Find the equation of the line with slope m= 1/5
that contains the point (-10, 5).

Answer: 2(y + 6)(-y + 6)

Step-by-step explanation: Factor 72 - 2y^2

                                             -2y^2 + 72

                                             = 2(y + 6)(-y + 6)

Answer:

[tex]-2\left(y+6\right)\left(y-6\right)[/tex]

Step-by-step explanation:

[tex]72-2y^2[/tex]

[tex]-2y^2+72[/tex]

Factor out GCF.

[tex]2(-y^2+36)[/tex]

Apply difference of two squares formula.

[tex]-2\left(y+6\right)\left(y-6\right)[/tex]

Answer:   [tex]6\dfrac{3}{8}\text{ inches}[/tex]

Step-by-step explanation:

Given: Original length = [tex]15\dfrac{1}{8}[/tex] inches

[tex]=\dfrac{8\times15+1}{8}=\dfrac{121}{8}[/tex] inches                      ( In improper fraction )

Length of piece cut from original = [tex]8\dfrac{3}{4}[/tex] inches

[tex]=\dfrac{4\times8+3}{4}[/tex][tex]= \dfrac{35}{4}[/tex] inches                 ( In improper fraction )

Length of piece leftover piece =  (Original length ) - (Length of piece cut )

[tex]=\dfrac{121}{8}-\dfrac{35}{4}\\\\=\dfrac{121-2\times35}{8}\\\\=\dfrac{121-70}{8}\\\\=\dfrac{51}{8}\\\\=6\dfrac{3}{8}\text{ inches}[/tex]

Hence, the leftover piece will be [tex]6\dfrac{3}{8}\text{ inches}[/tex]  long.

Answer:

875

Step-by-step explanation:

35 x 25 =

30x25 + 5x25

750 + 125

875

The Answer is 875

✍️(◔◡◔) hope this helps <3

Answer:

B.

Step-by-step explanation:

Since we are moving the graph f(x) to the right 2 and down 1 with a reflection over the x-axis, we modify a, h, and k in f(x) = a(bx - h)² + k:

We would get f(x) = -(x - 2)² - 1 as our answer.

Answer:

y intercept is -19/6

Step-by-step explanation:

The slope intercept form of a line is given by

y = mx+b where m is the slope and b is the y intercept

y = 16/13x - 19/6

The slope is 16/13 and the y intercept is -19/6

Answer:

[tex]\boxed{-\frac{19}{6} }[/tex]

Step-by-step explanation:

Use slope-intercept formula.

[tex]y=mx+b[/tex]

[tex]m[/tex] is the slope of the line.

[tex]b[/tex] is the y-intercept of the line.

The equation of the line is already in slope-intercept form.

[tex]y=\frac{16}{3} x+-\frac{19}{6}[/tex]

[tex]b= -\frac{19}{6}[/tex]

Answer:

A. m∠2 + m∠3

Step-by-step explanation:

The exterior angle theorem states that the exterior angle formed when you extend the side of a triangle is equal to the sum of its non-adjacent angles.

So m∠4's non-adjacent angles are 2 and 3 NOT 1. Therefore, the measure of ∠4 = m∠2 + m∠3.

Hope this helps!

Answer:

A) m∠2 + m∠3

Step-by-step explanation:

Triangle Exterior Angle Theorem: The Sum of the outside angle is found using by adding the two opposite interior angles.

In the case of ∠4, the opposite interior angles are ∠2 & ∠3.

~

Answer: B C D

Step-by-step explanation:

just answered it for AP3X

Reasons used in the proof that the angle-bisector construction can be used to bisect any angle are as follows:

B. All of the radii of a circle are congruent

C .CPCTC

D. SSS triangle congruence postulate

" Angle bisector is defined as the ray which divides the angle into two equal parts."

According to the question,

A. Any Line segment can be extended indefinitely is not required to bisect any angle .

Therefore , it is not a correct option.

B. All of the radii of a circle are congruent : To bisect an angle draw an arc with same radii is used in constructing an angle bisector .

Therefore , Option B is a correct option.

C. CPCTC : Corresponding parts of a congruent triangle are congruent is required to proof angle bisector. As it proofs two triangles are congruent.

Therefore, Option C is the correct option.

D. SSS triangle congruence postulate : It is required an important step to prove that two triangles are congruent which imply proof of angle - bisector construction.

Therefore, Option D is the correct option.

Hence, Option B, Option C , Option D are the correct answer.

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Answer:

-17.5℃

Step-by-step explanation:

Current temperature = 0 ℃

Rate of falling per hour = -3.5 ℃

Temperature in 5 hours = -3.5 * 5 = -17.5 ℃  

Answer:

x=pm-rm

Step-by-step explanation:

[tex]\frac{x}{m}+r=p\\\\ \frac{x}{m}+r-r=p-r\\\\\frac{x}{m}=p-r\\\\\frac{x}{m}*m=(p-r)*m\\\\\boxed{x=pm-rm; m\neq 0}[/tex]

Answer:

Step-by-step explanation:

[tex]5 - 8x = - 1[/tex]

Move constant to R.H.S and change its sign:

[tex] - 8x = - 1 - 5[/tex]

Calculate

[tex] - 8x = - 6[/tex]

The difference sign (-) will be cancelled in both sides

[tex]8x = 6[/tex]

Divide both sides of the equation by 8

[tex] \frac{8x}{8} = \frac{6}{8} [/tex]

Calculate

[tex]x = \frac{3}{4} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Hey there!

5-8x=-1

-8x=-6

x=3/4

Hope this helps!

Answer:

a)3/6 and 4/6

b)15/20 and 12/20

c)4/6 and 5/6

d)15/20 and 14/20

Step-by-step explanation:

Change the demonimator to the lowest common demonimator. What ever you do to the bottom number to get to the lowest common denominator, multiply the numerator by the same number.

Hey there! :)

Answer:

x = 5, x = -i√7, x = i√7

Step-by-step explanation:

We can factor the equation x³ - 5x² + 7x - 35 = 0 by grouping:

x²(x - 5) + 7(x -5) = 0

We get:

(x² + 7)(x - 5) = 0

or

(x + i√7)(x - i√7)(x - 5) = 0

Use the Zero Product Property to solve for the solutions:

x - 5 = 0

x = 5.

-----------

x² + 7 = 0

x² = -7 (We will have imaginary solutions in this instance)

x = ±i√7

Therefore, the zeros of this equation are:

x = 5, x = -i√7, x = i√7

Answer:

20

Step-by-step explanation:

Answer:

Answer attached

Answer:

remove insulation ,,,eat low on the food chain

Step-by-step explanation:

u can reduce it by 8 pounds

Answer:

remove insulation

Answer:

Step-by-step explanation:

The total sum of the answers or sums that we can get when we roll a pair(2) dice is 36. Yes, there are repeated sums.

All the even sums: 2,4,6,4,6,8,4,6,8,6,8,10..., if you notice, there are 18 even sums.

All the sums that are odd by greater than 7: 9,9,9,11,9,11, if you notice, there are 6 of them.

Total: 6 + 18 = 24

Probability(A) = number of favorable outcomes/ total number of outcomes

The probability is 24/36 = 2/3

The probability of rolling an even sum or a sum greater than 7 when a pair of dice is rolled is 2/3.

Probability refers to a possibility that deals with the occurrence of random events.

We need to find the probability of rolling an even sum or a sum greater than 7 when a pair of dice is rolled.

The total sum of the answers or sums that we can get when we roll a pair(2) dice is 36.

All the even sums: 2,4,6,4,6,8,4,6,8,6,8,10...,

there are 18 even sums.

All the sums that are odd by greater than 7: 9,9,9,11,9,11, there are 6 of them.

Total: 6 + 18 = 24

Probability(A) = number of favorable outcomes/ total number of outcomes

Therefore, The probability is 24/36 = 2/3

Hence, the probability of rolling an even sum or a sum greater than 7 when a pair of dice is rolled is 2/3.

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The number of buttons in C is 17 buttons

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the three tins be A , B and C respectively

The number of buttons in tin A = x

The number of buttons in tin B = 4 times the number of buttons in tin A

                                                   = 4x

The number of buttons in tin C = 7 fewer buttons than tin A

                                                    = x - 7

The total number of buttons in tin A , tin B and tin C together = 137 buttons

So , the total number of buttons =
number of buttons in tin A + number of buttons in tin B + number of buttons in tin C

So , the equation will be

Total number of buttons = x + 4x + ( x - 7 )

x + 4x + ( x - 7 ) = 137

6x - 7 = 137

Adding 7 on both sides , we get

6x = 144

Divide by 6 on both sides , we get

x = 24 buttons

So , the number of buttons in tin A is 24 buttons

So , number of buttons in tin B = 4 x 24

                                                   = 96 buttons

Therefore , the number of buttons in tin C = 17 buttons

Hence , the number of buttons in tin C is 17 buttons

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Answer:

A. It is a series of points that fall in a straight line but are unconnected.

Step-by-step explanation:

Given variables y and x, and a proportional factor k, the proportional relationship is :

y/x = k or y = k*x

This means that points fall in a straight line.

Discrete data means that the function is also discrete, that is, points are not connected between them like in a continuous function.

Answer:

its a

Step-by-step explanation:

got it right

Answer:

225

Step-by-step explanation:

Answer:

I'm confused what's the question ?

Answer:

y-intercept: (0, 2.5)

x-intercept: (1.67, 0)

Step-by-step explanation:

Right now, you have 3x + 2y = 5. You want to change it into slope-intercept form to make the problem easier to solve.

2y = -3x + 5

y = -3/2x + 5/2

From here, you can see that the y-intercept is (0, 5/2). You can also say that the y-intercept is (0, 2.5).

To get the x-intercept, substitute 0 for y.

0 = -3/2x + 5/2

3/2x = 5/2

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0). You can also say that the x-intercept is (1.67, 0).

Hope this helps!

Answer:

Step-by-step explanation:

To find the x-intercept, let y = 0.  Then 3x = 5 and x = 5/3, or x = 1.667, and the x-intercept is (1.667, 0).

To find the y-intercept, let x = 0.  Then 2y = 5 and y = 5/2 or 2.5.  Then the y-intercept is (0, 2.5).

Answer:

(a) The probability that a male is selected, then two females is 0.4352.

(b) The probability that a female is selected, then two males is 0.3348.

(c) The probability that two females are selected, then one male is 0.4352.

(d) The probability that three males are selected is 0.0717.

(e) The probability that three females are selected is 0.1583.

Step-by-step explanation:

We are given that a math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment.

(a) The probability that a male is selected, then two females is given by;

Number of ways of selecting a male from a total of 11 male = [tex]^{11}C_1[/tex]

Number of ways of selecting two female from a total of 14 female = [tex]^{14}C_2[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{11}C_1 \times ^{14}C_2}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{11!}{1! \times 10!} \times \frac{14!}{2! \times 12!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{1001}{2300}[/tex]  =  0.4352

(b) The probability that a female is selected, then two males is given by;

Number of ways of selecting a female from a total of 14 female = [tex]^{14}C_1[/tex]

Number of ways of selecting two males from a total of 11 male = [tex]^{11}C_2[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_1 \times ^{11}C_2}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{14!}{1! \times 13!} \times \frac{11!}{2! \times 9!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{770}{2300}[/tex]  =  0.3348

(c) The probability that two females is selected, then one male is given by;

Number of ways of selecting two females from a total of 14 female = [tex]^{14}C_2[/tex]

Number of ways of selecting one male from a total of 11 male = [tex]^{11}C_1[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_2 \times ^{11}C_1}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{14!}{2! \times 12!} \times \frac{11!}{1! \times 10!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{1001}{2300}[/tex]  =  0.4352

(d) The probability that three males are selected is given by;

Number of ways of selecting three males from a total of 11 male = [tex]^{11}C_3[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{11}C_3}{^{25}C_3}[/tex]

                                           =  [tex]\frac{ \frac{11!}{3! \times 8!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{165}{2300}[/tex]  =  0.0717

(e) The probability that three females are selected is given by;

Number of ways of selecting three females from a total of 14 female = [tex]^{14}C_3[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_3}{^{25}C_3}[/tex]

                                           =  [tex]\frac{ \frac{14!}{3! \times 11!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{364}{2300}[/tex]  =  0.1583

(a) The probability that a male is selected, then two females is 0.4352.

(b) The probability that a female is selected, then two males is 0.3348.

(c) The probability that two females are selected, then one male is 0.4352.

(d) The probability that three males are selected is 0.0717.

(e) The probability that three females are selected is 0.1583.

Answer:

There are 90 different ways

Step-by-step explanation:

We can apply factorials to help solve this equation.

Just to review, 4!= 4x3x2x1

To solve this problem, we need to use factorials but only a portion of it.

Since there are only 2 roles, we only have to go down two numbers

For captain, there are 10 players available,

But for co captain, there are 9, because the captain can't also be the co captain

So the result is 10x9

We don't have to go further since there are no more further roles to occupy

10x9=90

There are 90 different ways

Answer:

45 if two co-captains or 90 if captain and co-captain are two DISTINCT roles.

Step-by-step explanation:

METHOD ONE

Label each player (either a through j OR 1 - 10).

List combinations:

METHOD 2

use formula

Answer:

See below

Step-by-step explanation:

[tex]\sqrt{6}[/tex] = 2.449

So, While plotting to the number line it will be like:

Answer:

Step-by-step explanation:

Hello!

You have to plot √6 on the number line.

The √6 is equal to 2.4494

In the given number line is depicted the scale between 2.4 and 2.5, the lines between corresponds to the second decimal digit between these two numbers, so the given scale is:

   |    *    |        |           |  *      |    *   |          |        |    *    |          |          |

2.40   2.41   2.42   2.43   2.44   2.45   2.46   2.47   2.48   2.49   2.50

The dot corresponding to √6  is the third counting from left to right.

(See attachment)

I hope this helps!

Answer:

3) x = 27; m∠FDG = 62°; m∠GOF = 118°

Step-by-step explanation:

2x + 8 + 4x + 10 = 180

6x + 18 = 180

6x = 162

x = 27

Answer:

x = 27; m∠FDG = 62°; m∠GOF = 118°

Step-by-step explanation:I took the test

Answer:

x = 8

Step-by-step explanation:

In a circle if two chord intersects as shown in figure

and length of a chord at point of intersection is a and b

and  length of another  chord at point of intersection is c and b

a*b = c*d

using this relation here, we have

8*(x+7) = 10 * (4 +x)

=> 8x + 56 = 40 + 10x

subtracting 40  and 8x from both sides

=>8x + 56  - 8x -40= 40 + 10x -8x -40

=> 16 = 2x

=> x = 16/2 = 8

Thus, x = 8

Step-by-step explanation:

total ratio = 3+4+7 = 14

3/14×180= 38.57°

4/14×180= 51.43°

7/14×180 = 90°

Answer:

total ratio = 3+4+7 = 14

3/14×180= 38.57°

4/14×180= 51.43°

7/14×180 = 90°

Step-by-step explanation:

Answer:

See below hot to plot.

Step-by-step explanation:

You did part a correctly and now have 3 points of this graph. For part b you need to plot the line by first plotting the points.

Plot the points on the graph and then connect them with a line.

The three points are (-5, -3), (0, 2), and (3, 5).

To plot (-5, -3):

Start at (0, 0), the origin, where the x-axis and y-axis intersect.

Go 5 units left to the -5. Now go 3 units down. That is point (-5, -3). Put a dot on it.

To plot (0, 2):

Start at (0, 0), the origin, where the x-axis and y-axis intersect.

Since the x-coordinate is 0, don't go right or left. Now go 2 units up to where you see a 2 on the y-axis. That is point (0, 2). Put a dot on it.

To plot (3, 5):

Start at (0, 0), the origin, where the x-axis and y-axis intersect.

Go 3 units right to the 3 on the x-axis. Now go 5 units up. That is point (3, 5). Put a dot on it.

Now connect the three dots with a line. Put arrow heads at both ends of the line.

Answer:

Hope this helps

Problem 9, part a)

Compass bearings always have north as the starting point. This is where 0 degrees is situated, and 360 degrees as well. As the bearing angle increases, you'll turn to the right toward the eastward direction. Effectively you're sweeping out a clockwise rotation. The bearing 322 degrees is in a northwest position as the diagram shows (place the ship at the bottom right corner of the triangle). The bottom right acute angle of the triangle is 322 - 270 = 52 degrees. This is the reference angle we'll use for finding the distance d.

With respect to the reference angle of 52 degrees, the side 18.5 is the opposite side and d is the adjacent side. Use the tangent ratio to get...

tan(angle) = opposite/adjacent

tan(52) = 18.5/d

d*tan(52) = 18.5

d = 18.5/tan(52)

d = 14.4537840903742

The approximate value of d is 14.4537840903742 km

This rounds to 14.5 when rounding to one decimal place.

=======================================================

Problem 9, part b)

Recall that

distance = rate*time

where "rate" is another term for "speed" or "velocity"

We can solve this for the time to get

time = distance/rate

------

We found the distance back in part a) above. We are given the rate of 48 km/h

So,

time = distance/rate

time = 14.4537840903742/48

time = 0.3011205018828

This is the time it takes in hours. Multiply by 60 to convert to minutes

0.3011205018828 hours = 60*0.3011205018828 = 18.067230112968 minutes

This rounds to the whole number 18

Answer:

3200000

Step-by-step explanation:

multiply the volume value by 1000