The system of equations is graphed on the coordinate plane.

y=−x−2
y=3x+2

Enter the coordinates of the solution to the system of equations in the boxes.

(__,__)

Frank has memorized 6 words which is two-thirds of his vocabulary list, so by dividing 6 by 2/3, we find out that the total number of words on the list is 9.

Frank has memorized 6 words on his Latin vocabulary list, which is two-thirds of the total number of words. To find out the total number of words on the list, we can set up a proportion where 6 words corresponds to 2/3. Therefore, we need to find a number that, when multiplied by 3/2 or 1.5, gives us 6.

We can set up the equation like this: 2/3 * total words = 6 words. To find the total words, we divide 6 by 2/3:

total words = 6 ÷ (2/3)

total words = 6 * 3/2

total words = 9

So, the vocabulary list has a total of 9 words.

[tex]\text{Answer: The fence post will be }3\frac{5}{8}\ feet\text{ far above the ground when it is placed in the hole.}[/tex]

Explanation:

Since we have given that

Length of hole dug for a fence post is given by

[tex]2\frac{3}{8}\ feet=\frac{19}{8}\ feet[/tex]

Length of the fence post = 6 feet

we need to find the length of the fence post above the ground is seen when it is placed in the hole.

So, Length of the fence post above the ground is given by

[tex]6-\frac{19}{8}\\\\=\frac{48-19}{8}\\\\=\frac{29}{8}\\\\=3\frac{5}{8}\ feet[/tex]

[tex]\text{Hence, the fence post will be }3\frac{5}{8}\ feet\text{ far above the ground when it is placed in the hole.}[/tex]

The skateboarder's rate of ollies per minute would be 68 ollies per minute. The skateboarder's rate of ollies per hour would be 4080 ollies per hour.

To find the rate of ollies per minute, we need to divide the number of ollies completed in 30 seconds by the number of seconds in a minute. In this case, the skateboarder completed 34 ollies in 30 seconds, so the rate of ollies per minute would be:

Rate per minute = (34 ollies / 30 seconds) × (60 seconds / 1 minute) = 68 ollies per minute

To find the rate of ollies per hour, we need to divide the number of ollies completed in 30 seconds by the number of seconds in an hour. In this case, the skateboarder completed 34 ollies in 30 seconds, so the rate of ollies per hour would be:

Rate per hour = (34 ollies / 30 seconds) × (3600 seconds / 1 hour) = 4080 ollies per hour

Final answer:

The slope of the line through points P(5,7) and Q(-1,7) is calculated to be 0, indicating a horizontal line.

Explanation:

To find the slope of the line through points P(5,7) and Q(-1,7), we can use the formula for the slope of a line through two points: slope (m) = (y2 - y1) / (x2 - x1). In this case, the coordinates for P are (x1, y1) = (5, 7) and the coordinates for Q are (x2, y2) = (-1, 7).

Plugging these values into the slope formula, we get:

m = (7 - 7) / (-1 - 5)

m = 0 / (-6)

m = 0

So the slope of the line is 0, which means that the line is horizontal.

Answer:

48 grams

Step-by-step explanation:

= 32 + 25      because 32 grams and 25 %

= 57 - 10        because there's 10%

= 47 + 1          because 10 ÷ 10 = 1

= 48

My teacher taught me it this way!☺

A is 16 and B is 28.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given

A:B = 4:7

A + B = 44

Let the common factor between A and B is x

then

4x + 7x = 44

11x = 44

x = 4

Therefore,

A = 16

B = 28

Hence, 16 and 28 are A and B respectively.

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Answer:

1. A line passes through (2, −1) and (4, 5).

Which answer is the equation of the line?

−3x+y=−7

2. A line has slope −3/4 and y–intercept 5.

Which answer is the equation of the line?

y=−3/4x+5

3. There are 6 quarters in a jar. Jill adds 2 quarters to the jar every day.

Which linear equation represents the total amount of quarters in the jar after x days?

y = 2x + 6

4. Which answer is an equation in point-slope form for the given point and slope?

Point: (1, 9); Slope: 5

y−9=5(x−1)

Step-by-step explanation:

[tex]\left(-\dfrac{2}{3}\right)\left(\dfrac{1}{6}\right)=-\dfrac{1}{3}\cdot\dfrac{1}{3}=-\dfrac{1}{9}[/tex]

10 trees /  2 hours = 5 trees per hour

150 trees /  5 per hour = 30 hours

The ratio of soccer balls to all balls is 4:25.

Given that;

The table shows the number of balls, by sport, in the gym.

Now, We have;

Number of soccer balls = 8

And, Total number of balls = 50

Hence, The ratio of soccer balls to all balls is,

⇒ 8 : 50

⇒ 4 : 25

Thus, We get;

The ratio of soccer balls to all balls is 4:25.

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The measure of angle KLM is 64⁰

Supplementary angles are two angles whose measures add up to 180⁰ In other words, when placed adjacent to each other, they form a straight line.

From the figure

Given

<J = (6x+4)⁰

<K = (8x + 18)⁰

<KLN = 180 -(20x +4) (supplementary angles)

In Triangle KLN

<J + <K + <L = 180⁰(sum of angles in triangle)

Substitute

(6x + 4) + (8x + 18) = (20x + 4)(sum of 2 int.<s is equal to exterior<)

Simplifying

6x + 8x - 20x = 4 - 4 - 18

14x -20x = -18

-6x = -18

x = -18/-6

= 3

Substitute into (20x + 4) to find the measure of angle KLM

20x +4 = 20(3) + 4

= 60 + 4

= 64⁰

The measure of angle KLM is 64⁰

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