solve the system of equations by substitution -6x+7y=23, -5x+y=24

Final answer:

To find the area of the basement, we started with the given perimeter of 130 feet and the known length of 25 feet and solved for the missing width. Once we determined the width was 40 feet, we used the formula for the area of a rectangle (Area = length × width) to calculate that the basement's area is 1000 square feet.

Explanation:

To solve the question regarding the area of a rectangle where the length is 25 feet and the perimeter is 130 feet, we must first deduce the width of the rectangle using the perimeter formula: P = 2l + 2w (where P is the perimeter, l is the length, and w is the width). Since we know the perimeter (P) and the length (l), we can rearrange this formula to solve for the width (w).

The perimeter formula is expressed as:

130 = 2(25) + 2w

130 = 50 + 2w

2w = 130 - 50

2w = 80

w = 40 feet

Now that we have both the length and the width, we can calculate the area of the rectangle using the formula Area = length × width.

Therefore, the area of the rectangle is:

Area = 25 feet × 40 feet
Area = 1000 square feet

The value of -36 divided by (-4/9) is 81, which is found by multiplying -36 with the reciprocal of (-4/9), giving the result 324/4, which simplifies to 81.

To find the value of -36 divided by (-4/9), you can think of division by a fraction as multiplication by its reciprocal. So, the problem changes from division to multiplication: -36 * (-9/4). To solve this:

First, multiply the numerators: -36 * -9 = 324.

Then, multiply the denominators: 1 * 4 = 4.

Now, divide 324 by 4 to get 81.

Therefore, the value of -36 divided by (-4/9) is 81.

Answer:

two to the power of one multiply by two hundred twenty seven to the power of one.

Step-by-step explanation:

456÷2=227

227 can not be divided any further so it would be two to the power of one multiply by two hundred twenty seven to the power of one.

You are supposed to find prime factorization by dividing the number by prime numbers.

Answer: They each paid $2.40.

Answer:

all books to new books- 14:5

used books to new books- 5:9

Step-by-step explanation:

Answer: a. 14:5 b. 5:9

Step-by-step explanation:

There are 14 books and 9 are new so subtract 9 from 14 and get 5 and your ration would be 14:5. Once you have the answer to a you know how many new books there are and how many old books there are, so you can easily figure out the ratio would be 5:9.

I'll do the first part to get you started.

--------------------

Area = 1/2

Length = 7/8

Width = W

Area of rectangle = Length*Width

A = L*W

1/2 = (7/8)*W

(8/7)*(1/2) = (8/7)*(7/8)*W .... see note1 below

(8*1)/(7*2) = (8*7)/(7*8)*W .... see note2

8/14 = (56/56)*W

4/7 = 1*W .... see note3 and note4

--------------------

Foot notes

Answer:

x = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Given

3x = 6x - 2 ( subtract 6x from both sides )

- 3x = - 2 ( divide both sides by - 3 )

x = [tex]\frac{-2}{-3}[/tex] = [tex]\frac{2}{3}[/tex]

Answer:

x=2/3

Step-by-step explanation:

Its just right

1. Find how much one pound is.

- to do this, divide 1.50 by 9. This will give you one pound.

2. Figure out how many times 1 pound can go in a dollar.

proportion

[tex]\frac{9}{1,5} = \frac{x}{1} \\[/tex]

1.5x=9*1

1.5x=9

x=[tex]\frac{9}{1.5}[/tex]

x=6

Answer:

22

Step-by-step explanation:

Let x be a number

Other number = 39 -x

x - (39 - x) =5

x - 39 + x = 5

2x = 5 + 39 = 44

x = 44/2

x = 22

Other number = 39 - 22 = 17

Answer:

The larger number = 22

Step-by-step explanation:

Let the two number x and y

The sum of two numbers is 39 can be represented as:

x + y = 39----------------1

The difference of two numbers is 5 can be represented as:

x - y = 5------------------2

x + y = 39----------------1

x - y = 5------------------2

Using Elimination Method and subtracting 2 from 1

x-x + y-(-y) = 39 - 5

0+y+y=34

2y=34

y=34/2

y=17

substituting y=17 in 1

x+17=39

x=39-17

x=22

∴ The larger number = 22

Answer:

[tex]The \: circle \: has \: a \: bigger \: area \: by \approx 438 \: {ft}^{2} [/tex]

Explanation:

[tex]Diameter \: of \: circle:160 \div 3.14 \approx 51 \: ft \\ Area \: of \: circle : \frac{3.14 \times {51}^{2} }{4} \approx 2038 \: {ft}^{2} \\ Sides \: of \: square:160 \div 4 = 40 \: ft \\

Area \: of \: square: \: {40}^{2} = 1600 \: {ft}^{2} \\ 2038 - 1600\approx 438 \: {ft}^{2} [/tex]

Final answer:

Comparing the areas of a circle and a square with the same perimeter of 160 feet, the circle has a greater area by approximately 435.75 square feet.

Explanation:

We are comparing the areas of a circle and a square which both have a perimeter of 160 feet. For the square, since the perimeter (P) is 160 feet, each side (s) will be P/4, which gives us s = 40 feet. The area of the square (Asquare) is s², so Asquare = 40² = 1600 square feet.

For the circle, the perimeter is the circumference (C), which is 160 feet. The formula for the circumference of a circle is C = 2πr, where r is the radius. So, 160 = 2πr, giving us r = 160/(2π). The area of the circle (Acircle) is πr², so Acircle = π(160/(2π))². After calculation, we find that Acircle ≈ 2035.75 square feet.

Comparing the two areas, the circle has a greater area than the square by Acircle - Asquare ≈ 2035.75 - 1600 ≈ 435.75 square feet.

Answer:

30, 42

Step-by-step explanation:

You add 2 to the additional 2 you started with

0+2=2

2+(2x2)=6

6+(2x3)=12

The required next two-term of the sequence is 30 and 42.

Given that,
To determine the pattern and next two-term of numbers 0, 2, 6, 12, 20.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
The given sequence is,
0, 2, 6, 12, 20,
a0 = 0,
a1 = 2
nth term an = a(n - 1) + 2(n - 1)
For 6th term
n = 6
6th term = a(6 - 1) + 2(6 - 1)
        a6 = a5 + 10
        a6 = 20 + 10
        a6  = 30
7th term,
an = a(n -1) + 2 (n - 1)
a7 = a6 + 2*6
a7 = 30 + 12
a7 = 42

Thus, the required next two-term of the sequence is 30 and 42.

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Answer:

B. 2/12 = 78/x ; x = 468

Step-by-step explanation:

12/2 = 78/x

6 = 78/x

6 x 78 = x

468

Answer: It’s D, i got it right!!

Step-by-step explanation:

Answer: The dimensions of the rectangle are

Length = 75 and Width = 63

Step-by-step explanation: We would start with the information about the sides of the rectangle which states that the length is twelve inches more than it's width. In other words, if the width is represented by the letter w, then the length will be w + 12.

Also the perimeter of a rectangle is given as

2(L + W) where L is the length and W is the width of the rectangle

Therefore

Perimeter = 2( {w +12} + w)

276 = 2(2w + 12)

276 = 4w + 24

Subtract 24 from both sides of the equation

252 = 4w

Divide both sides of the equation by 4

63 = w

Therefore the width of the rectangle is 63 and the length is 75 (63 + 12).

L = 75 inches

W = 63 inches

Answer:  1.75 cubic feet concrete is needed.

Step-by-step explanation:

Alright, lets get started.

The volume of the pillar is : [tex]\pi r^2h[/tex]

We have given the height is 5 feet.

We have given the diameter is 4 inches.

So the radius will be : [tex]\frac{4}{2}=2 \ inches[/tex]

Converting inches into feet.

The radius will be : [tex]\frac{2}{12} \ feet[/tex] [tex]= 0.167 feet[/tex]

So the volume of the cylinder will be : [tex]\pi * 0.167^2*5[/tex]

So the volume of the cylinder will be : [tex]0.4380 \ cubic \ feet[/tex]

As there are 4 pillars, so total volume will be : [tex]4*0.4380[/tex]

So, total volume will be : [tex]1.75 \ cubic \ feet[/tex]

Hence 1.75 cubic feet concrete is needed.   :   Answer

Hope it will help :)

Answer:

1.75 cubic feet

Step-by-step explanation:

Measure the diameter of the cylinder. ...

Hope this helps

the equation line of the scatter plot is y = ×+10

Answer:

Step-by-step explanation:

Correct option:

[tex]\boxed{x-y=P-Q}[/tex]

Given that the line we are looking for is parallel to g, then the slope of that line and g is the same, therefore:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ (x_{1},y_{1})=(-3,2) \\ \\ (x_{2},y_{2})=(0,5) \\ \\ \\ m=\frac{5-2}{0-(-3)}=1[/tex]

So we can write the point-slope form of the equation of the line as follows:

[tex]y-y_{0}=m(x-x_{0}) \\ \\ (x_{0},y_{0})=(P,Q) \\ \\ \\ y-Q=1(x-P) \\ \\ y-Q=x-P \\ \\ \\ Arranging: \\ \\ P-Q=x-y \\ \\ \boxed{x-y=P-Q}[/tex]

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A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope and b is the y intercept.

Line g passes through (-3,2) and (0,5). hence:

Two lines are parallel if they have the same slope. Hence:

Line parallel to line g has a slope of 1. Since it passes through (P, Q), hence:

[tex]y-y_1=m(x-x_1)\\\\y-Q=1(x-P)\\\\y-Q=x-P\\\\x-y=P-Q[/tex]

The equation of a line that is parallel to line g that contains (P, Q) is x - y = P - Q

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Answer:

  0

Step-by-step explanation:

Put the numbers where the letters are and do the arithmetic.

  (1)^2(-1)^2 +(1)(-1) -(-1)^3 -(1)^3

  = 1·1 -1 -(-1) -1

  = 1 - 1 + 1 - 1 = 0

The value of the expression is 0.

Answer:

Length = 24 cm

Width = 6 cm.

Step-by-step explanation:

The formula to compute the perimeter of a rectangle is,

[tex]Perimeter=2(length+width)[/tex]

Given:

Perimeter = 60 cm

width = w

length = 4w

Determine the value of width as follows:

[tex]Perimeter=2(length+width)\\60=2\times(4w+w)\\60=10w\\w=6[/tex]

The value of length is:

[tex]length(l)=4\times w\\l=4\times6\\l=24[/tex]

Thus, the length and the width of the rectangle are 24 cm and 6 cm respectively.

Answer:

The area of the composite figure = 12.785 square units

Step-by-step explanation:

The figure composite of :

A ⇒ Rectangle with coordinates (0,0) , (0,5) , (2,5) and (2,0)

B ⇒ Rectangle with coordinates (2,0) , (2,1) , (4,1) and (4.0)

C ⇒ Quarter of a circle with coordinates (2,1) , (2,2) and (3,1)

Area of A: Length = 5 and Width =2

Area of A = Length times the width = 5*2 = 10 square units

Area of B: Length = 2 and Width =1

Area of B = Length times the width = 2*1 = 2 square units

Area of C: radius = 1

Area of C = 0.25 * pi * r² = 0.25 * 3.14 * 1² = 0.785 square units

Total Area = 10 + 2 + 0.785 = 12.785 square units

Answer:

the answer is 12.785

Step-by-step explanation:

i took the test

Answer:

[tex]\frac{7}{2}[/tex] square units.

Step-by-step explanation:

We have to use limits to find the area of the region bounded by the graph [tex]f(x) = 4 - 2x^{3}[/tex] , the x-axis, and the vertical lines x=0 and x=1.

So, the area will be

A = [tex]\int\limits^1_0 {(4 - 2x^{3})} \, dx[/tex]

= [tex][4x - \frac{x^{4}}{2} ]^{1} _{0}[/tex]

= [tex]4 - \frac{1}{2}[/tex]

= [tex]\frac{7}{2}[/tex] square units. (Answer)

Answer: $36

Step-by-step explanation:

Each cantaloupe is $1.5.

Answer:

he will spend 36 dollars because 24 ÷ 6 = 4 and 9$ times 4 = 36$

Answer:

5 days to spend exactly $710

Step-by-step explanation:

Answer:

5 days

Step-by-step explanation:

5 x 120 = 600

600 + 110 = 710

Answer:

[tex]\dfrac{14\pi }{3}\ cm[/tex]

Step-by-step explanation:

The circumference of the circle with radius of 7 cm is

[tex]C=2\pi r\\ \\C=2\pi \cdot 7=14\pi \ cm[/tex]

An arc of a circle o subtends an angle of [tex]120^{\circ}[/tex] at the centre.

The circle has the full angle of [tex]360^{\circ},[/tex] then

[tex]14\pi \ cm - 360^{\circ}\\ \\x\ cm - 120^{\circ}[/tex]

Write a proportion:

[tex]\dfrac{14\pi }{x}=\dfrac{360}{120}\\ \\\dfrac{14\pi }{x}=\dfrac{3}{1}\\ \\14\pi =3x\\ \\x=\dfrac{14\pi }{3}\ cm[/tex]

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{3}[/tex] x - 6 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{3} }[/tex] = 3

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 3 and (a, b) = (- 1, 5), thus

y - 5 = 3(x - (- 1)), that is

y - 5 = 3(x + 1) → A

We know x in f(x) is g(x) which is 2x^2 because we are to find (fg)(x)

f(x)=4(2x^2)+6

f(x)=8x^2+6

So (fg)(x) is 8x^2+6

Hope this helped!

(4x+6)(2x^2) = 8x3 + 12x2

Answer:

The value of tan P  = 1.875

Step-by-step explanation:

Given:

PR=17

RQ=15

PQ =8

To find:

tan P = ?

Solution:

In trigonometric ratio

tan = [tex]\frac{opposite}{adjacent}[/tex]

Now on substituting the given values(refer the figure)

tan (P) =[tex]\frac{15}{8}[/tex]

tan (P) = 1.875

Answer: 18

Step-by-step explanation: 2 x 2 x 2= 8

8 x 4 = 32

32 / 2 = 16

16 + 2 = 18