Cool Down
Lesson 3: Reasoning about Equations with Tape Diagrams
Cool Down: Three of These Equations Belong Together
Here is a diagram.
X
1. Circle the equation that the diagram does not match.
06+3x=30
03(x+6)=30
0 3x-30-6
030-3x+6
2. Draw a diagram that matches the equation you circled.

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:

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.

The function g(x) = √(x - 8) represents a horizontal shift of the square root parent function f(x) = √x, to the right by eight units. Option B.

To horizontally shift the square root parent function, f(x) = √x, right eight units, we need to replace x with (x - 8) in the function. This shift will move the entire graph eight units to the right.

So, the equation of the new function, let's call it g(x), will be:

g(x) = √(x - 8)

Therefore, the correct choice is  g(x) = √(x - 8).

This means that for any given value of x, we substitute (x - 8) in the original square root function. The effect of this shift is that all x-values on the graph of g(x) will be eight units greater than their corresponding x-values on the graph of f(x).

For example, if we consider the point (8, 2) on the graph of f(x), after the horizontal shift, it will be located at (16, 2) on the graph of g(x). Similarly, the point (0, 0) on the graph of f(x) will shift to (8, 0) on the graph of g(x).

The function g(x) = √(x - 8) represents a horizontal shift of the square root parent function f(x) = √x, to the right by eight units. This transformation allows us to analyze and understand how the graph of the square root function is affected by horizontal shifts. SO Option B is correct.

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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:

1218 inches

Step-by-step explanation:

First, let's make our numbers equivalent to a certain unit. Preferably inches, since we can't turn inches into yards or feet, but we can turn yards and feet into inches.

3 yards is 9 feet, which when multiplied by 12 (12 inches in a foot) is 108.

5 feet times 12 is 60 inches.

6 inches is 6 inches.

108+60+6 is 174

Multiply all that by 7 and you get your answer of 1218 inches.

Hope this helps!

Answer:

381

Step-by-step explanation:

232 + 88 = 320

320 + 61 = 381

Hope this helped and brainliest please

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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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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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 )

Answer:

see the attachment photo!

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:

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:

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

Answer:

i think the answer is 278.75

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

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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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°....

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  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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Answer:

2 up 3 run

Step-by-step explanation:

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

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)

Answer:

u should subract those not add

Answer:

[tex]\boxed{ \rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3} } \rm (rounded \: to \: nearest \: tenth)[/tex]

Step-by-step explanation:

Given dimensions:

Given value of π :

To find:

Solution:

Here, we'll need to use the formulae of the volume of cylinder,to find it's volume.Its actually like a savior while solving these type of questions.

[tex] \pink{\star}\boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}\pink{\star}[/tex]

where,

Plug/substitute them onto the formulae,then simplify it using PEMDAS.

[tex] \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} \times 3[/tex]

[tex] \rm \: Volume_{(Cylinder)} = \pi(49)(3)[/tex]

[tex] \rm \: Volume_{(Cylinder)} = 147\pi \: [/tex]

[tex] \rm \: Volume_{(Cylinder)} = 147 \times 3.14[/tex]

[tex] \rm \: Volume_{(Cylinder)} = 461.58 \: {m}^{3} [/tex]

[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3}} \rm (rounded \: to \: nearest \: tenth) \: [/tex]

Hence, we can conclude that:

The volume of the cylinder is approximately

461.6 m³.

[tex] \rule{225pt}{2pt}[/tex]

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 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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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