What ratio is equivalent to 6 to 2? Complete the statement.

What is the solution to the system of equations?

Minchanka [31]

Answer:

(1, –5)

Step-by-step explanation:

It is relatively easy to try the offered solutions to see what works.

(1, -5)

3(1) +10(-5) = -47 . . . true

5(1) -7(-5) = 40 . . . true

(1, -5) is the solution

_____

As a check, you can try some of the other choices:

(1, 5)

3(1) +10(5) ≠ -47

(-1, -5)

3(-1) +10(-5) ≠ -47

(-1, 5)

3(-1) +10(5) ≠ -47

None of the other choices works in the first equation, so they're not the solution.

4 0

3 years ago

The difference between two integers is 8 and their product is 65. Assume that the larger of the two numbers is x. Write a quadra

zzz [600]

A quadratic equation in standard form that can be used to determine the value of x is $x^{2}$ - 8x - 65 = 0.

The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5.

The value for the second number is 5

<h3>Word Problem Leading To Quadratic Equation.</h3>

The general formula for quadratic equation in a in standard form is

a $x^{2}$ + bx + c = 0

Given that the difference between two integers is 8

Let the two integers = x and y,

and their product is 65. If the larger of the two numbers is x. Then,

x - y = 8 and xy = 65

Since we are looking for the value of x, make y the subject of formula in the first equation.

y = x - 8

Substitute y in the second equation.

x(x - 8) = 65

$x^{2}$ - 8x - 65 = 0

$x^{2}$ - 13x + 5x - 65 = 0

(x - 13)(x + 5) = 0

x = 13 or -5

We will ignore -5 since x is the larger number.

To get y Substitute x in the second equation.

xy = 65

13y = 65

y = 65/13

y = 5

Therefore, a quadratic equation in standard form that can be used to determine the value of x is $x^{2}$ - 8x - 65 = 0. The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5. The value for the second number is 5

Learn more about Quadratic Equation here: brainly.com/question/25841119

#SPJ1

5 0

1 year ago

Find the area of a circle with a

lina2011 [118]

Answer:

254.34 in.²

Step-by-step explanation:

area = πr²

given, radius = 9 cm

according to formula

→ 3.14 × (9)²

→ 3.14 × 81

→ 254.34 in.² ans.

hope this helps you !

6 0

2 years ago

You have the numbers 1-24 written on slips of paper. If you choose one slip at random, what is the probability that you will not

ra1l [238]

The probability of selecting a number not divisible by 3 is: 2/3

Step-by-step explanation:

There are two methods to solve the question.

We can find the probability of numbers not divisible by 3
We can find the probability of numbers divisible by 3 and then find the complement of it

We will use the second method:

Given:

There are 24 slips

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}

n(S) = 24

Let A be the event that the slip number is divisible by 3

Then

A = {3,6,9,12,15,18,21,24}

n(A) = 8

The probability of number divisible by 3 is:

$P(A) = \frac{n(A)}{n(S)}\\=\frac{8}{24}\\=\frac{1}{3}$

The sum of the probability of an event's occurrence and non-occurrence is 1. So the probability of numbers divisible by 3 will be subtracted from 1 to find the probability of selecting a number not divisible by 3.

The probability of selecting a number not divisible by 3 will be:

$=1-\frac{1}{3}\\=\frac{3-1}{3}\\=\frac{2}{3}$