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4 years ago

Which equation is in slope-intercept form and represents a line with slope 3 through the point (9, –4)?

1 answer:

8 0

The slope-intercept form of a line is:

$y = mx + q$

Where m is the slope and y is the y-intercept:

$y = 3x + q$

To find q (y-intercept), substitute the coordinates of the point (9, -4) in the equation of the line and solve it as an equation:

-4=3(9)+q
-4=27+q
q=-27-4=-31

The equation of the line is: y=3x-31

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11. How many different ways can the 16 numbered pool balls be placed in a line on the pool table?

nikklg [1K]

Answer:

The number of ways are 16! or 20,922,789,888,000.

Step-by-step explanation:

Consider the provided information.

We need to determine the number of different ways 16 numbered pool balls be placed in a line on the pool table.

For the first place we have 16 balls.

For the second place we have 15 balls left.

Similarly for the third place we have 14 balls as two balls are already arranged and so on.

Or we can say that this is the permutation of 16 things taking 16 at a time.

Thus the number of ways are: $16!$ or $^{16}P_{16}$

$16!=16\times15\times14\times13......\times2\times1=20,922,789,888,000$

Hence, the number of ways are 16! or 20,922,789,888,000.

7 0

3 years ago

Hi someone please help. 5TH GRADE HELP

Effectus [21]

Answer:

Step-by-step explanation:

2 [32 - (4 - 1)³]

2[32 - (3)³]

2[32 - 27]

2[5]

4 0

3 years ago

Explain why a + b = d. B A C swer

bixtya [17]

Answer:

Explanation below

Step-by-step explanation:

Angles in a Triangle

There are two basic relations of angles we need to recall:

Supplementary angles add up to 180°
Internal angles of a triangle add up to 180°

Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:

c = 180 - ( a + b )

Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus

c = 180 - d

From the two relations above, it follows that:

a + b = d

4 0

3 years ago

Geometry problem help! Please refer to the image below...

Vinil7 [7]

Answer:

A. 1/3

B. √10

C. -1, 1

D. √8, 6

E. congruent and opposite pairs parallel

F. perpendicular, not congruent

G. rhombus, explanation below

Step-by-step explanation:

Hey there! I'm happy to help!

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Slope is the rise over the run. Let's look at F to G.

We are going from -1 to 2 on our x-axis (run), so our run is 3 units.

Our rise is 1 unit as we go from 2 to 3 on the y-axis.

$slope=\frac{rise}{run} =\frac{1}{3}$

This slope is the same for all of the sides.

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We will use the distance formula (which is basically just the Pythagorean Theorem) to calculate the length of each side. Let's go between F and G again, but this distance is the same for all the sides.

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+1)^2+(3-2)^2 } \\\\\sqrt{(3)^2+(1)^2 }\\\\\sqrt{9+1 }\\\\\sqrt{10}$

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The diagonals are the lines that connect the non-adjacent vertices.

Our two diagonals are FH and GE.

-----------------------------

FH

We go from x-value -1 to 1 from F to H, so our run is 2.

We go from y-value 2 to 0. so our rise is -2.

$slope=\frac{rise}{run} =-\frac{2}{2} =-1$

-----------------------------

GE

We go from x-value -2 to 2 from E to G, so our run is 4.

We go from y-value -1 to 3. so our rise is 4.

$slope=\frac{rise}{run} =\frac{4}{4} =1$

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Let's use the distance formula on each of our diagonals.

-----------------------------

FH

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(1,0)\\\\\\\sqrt{(1+1)^2+(0-2)^2 } \\\\\sqrt{(2)^2+(-2)^2 }\\\\\sqrt{4+4 }\\\\\sqrt{8}$

-----------------------------

GE

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-2,-1)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+2)^2+(3+1)^2 } \\\\\sqrt{(4)^2+(4)^2 }\\\\\sqrt{16+16 }\\\\\sqrt{36}\\\\6$

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They are congruent as they all have the same length (√10) and the opposite sides are parallel as they have the same slope (1/3)

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They are perpendicular diagonals as their slopes are negative reciprocals (1 and -1), and they are not congruent as they have different lengths (√8 and 6).

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Parallelogram- quadrilateral with opposite pairs of parallel sides.

Rhombus- a parallelogram with four equal sides

Square- a rhombus with four right angles

We can see that this is a parallelogram as we saw that the opposite sides are parallel due to having the same slope, and the perpendicular diagonals show that as well. This is also a rhombus because if we use that distance formula on all the sides, it will be the same. It is not a square though because it does not have four right angles, so this is a rhombus.

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Have a wonderful day and keep on learning!

8 0

3 years ago

A circular swimming pool is 21 feet in diameter. What is the circumstances of the swimming pool?

Reptile [31]

Hello there!

21 * 3.14 = 65.94

Thus,

The circumstances of the swimming pool is 65.94

4 0

3 years ago