Solve the system by substitution y=6x and 7x-8y=-41

Given:

A figure.

To find:

The value of x and y.

Solution:

In triangle ADC, all angles are equal, so it is an equilateral triangle.

We know that, all sides of an equilateral triangle are equal.

[tex]AD=AC[/tex]       ...(i)

[tex]3x-5=5y-4[/tex]                   ...(ii)

In triangle ABD,

[tex]\angle BAD=\angle ABD[/tex]

Base angles are equal, so triangle ABD is an isosceles triangle.

[tex]AD=BD[/tex]     ...(iii)

Using (i) and (iii), we get

[tex]AC=BD[/tex]

[tex]5y-4=y+12[/tex]

[tex]5y-y=4+12[/tex]

[tex]4y=16[/tex]

Divide both sides by 4.

[tex]y=4[/tex]

Putting y=4 in (ii), we get

[tex]3x-5=5(4)-4[/tex]

[tex]3x-5=20-4[/tex]

[tex]3x-5=16[/tex]

Adding 5 on both sides, we get

[tex]3x=16+5[/tex]

[tex]3x=21[/tex]

Divide both sides by 3.

[tex]x=7/tex]

Therefore, the value of x is 7 and the value of y is 4.

Answer: Braulio is 15 years old, and Alejandro is 6 years old.

Step-by-step explanation:

Let's define:

B = Age of Braulio

A = Age of Alejandro.

"Three years from now, Braulio will be 3 times Alejandro's present age"

We can write this as:

B + 3 = 3*A

"At that time, Alejandro will then be half as old as Braulio"

A + 3 = (B + 3)/2

Then we have a system of equations:

B + 3 = 3*A

A + 3 = (B + 3)/2

To solve this, we first need to isolate one of the variables in one of the equations.

Let's isolate A in the second equation:

A = (B + 3)/2 - 3

Now we can replace this in the other equation to get:

B + 3 = 3*A

B + 3 = 3*((B + 3)/2 - 3)

B + 3 = (3/2)*B + 9/2 - 9

Now let´s move all the terms with B to the left side, and the other terms to the right side.

B - (3/2)*B = 9/2 - 9 - 3

-(1/2)*B = 9/2 - 18/2 - 6/2 = -15/2

B = (-2)*(-15/2) = 15

Braulio is 15 years old.

And from the first equation:

B + 3 = 3*A

15 + 3 = 3*A

18 = 3*A

18/3 = A = 6

Alejandro is 6 years old.

Answer:

It takes 1 year.

Step-by-step explanation:

You have to apply simple interest formula, I = (P×R×T)/100 where I represent interest amount, P is principle, R is interest rate and T is number of years :

[tex]I = \frac{PRT}{100} [/tex]

[tex]200 = \frac{4000 \times 5 \times T}{100} [/tex]

[tex]20000 = 20000T[/tex]

[tex]T = 1[/tex]

We, know that :

[tex] \underline{\boxed{\sf Interest \: amount = \dfrac{Principal \times Rate \times Time}{100}}}[/tex]

[tex] \underline{\boxed{\sf I = \dfrac{P \times R \times T}{100}}}[/tex]

By putting values, we have

[tex] \sf : \implies 200 = \dfrac{4000 \times 5 \times T}{100}[/tex]

[tex] \sf : \implies 200 \times 100 = 20000 \times T[/tex]

[tex] \sf : \implies 20000 = 20000 \times T[/tex]

[tex] \sf : \implies \cancel{\dfrac{20000}{20000}} = T[/tex]

[tex] \sf : \implies 1 = T[/tex]

[tex] \underline{\boxed{\sf T = 1 \: year}}[/tex]

It takes 1 year for him to earn $ 200 in simple interest.

Answer:

4

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

Given the points :

(-5, 2) and (2, 8)

Slope can be obtained by using the relation :

(y2 - y1) / (x2 - x1)

From the points given :

x1 = - 5 ; y1 = 2 ; x2 = 2 ; y2 = 8

(8 - 2) / (2 - (-5))

(8 - 2) / (2 + 5)

6 / 7

Hence, slope between the two points = 6/7

Answer:

Domain = 1,3,5,7

Range = 8,7,6,5

Step-by-step explanation:

We need to identify the domain and range of the function: input 1,3,5,7 output 8,7,6,5

Domain of function:

For any function domain is set of input values.

Range of function:

For any function range is set of output values.

So, for the given function we have : input 1,3,5,7 output 8,7,6,5

Domain = 1,3,5,7 (set of input values is domain of function)

Range = 8,7,6,5 (set of output values is range of function)

Answer:

✔️The arithmetic sequence: 16, 11, 6, 1, -4. . .

✔️The Geometric Sequence: ⁵/9, ⁵/3, 5, 15, 45 . . .

✔️Neither is: ½, 1, 2, 3, 4 . . .

Step-by-step explanation:

In an arithmetic sequence, a constant number called common difference is added or subtracted from each term to get the next successive term in the sequence.

On the other hand, in a geometric sequence, a constant number called common ratio is used to multiply or divide each term to get the next successive term in the sequence.

✔️The arithmetic sequence is:

16, 11, 6, 1, -4. . .

This is because it has a common difference of -5. Thus, 5 is subtracted from each term to get the next successive term.

✔️The Geometric Sequence is:

⁵/9, ⁵/3, 5, 15, 45 . . .

The common ratio is 3. Each term is multiplied by 3 to get the next successive term in the sequence.

✔️Neither is:

½, 1, 2, 3, 4 . . .

This sequence lacks either a common difference or a common ratio.

Answer:

x=2

Step-by-step explanation:

25/625 is 1/25

1/25 = 1/5^x

1/5 =sqrt 1/25 and that is 2

so x=2.

Hope this helps plz hit the crown :D

Answer:

22.5

Step-by-step explanation:

Brainliest plzzz

Answer:

Negative and positive

Step-by-step explanation:

Complete the statements about the key features of the graph of f(x) = x5 – 9x3.

As x goes to negative infinity, f(x) goes to "NEGATIVE" infinity, and as x goes to positive infinity, f(x) goes to "POSITIVE" infinity.

The complete statement is:

As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity

The function is given as:

[tex]f(x) = x^5 - 9x^3[/tex]

Set x to 2

So, we have:

[tex]f(2) = 2^5 - 9(2)^3[/tex]

[tex]f(2) = -40[/tex]

Set x to 5

[tex]f(5) = 5^5 - 9(5)^3[/tex]

[tex]f(5) = 2000[/tex]

Notice that, as the value of x increases from 2 to 5, the function increases from -40 to 2000

Hence, the texts that complete the blanks are (a) negative and (b) positive, respectively

Read more about function behaviors at:

https://brainly.com/question/24114085

Answer:

D

Step-by-step explanation:

Area = 1/2 a * p

Multiply both sides by 2

2*A = ap

Divide by p

2A / p = a

D

Answer: D

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

I got it correct.

Answer: 382

You put the 3 in the hundred then add 70+12=82 So this is right

Just add 70+12 then add 300

Answer:

FV= $17,321.20

Step-by-step explanation:

Giving the following information:

Annual deposit (A)= $3,000

Number of periods (n)= 5 years

Interest rate (i)= 7.2% = 0.072

To calculate the future value (FV), we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {3,000*[(1.072^5) - 1]} / 0.072

FV= $17,321.20

Answer:

Step-by-step explanation:

Alina=2x---eq(1)

Asim=5x----eq---(2)

So,we get

2x+5x=210

7x=210

x=30

Now,Putting '30' in eq 1 and eq 2

2*30=60

5*30=150

Therefore Alina got 60 Rs while Asim got 150 Rs

Answer: 71 coins

Step-by-step explanation:

First and foremost, we should note that:

12 months = 1 year

2 years = 12 × 2 = 24 months

Since she has 25 coins in her first month and adds 2 coins to her monthly collections, this means that she has 23 more months. This can be expressed as:

= 25 + 2x

where, x = number of months

= 25 + 2(23)

= 25 + 46

= 71 coins

She will have 71 coins after 2 years.

Answer:

larry is 19

Step-by-step explanation:

ok, so larry's age is y, his sisters age is x

x + 8 = y

thats the equation for him being 8 years older

now 2y = 3x + 5

his sisters age is 3x + 5 to get larry's age when its doubled

substitute x + 8 in for y

2 (x+8) = 3x + 5

2x + 16 = 3x + 5

16 = x + 5

x = 11

11 + 8 = y

y = 19

Answer:

No

Step-by-step explanation:

Answer:

I don't think so.

Step-by-step explanation:

3(5b - 2) would be equivalent to 15b - 6

Answer:

I think it would be 13

Step-by-step explanation:

Answer:

Your slope is -1 and you y is 2 and the equation is -1y+ 0x

Step-by-step explanation:

Answer: She had $1.16 left

Step-by-step explanation:

Step-by-step explanation:

1.16 dollars left

Answer:

St rt ok is et cell pic ch se art on FB

[tex] \bf {(2x)}^{0} = 1[/tex]

The rule is that any number raised to the power of 0 equals to 1.

So if 2 or 1,000,000 is raised to the power of 0 it equals 1.

But 0 to the power 0 is undefined!

0 to any positive power is 0, so 0 to the power 0 should be 0. But any positive number to the power 0 is 1, so 0 to the power 0 should be 1. We can't have it both ways. Underlying this argument is the same idea as was used in the attempt to define 0 divided by 0.

Answer

slight

Step-by-step explanation:

But Never zero

Answer:

The first one is 9/50 and the second one is 1/2

Step-by-step explanation:

you multiply the numerators by each other then you multiply the denominators by each other then you should have your answer :)

Answer:

- 1

Step-by-step explanation:

y = mx + b ( "m" is slope and "b" is y-intercept )

The equation of a given line is

y = - 2x - 2

Coordinates of x-intercept are ( x, 0 ) ⇒ 0 = - 2x - 2 ⇒ x = - 1

The x-intercept of the line is ( - 1 )