Solve by the elimination method. [tex]4x+8y=40\\-4x+y=14[/tex]

Answers

Answer 1

Answer:

[tex]x=-2,y=6[/tex]

Step-by-step explanation:

We can add these 2 equations together to eliminate [tex]x[/tex] from the equation, leaving us to solve for [tex]y[/tex].

[tex](4x+8y) + (-4x+y) = (40) + (14)\\9y = 54\\\boxed{y = 6}[/tex]

Now we can solve for [tex]x[/tex] through substituting [tex]y[/tex].

[tex]4x+8y=40\\4x+8(6)=40\\4x+48=40\\4x=-8\\\boxed{x=-2}[/tex]

We can check our answers by substituting [tex]x[/tex] and [tex]y[/tex] into one of the equations and seeing if the equation is true.

[tex]-4x+y=14\\-4(-2)+6=14\\8+6=14\\14=14[/tex]

LHS = RHS so our answers are correct.


Related Questions

Which algebraic expression is equivalent to the expression below? 2(x - 5) + 13(x + 7) please help!!

Answers

Answer:

C

Step-by-step explanation:

The population in the United States was roughly 161,000,000 in 1950. By 2000, it had grown to roughly 291,000,000. Assume that the population in the United States grew linearly during that period. Find a linear equation which models the population in the United States during the period 1950 to 2000

Answers

to get the equation of any straight line, we simply need two points off of it, so let's use the ones provided in the table above.

[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{millions}{population}&year\\ \cline{1-2} 161&1950\\ 291&2000\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{161}~,~\stackrel{y_1}{1950})\qquad (\stackrel{x_2}{291}~,~\stackrel{y_2}{2000}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2000}-\stackrel{y1}{1950}}}{\underset{run} {\underset{x_2}{291}-\underset{x_1}{161}}} \implies \cfrac{ 50 }{ 130 }\implies \cfrac{5}{13}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1950}=\stackrel{m}{\cfrac{5}{13}}(x-\stackrel{x_1}{161}) \\\\\\ y-1950=\cfrac{5}{13}x-\cfrac{805}{13}\implies y=\cfrac{5}{13}x-\cfrac{805}{13}+1950\implies y=\cfrac{5}{13}x+\cfrac{24545}{13}[/tex]

This set of points is on the graph of a function.
{(-3, 9), (-1, 1), (0, 0), (2, 4)}
Which points are on the graph of the inverse?
Select each correct answer.
(-9, 3)
(1, − 1)
(4,2)
(0, 0)

Answers

Answer:

Points on the inverse are [tex](1,-1), (4,2), \text{and } (0,0)[/tex]

Step-by-step explanation:

When writing the inverse function of a set of points, you simply switch the coordinates:

[tex]\text{Function}: (x,y)\\\text{Inverse}: (y,x)[/tex]

We are given the points

[tex](-3,9), (-1,1), (0,0), \text{and } (2,4)[/tex]

Using our rule for function, our new points will be

[tex](9,-3), (1,-1), (0,0), \text{and } (4,2)[/tex]

From the list, the points we have for the graph of the inverse are

[tex](1,-1), (4,2), \text{and } (0,0).[/tex]

find the height of a a cuboid if it's length is 10m , breadth is 5m and LSA is 180m² .

NONSENSE = REPORT ​

Answers

[tex]\huge\sf\underline{Answer}[/tex]

Let's find out ~

Given :-

Length ( l ) = 10m Breadth ( b ) = 5m LSA = 180m²

Solution :-

[tex]\sf\rightarrow \:LSA \: of \: cuboid \: = 2h \: ( \: l + b \: )[/tex]

[tex]\sf\rightarrow \: 180 = 2h \: (10 + 5)[/tex]

[tex]\sf\rightarrow180 = 2h \: \times 15[/tex]

[tex]\sf\rightarrow 180 = 30h \: [/tex]

[tex]\sf\rightarrow \: 30h \: = 180[/tex]

[tex]\sf\rightarrow \: h = \frac{180}{30} [/tex]

[tex]\sf\rightarrow \: 6[/tex]

Thus , the height of cuboid is 6m

If f(x) = x³ +7x²-x and g(x)=x²-3, What is the degree of g(f(x))?
a)2
b)3
c)6
d)8

Answers

Answer:

c) 6

Step-by-step explanation:

Given :

⇒ f(x) = x³ + 7x² - x

⇒ g(x) = x² - 3

===============================================================

Finding the degree of g(f(x)) :

⇒ Degree of f(x) = 3

⇒ Degree of g(x) = 2

⇒ Therefore, degree of g(f(x)) = degree of f(x) × degree of g(x)

⇒ Degree of g(f(x)) = 3 × 2

⇒ Degree of g(f(x)) = 6

g(f(x))g(x³+7x²-x)(x³+7x²-x)²-3

Degree of g(f(x))

Use Pascal's law

3×26

Option C

what is the area of this rectangle

Answers

Answer:

6 cm^2

Step-by-step explanation:

Area of Rectangle is L*W

L=3 and W=2

3*2=6

Jessie invests $33 in the stock market. Over the 3 years she has this invested she gets an average return of 7,8%. How much will her investment be worth after the 3 years?

Answers

Answer:

it would end up being about $40.73

Step-by-step explanation:

multiply 0.078 by 3 then multiply that by 33

Answer:

hope you can understand

Can someone please help me with this? it's really important, ill give 10 points for this.

Answers

Answer:

ill answer

Step-by-step explanation:

but what is the question please make me brillianist

Select the correct answer. in which career would you most likely apply concepts from geometry? a. food critic b. social worker c. radio dj d. computer game designer

Answers

Answer:

Computer game designer.

Step-by-step explanation:

If you want to design a game, you need to have some basic shapes and stuff in it. I'm not sure what else needs to be explained here lol

please help... The triangle represents a cross section from a 3D prism. Draw or describe the 3D prism that produced this cross section. ​

Answers

The 3D prism that produced the cross-section of a triangle is a triangular prism.

How to describe the 3D prism?

From the given figure, we can see that the cross-section is a triangle

One of the faces of a triangular prism is a triangle.

This means that when the triangular prism is cut vertically, a triangle face is created

Hence, the 3D prism that produced the cross-section of a triangle is a triangular prism.

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7/8 - 6/7. what is the answer.???

Answers

Answer:

0.0178 is the answer

The sum of the volume of two rectangular prisms, box a and box b are 14.325cm cubed. Box a has a volume of 5.61cm.

Answers

The equation that could be used to determine the volume of Box B is (B = 14.325cm³ - 5.61cm³) and the volume of Box B is 8.715cm³.

This question is incomplete, the complete question is:

The sum of the volume of two rectangular prisms, box a and box b are 14.325cm cubed. Box a has a volume of 5.61cm.

a. Let B represent the volume of Box B in cubic centimeters. Write an equation that could be used to determine the volume of Box B.

b. Solve the equation to determine the volume of Box B

What is volume?

Volume is simply the amount of space that is enclosed within a container.

Given that;

Sum of the volume of two rectangular prisms A&B = 14.325cm³Volume of Box A = 5.61cm³

a)

Let B represent the volume of Box B in cubic centimeters. The equation that could be used to determine the volume of Box B will be;

Sum of the volume of two rectangular prisms A&B = Volume of Box A + Volume of Box B

14.325cm³ = 5.61cm³ + B

B = 14.325cm³ - 5.61cm³

Hence, The equation that could be used to determine the volume of Box B is B = 14.325cm³ - 5.61cm³

b)

To determine the volume of Box B, we solve the equation.

B = 14.325cm³ - 5.61cm³

B = 8.715cm³

Hence, the volume of Box B is 8.715cm³.

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i need help on this may you help

Answers

Answer:

should be 63

Step-by-step explanation:

Set A= 1, 3, 4, 5, 9, 10, 11
Set B= 2, 4, 6, 7, 11, 12
What is the union of sets A and B?

Answers

Answer:

1 ,2,3,4,5,6,7,9,10,11,12 is the union

Answer:

A U B = {1,2,3,4,5,6,7,9,10,11,12}

Step-by-step explanation:

Union of sets is a set containing all elements that are in A or  B.

A = {1,3,4,5,9,10,11}

B= {2,4,6,7,11,12}

A U B = {1,2,3,4,5,6,7,9,10,11,12}

Solve the equation for x
z=m+x-y a)x=-z+m+y b)x=z-m+y c)x=z+m-y d)x=z+y+m

Answers

Answer:

x = z - m + y

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z = m+x-y}[/tex]

To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.

[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]

Therefore, the answer to this question is x = z - m + y

Please let me know if you have any questions regarding my answer or explanation!

PLEASE HELP!

Martha and Emily had to sew dresses with beads. Emily had 20% more beads than Martha. Then Emily gave 25% of her beads to Martha. Now Martha has 80 beads more than Emily. How many beads did each dressmaker had at the start?​​

Answers

Answer:

Emily has about 73 beads and Martha has about 62

Step-by-step explanation:

E = M · 1.2

M + ( .25 · E ) = m

m = 80

Now work backwards to find the answer.

Note that to find the answer you must get rid of the variable E, so you must use the expression M · 1.2 to represent E.

M + ( .25 · M · 1.2 ) = 80

M + .3M = 80

1.3M = 80

Divide both sides by 1.3

M = 61.5

Round to the nearest one

M = 62

Now use this to find E

E = 62 · 1.2

E = 74.4

Round to nearest one

E = 73

This might be confusing but I hope it was helpful!

Also, can I get brainliest because this took a lot of work to figure out.

A triangular prism. The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet. The 2 triangular sides have a base of 2 feet and height of 1.5 feet.

Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.



If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?


Trenton will need
square feet of plywood.

Answers

The amount of plywood that he needs to buy will be 21 square feet.

What is the surface area of the triangular prism?

Let the prism with a length of L of the rectangular surface.

And the dimension of the triangle is A, B, and C. Then we have

SA = 2(area of triangle) + 3(area of rectangle surface)

A triangular prism.

The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet.

The 2 triangular sides have a base of 2 feet and a height of 1.5 feet.

Then the area of the triangle will be

⇒ 1/2 x 2 x 1.5

⇒ 1.5 square feet

The area of the rectangles will be

⇒ 3 x 2 + 3 x 2.5 + 3 x 1.5

⇒ 18 square feet

Then the surface area of the triangular prism will be

Surface area = 2 x 1.5 + 18

Surface arae = 3 + 18

Surface area = 21 square feet

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Given that 2x³-5x² - 4x+8 = (Ax - 1)(x-B)(x + 1) + C for all values of x, find the
values of A, B and C.

Answers

Answer:

A=2, B=3, C=5

Step-by-step explanation:

Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way

[tex](Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C[/tex]

Now, for the two polynomials to be the same we need to have, at the same time

[tex]x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8[/tex]

You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.

Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.

Fill in the blank. using decimals write the number 348.562 in expanded form:

348.562 =

Answers

Answer / Step-by-step explanation:

(300.500+40.60+8.2)=348.562

What is the surface area of the cylinder? Please show work.

Answers

Answer:

Surface area is 288π cm² (exact solution), which is approximately 904.78 cm² (if you use pi on calculator) or 904.32 cm² (if you use 3.14 for pi).

Step-by-step explanation:

Surface area of cylinder

[tex]SA = 2 \times \text{area of base} + \text{lateral area}\\SA = 2 \pi r^2 + 2 \pi r h[/tex]

SA ... surface area

r ... radius

h ... height of cylinder

Given:

d = 12 cm

h = 18 cm

Since diameter d is 12 cm, that means that radius is half of that, so 6 cm.

r = 6 cm

Insert in formula:

[tex]SA = 2 \pi r^2 + 2 \pi r h\\SA = 2 \pi (6)^2 + 2 \pi (6)(18)\\SA = 72 \pi + 216 \pi\\SA = 288 \pi \text{ cm}^2 \approx 904.78 \text{ cm}^2[/tex]

what is the answer to −1.4+(−1.2)

Answers

Answer:

-2.6

Step-by-step explanation:

-1.4+(-1.2)

-1.4-1.2=-2.6

Hope this helps!

If not, I am sorry.

Find the values of x in the following figures.
Please help​

Answers

Answer:

1) x = 15°2) x = 60°

Step-by-step explanation:

1)

(2x + 4x + 6x) * 2  = 360*

2x + 4x + 6x = 180°

12x = 180°

x = 180 : 12

x = 15

2)

(2x + x) * 2 = 360

2x + x = 180

3x = 180

x = 180 : 3

x = 60°

Cut-1 Cut-2 Number of rope cutting 1 2 3 Resulting pieces 3 5 7 1.2.1 The number of pieces of ropes for FIVE cuts. 4 S​

Answers

The answer to the all parts given below.

What is sequence?

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

For 5 cuts number of pieces will be 11 pieces.

General formula:

Tn= 2n+1

For 153 rope pieces number of rope cutting

2n+1=153

2n= 152

n= 76

For 11 cuttings rope pieces will be

2(11)+1

= 23

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6
the incomplete pictogram shows information about the number of eggs sold
shop on monday.
monday
tuesday
wednesday
on monday the shop sold 18 eggs.
on tuesday the shop sold 24 eggs.
on wednesday the shop sold 27 eggs.
use this information

Answers

The number of eggs sold on Tuesday is 2 complete circles, while the number of eggs sold on Wednesday is 2 complete circles and 1 quarter of the circle.

What is a graph?

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

Given on Monday the shop sold 18 eggs. Therefore, each quarter of the circle represents 3 eggs.

Hence, the number of eggs sold on Tuesday is 2 complete circles, while the number of eggs sold on Wednesday is 2 complete circles and 1 quarter of the circle.

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A number cube is rolled 14 times and the results are recorded in the table.

what, in simplest form, is the experimental probability that the number 4?

Answers

Answer:

2.3333 ≈ 2

Step-by-step explanation:

The first step is the 1/6 because you are only counting the value 4 not the other ones like 1,2,3,5,6. So then that is 0.1666666. Then you multiply it by 14 which is rounded to 2. I can tell you are a 6th grader.

DISCLAIMER: THIS ANSWER MAY BE FALSE BECAUSE THERE IS NO PICTURE ATTACHED TO THIS POST. THUS, NEXT TIME YOU SHOULD UPLOAD A PICTURE. THIS IS ONLY A GUESS NOT A REAL ANSWER.

Solve for x. Round your answer to the nearest tenth if necessary.

Answers

Answer: 8.8

Step-by-step explanation:

Because [tex]\angle S \cong \angle S[/tex] by the reflexive property, we know that [tex]\triangle STU \sim \triangle SQR[/tex] by AA.

So, by the triangle proportionality theorem,

[tex]\frac{x}{5.3}=\frac{11.1}{6.7}\\x=(11.1/6.7)(5.3) \approx \boxed{8.8}[/tex]

At a football game, the quarterback threw the football and the receiver caught it for a 12-yard gain. What integer represents the yards gained?


1/12

12

-12

6

Answers

12 because it’s a positive gain


What percentage of 2 hours is 12 minutes?

Answers

Answer:

10%

Step-by-step explanation:

1. Convert 2 hours to minutes

            2(60) = 120 min.

2.Calculate the percentage

[tex](\frac{12}{120} )(100)=10[/tex]

12 minutes is 10% of 2 hours

Hope this helps

What is the value of y?
log^464 = y
OA. 16
OB. 8
OC. 3
OD. 4

Answers

The value of y in the given logarithmic equation is 3. The correct option is C. 3

Evaluating Logarithmic equation

From the question, we are to determine the value of y in the given logarithmic equation

The given equation is

[tex]log_{4}64=y[/tex]

By applying one of the laws of logarithm, we get

[tex]64 = 4^{y}[/tex]

Now, express 64 in index form,

[tex]4^{3} = 4^{y}[/tex]

Since the bases are equal, we can equal the powers to get

3 = y

∴ y = 3

Hence, the value of y in the given logarithmic equation is 3. The correct option is C. 3

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Please answer this question

Answers

Answer:

A: Isosceles B: EquilateralC: ScaleneD: Isosceles E: Isosceles F: Scalene

Step-by-step explanation:

We can classify triangles by their sides into three types:

Equilateral: It is when the triangle has all the equal sides.Isosceles: It is when the triangle has only two equal sides.Scalene: It is when none of the sides of a triangle are equal.

MissSpanish
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