Henrique began to solve a system of linear equations using the linear combination method. His work is shown below:
3(4x – 7y = 28) → 12x – 21y = 84
–2(6x – 5y = 31) → –12x + 10y = –62 
      12x – 21y = 84
+   –12x + 10y = –62
              –11y = 22
y = –2
Complete the steps used to solve a system of linear equations by substituting the value of y into one of the original equations to find the value of x.
What is the solution to the system?

Answer:

Step-by-step explanation:

25b * (3a² - 1) = 25b * 3a² - 25b * 1

                     = 75ba² - 25b

Distributive law upon subtraction:

a(x - y) = ax - ay

Answer:

[tex]25b(3a*2-1)=25b(6a-1)[/tex]

Step-by-step explanation:

[tex]25b(3a*2-1)[/tex]

Multiply the numbers: [tex]3 * 2 = 6[/tex]

[tex]=25b(6a-1)[/tex]

Hope I helped, may I get brainliest and a thanks?

Thank you, have a good day! =)

Answer:yes

Step-by-step explanation: 20<_x-8 = 20 <_20 which is correct

Answer:

24

Step-by-step explanation:

m-n = 16

Let n = 8

m-8 = 16

Add 8 to each side

m-8+8 =16+8

m = 24

Answer:

(2,-3)

Step-by-step explanation:

have to multiply (-3) to the second equation to get -3x + 15y = 51 then you add  both equations .the 3 is remove (postive and negative cancels out )

2y+15y= 17y

0-51+-51

divide both sides by 17 y

-51/17= -3

then you plug -3 into the first equation  and get

x= 2

y=-3

Answer:

x=2 y=- 3

Step-by-step explanation:

Answer:

39200

Step-by-step explanation:

Revenue = number of cameras * cost

R(m) = N(m) * C(m)

        = (50m+600) * (4m^2-15m+45)

The months since may is June July August September = 4 months

R(4) = (50*4+600) * (4*4^2-15*4+45)

        (200+600) * (64-60+45)

           800*49

                39200

Answer:

39,200

Step-by-step explanation:

September is 4 months after may, so m = 4

No. of cameras:

N(4)=50(4)+600 = 800

Cost per camera:

C(4)=4(4²)-15(4)+45 = 49

Total cost:

N × C

800 × 49

39200

Answer:

False. 0.17

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the last number is the y intercept so the intercept in the line is -3.5 so I just matched them up.

Answer:

Option (3). 1571 in³

Step-by-step explanation:

Amount of cement required to fill the cement = Volume of the cone

Formula for the volume of the cone is

Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here r = radius of the cone

h = height of the cone

Volume = [tex]\frac{1}{3}\pi (10^{2})(15)[/tex]

             = [tex]\frac{1}{3}\pi (100)(15)[/tex]

             = [tex]\frac{1500\pi }{3}[/tex]

             = 500π

             = 1570.8

             ≈ 1571 in³

Therefore, Option (3) is correct.

Answer: y + 5 = 2 ( x + 1 ) = 2 x − y + 2 = 5

Answer:

 Slope = 4.000/2.000 = 2.000

 x-intercept = 3/2 = 1.50000

 y-intercept = -3/1 = -3.00000

Step-by-step explanation:

I hope this helped!

Answer:

The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles.

Step-by-step explanation:

Any prism has two bases.  Since we are talking about a rectangular prism and a triangular prism both must have two bases.

For example, a square prism has two bases and they are both square.

In this case a rectangular prism has two bases that are rectangles and a triangular prism also has two bases and both bases are triangles.

Note: For the figure to have only one base it must be called a pyramid.

Thus, the answer is:

The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles

Answer:

a

Step-by-step explanation:

Answer: it’s answer C.

Step-by-step explanation: 708.6 ÷ 6 = 118.1(0)

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

rectangle and triangle is here

area of triangle = 1/2 * 5 * 12 = 30

area of rectangle = 1 * 12 = 12

total is 12 + 30 = 42

Answer:

  512

Step-by-step explanation:

You can figure this a couple of ways.

1) Figure the number of muffin boxes that goes into each dimension of the larger box:

  (2 ft)/(3 in) = (24 in)/(3 in) = 8 . . . . muffin boxes in each direction.

Then the total number of muffin boxes that will fit in a larger box is ...

  8×8×8 = 512

512 muffin boxes can fit into the larger box.

__

2) The volume of a muffin box in cubic feet is ...

  ((3 in)/(12 in/ft))^3 = (1/4 ft)^3 = 1/64 ft^3

The volume of a larger box in cubic feet is ...

  (2 ft)^3 = 8 ft^3

Then the number of smaller boxes that will fit in the larger box is ...

  (8 ft^3)/(1/64 ft^3) = 8×64 = 512

512 muffin boxes can fit into the larger box.

Answer:

V = π*r^2*h/3

the formula not sure which answer represent that

117.29 ft^3

Step-by-step explanation:

Answer:

a = 47

b = 23.87

c = 90

d = 35.59

Step-by-step explanation:

I can only help this much. Not sure what the other two others below are asking

Answer: [tex]x=12[/tex]

Step-by-step explanation:

[tex]9+9=3(x-6)[/tex]

simplify: add the 9's together and distribute the 3

[tex]18=3x-18[/tex]

add 18 to both sides

[tex]36=3x[/tex]

divide by 3

[tex]12=x[/tex]

[tex]x=12[/tex]

I hope this helps you

Answer:

integer and rational hth

Step-by-step explanation:

Answer:

Uhhh the previous campers?

Step-by-step explanation:

No idea if this is some sort of trick question but I'm just going to go ahead and say the campers.

Answer:

a

Step-by-step explanation:

Answer:

The population density is 150 persons per square mile

Step-by-step explanation:

Firstly, we need to calculate the area of the trapezoid.

Mathematically, the area of a trapezoid is

(a+b)/2 * h

from the grid, we can obtain the lengths

on the x-axis , each line is 40(200/5 thin lines)

on the y-axis, each thin line also is 40(200/5 thin lines)

thus a = (8 * 40) = 320

b = (10* 40) = 400

h = (3 * 40) = 120

Inserting this into the area equation, we have the area of the trapezoid as (320 + 400)/2 * 120 = 43,200 units

since each unit = 1 mile, the area of Tennessee = 43,200 units

The population density is thus ; 6,495,978/43,200= which is approximately 150 persons per square mile

The population density is a number that gives the number of people located within the state.

[tex]\mathrm{The \ population \ density \ is \ approximately}\ \underline{150}\ \frac{persons}{mi.^2}[/tex]

Reasons:

The population of Tennessee = 6,495,978

The dimensions of the trapezoid model of the territory are;

Base length, a = 320

Base length, b = 400

Height of the trapezoid, h = 120

[tex]Area \ of \ the \ trapezoid = \mathbf{\dfrac{a + b}{2} \cdot h}[/tex]

Which gives;

[tex]Area \ of \ the \ trapezoidal \ territory = \mathbf{\dfrac{320 + 400}{2} \times 120 }= 43,200[/tex]

Area of the trapezoidal territory of the state = 43,200 mi²

[tex]The \ ratio \ of \ the \ population \ to \ the \ territory = \dfrac{6,495,978}{43,200} = 150.36986\overline 1[/tex]

Therefore;

[tex]The \ population \ density \approx \underline{150}\ \frac{persons}{mi.^2}[/tex]

Learn more here:

https://brainly.com/question/16098011

Answer:

Could u help me with my question

Step-by-step explanation:

Answer:

6dquare 2

Step-by-step explanation:

The square root of 108 in radical form is 6√(3). In general, to find √(a) in radical form, when a is not a perfect square, we use the.

Answer:

r  =  22 ft  the sprinkler sends water until 22 feet away

Step-by-step explanation:

A circular pattern has an area of  1,519,76 ft²

And  the areaof a circle is:

A(c) = π*r²

A(c) = 3,14 * r²     ⇒   1,519,76  =  3,14 * r²

r²  =  1,519,76/3,14      ⇒   r²  = 484

r  = √484

r  =  22 ft

Answer:

22 ft

Step-by-step explanation:

The sprinkler is located in the middle of the circular pattern created by the sprinkler therefore the distance from the center to the end of the circular pattern is called the RADIUS

note:

area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

      1519.76 = 3.14 * [tex]r^{2}[/tex]

therefore [tex]r^{2}[/tex] = 1519.76 / 3.14 = 484

therefore radius ( r ) = [tex]\sqrt{484}[/tex]  =  22 ft

The sprinkler is 22 feet away from the spread water

Answer:

a² - a  + 12

Step-by-step explanation:

(see attached)

using the Foil Method :

(-a + 3)(a + 4)

= (-a)(a) + (-a)(4) + (3)(a) + (3)(4)

= -a² - 4a + 3a + 12

= -a² - a  + 12

Answer: 70 meters

Step-by-step explanation:

Hi, since the situation forms a right triangle and a rectangle, we have to apply the Pythagorean Theorem (for the triangle)

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (the longest side) and a and b are the other sides.  

Replacing with the values given:  

65^2 = 16^2 + x^2  

4,225 = 256 + x^2

4,225-256 = x^2

3,969=x^2

√3,969 =x

63=x

We have calculated the missing side of the triangle, now we have to add the height of the rectangle:

63 +7 =70 meters

Feel free to ask for more if needed or if you did not understand something.  

Answer:

The answer would be {y|y>0}

Step-by-step explanation:

hope this helps

Answer:

x >-2

Step-by-step explanation:

-4(x-1)<12

Divide each side by -4, remembering to flip the inequality

-4/-4(x-1)<12/-4

x-1 > -3

Add 1 to each side

x-1+1 > -3+1

x >-2

open circle at -2  

line extending to the right