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3 years ago

5

Katie bought 2 one-gallon bottles of juice for a party. Her guests drank 6/4 gallons of juice. What fraction of a gallon of juic

e is left over? Draw a number line to show, and explain your answer.

2 answers:

suter [353]3 years ago

6 0

Her guests are really gonna needa use the bathroom after the party

Alenkasestr [34]3 years ago

3 0

6/4 = 1 1/2 gallons
2 - 1 1/2 = 1/2 gallon

She has 1/2 a gallon left over

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Place the quadratic y=2x^2+24x+79 into vertex form by using the method of completing the square and then state the coordinates o

katrin2010 [14]

Answer:

$y=2(x+6)^2+7$

$(-6,7)$

Step-by-step explanation:

$y=2x^2+24x+79$

Completing the square is a process of converting a quadratic equation in standard form into vertex form.

The first step in completing the square is grouping the quadratic and linear terms of the quadratic equation.

$y=(2x^2+24x)+79$

Factor out the coefficient of the quadratic term,

$y=2(x^2+12x)+79$

Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.

$y=2(x^2+12x+36-36)+79$

Simplify,

$y=2(x^2+12x+36)+79+(2)(-36)$

$y=2(x+6)^2+79-72$

$y=2(x+6)^2+7$

The x-coordinate of the vertex of the equation is equal to (-1) times the numerical part of the quadratic term, and the y-coordinate is equal to the constant.

$(-6,7)$

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3 years ago

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iragen [17]

Answer:

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3 years ago

Can someone also help me with this please and thankss

VMariaS [17]

Answer: The measure of angle 3 is 50 degrees.

Step-by-step explanation:

We know that angle 2 is 130 degrees.

Angle 1 and angle 2 are verticle angles which means that they are across and equal to each other.

So angle 1 and angle 2 are 130 degrees.

Add up both angle 1 and angle 2, 130 + 130 = 260.

Now, all of these angles add up to be 360 degrees in total as they make a circle and there are 360 degrees in one.

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3 years ago

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3 years ago

Find the distance and midpoint of a segment with the following endpoints: (5,-1) and (-9,-1)

Likurg_2 [28]

Answer:

$d = 14$

$(-2,-1)$

General Formulas and Concepts:

Order of Operations: BPEMDAS
Distance Formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Midpoint Formula: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Step-by-step explanation:

<u>Step 1: Define</u>

(5, -1)

(-9, -1)

<u>Step 2: Find distance </u><em><u>d</u></em>

Substitute: $d = \sqrt{(-9-5)^2+(-1-(-1))^2}$
Simplify: $d = \sqrt{(-9-5)^2+(-1+1)^2}$
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Evaluate: $d = \sqrt{196}$
Evaluate: $d = \14$

<u>Step 3: Find Midpoint</u>

Substitute: $(\frac{5-9}{2},\frac{-1-1}{2})$
Subtract: $(\frac{-4}{2},\frac{-2}{2})$
Divide: $(-2,-1)$

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3 years ago