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NISA [10]
3 years ago
8

What is the solution to the system of equations?

Mathematics
1 answer:
Jlenok [28]3 years ago
4 0

Answer:

The solution would be (-19, 40)

Step-by-step explanation:

In order to solve this system by substitution, simply take the value of y in the first equation and use it in place of y in the second. This will allow you to solve for x.

5x + 2y = 15

5x + 2(-3x - 2) = 15

5x - 6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

Now that we have the value of x, we can find the value of y.

y = -3x - 3

y = -3(-19) - 3

y = 43 - 3

y = 40

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Five students plan to rent a minivan for the weekend and equally share the rental cost. By adding one more people, they can each
Novay_Z [31]

Answer:

  $180

Step-by-step explanation:

The difference between 1/5 and 1/6 of the rental price is ...

  1/5 - 1/6 = 6/30 -5/30 = 1/30 . . . of the rental price

If 1/30 of the rental price is $6, then the full rental price is $6 × 30 = $180.

The total rent of the car is $180.

7 0
3 years ago
Evaluate. Write your answer as a whole number or as a simplified fraction.<br> 12-².4³ =<br> Submit
Delicious77 [7]

12^{-2} \times 4^3\\\\=(4 \times 3)^{-2} \times 4^3\\\\=4^{-2} \times 4^3 \times 3^{-2}\\\\=4^{-2+3} \times 3^{-2}\\\\=4^1 \times \dfrac1{3^2}\\\\=\dfrac 49

7 0
2 years ago
I dont understand please help Which expression is equivalent to 8-(6r+2) A -6r+6 B 2r+2 C 6r+10 D -6r+10
Goryan [66]

Answer:

-6r+6

Step-by-step explanation:

Given data

We are given the expression

8-(6r+2)

let us expand it by opening the bracket

=8-6r-2

collect like terms

=8-2-6r

=6-6r

rearrange

=-6r+6

Hence option A is correct

8 0
3 years ago
The eccentricity e of an ellipse is defined as the number c/a, where a is the distance of a vertex from the center and c is the
Anna71 [15]

Answer:

Check below, please.

Step-by-step explanation:

Hi, there!

Since we can describe eccentricity as e=\frac{c}{a}

a) Eccentricity close to 0

An ellipsis with eccentricity whose value is 0, is in fact, a degenerate one almost a circle. An ellipse whose value is close to zero is almost a degenerate circle. The closer the eccentricity comes to zero, the more rounded gets the ellipse just like a circle. (Check picture, please)

\frac{x^2}{a^2} +\frac{y^2}{b^2} =1 \:(Ellipse \:formula)\\a^2=b^2+c^2 \: (Pythagorean\: Theorem)\:a=longer \:axis.\:b=shorter \:axis)\\a^2=b^2+(0)^2 \:(c\:is \:the\: distance \: the\: Foci)\\\\a^2=b^2 \\a=b\: (the \:halves \:of \:each\:axes \:measure \:the \:same)

b) Eccentricity =5

5=\frac{c}{a} \:c=5a

An eccentricity equal to 5 implies that the distance between the Foci has to be five (5) times larger than the half of its longer axis! In this case, there can't be an ellipse since the eccentricity must be between 0 and 1 in other words:

If\:e=\frac{c}{a} \:then\:c>0 , and\: c>0 \:then \:1>e>0

c) Eccentricity close to 1

In this case, the eccentricity close or equal to 1 We must conceive an ellipse whose measure for the half of the longer axis a and the distance between the Foci 'c' they both have the same size.

a=c\\\\a^2=b^2+c^2\:(In \:the\:Pythagorean\:Theorem\: we \:should\:conceive \:b=0)

Then:\\\\a=c\\e=\frac{c}{a}\therefore e=1

7 0
3 years ago
Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1? (1, –1) (0, 0) and (0, –1) (0,
olganol [36]

ANSWER

No solution

EXPLANATION

The first equation is

y =  {x}^{2}  - 2x

and the second equation is

y =  - 2x  - 1

We equate the two equations to obtain;

{x}^{2}  - 2x =  - 2x - 1

This implies that

{x}^{2}  =  - 2x + 2x - 1

{x}^{2}  =  - 1

There is no real number whose square is -1.

Therefore, the equation has no solution.

6 0
3 years ago
Read 2 more answers
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