex]
[tex]Average\ rate=2[/tex]
Hence final answer is 2.
what is 181x182 if you guess this right you get a follow and a thank you and you can get 30$
Answer: c[p(g)] = 0.896g
Step-by-step explanation:
All polygons can be decomposed into?
Answer:
Triangles
Step-by-step explanation:
A polygon is a two dimensional plane figure having at least three straight sides and angles. It can have more than three sides but the simplest and basic polygon we can draw is a triangle.
Hence all polygons can be decomposed into the smaller basic polygons which are triangles.
What is the product of z1 and its conjugate?
From the plot, we see that [tex]z_1=-4-3i[/tex]. Its conjugate would be [tex]\bar{z_1}=-4+3i[/tex], so that the product of the two is
[tex]z_1\bar{z_1}=(-4-3i)(-4+3i)=16-9i^2=16+9=25[/tex]
More generally, note that if [tex]z=x+yi[/tex], then
[tex]z\bar z=(x+yi)(x-yi)=x^2+y^2=|z|^2[/tex]
Answer:
The product of z1 and its conjugate is 25.
Step-by-step explanation:
In the given graph x-axis represents the real axis and y-axis represents the imaginary axis.
The end point of z1 are (0,0) and (-4,-3). So, the complex number z1 is defined as
[tex]z_1=x+iy=-4-3i[/tex]
The conjugate of z1 is
[tex]\overline {z_1}=x-iy=-4+3i[/tex]
The product of z1 and its conjugate is
[tex]z_1\overline {z_1}=(-4-3i)(-4+3i)[/tex]
[tex]z_1\overline {z_1}=-4(-4+3i)-3i(-4+3i)[/tex]
[tex]z_1\overline {z_1}=16-12i+12i-(3i)^2[/tex]
[tex]z_1\overline {z_1}=16-9(i)^2[/tex]
[tex]z_1\overline {z_1}=16-9(-1)[/tex] [tex][\because i^2=-1][/tex]
[tex]z_1\overline {z_1}=16+9=25[/tex]
Therefore the product of z1 and its conjugate is 25.
what is the result when 2x^3 -9x^2 +11x-6 is divided by x-3 ? show the work?
Step-by-step explanation:
2x^3 -9x^2 +11x-6 divided by x-3
We use long division
2x^2 - 3x + 2
------------------------------
x - 3 2x^3 - 9x^2 + 11x - 6
2x^3 - 6x^2
--------------------------------------(subtract)
-3x^2 + 11x
-3x^2 + 9 x
----------------------------------------(subtract)
2x - 6
2x - 6
-----------------------------(subtract)
0
Quotient : 2x^2 - 3x + 2
an animal shelter has a ratio of dogs and two cats that are a 3.2 and there are 30 cats at the shelter how many dogs are there
Answer:
We have 45 dogs when we have 30 cats
Step-by-step explanation:
If the ratio of dogs to cats is 3:2
We want to get to 30 cats so we need to multiply by 15 (2*15 =30)
What we do on one side we do on the other
3*15 : 2 * 15
45 :30
We have 45 dogs when we have 30 cats
solve this problem please
Answer:
x=22
Step-by-step explanation:
1408/64
Answer:
22
Step-by-step explanation:
1,408/64
The “Let’s Roll” game uses a number cube with the numbers 2,4,6,8,10 and 12. There are prizes for rolling any number less than 6.
Answer:
unlikely
Step-by-step explanation:
there is less that a 50 % chance
Answer:
unlikely is the answer
Pls solve this plèeeeeeeeease
Answer:
[tex] \dfrac{5^7}{2} = \dfrac{78125}{2} [/tex]
Step-by-step explanation:
[tex] \left( \dfrac{4}{5} \right)^2 \times 5^4 \times \left( \dfrac{2}{5} \right)^{-2} \div \left( \dfrac{5}{2} \right)^{-3} = [/tex]
[tex] = \dfrac{4^2}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]
[tex] = \dfrac{(2^2)^2}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]
[tex] = \dfrac{2^4}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]
[tex] = 2^{4 - 2 - 3} \times 5^{- 2 + 4 + 2 + 3} [/tex]
[tex] = 2^{-1} \times 5^{7} [/tex]
[tex] = \dfrac{5^7}{2} [/tex]
[tex] = \dfrac{78125}{2} [/tex]
What is 3/4 of 4/9 kilogram?
Hey there!
The word "of" means multiply in mathematical terms
"What is [tex]\frac{3}{4}[/tex] of [tex]\frac{4}{9}[/tex] kilogram? "
So, now that we know what of means we could now solve this equation '
[tex]\frac{3}{4} * \frac{4}{9}[/tex] [tex]3*4 [/tex][tex]4*9[/tex][tex]3*4 = 12[/tex][tex]4*9 = 36[/tex]We get: [tex]\frac{12}{36}[/tex] both terms go into [tex]12[/tex] ← so you could simply that fraction[tex]\frac{12/12}{36/12}[/tex][tex]\frac{12}{12} = 1[/tex][tex]\frac{36}{12} = 3[/tex][tex]\boxed{Answer: \frac{1}{3} }[/tex]Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Michelle earns seven dollars per hour and get the 10% commission on the sale price of each item she sells. She wants the work only 10 hours each week and has a weekly earnings goal of $200. Chief the inequality to find the total sale she mismate to reach her goal
Answer:
She must sell $1,300 to make her goal.
Step-by-step explanation:
In order to find this you can create an equation in which x is the total number of sales she makes. Firstly, you know she gets 10% (or .1) of that number.
y = .1x
We also know that she works 10 hours at $7 per hour. That means we can add $70 to the end.
y = .1x + 70
Now we are looking to make $200, which means we can put 200 in for y and solve for the total amount of sales.
200 = .1x + 70
130 = .1x
1,300 = x
Final answer:
Michelle must generate at least $1300 in sales each week to achieve her weekly earnings goal of $200, given that she works 10 hours per week at an hourly wage of $7 and earns a 10% commission on sales.
Explanation:
To calculate the total sales Michelle must achieve to reach her goal of $200 per week when she earns $7 per hour and a 10% commission on the sale price of each item, we'll set up an inequality. Michelle wants to work only 10 hours each week.
Her earnings from the hourly wage are $7hour times 10 hours, which gives us $70. Now, let's say the total sales she needs to make are represented by x. Therefore, 10% of x represents her earnings from commission. Michelle's weekly earnings goal is $200, so we can write the inequality as:
Hourly earnings: $7*10 hours = $70
Commission earnings: 10% of x (0.10x)
Total earnings (hourly + commission): $70 + 0.10x [tex]\geq[/tex] $200
To find the total sales required, we solve the inequality for x:
$70 + 0.10x [tex]\geq[/tex]$200
0.10x [tex]\geq[/tex]$130
x [tex]\geq[/tex] $1300
So Michelle must generate at least $1300 in sales to meet her weekly earnings goal of $200.
Which shows one way to determine the factors of x3 – 12x2 – 2x + 24 by grouping?
Answer:
(x - 12)(x^2 - 2) or (x - 12)(x + sqrt(2) ) (x - sqrt(2))
Step-by-step explanation:
It looks like grouping is the quickest way to do this.Put brackets around the 1st and second trems and around the 3rd and 4th terms.(x^3- 12x^2) - (2x -24) Pull out x^2 from the first 2 terms and 2 from the last 2.x^2(x - 12) - 2(x - 12) Now pull out x - 12 which is common on either side of the minus(x - 12)(x^2 - 2) You can leave this as it is, or you can factor x^2 - 2 intox^2 - 2: (x + sqrt(2) ) ( x - sqrt(2) )(x - 12)(x - sqrt(2) ) (x + sqrt(2) )Just to show you that these are possible factors, I've included a graph.The sqrt(2) = 1.4142The exact answer depends on your answer choices.guys I really need help with part c) I literally have no idea how to this. given that tan(pi/8)=sqrt(2)-1. I am really looking forward to step-by-step explanation.
Answer:
[tex]a \geq \frac{1}{\sqrt{2} -1}[/tex]
Step-by-step explanation:
This equation is more intimidating than the problem you have to solve.
You know that the sine of everything is always between -1 and +1. So for the entire expression to be >= 0, the a*tan(pi/8) bit has to be 1 at least. Given this, we can forget about the sin(...) term of the equation for the remainder of solving it.
You already figured out that tan(pi/8) is sqrt(2)-1.
So what we're saying is a * (sqrt(2) - 1) has to be 1 at least.
If we solve a(sqrt(2)-1) >= 1 for a we get:
a = 1/(sqrt(2)-1)
[tex]c)\\\tan\left(\dfrac{\pi}{8}\right)=\tan\left(\pi-\dfrac{7\pi}{8}\right)=\tan\left(-\dfrac{7\pi}{8}\right)=-\tan\left(\dfrac{7\pi}{8}\right)\\\\=-(1-\sqrt2)=\sqrt2-1\\\\y=\sin(2x-1)+a\tan\dfrac{\pi}{8}\\\\\text{We know}\ -1\leq\sin(2x-1)\leq1.\\\\y\geq0\ \text{therefore}\ a\tan\dfrac{\pi}{8}\geq1\\\\\text{We have to move the graph at least one unit up}\\\\a(\sqrt2-1)\geq1\qquad\text{divide both sides by}\ (\sqrt2-1)>0\\\\a\geq\dfrac{1}{\sqrt2-1}\cdot\dfrac{\sqrt2+1}{\sqrt2+1}\\\\a\geq\dfrac{\sqrt2+1}{(\sqrt2)^2-1^2}[/tex]
[tex]a\geq\dfrac{\sqrt2+1}{2-1}\\\\a\geq\dfrac{\sqrt2+1}{1}\\\\a\geq\sqrt2+1\\\\Answer:\ \boxed{a=\sqrt2+1}[/tex]
A bag has 4 green marbles, 3 red marbles, and 3 yellow marbles. What is the probability that you pick a green marble, do not replace it, and pick a red marble?
Answer:
1/10
Step-by-step explanation:
Assuming there are 3 red marbles:
3/10 × 3/9 = 9/90 = 1/10
There are 3 red, that is where the first numerator comes from and there are 10 marbles so that is where the denominator comes from. There are 3 yellows, hence the second numerator but as we have taken a marble out there are now only 9 marbles in total.
PLEASE SHOW WORK
Solve using substitution
y=x+4
x-y=-4
y = x + 4 (*)
x - y = -4 (**)
Substitute (*) to (**):
x - (x + 4) = - 4
x - x - 4 = - 4
- 4 = - 4 TRUE
Answer: Infinitely many solutions.x ∈ R
y = x + 4
Answer:
x= -8 y= -4
Step-by-step explanation:
SOLVING FOR X
y=x+4
x-y=-4
----------------------
x-x+4= -4
-4 -4
---------------------
x-x= -8
x= -8
SOLVING FOR Y
plug in the x in any equation
y=(-8)+4
y= -8+4
y= -4
Justin buys candy that cost 6$ per pound he will spend at most $66 on candy what are the possible numbers of pounds he will buy