Answer:
w = 2.5
Step-by-step explanation:
Write these 2 equations to represent the problem:
[tex]l=w+5\\2w+2l=20[/tex]
where w is width and l is length. This can then be solved as a system of equatios. I'll solve by substitution, and as the [tex]l[/tex] is already solved for at the top:
[tex]2w+2l=20\\2w+2(w+5)=20\\2w+2w+10=20\\4w+10=20\\4w=10\\w=2.5[/tex]
If you just need the width, then you're already done there. I'll find the other variable too, and then check it to be sure it's correct.
[tex]l=w+5\\l=(2.5)+5\\l=7.5[/tex]
Now, confirm that with the second equation:
[tex]2w+2l=20\\2(2.5)+2(7.5)=20\\5+15=20\\20=20[/tex]
The perimeter of a rectangle is the sum of its side lengths.
The width of the rectangle is 2.5 units
Represent the length with l and the width with w.
So, we have:
[tex]P =2 \times (l + w)[/tex] --- the formula of perimeter
The perimeter is 20 units.
So, we have:
[tex]20 =2 \times (l + w)[/tex]
Divide both sides of the equation by 2
[tex]10 =l + w[/tex]
The length is said to be 5 more than its width.
So, we have:
[tex]l =5 + w[/tex]
Substitute 5 + w for l in [tex]10 =l + w[/tex]
[tex]10 = 5 + w + w[/tex]
[tex]10 = 5 + 2w[/tex]
Subtract 5 from both sides
[tex]5 = 2w[/tex]
Divide both sides by 2
[tex]2.5 = w[/tex]
Rewrite as:
[tex]w =2.5[/tex]
Hence, the width of the rectangle is 2.5 units
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Sally bought shirts and pants for school. She bought a total of 8 items. Each pair of pants cost
$28, and each shirt cost $12. She spent a total of $144. How many pairs of pants did Sally buy?
How many shirts did she buy?
ONLY ORIGINAL ANSWERS OR NO BRAINLIEST WILL BE GIVEN AND NO SITES OR CHEET SHEETS
If my calculations are correct, Sally would be able to buy 3 pairs for 84 bucks and 5 pairs of shirts for 60 bucks, making a total of 144 bucks.
Which of the following is a triangle circumscribed by a circle?
Answer:
Hi again
Its your 3rd option
Step-by-step explanation:
Answer:
Step-by-step explanation:
Option 3 is correct just got the test!
Solve the system of equations -6x+5y=0 and −5x+5y=−5 by combining the equations.
Answer:
Step-by-step explanation:
-6x+5y=0 and −5x+5y=−5
Subtract the second from the first:
-6x+5y=0
5x-5y= 5
-x = 5
x = -5
Hamilton's rule is "Add 4." If he starts with 8, which number would be the 5th number in his pattern?
A. 28
B. 24
C. 20
D. 12
Answer:
B. 24
Step-by-step explanation:
If N1 = 8;
N1 + 4
8 + 4 = 12 =N2
N2 + 4
12 + 4 = 16 = N3
N3 + 4
16 + 4 =20 = N4
N4 + 4
20 + 4= 24 = N5
I need help long dividing this equation.
(x^2 - x +5) / (x + 1)
I already know the answer however I’m having a bit of trouble understanding how to get to it. At the second to last operation you come to,
- x^2 + 4x
- x^2 - x
= 5x
I’m having trouble understanding how you get 5x from that? Someone please help!
First, we'll look at the first term of each expression.
---x times what is equal to x^3? = x times x^2 = x^3
So, we'll multiply everything in the divisor by x^2 and subtract that from the dividend.
x^2(x + 1) = x^3 + x^2
(x^3 + 4x + 5) - (x^3 + x^2)
x^3 - x^3 = 0
0 - x^2 = -x^2
4x - 0 = 4x
5 - 0 = 5
Our new expression is -x^2 + 4x + 5.
So we again ask ourselves, x times what is equal to -x^2? = -x
-x(x + 1) = -x^2 - x
And subtract!
(-x^2 + 4x + 5) - (-x^2 - x)
-x^2 - - x^2 = -x^2 + x^2 = 0
4x - - x = 4x + x = 5x
5 - 0 = 5
Our new expression is 5x + 5. Let's ask ourselves once again, x times what is equal to 5x? = 5.
Multiply, then subtract!
5(x + 1) = 5x + 1
(5x + 1) - (5x + 1) = 0
Now that we have nothing left to divide, let's go back and get our answer.
x^2 - x + 5
Notice that when I was dividing, I always looked at the first term of the dividend (as the expression changed) and divisor. Whatever comes after the first term doesn't matter at the time.
Hope this helps and if you have any further questions, please let me know! :)
Answer:
Step-by-step explanation:
x - 2 <--- quotient
x + 1) x^2 - x + 5 First divide x^2 by x giving x then multiply x + 1 by x:
x^2 + x Now subtract x^2 + x from x^2 - x and bring down +5:
-2x + 5 Now divide -2x by x to get -2 and multiply X+1 by -2 -2x - 2 Subtract:
7
The result is x - 2 (see above) remainder 7
or you could write it as
x - 2 + 7/(x + 1)
HELP ME PLEASEEEE I NEED ITT !
Answer:
10
Explanation:
130 divided by 13 equals 10
10 times 13 equals 130
⦁ Determine the zeros of f(x) = (x + 1)^2(x – 3)(x – 4). Indicate the multiplicity of any factors that occur more than once.
Answer:
see explanation
Step-by-step explanation:
To find the zeros equate f(x) to zero , that is
(x + 1)²(x - 3)(x - 4) = 0
Equate each factor to zero and solve for x
x- 4 = 0 ⇒ x = 4
x - 3 = 0 ⇒ x = 3
(x + 1)² = 0 ⇒ (x + 1) = 0 , x + 1 = 0 ( 2 factors ) , then
x = - 1 with multiplicity 2
The oblique prism below has an isosceles right triangle base.
An oblique right triangular prism is shown. The triangular bases have 2 sides with a length of x. The length of they hypotenuse is unknown. The distance from the 2 triangular bases is (x + 3). The vertical height of the prism is (x + 2).
What expression represents the volume of the prism, in cubic units?
One-halfx3 + x2
One-halfx3 + Three-halves x2
x3 + x2
x3 + 3x2
The volume of the prism, in cubic units is 1/2x³ + x²
The volume of the oblique prism is given as:
V = Base area * Height
Given the following
Height = x + 2Base area = area of the triangleBase area = 1/2 (x*x)
Base area = 1/2 x²
Get the volume of the prism;
Volume of the prism = 1/2(x²)(x+2)
Volume of the prism = 1/2(x³+2x²)
Volume of the prism = 1/2x³ + 1/2(2x²)
Volume of the prism = 1/2x³ + x²
Hence the volume of the prism, in cubic units is 1/2x³ + x²
Learn more on the volume of prism here: https://brainly.com/question/23963432
Answer:
1/2x³ + x²
Step-by-step explanation:
edg
What is the remainder when (x3 1) is divided by (x2 â€"" x 1)?.
The remainder of the equation is [tex]\rm x+1[/tex].
Given that,
When the equation is [tex]x^3+1[/tex] divided by [tex]x^2-x+1[/tex].
We have to determine,
The remainder for the equation?
According to the question,
The equation [tex]x^3+1[/tex] is divided by [tex]x^2-x+1[/tex].
On the division of the polynomial, the remainder is,
[tex]\dfrac{\rm x^3+1}{x^2-x+1}[/tex]
Factorize the equation to convert this into the simplest form,
[tex]\rm = x^3+1\\\\=x^3-x^2+x + x^2-x+1\\\\= x ( x^2-x+1) + 1(x^2-x+1)\\\\= (x+1) (x^2-x+1)[/tex]
Now, the equation can be written as,
[tex]\rm = \dfrac{(x+1) (x^2-x+1) }{ x^2-x+1}\\\\= x+1[/tex]
Hence, The required remainder of the equation is [tex]\rm x+1[/tex].
For more details refer to the link given below.
https://brainly.com/question/25880057
Answer: a
Step-by-step explanation:
on edge
HELP!!!
n – 3 = ‐1
Please do not just type in the answer please explain how you got your answer! Whoever explains (CORRECTLY) first gets brainliest!
Answer:
n = 2
Step 1: Add 3 to both sides to isolate x.
n – 3 = ‐1
Step 2: Solve
=> n = -1 + 3
Final Answer: Answer to the question.
=> n = 2
Therefore, n = 2 is our answer.
Hoped this helped.
What is the y-intercept of a line through (2, 7) and perpendicular to the graph of y =-3 /2 x +6
Answer:
5.5
Step-by-step explanation:
The line perpendicular to y =-3 /2 x + 6 is y = 2/3 x + 6. When you find the y-int from the graph you drew, the y-int is about 5.5
Hope that helps
pls help what is the answer
James makes $44,059 per year, how much would he make monthly?
Answer:
$3671.58
Step-by-step explanation:
Take the annual salary and divide it by the number of months
please i need help ASAP!!!
Use the graph below to answer the question.
The statements that are true are:
a. The rate of change of segment T is decreasing
b. Difference between the rate of change of segments S and R is 3½
How to Find Rate of ChangeRate of change (slope) = change in y / change in x = rise/runRate of change for horizontal line/graph are always zero.To determine which statements are true, find the rate of change of each segment in the graph.
Rate of change for Segment R:
Segment R is horizontal, therefore the rate of change = 0.
Rate of change for Segment S:
Rate of change = rise/run = 7/2 = 3½.
Rate of change for Segment T:
Rate of change = rise/run = 8/-8 = -1.
Rate of change for Segment U:
Rate of change = rise/run = 5/3 = 2⅔.
The rate of change of segment T is negative, therefore, it is decreasing. (Option 1 is true).
Difference between Rate of change of segment S and R = 3½ - 0 = 3½. (Option 2 is also true).
Rate of change for segment T, -1, is less than rate of change for segment S, 3½. (Option 3 is not true).
Option 4 is false. Rate of change for segment U is rather 2⅔.
Option 5 is also not true. Segment R has a rate of change of 0.
Therefore, the statements that are true are:
a. The rate of change of segment T is decreasing
b. Difference between the rate of change of segments S and R is 3½
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HELP ME PLEASEEEE I NEED ITT !
Answer:
p=12
Step-by-step explanation:
a=l×b
a=219.6
l=18.3
b=?
219.6=18.3×b
Divide both sides by 18.3
And therefore b=12 yards
6.4f 24 water bottles weigh 30 pounds, how much would a shipment of 150 water bottles weigh?
Answer:
120 pounds
Step-by-step explanation:
24÷30 =0.8
0.8 x 150= 120 pounds
Question 7 of 25
If f(x) = 3x2 - 2x + 4 and g(x) = 5x2 + 6x - 8, find (f+ g)(x).
A. (f+ g)(x) = -2x2 - 8x+ 12
B. (f+g)(x) = 8x2 + 8x + 12
O C. (f+g)(x) = 2x2 + 8x - 12
D. (f+g)(x) = 8x2 + 4x - 4
Answer:
D. (f+g)(x) = 8x^2 + 4x - 4
Step-by-step explanation:
The notation (f+g)(x) is shorthand for f(x) +g(x).
(f +g)(x) = f(x) +g(x) = (3x^2 -2x +4) +(5x^2 +6x -8)
= (3 +5)x^2 +(-2 +6)x +(4 -8)
(f +g)(x) = 8x^2 +4x -4
Melissa bought a sofa on sale for $630. This price was 28% less than the original price.
What was the original price?
Answer:
630 is 28% of 2250.
Step-by-step explanation:
28 / 100 = .28
2250 X .28 = 630.
What is the answer to this?
Answer:
56
Step-by-step explanation:
Answer:
i think its 140 because u got to add all the sides in order to subtract from 180
i dont know if its right but that is what i think UwU
if 3 chickens in 3 days layed 3 eggs how many eggs would be layed by 12 chickens in 12 days
Answer:
142
Step-by-step explanation:
(if I'm doing the math in my head right)3×3×3 to find the number of eggs that three chickens would lay in three days, so that would be 27it seems like it's saying that chickens can only lay 3 eggs per day, so what I would do is multiply 12*12 (144) and then multiply 144 by 3so maybe 142?Solve (x 3)2 (x 3) â€"" 2 = 0. Let u =.
The solution to the original equation will be -2 and -6
Given the function [tex](x + 3)^2 + (x + 3) - 2 = 0.[/tex]
If u = x + 3, the function in terms of "u" will be;
[tex]u^2+u-2=0[/tex]
Factorize the resulting equation as shown:
[tex]u^2+u-2=0\\u^2+2u-u-2=0\\u(u+2)-1(u+2)=0\\(u-1)(u+3) = 0\\u=1 \ and \ -3[/tex]
Since x + 3 = u
x = u - 3
If u = 1
x = 1 - 3 = -2
If u = -3
x = -3 - 3 = -6
Hence the solution to the original equation will be -2 and -6
Correct question:
Solve (x + 3)^2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u – 2 = 0 u2 + u + 1 = 0 Factor the equation. What are the solutions of the original equation?
Learn more on factorization here: https://brainly.com/question/25829061
Which equation could be used to solve the question below?
Justine went to the doughnut shop and bought d boxes of 24 doughnut holes. Then, she took 37 doughnut holes to her morning meeting. Now, she has 83 doughnut holes left. How many boxes of doughnut holes did Justine buy in all?
Answer:
5 PLZ GIVE BRAINLIEST
Step-by-step explanation:
83+37 = 120
120/5=24
If a city with a population of 500,000 doubles in size every 85 years, what will the population
be 340 years from now?
Answer:
8,000,000
Step-by-step explanation:
if 500,00 is the first year and in 85 years it will be 1,000,000, then after 180 years 2,000,000 and then 4,000,000 after 265 years then 8,000,000 after 340 years
ax4 + bx2 + c=0 (a>0) (c>0)
The quadratic equation has two solutions If
1)b2>4ac
2) b2-4ac>0
The quadratic equation has two solutions if b^2 - 4ac > 0
Given the equation ax^4 + bx^2 + c=0
Let P = x^2Substitute into the formula to have:
a(x^2)^2 + bx^2 + c =0The equation becomes aP^2 + bP + c = 0
For us to have a unique solution, the discriminant b^2 - 4ac must be greater than zero. Hence the quadratic equation has two solutions if b^2 - 4ac > 0
learn more on discriminant here; https://brainly.com/question/1537997
when we simplify (ab + 3c)^2 we get
Answer:
a^2b^2+6abx+9c^2
Step-by-step explanation:
(a + b)2 = a2 + 2ab + b2
(ab+3c)^2=(ab)^2+2ab*3c+(3c)^2
Hey there!
(ab + 3c)^2
= (ab + 3c)(ab + 3c)
DISTRIBUTE
= ab(ab) + ab(3c) + 3c(ab) + 3c(3c)
= a^2 b^2 + 3abc + 3abc + 9c^2
COMBINE the LIKE TERMS
= a^2 b^2 + 6abc + 9c^2
Therefore, your answer is:
a^2 b^2 + 6abc + 9c^2
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
What is the value of log3 27?
Answer:
Logarithm base 3 of 27 is 3 .Step-by-step explanation:
hope it helpsAnswer:
3
Step-by-step explanation:
27 = 3 x 3 x 3 = 3³
log3 27
= log3 3³
= 3 log3 3
= 3 x 1
= 3
Note : -
Formulas : -
Logn n = 1
Logn n^n = n Logn n
1) The graph below represents the function y = f(x). State the domain and range of this
function in interval notation.
Please use the graph below and not some other graph. A 20,000 gallon swimming pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1250 gallons per hour.
Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full.
Answer:
see attached
Step-by-step explanation:
The graph starts at 5000 gallons on the vertical axis, and increases at the rate of 1250 gallons per hour, or 5000 gallons per 4 hours until 20,000 gallons is reached after 12 hours.
__
Additional comment
We don't have access to your segment tool, so you will have to copy the graph.
please help dont want to fail final exam
How much does she earn if she does not make any sales on a given day?
Question 7 options:
$75
$175
$0
$25
Answer:
$75 I think. Not 100% sure but like 95% sure :)