Benny thinks of a number, subtracts 18 from it, and divides the difference by 3, the result is (-4). What is the number?

Problem 22

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Explanation:

Segments XY and YZ add up to segment XZ

XY + YZ = XZ

(x+6) + (3x+1) = 5x

4x+7 = 5x

7 = 5x-4x

7 = x

x = 7

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Problem 23

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Explanation:

We'll use the result in the previous problem to find that,

XY = x+6

XY = 7+6

XY = 13

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Problem 24

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Explanation:

Similar to problem 23, we'll use the value of x = 7 to find that,

YZ = 3x+1

YZ = 3*7+1

YZ = 21+1

YZ = 22

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Problem 25

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Explanation:

We have two options. We could add the results of the last two problems

XZ = XY + YZ = 13+22 = 35

Or we could compute XZ directly like so

XZ = 5x = 5*7 = 35

Either way, we get the same result. The fact we get the same value both times helps confirm we have the correct x value and the correct lengths of XY and YZ.

Answer:

Concept:

Here, we need to know the idea of the segment addition postulate.

The segment addition postulate states the given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC. In another word, if 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

Given information

XY = x + 6

YZ = 3x + 1

XZ = 5x

Given expression deducted according to the segment addition postulate

XY +YZ = XZ

Substitute values into the expression

x + 6 + 3x + 1 = 5x

Combine like terms

4x + 7 = 5x

Subtract 4x on both sides

4x + 7 - 4x = 5x - 4x

x = 7

Find the value of XY

XY = x + 6 = (7) + 6 = 13

Find the value of YZ

YZ = 3x + 1 = 3 (7) + 1 = 22

Find the value of XZ

XZ = 5x = 5 (7) = 35

Check:

Left-hand side: XY + YZ = 13 + 22 = 35

Right-hand side: XZ = 35

35 = 35

Hope this helps!! :)

Please let me know if you have any questions

Answer:

2/5k + 31/4

Step-by-step explanation:

8+ 2/3k-4/15k-1/4

2/3k - 4/15k + 8 - 1/4

(5)(2/3k) - 4/15k + 8 - 1/4

10/15k - 4/15k + 31/4

6/15k + 31/4

2/5k + 31/4

Answer:

2.8

Step-by-step explanation:

If u divide 14 into 5, you get a decimal, 2.8.

2.8

simply asking for the answer to 14 divided by 5 it is 2.8

(if anything further is required i’ll try my best to help! )

Answer:

p is 16

Step-by-step explanation:

[tex]p \: \alpha {(q + 2)}^{2} [/tex]

introduce a constant on a right hand side:

[tex]p = k {(q + 2)}^{2} - - - eqn \: (a)[/tex]

[ when q is 1, also p is 1 ]

[tex]1 = k(1 + 2) {}^{2} \\ 1 = 9k \\ k = \frac{1}{9} [/tex]

substitute for k in eqn (a):

[tex]p = \frac{1}{9} (q + 2) {}^{2} [/tex]

so, when q is 10:

[tex]p = \frac{1}{9} (10 + 2) {}^{2} \\ \\ p = \frac{1}{9} (144) \\ \\ p = 16[/tex]

Answer:

The circumference is the perimeter, specifically the perimeter of a circle. It can be solved by using the following formula:  

C = 2πr

C stands for circumference.

π stands for pi, or 3.14 (rounded).

r stands for radius.

The radius is the distance from the center point of the circle to any point on the circle. It is denoted by the variable, r, as stated above. It is 1/2 of the diameter.

Answer:

the radius is the line from center to perimeter and circumference is the enclosed boundary

Step-by-step explanation:

radius- is any of the line segments from a circle or spheres center to its perimeter

circumference- the enclosed boundary a curved geometric figure, especially a circle

Answer:

x= -0.5

Step-by-step explanation:

2x-4+2x+16=10

4x+12=10

4x=-2

x=-1/2

Step-by-step explanation:

(x-2) 2 +(x+8) 2 = 10

x-2 + 2× x 2×8 + 2 = 10

x - 2 + 2x + 16 + 2 = 10

x + 2x + 16 - 2 + 2 = 10

3x + 16 = 10

3x = 10-16

3x = -6

3x÷3x = 6 ÷ 3

x = -2

Answer:

1/8 or 12.5% probability

Step-by-step explanation:

Compound probability is what you would want to use here which is the probability of the first event multiplied by the second event.

So, if 1/4 is the probability of spinning a 1 on the spinner and 1/2 is the probability of flipping heads, you would multiply 1/4 • 1/2 to get 1/8, or 12.5%

Hope this helped!

Answer:

3.2×10^-7 hope this will be of help

Answer:

-2

Step-by-step explanation:

Triangle S

Triangle L

For the base you must multiply 4 by -2 to get 2. Likewise for the height you must multiply 8 by -2 to get 4. Thus the scale factor from L to S is -2

Hope it helps,... Chow,...!

I assume you're asked to find [tex]7^{4k}\pmod{100}[/tex] for positive integer k. To start, notice that

[tex]7^4 \equiv 7^3\times7 \equiv 343\times7 \equiv 43\times7 \equiv 301 \equiv 1\pmod{100}[/tex]

Then for every k, we have

[tex]7^{4k} \equiv (7^4)^k \equiv 1^k \equiv 1 \pmod{100}[/tex]

Answer:

59000.000 nanometres

Answer:

59μm

Please give branliest

Step-by-step explanation:

1e-6m=1μm

5.9e-5m=59μm

Answer:

Option b 12+6÷(3+3)

Step-by-step explanation:

12+6÷(3+3)

= 12+6÷6

= 12+1

= 13

Answer:

t(5x + 4)

Step-by-step explanation:

im not entirely sure if this is correct

Answer:

t×(5x+4)

Step-by-step explanation:

factor out t from the expression

Answer:

Opposite numbers are numbers that, when placed on a number line, are the exact same distance away from the 0, but on opposite sides, or in opposite directions. They look the same except for their signs.

this is based off what I know I hope it helps

Answer:

Step-by-step explanation:

3/5 divide each by 3

Answer:

lowest term is 3/5

Step-by-step explanation:

Answer:

the value of x = 61

I hope it's helps you

Answer:

2/3

Step-by-step explanation:

Well, I don't know and the answer might not be correct*

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, B to A , then

scale factor = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex] ( = 1.5 )

Answer:

140

Step-by-step explanation:

For every 2 hours, the number goes up 140 miles.

Note: it does not ask for the MPH, it asks for Rate of Change.

Rate of Change is asking for the difference between numbers from one circumstance to the next. For example, in this question, as the table goes up 2 hours in each section, so does miles traveled. Calculate the difference in miles driven for each section to concur that the Rate of Change is 140.

Answer:

70 mph

Step-by-step explanation:

The rate of change is measured as the ratio of the difference between any 2 ordered pairs from the table

Using (4, 280 ) and (6, 420 ) , then

rate of change = [tex]\frac{420-280}{6-4}[/tex] = [tex]\frac{140}{2}[/tex] = 70 mph

The equations are alike because all of their variables are equivalent to 6. Another similarity is that they are all one-step equations, meaning they can be solved with just one operation.

[tex]4a=24\\a=6[/tex]

[tex]c-1.2=4.8\\c=6[/tex]

[tex].5b=3\\b=6[/tex]

[tex]d + 5.5=11.5\\d=6[/tex]

These equations are different because require different operations to find their variables. Their terms, excluding the variable, also have differnt values.

Have a nice day. Feel Free to ask Questions. Spread The Love.

Answer:

x =24

Step-by-step explanation:

3(x + 4) = 4(x -3)

3x + 12 = 4x -12

add 12 to both side

3x + 24 = 4x

subtract 3x

24 = x

Answer:

(5,2)

Step-by-step explanation:

midpoint formula for future reference

(x1+x2/2),(y1+y2/2)

(3+7/2),(-5+9/2)

(10/2),(4/2)

(5,2)

Answer:

D this will be your answer

d.between 44 and 46

for sure it is the correct answer

Answer:

49.0(714285) or 49 and remain 1

Step-by-step explanation  

687/14 = 49

49*14 = 686

687 - 686 = 1

49 and remain 1 (Remain Method)

1/14 = .0714285714285714285.... => .0(714285)

Now add 49 to the result, we get 49.0(714285)

Good luck!

Answer:

V = 315 degrees

K = 280 degrees

Y = 190 degrees

Q = 225 degrees

Step-by-step explanation:

since its estimated its ok if im a little wrong right?

Answer: Filled circle at -1 shading to the left.

Step-by-step explanation:

-3x+3<6

     -3 -3

_________

-3x<3

-3x/-3     3/-3

=  -1

and the < sign means less than or equal to. Hope this helps!

Answer:Option D

Step-by-step explanation:

Answer:

40.3

Step-by-step explanation:

62×(1-35%)= 40.3

100% - 35% = 65%

The toasters sale price is 65% of the original price:

$62 x 0.65 = $40.30

Sale price = $40.30

Answer:

Y-2x=8

Y-x=8/2

Yx=4

Maths gradients

Answer:

b

Step-by-step explanation:

Answer:

New length is 3 3/20 ft.

Step-by-step explanation:

The total board is 2 5/8 feet long. And since 5/6 of a foot is trimmed off, that means each piece of wood is 5/6 feet.

We can now set up an equation like this ---> 5/6 ⋅ x = 2 5/8

Now we're going to simplify --->  5/6 ⋅ x = 2 5/8

                                                      5/6 ⋅ x = 21/8              

                                                      (multiply both sides by 6)

                                                      5x = 63/4

                                                      (divide both sides by 5)

                                                      x = 63/20

                                                      x= 3.15

So, the new length is 3.15 feet long, or 3 3/20 in mixed fraction.

am I supposed to do the picture one or the you type