Given Segment AC with point B contained on the segment, as shown below.


Write a complete two-column proof for following information:

Given: Segment AB = x + 16, Segment BC = 4x + 11

Segment AC = 77

Prove: AB = 26

Answer:

Only b we can check

The rule is sum of two sides must be greater than third side

Check

They can't form a triangle

Answer:

b ≈ 7.8

Step-by-step explanation:

using the law of sines

∠ A = 180° - 105° - 40° = 180° - 145° = 35° , then

[tex]\frac{b}{sin40}[/tex] = [tex]\frac{7}{sin35}[/tex] ( cross- multiply )

b × sin35° = 7 × sin40° ( divide both sides by sin35° )

b = [tex]\frac{7sin40}{sin35}[/tex] ≈ 7.8 ( to the nearest tenth )

The true solution to the system of inequities shown is B; All values that satisfy  [tex]y \leq \dfrac{ 1}{3}x - 3[/tex] are solutions.

When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalities.

A collection of inequalities for which we consider a common solution for all inequalities is called a system of inequalities.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true.

A set of such values is called a solution set to the considered equation or inequality.

The true solution to the system of inequities shown is B;

All values that satisfy  [tex]y \leq \dfrac{ 1}{3}x - 3[/tex] are solutions.

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Step-by-step explanation:

2x + 28° + 90° = 180° ( The sum of all angle of triangle is 180° )

Now you may add 28° and 90° and subtract it from 180° ...

2x = 62° ..

Now...divide 62 by 2 ...

x = 31°

hence the value of x is 31°....

Step-by-step explanation:

Ashley is the utilities manager at a paper mill. She's watching over one of her holding tanks. It takes 4/5 of an hour to fill 1/2 the tank

First we convert 4/5 of an hour in to

minutes

4/5 6048 minutes

In 48 minutes ----> 1/2 tank filled

In 60 minutes ----> 60 * 1/2 divide by 48

30 divide by 48=\frac{30}{48}

48

30

All 15%

Simplify the fraction by dividing top and

bottom by 6

30/48 = 5/8

Answer:

u should subract those not add

Using the normal distribution, it is found that there is a 0.2776 = 27.76% probability that the life span of the monitor will be more than 20,179 hours.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 19000, \sigma = \sqrt{4000000} = 2000[/tex]

The probability that the life span of the monitor will be more than 20,179 hours is one subtracted by the p-value of Z when X = 20179, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20179 - 19000}{2000}[/tex]

Z = 0.59.

Z = 0.59 has a p-value of 0.7224.

1 - 0.7224 = 0.2776.

0.2776 = 27.76% probability that the life span of the monitor will be more than 20,179 hours.

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Answer:

see the attachment photo!

Answer:

2 up 3 run

Step-by-step explanation:

just count the squares until u reach a part where the line touches again

Answer:

x = 7

Step-by-step explanation:

8*7 - 6 = 50

The capacity or volume of the rectangular water tank is 100000 cm³.

volume of a rectangular water tank = base area × height

where

Therefore,

base area = 1000 cm²

height = 100 cm

Therefore,

capacity(volume) of the water tank = 1000 × 100 = 100000 cm³

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Answer:

20%

Step-by-step explanation:

the units of measure must be the same, so

2m = 2 × 100 cm = 200 cm

then

[tex]\frac{40}{200}[/tex] × 100%

= 0.2 × 100%

= 20%

Answer:

20%

Step-by-step explanation:

The volume of the given rectangular prism.

[tex]\huge\boxed{Formula: lwh}[/tex]

To find the the volume we'll have to multiply the height, width and length.

[tex]V=\: 13×7×5 [/tex]

[tex]\large\boxed{V= \:455\: {cm}^{3}}[/tex]

Therefore, the volume of the given rectangular prism is 455 cubic centimeters.

A ratio shows us the number of times a number contains another number. The number of baskets Jasmine made is 24.

A ratio shows us the number of times a number contains another number.

The ratio of the number of baskets she missed during the tournament to the number of baskets she made is 3:8. Therefore, we can write,

(Number of baskets Missed)/ (Number of baskets made) = 3/8

If Jasmine missed 9 baskets during the tournament, then the ratio can be rewritten as,

(Number of baskets Missed)/ (Number of baskets made) = 3/8

9 / (Number of baskets made) = 3/8

(9×8)/3 = (Number of baskets made)

Number of baskets made = 24 baskets

Hence, the number of baskets Jasmine made is 24.

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Answer:

No

Step-by-step explanation:

If a ordered pair is a solution for an equation, then it will satisfy the equation. That is, after substituting the x and y values in the equation, both sides of the equation will be same.

Here 29 ≠ 45.

So, (4,7) is not a solution

The statement (C) the number of juice boxes must be an even number is correct.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a rule is “Multiply by 8"

Number of Packages:         3    5   6    8

Number of Juice Boxes:     24  40  48

The statements are:

Number of package starts from 3

Applying the rule: "Multiply by 8.

Number of Juice Boxes = 3×8 = 24

The statement should be the number of juice boxes will always be greater than and equal to 24.

When we multiply even with odd we get an even number.

8 is an even number.

Thus, the statement (C) the number of juice boxes must be an even number is correct.

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Answer:

(2, 5)

Step-by-step explanation:

Given:

To find the components of [tex]\overrightarrow{RS}[/tex] we need to go from R to O and then O to S.  Remember that [tex]\overrightarrow{RO}[/tex] is the negative of [tex]\overrightarrow{OR}[/tex].  Therefore:

[tex]\begin{aligned} \displaystyle \overrightarrow{RS} & =\overrightarrow{RO}+\overrightarrow{OS}\\& = \overrightarrow{OS}-\overrightarrow{OR}\\& =\binom{-2}{12}-\binom{-4}{7}\\& =\binom{2}{5}\end{aligned}[/tex]

Therefore, the component form (x, y) of the vector [tex]\overrightarrow{RS}[/tex] is (2, 5)

The  equation  that can be used to find how many nickels logan uses is: 50÷5.

Given:

Total pennies=50

Logan got a nickel of 5 pennies=1

Hence:

Number of nickels=1÷5×50

Number of nickels=50÷5

Number of nickels=10 nickels

Therefore the  equation  that can be used to find how many nickels logan uses is: 50÷5.

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For fraction multiplication, multiply the numerators and then multiply the denominators to get

This fraction cannot be reduced.

Therefore:

Apply the fractions formula for multiplication, to

and solve

Answer:

1) 5
2) 0.8
3)  -1.3

4) -[tex]\frac{4}{9}[/tex]

5) ±10

6) ±[tex]\frac{7}{12}[/tex]

Step-by-step explanation:

Answer:

i think the answer is 278.75

Answer:

6.5m

Step-by-step explanation:

V=TTr²h

507TT=TTr²12

cancel TT on both sides

507=12r²

169\4=r²

r=13/2

Area of the plot = 193 sq.yd.  , Option B is the correct answer.

Area is the space occupied by a flat surface or an object .

It is measured in square units

It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.

It is given that

A developer buys an empty lot to build a small house.

area of the lot = ?

The figure is incomplete and the complete figure is attached with the answer.

To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure

Area of the first triangle = (1/2) * base * height

By Calculation

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5

=85 sq.unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq.unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

The area of the plot = 85+36+63+9

Area of the plot = 193 sq.yd.

Therefore , Option B is the correct answer.

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Answer:

Step-by-step explanation:

Area of the plot = 193 sq.yd.  , Option B is the correct answer.

What is Area ?

Area is the space occupied by a flat surface or an object .

It is measured in square units

It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.

It is given that

A developer buys an empty lot to build a small house.

area of the lot = ?

The figure is incomplete and the complete figure is attached with the answer.

To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure

Area of the first triangle = (1/2) * base * height

By Calculation

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5

=85 sq.unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq.unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

The area of the plot = 85+36+63+9

Area of the plot = 193 sq.yd.

Therefore , Option B is the correct answer.

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Answer:

see the attachment photo!

Answer: The correct answer is 135 in².

Step-by-step explanation: An area of a polygon is this:

Area = (number of sides × length of one side × apothem)/2

(5 x 6 x 9) / 2 = 135

The value of the perpendicular is 12 and the hypotenuse is 8√3.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The value of the sides will be calculated as:-

The perpendicular side will be calculated by using tan theta.

tan Ф = Perpendicular / BAse = P / 4√3

P = 4√3 x tan(60)= 4 √3 x √3 =12

The value of the hypotenuse will be calculated by using the Cos angle:-

Cos 60 = Base \ Hyputenuse.

Cos 60 = 4√3 / Hypotenuse

1 / 2 = 4√3 / Hypotenuse

Hypotenuse = 2 x 4 x √3 = 8√3

Therefore the value of the perpendicular is 12 and the hypotenuse is 8√3.

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