What is the solution to the system of equations?
y = -3x + 5
5x – 4y = -3

Answer:

[tex] \overline{EG} \cong \overline{HK} [/tex]

[tex] \overline{HJ} \cong \overline{EF} [/tex]

[tex] \angle F \cong \angle J [/tex]

[tex] \angle H \cong \angle E [/tex]

∆FGE ≅ ∆JKH

Step-by-step explanation:

Since ∆EFG ≅ ∆HJK, therefore, the corresponding sides and angles of both ∆s are congruent.

Thus:

[tex] \overline{EG} \cong \overline{HK} [/tex]

[tex] \overline{HJ} \cong \overline{EF} [/tex]

[tex] \angle F \cong \angle J [/tex]

[tex] \angle H \cong \angle E [/tex]

∆FGE ≅ ∆JKH (take note of the arrangement of the letters or naming of each vertex of both triangles. Each vertex of in one ∆ must correspond to the vertex of the other for the ∆s to be congruent)

△EFG ≅ △HJK,

From the figure attached we can conclude  that

  [tex]\rm \bar {EG}[/tex] ≅ [tex]\rm \bar {HK}[/tex]

  [tex]\rm \bar HJ[/tex] ≅ [tex]\rm \bar FE[/tex]

   ∠[tex]\rm F[/tex] ≅∠[tex]\rm J[/tex]

   ∠[tex]\rm H[/tex] ≅∠[tex]\rm E[/tex]

△FGE ≅ △JKH

Given that

△EFG ≅ △HJK,

Since △EFG ≅ △HJK is given hence we can conclude that corresponding sides and corresponding angles of both the triangles will be equal.

Two triangles are said to be congruent when they are of similar shape and size means all the angles of one triangle are  equal to the corresponding angles of other triangle and  all the  sides of one triangle are equal to  corresponding sides of other triangle.

From the figure attached we can conclude  that

  [tex]\rm \bar {EG}[/tex] ≅ [tex]\rm \bar {HK}[/tex]

  [tex]\rm \bar HJ[/tex] ≅ [tex]\rm \bar FE[/tex]

   ∠[tex]\rm F[/tex] ≅∠[tex]\rm J[/tex]

   ∠[tex]\rm H[/tex] ≅∠[tex]\rm E[/tex]

△FGE ≅ △JKH

For more information please refer to the link below

https://brainly.com/question/25063327

Answer:

16 = x

Step-by-step explanation:

Since angle B and E are congruent to each other (because triangle ABC is congruent to triangle DEC), We can set up an equation to find x.

x + 15 = 6x - 65

Add 65 and subtract x to and from both sides.

80 = 5x

Divide by x.

16 = x.

Answer:

she decorated two cookies per minute

Step-by-step explanation:

72 cookies divided by 36 minutes

Answer:

11x+11

Step-by-step explanation:

4x+8+7x-3=11x+11

Hope this helps :D

Answer:

11x + 11

Step-by-step explanation:

( 4x + 8 ) + ( 7x + 3 )

Remove parenthesis;

Note: Remember, the associate property states that if an equation is either all multiplication or addition, then it can be done in any order, hence the parenthesis holds no weight in this case.

4x + 8 + 7x + 3

Combine like terms;

11x + 11

Answer:

The Value of "A" is 10.0 Inches

The Value of "B" is 35 Inches

Step-by-step explanation:

Got it right on

E D G E N U I T Y 2021

The value of A is 10.

The value of B is 35.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A 3-column table with 2 rows. Column 1 is labeled Scale factor with entries 1, 1.25. Column 2 is labeled Width with entries 8 inches, A. Column 3 is labeled Length with entries 28 inches, B.

Hence, We can formulate;

The value of A = 1.25 × 8

                       = 10

And, The value of B is,

⇒ 1.25 × 28

⇒ 35

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ6

Answer:

33

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

3(11)=33

hope this help

Answer:

5 to 8  &  5/8

Step-by-step explanation:

Answer:

832,000

Step-by-step explanation:

Answer:

The area of the square is 15²

the area of a square and the length of its side are directly proportional because The area of the square is x²=> when its edge decreases, the area of ​​the figure decreases

Step-by-step explanation:

Answer:

It will take 5.3 years to reach $39,500

Step-by-step explanation:

Compound Interest

It occurs when the interest is reinvested rather than paying it out.

Interest in the next compound period is then earned on the principal sum plus the previously accumulated interest.

The formula is:

[tex]\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

We are required to find the time needed to convert the principal P into a given final amount.

Solving the above equation for t, we get:

[tex]\displaystyle t=\frac{log(A/P)}{n\cdot log\left(1+r/n\right)}[/tex]

Anne invested P=$28,000 in an account at r=6.5%=0.065 compounded daily. There are 360 days in a year, so n=360. The final amount A=$39,500.

Substituting into the formula:

[tex]\displaystyle t=\frac{log(39,500/28,000)}{360\cdot log\left(1+0.065/360\right)}[/tex]

t=5.3 years

It will take 5.3 years to reach $39,500

Answer:5.3

Step-by-step explanation:

Answer:

0.26 possibly

Step-by-step explanation:

Answer:

Thanks for the free points

Answer:

So, the answer for b is 20.

The way to figure this out is:

angle N is congruent to angle S

angle M is congruent to angle M

side NM is 10

because of the three things above, triangle NHM is congruent to triangle SML because of SAS(side angle side postulate)

Hope that helps! Let me know if it does! ;P

Answer:

No

Step-by-step explanation:

The sum of 312+18 is 330.

To simplify the sum of 312 + 18, we add the two numbers together:

When three hundred twelve is added with eighteen we get three hundred thirty.

312

+18

________

330

Hence, the value of 312+18 is 330.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ6

Answer:

true!

Step-by-step explanation:

Answer

D

Step-by-step explanation:

y=2x+15

7=2(-4)+15

7=15-8

7=7

7x+2y=-14

7(-4)+2(7)=-14

-28+14=-14

-14=-14

Answer:

P(x)=8x-20

P(x)=8x-(2x+20(

Step-by-step explanation:

A number written in the form p/q such that q ≠ 0 will be rational if and only if p and q both are integers so option (A) will be correct.

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.

Let's suppose a decimal number,

2.256

By removing decimal

2.256 → 2256/1000 here 2256 and 1000 both are integers which means they will be a rational numbers.

Now take another example,

√2 → √2/1 here √2 is not an integer and if we expand √2 then it will be non-repeating and non-terminating so we cannot write in form of p/q.

Hence "A number written in the form p/q such that q ≠ 0 will be rational if and only if p and q both are integers".

For more about the irrational number,

https://brainly.com/question/4031928

#SPJ2

Answer:

The slope is most easily defined as rise over run.

First, find a point you like because it is directly on the line and is where for example starting from the origin which you know should be always (0, 0).

Then find another point that is on the line and is perfectly aligned where on the graph is like (1, 2).

Then, as I said earlier, rise over run. So you climb up from for example the origin which is in the graph and climb up to the (1, 2) point. It should go up two units because it is increasing in intervals of 2 but has the notches in the half mark of 1.

So the rise is 2 because it climbed from 0 to 2.

The run is running from the 0 in the origin on the x-axis and running to the 1 because it is (1, 2) where it is in the form (x,y).

Since it is rise over run, the rise is 2 and the run is 1 so 2 over 1 is 2.

Hence the slope is 2.

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

3-1/5-2=

2/3

We want to imagine where the shading should be, and with that determine which point is a solution for both inequalities. We will see that the solution is the point (7, -8)

In this case, the inqualities are:

You can see that in both cases, y is smaller than the line, thus, for both inequalities, we must shade the part that is below the lines.

With that in mind, the region of solution will be the region that is below both lines at the same time, and that region will be the "triangle" that you can see at the middle below the horizontal axis.

Now that we know the region of solutions, we only need to see which point belongs there, from the given options the only that belongs to that region is the point (7, -8), which means that this point is a solution for both inequalities.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/11234618

Answer:

1

Step-by-step explanation:

(-4) + (-8) + 11 - (-2)

~Simplify

-4 - 8 + 11 + 2

~Subtract

-12 + 11 + 2

~Add

-1 + 2

~Add

1

Best of Luck!

Explanation: 1 / 2 = 9 / 18 Halfway that and 0 would be 4.5 / 18 Since 3 / 18 is below that, we would round to 0

The equation that best represents this solution is:

40t + 1,280 = 2,680

What is the algebraic equations?

An algebraic expression is when we use numbers and words in solving a particular mathematical question.

Each time Sophia shops at the grocery store, she earns 40 points. If she needs a total of 2,680 points to receive a free prize and she has already earned 1,280 points, then she needs to earn an additional 2,680 - 1,280 = 1,400 points. Let t represent the number of times Sophia visits the store.

Since Sophia earns 40 points every time she shops at the grocery store, the total number of points she will earn after t visits is 40t. Therefore, we can set up the following equation:

40t = 1,400

Solving for t, we can divide both sides of the equation by 40:

t = 1,400/40

t = 35

Hence, Sophia will need to shop at the grocery store 35 more times in order to earn the additional points she needs for a free prize.

The equation that best represents this solution is:

40t + 1,280 = 2,680

To learn more about algebraic equations, Visit

https://brainly.com/question/4344214

#SPJ1

Answer:

x=5 and y=1

Step-by-step explanation:

Answer:

You would multiply $8200 by .075, giving you 615. Then to find the decrease. Take the starting value (8200) by the end value (615). and you would get 7,585.

Answer:

the answer is x = 4

Step-by-step explanation:

first you wanna subtract 8 from both sides

then it should look like this...  [tex]4\left(x+3\right)-2x=20[/tex]

then this... 2x+12=20

next you need to subtract 12 from both sides

then it'll look like this 2x=8

then this... [tex]\frac{2x}{2}=\frac{8}{2}[/tex]

lastly your gonna simplify it and and your answer will be...

x = 4

hope this helps :)