Joe made a scale drawing of the community pool in his town. the pool has a perimeter of 77 meters, what is the length and width in meters?
Answer:
The length of the pool is 28 meters and the width of the pool is 10.5 meters.
Step-by-step explanation:
In the scale drawing of Joe, the community pool has (length : width) = 8 : 3
Let the actual length of the pool is 8x meters and the actual width is 3x meters.
Now, given that the actual pool has a perimeter of 77 meters.
So, 2(8x + 3x) = 77
⇒ 22x = 77
⇒ x = 3.5
So, the length of the pool is 8x = 8(3.5) = 28 meters and the width of the pool is 3x = 3(3.5) = 10.5 meters. (Answer)
Answer:
The length of the pool is 28 meters and the width of the pool is 10.5 meters.
Step-by-step explanation:
A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 12.5, 2.5, 0.5, 0.1, 0.02.
Which exponential function is represented by the table?
f(x) = 0.2(0.5x)
f(x) = 0.5(5x)
f(x) = 0.5(0.2x)
f(x) = 0.2(0.2x)
Answer:
[tex]f(x)=0.5\cdot (0.2)^x[/tex]
Step-by-step explanation:
Given the table
[tex]\begin{array}{cc}x&f(x)\\ \\-2&12.5\\ -1&2.5\\0&0.5\\1&0.1\\2&0.02\end{array}[/tex]
The exponential function can be written [tex]f(x)=a\cdot b^x.[/tex] To find [tex]a[/tex] and [tex]b,[/tex] substitute some values:
When [tex]x=0,\ f(x)=0.5,[/tex] then
[tex]0.5=a\cdot b^0\Rightarrow a=0.5\ [ b^0=1][/tex]
When [tex]x=1,\ f(x)=0.1,[/tex] then
[tex]0.1=0.5\cdot b^1\Rightarrow 0.5b=0.1,\ b=0.2[/tex]
Thus,
[tex]f(x)=0.5\cdot (0.2)^x[/tex]
Check remaining values:
[tex]f(-2)=0.5\cdot 0.02^{-2}=0.5\cdot 5^2=0.5\cdot 25=12.5\\ \\f(-1)=0.5\cdot 0.2^{-1}=0.5\cdot 5=2.5\\ \\f(2)=0.5\cdot 0.2^2=0.5\cdot 0.04=0.02[/tex]
-x3+3x2+5x+1
Evaluate when x=-12
Can someone help me I don’t understand this :(
Answer:
2102
Step-by-step explanation:
Evaluate -x³+3x²+5x+1 when x = -12
simply substitue x = -12 into the equation
-x³+3x²+5x+1 when x = -12
= - (-12)³ + 3(-12)² + 5(-12)+1
= -(-1728) + 3(144) - 60 + 1
= 1728 + 432 - 60 +1
= 2102
To evaluate the polynomial -x^3 + 3x^2 + 5x + 1 for x = -12, we substitute -12 for x and simplify, resulting in a final value of 2101.
The student is asking to evaluate the polynomial -x^3 + 3x^2 + 5x + 1 when x = -12. To solve this, we substitute -12 for x in the polynomial and simplify:
Substitute x with -12: -(-12)^3 + 3(-12)^2 + 5(-12) + 1Simplify the equation: -( -12 x -12 x -12) + 3( -12 x -12) + 5( -12) + 1Calculate the powers: -(-1728) + 3(144) - 60 + 1Multiply and add: 1728 + 432 - 60 + 1Combine like terms: 1728 + 432 - 60 + 1 = 2101Therefore, when x = -12, the polynomial evaluates to 2101.
Which data set below has the weakest correlation?
Answer:
C.
Step-by-step explanation:
I just got it right
solve the inequality. (x-3)(x-4)/(x-5)(x+6)^2>0
Answer:
C
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
Consider the numerator;
When (x - 3)(x - 4) = 0
x = 3 or x = 4.
When x > 3 and < 4 (x - 3)(x- 4) will be negative and the denominator (x - 5(x + 6)^2 will be negative so the function will be positive.
So 3 < x < 4 is a part of the answer.
When x > 5 the denominator will be positive and so will be the numerator.
So x > 5 also is a solution.
When x < 3 the numerator will be positive and the denominator will be negative so the function will be negative.
PLEASE HURRY !!
Washington Park is a grassy area bordered by three streets as pictured below. A park is shaped like a triangle. The base is 400 yards and the height if 500 yards. What is the area of the park to the nearest square yard?
Answer:
a, it should be 10000
Step-by-step explanation:
400 x 500 is 200000 and the formula is
A=(b)(h)1/2 so half of 200000 is 100000.
Answer:
A
Step-by-step explanation:
Austin correctly answered 92% of the questions on a geography quiz. Liz answered 47 of the 50 questions correctly. Who earned the higher score? Explain
Liz scored higher.
Step-by-step explanation:
Given,
Correct answers by Austin = 92%
Total questions = 50
Correctly answered by Liz = 47
Percent of Liz's correct answers = [tex]\frac{Correct\ answers}{Total\ questions}*100[/tex]
Percent of Liz's correct answers = [tex]\frac{47}{50}*100[/tex]
Percent of Liz's correct answers = [tex]\frac{4700}{50} = 94\%[/tex]
As 94% is higher than 92%, therefore;
Liz scored higher.
Keywords: percent, division
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A. Suppose you have just inherited a sum of money. Let’s say you choose to invest the money. How much did you inherit? Choose an amount between $1000 and $100,000. Do not choose an increment of 1000. In other words, do not choose $1000, $2000, $5000, $14000, etc.
B. What is your interest rate? Choose a rate between 0.5% and 3%.
C. Using yearly compounding, calculate the accrued value after 5 years, 10 years, and 15 years. Show all work. You may show your work as an inserted image.
Amount =$48003.20
Step-by-step explanation:
Here apply the compound interest formula;
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
where;
P=Principal amount invested = $37500
r=rate of interest as a decimal, 2.5% =0.025
n=number of compounding per year=1
t=time period the amount in invested=10
In our case, the amount after investing will be;
[tex]A=37,500(1+0.025)^{10} \\\\A=37,500(1.025)^{10} \\\\A=48003.20[/tex]
Interest earned after the period= $48003.20-$37500 =$10503.20
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Keywords: inherit, sum, money, interest
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A 22inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is one inch more than four times the length of the first piece. Find the length of the pieces
Answer:
The length of the pieces is 3 inch, 6 inch and 13 inch.Step-by-step explanation:
Let, the length of the first piece is x inch.
Hence, the length of the second piece is 2x.
It is given that, the length of the third piece is one inch more than four times of the first piece. Hence, the length of the third piece is 4x + 1 inch.
The total length of the steel is 22 inch.
Hence, x + 2x + 4x + 1 = 22
or, 7x = 21
or, x = 3.
The length of the second piece is [tex]2x = 2\times3 =[/tex] 6 inch.
The length of the third piece is [tex]4x + 1 = 12 + 1 =[/tex] 13 inch.
The lengths of the three pieces of steel are 3 inches, 6 inches, and 13 inches respectively.
Explanation:Let's denote the length of the first piece as x. According to the problemm, the second piece is twice as long as the first piece, which could be represented as 2x. The third piece is said to be one inch more than four times the length of the first piece, which could be represented as 4x + 1. Since the total length of the steel is given as 22 inches, we write down this equation: x + 2x + 4x + 1 = 22.
Simplifying this equation, we get: 7x + 1 = 22. We then subtraact 1 from both sides to isolate the term with x on one side: 7x = 21. Finally, we solve for x by dividing both sides by 7: x = 3.
Therefore, the length of the first piece of steel is 3 inches. The length of the second piece is twice that, or 6 inches. The length of the third piece is four times the length of the first piece plus one inch, or 13 inches.
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6ab-8ab how do you simplify this monomials
To simplify the monomials 6ab-8ab, subtract the coefficients of the like terms and combine the result with the common variables, resulting in -2ab.
The question asks how to simplify the monomials 6ab-8ab. This simplification process involves combining like terms. Both terms have the same variables (a and b), so they are like terms and can be combined by subtracting their coefficients.
Here are the steps to simplify:
Identify the coefficients of the like terms: 6 and -8.
Subtract the coefficients: 6 - 8 = -2.
Combine the result with the common variables: -2ab.
Therefore, the simplified form of 6ab-8ab is -2ab.
What steps would you do to solve n/7 + 3 ≥ -4?
a Multiply by seven, then subtract three.
b Add three, then multiply by seven.
c Subtract three, then multiply by seven.
d Subtract three, then divide by seven.
The right answer is Option C.
Step-by-step explanation:
Given inequality is
[tex]\frac{n}{7}+3\geq -4[/tex]
We will first subtract three from both sides.
[tex]\frac{n}{7}+3-3\geq -4-3\\\frac{n}{7}\geq -7[/tex]
In the next step we will multiply both sides with 7 to determine n.
Therefore,
Subtract three, then multiply by 7.
The right answer is Option C.
Keywords: inequality, subtraction
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Find the maximum value or minimum value for the function f(x) = 0.15(x + 1)² - 3.
0.15
3
1
-3
Answer:
The minimum value for [tex]f(x) = 0.15(x + 1)^2 - 3[/tex] is [tex]-3[/tex].
Step-by-step explanation:
Given function is [tex]f(x) = 0.15(x + 1)^2 - 3[/tex]
We need to find the maximum value or the minimum value for the function.
Now, differentiate [tex]f(x) = 0.15(x + 1)^2 - 3[/tex] w.r.t [tex]x[/tex].
[tex]f'(x) =\frac{d}{dx}(0.15(x + 1)^2 - 3)\\f'(x)=\frac{d}{dx}(0.15(x+1)^2-\frac{d}{dx}(3)\\[/tex]
[tex]f'(x)=2\times 0.15(x+1)\frac{d}{dx}(x+1)-0\\f'(x)=0.3(x+1)(1)\\f'(x)=0.3(x+1)[/tex]
Now, we will equate [tex]f'(x)=0[/tex] to find critical point.
[tex]0.3(x+1)=0\\x=-1[/tex]
Plug this critical point in to the function [tex]f(x) = 0.15(x + 1)^2 - 3[/tex] we get,
[tex]f(-1) = 0.15(-1 + 1)^2 - 3\\f(-1)=-3[/tex]
Also, [tex]f''(x)=0.3[/tex] which is positive, We have minimum value.
So, the minimum value for [tex]f(x) = 0.15(x + 1)^2 - 3[/tex] is [tex]-3[/tex].
what is an expression equivalent to 48+30
Answer:
Step-by-step explanation:
48 + 30 = 6(8 + 5)
Answer:78
Step-by-step explanation:
Equivalent expression is to carry out the addition process.
48 + 30 = 78
Quadrilateral TRPK ~ Quadrilateral EWMN Which statements are correct? Select all that apply. Question 8 options:
TK/NM = RP/EW
∠R≅∠W
∠P≅∠N
RP/WM = TR/EW = TK/EN
Ricardo is building a new garden and is buying soil to fill it up. he buys 4 kilograms of soil for $10.00.
what is the unit rate for the soil in kilograms?
The difference of r and 18 is equal to five
Answer: 23
Step-by-step explanation: 18+5=23
23-5=18
R=23
The difference of r and 18 means subtraction: r - 18 = 5
To isolate r, you add 18:
r = 18 + 5 or 23
r = 23
(6c)^3
---------
c
please help
Answer:
216c^3
Step-by-step explanation
You have 125% of the tickets required for a souvenir. What fraction of the required tickets do you have? Do you need more tickets for the souvenir?
Explain. Write your answer in simplest form.
PLEASEEEE HELP!!
Answer:
The answer is that it requires 4/5 of your total amount of tickets
Step-by-step explanation:
You break it down originally into fourths, 25x4 = 100% or 100. 125% would be 125 tickets since its by percentage. you'd have a remaining 25 tickets after purchase
Answer:
It is 4/5
Step-by-step explanation:
dont worry
How do dhhdhdbsjjajsd
3.) mr. smith’s class sold wrapping paper for $3.50 each and mr. davis’ class sold magazines for $2.75 each. together, the classes sold 72 items and earned $222 for their school. a. write and solve a system of equations that model the problem. show all your work. Need answer ASAP!!!!!
Answer:
The number of wrapping paper sold was 32 and the number of magazines sold was 40
Step-by-step explanation:
Let
x ----> the number of wrapping paper sold
y ----> the number of magazines sold
we know that
The classes sold 72 items
so
[tex]x+y=72[/tex] ----> equation A
The classes earned $222 for their school
so
[tex]3.50x+2.75y=222[/tex] ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
using a graphing tool
The solution is (32,40)
see the attached figure
therefore
The number of wrapping paper sold was 32 and the number of magazines sold was 40
Adrian made the cakes shown below for a 3 cakes at the party Adrian will serve each guest 1/8 of a cake what is the greatest number of guests Adrian can serve?
Answer:
24 Guests
Step-by-step explanation:
3 x 8 = 24.
Answer:
since each guest is 1/8 of the cake and he has 3 cake . So the great number of the guest is 24....
Step-by-step explanation:
Should be 24 is the answer...
I hope this will help...Have a nice day...
What percent of your budget of $6000 would your rent be if you pay $600 in rent?
Answer:
ur answer ( I think so it will be correct)
Step-by-step explanation:
$6000 percent $600
= 6000/600
= 60÷6 percent
= 10 percent
I THINK ITS HELPFULL TK YOU
Suppose a refrigerator that sells for$700 costs $85 a year for electricity. Write an expression for the cost to buy and run the refrigerator for x years.
Answer:
Step-by-step explanation:
700 + 85x <=== ur expression
Part A: Write an equation of a line that is perpendicular to the line y = 2/3x + 5 and passes through the point (4, 0).
Part B: Explain how you determine the equation in 3-4 sentences using at least 6 of the words below.
Slope
y-intercept
x-intercept
perpendicular
opposite
reciprocal
substituted/substitution
slope-intercept
ordered pair
Step-by-step explanation:
First you need to make a line perpendicular to y=2/3x+5. To do that you have to know that, if we use y=ax+b, a1*a2=-1. That is if a1 and a2 are perpendicular. So we get 2/3*a2=-1. -1/ 2/3=a2. a2=-1.5. We get y=-1.5x+b. Fill in (4,0) on y=-1.5x+b abd we get 0=-1.5(4)+b. b=6
Answer:
y = (-3/2)x - 6
Step-by-step explanation:
slope of the line y= 2/3x + 5
slope = 2/3
for two perpendicular lines
slope1*slope2 = -1
so, slope2 = (-1)*(3/2) = -3/2
hence for it to pass (4,0)
slope2=(y2 - y1)/(x2 - x1)
-3/2 = (y - 0)/(x - 4)
cross multiplying
-3x -12 = 2y
the equation of the line is
y = (-3/2)x - 6
PLZ HELP 20 points and brainliest
Select TWO equations that have infinitely many solutions.
A.
2(7 – 4x) = 4(5 – 2x) – 6
B.
6(x – 9) = 6x – 54 + x
C.
4(x + 4) = 2(2x + 5) + 6
D.
5(x – 8) + 10 = 5(x + 2)
Answer: A. 2(7 – 4x) = 4(5 – 2x) – 6
C. 4(x + 4) = 2(2x + 5) + 6
Step-by-step explanation:
Infinitely solution means when all numbers are solutions . Checking the equations given one by one
A. 2(7- 4x ) = 4(5 - 2x ) - 6
Expanding , we have
14 - 8x = 20 - 8x - 6
14 - 8x = 20 - 6 - 8x
14 - 8x = 14 - 8x , this is just a typical example of infinitely many solutions because any value of x chosen will satisfy the equation.
B. 6(x - 9 ) = 6x - 54 + x
Expanding , we have
6x - 54 = 6x + x - 54
6x - 54 = 7x - 54
collecting the like terms
6x - 7x = -54 + 54
- x = 0
x = 0
This equation has just one solution at x = 0 , because 0 is the only value of x that will satisfy the equation
C. 4( x + 4 ) = 2 ( 2x + 5 ) + 6
4x + 16 = 4x + 10 + 6
4x + 16 = 4x + 16
This equation also have infinitely many solutions
D. 5 ( x - 8 ) + 10 = 5 ( x + 2 )
5x - 40 + 10 = 5x + 10
5x - 30 = 5x + 10
This equation has no solution.
Therefore , the equations with infinitely many solutions are equations A and C
NEED HELP PLEASE!!!!
Answer:
The answer is 2.414213562
Step-by-step explanation:
The answer is shown in the image attached.
what is the value of (5r+1/5) squared when r=0
Answer:1/5
Explanation The answer is 1/5 because 05×0 is zero so 0+1/5 equals 1/5
Answer:
1/5
Step-by-step explanation:
Solve the proportion. Show all work. 2x/3=20/5
Answer:
2x/3 = 4
2x = 4*3
2x = 12
x = 12/2
x = 6
Hope it helps...
What is the rate of change in the equation y=-2x+7
Answer:
2
Step-by-step explanation:
m is the slope
y=mx+b
y is equation
m is slope (movement)
b is base
In the equation y=-2x+7, the rate of change (slope) is -2, denoting that for every unit increase in x, y decreases by 2. The +7 represents the y-intercept, the value of y when x equals zero. This concept is fundamental in understanding linear equations, where the rate of change is constant.
Explanation:In the equation y=-2x+7, the rate of change is represented by the coefficient of the x variable, which in this case is -2. This signifies that for each unit increase in x, the value of y decreases by 2. In the context of graphing, this slope (or rate of change) would mean for every step to the right (increase in x), you would take two steps down (decrease in y). For example, if x were to increase from 1 to 2, y would decrease from 5 (plugging x=1 into the equation gives y=5) to 3 (plugging x=2 into the equation gives y=3).
The rate of change is a crucial concept in algebra and lies at the heart of most mathematical models. It plays a vital role in calculus, physics, and engineering, amongst other disciplines. The second number in the equation, '+7', signifies the y-intercept, which is the value of y when x equals zero. This equation represents a straight line, as all linear equations do, and the rate of change (or the slope) is constant across this line.
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Solve for x and y:
28x-49y=35
4x-7y=5
A.The solution is (0, 0).
B.There are an infinite number of solutions.
C.X=3,y=1
D.There is no solution.
Answer:
D
Step-by-step explanation:
The lines are parallel, this means that they will never meet.
Answer: D no solution
Step-by-step explanation:
the first one is wrong because if they were both 0 than they would have to equal 0
the second one is wrong because no number works
the third one is wrong because it works on the second one but when you plug it into the first equation you get 95 = 35 which is incorrect.
D is the correct choice.