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2 years ago

Which function has the same y-intercept as the function?

Mathematics

1 answer:

rosijanka [135]2 years ago

8 0

Answer:

$6x -7y = 21$

Step-by-step explanation:

The $y$ -intercept of a line is the $y$ value when $x = 0$ . In the equation $y = \frac23 x -3 \\$ , we can solve for its equation when we plug in $x = 0$ .

Solving for $y$ when $x = 0$ :

$y = \frac23 x -3 \\ y = \frac23 (0) -3 \\ y = -3$ .

So the $y$ -intercept of the equation $y = \frac23 x -3 \\$ is $-3$ .

To find what equation has the same $y$ -intercept, we can do the same process for each equations given by the choices. However, I can see that the equation, $6x -7y = 21$ , has the $y$ -intercept. If in doubt, you can check for the solution below or solve each equations for yourself.

Solving for $y$ when $x = 0$ :

$6x -7y = 21 \\ 6(0) -7y = 21 \\ 0 -7y = 21 \\ -7y = 21 \\ \frac{-7y}{-7} = \frac{21}{-7} \\ y = -3$

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Answer: Meaghan is right.

Step-by-step explanation:

For a number like:

123.45

the tens place would be the "2" (second number at the left of the decimal point)

The ones place would be the "3" (first number at the left of the decimal point)

Let's suppose that Lily is correct.

Then the quotient of:

43.61/7

Will be a number with two digits in the left of the decimal point.

The smallest number that meets this condition, is the number 10.

Then let's see:

7*10 = 70

then:

70/7 = 10

and:

43.61 < 70

(70 is larger than 43.61)

then:

43.61/7 < 70/7 = 10

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This means that our quotient is smaller than 10, then the first digit of the quotient can not be on the tens place.

Then Meaghan is the correct one.

We also could perform the quotient to find:

43.61/7 = 6.23

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2 years ago

Given segments AB and CD intersect at E.

nata0808 [166]

The length of a segment is the distance between its endpoints.

$\mathbf{AB = 3\sqrt{2}}$
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(a) Length of AB

We have:

$\mathbf{A = (1,2)}$

$\mathbf{B = (4,5)}$

The length of AB is calculated using the following distance formula

$\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

So, we have:

$\mathbf{AB = \sqrt{(1 - 4)^2 + (2 - 5)^2}}$

$\mathbf{AB = \sqrt{18}}$

Simplify

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(b) Are AB and CD congruent

First, we calculate the length of CD using:

$\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

Where:

$\mathbf{C = (2, 4)}$

$\mathbf{D = (2, 1)}$

So, we have:

$\mathbf{CD = \sqrt{(2 -2)^2 + (4 - 1)^2}}$

$\mathbf{CD = \sqrt{9}}$

$\mathbf{CD = 3}$

By comparison

$\mathbf{CD \ne AB}$

Hence, AB and CD are not congruent

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If AB bisects CD, then:

$\mathbf{AB = \frac 12 \times CD}$

The above equation is not true, because:

$\mathbf{3\sqrt 2 \ne \frac 12 \times 3}$

Hence, AB does not bisect CD

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If CD bisects AB, then:

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$\mathbf{3 \ne \frac 12 \times 3\sqrt 2}$

Hence, CD does not bisect AB

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1 year ago

A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split

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The amount each friend paid for food is $8. 50 for the food and $1. 50 for the tip.

<h3>What is division?</h3>

The division is one of the most basic mathematical operators. It is used when a number is to be distributed equally in n number of parts.

As it is given that the total of 4 friends went to the lunch, the total amount paid by them is $40, but the food bill was just $34, therefore, the rest of the amount was paid in the tip. If we calculate the tip,

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Now, as it is that the total amount spend by all on the food is $34, and it is to be divided among the four friends, therefore, the amount paid by each of the friends is,

$\text{Total amount to be paid by each friend}=\dfrac{\text{Total amount spent by all on food}}{\text{Number of friends}}\\\\\text{Total amount to be paid by each friend}=\dfrac{\$34}{4}\\\\\text{Total amount to be paid by each friend}=\$8.5$

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1 year ago

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