Find the volume of the prism.

The value of the sum expression [tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex] is 1

The expression is given as:

[tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex]

Take the LCM of terms of the expression

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

Evaluate the quotient of x + 3 and x + 3

[tex]\frac{x}{x +3} + \frac{3}{x + 3} = 1[/tex]

Hence, the value of the sum expression [tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex] is 1

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The value of uv to the nearest tenth or as an integer is 3.1 units

uv is the adjacent side of the right triangle.

uv can be found using trigonometric ratios as follows:

Therefore,

tan 63 = opposite / adjacent

Hence,

tan 63 = 6 / adjacent

cross multiply

uv tan 63 = 6

divide both sides by tan 63

uv = 6 / tan 63

uv = 6 / 1.96261050551

uv  = 3.05716906145

uv = 3.1 units

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Answer:

The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Step-by-step explanation:

also it goes on and on so i dont think you meant but i hope this helps if it dosnt m very sorry

Answer:

371/999

Step-by-step explanation:

all repeating numbers like that just go over nines. Two repeating? Over 99. Four repeating? Over 9,999

The upper part of the x-axis is a quadratic function and the equation of the upper part is: y = 4 - x^2; -2 < x < 2

The equations are given as:

y = x^2 - 4

y = 4 - x^2

When these equations are plotted, the upper part of the x-axis is a quadratic function that has the following properties:

Zeros = -2 and 2

Because the upper x-axis is open upwards, the equation of the graph is:

y = -(x - zeros)

So, we have:

y - (x - 2)(x + 2)

Evaluate

y = 4 - x^2

Hence, the equation of the upper part is:

y = 4 - x^2; -2 < x < 2

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Answer:

the inequality, b ≤ 0 has interval Notation of -∞,0

Step-by-step explanation:

the inequality, b ≤ 0 has interval Notation of -∞,0

Answer:

x = 14

Step-by-step explanation:

Answer:

$54.6

Step-by-step explanation:

To solve the question, we need to find how much 5% of 52 is

For questions where we need to calculate the percentage, we will multiply the number by given percentage and then divide it by the whole, 100%

52*5/100 = 2.6

Now the price before the tax was 52 and the tax is 2.6

the total price:

2.6 + 52 = 54.6

Answer:

70%

Step-by-step explanation:

The segment area of the circle that's given in the envision geometry is 2.568.

It should be noted that the segment area is given as:

= (a/360)π × R² - Area of triangle

= (90/360)π × 3² - (1/2 × 3²)

= 9π/4 - 9/2

= 2.568

In conclusion, the segment area of the circle that's given in the envision geometry is 2.568.

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Answer:

Approximately 0.3.

Step-by-step explanation:

I can only estimate the value of the function when x = 2. it looks like it's about 2.4.

Average rate of change = [(f4) - f(2)] /  (4 - 2)

= (3 - 2.4) / 2

= 0.6/2

= 0.3.

The values of the temperature in degree Celsius (12 and 24) converted to degree Fahrenheit are 53.6°F and 75.2°F respectively.

In this exercise, you're required to convert the value of temperature in degree Celsius to degree Fahrenheit. Thus, we would use the following mathematical expression to do the conversion:

F(t) = 9/5C(t) + 32

When t = 12, we have:

F(t) = (9/5 × 12) + 32

F(t) = 21.6 + 32

F(t) = 53.6°F.

When t = 24, we have:

F(t) = (9⁄5 × 24) + 32

F(t) = 43.2 + 32

F(t) = 75.2°F.

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Answer:

See below ~

Step-by-step explanation:

Question 3 : (x, y - 5)

Question 4 : (x + 4, y + 1)

Answer:

(5,2) and (6,5)

length of side = sqrt10 ~= 3.16 units

Area = 12 sq units

Step-by-step explanation:

It really helps to graph the given information. See image. The sides have the same slope bc they are parallel. If you go UP3 & OVER1 to get from the first point to the second point, then do that again on the right side. See image. Use distance formula or pythagorean thm to find the length:

c^2 = 3^2 + 1^2

c^2 = 9+1

c^2 = 10

c = root10 ~= 3.16

Area of a parallelogram is b•h

A = 4•3

= 12

see image.

Answer:

F = 53.1°

Step-by-step explanation:

When you consider F as your angle

cos F = adjacent / hypotaneous

or, cos F = EF/DF

We do not have DF right now,

so DF² = DE² + EF²

DF = √ (12² + 9²)

DF = 15

cos F = adjacent / hypotaneous

or, cos F = EF/DF

cos F = 9 / 15

F = cos ⁻¹ (9/15)

F = 53.1°

The inside of a baking pan is to be lined with tinfoil. Then the amount of tinfoil needed will be 171 square inches.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

The inside of a baking pan is to be lined with tinfoil. the pan is 12 inches long, 9 inches wide, and 1.5 inches tall.

Then the amount of the tinfoil will be

The surface area of the rectangle with an open lid is given as

Surface area = 2(LH + WH) + LW

Then the surface area of the tinfoil will be

Surface area = 2(12 x 1.5 + 9 x 1.5) + 12 x 9

Surface area = 2 (18 + 13.5) + 108

Surface area = 2 x 31.5 + 108

Surface area = 63 + 108

Surface area = 171 square inches

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Answer:

21.6 units² (nearest tenth)

Step-by-step explanation:

[tex]\textsf{Area of a trapezoid}=\dfrac{1}{2}(a+b)h \quad \textsf{(where a and b are the bases and h is the height)}[/tex][tex]\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}[/tex]

Given:

[tex]\begin{aligned}\textsf{Area of figure} & =\textsf{area of trapezoid + area of semicircle}\\& = \dfrac{1}{2}(a+b)h+\dfrac{1}{2} \pi r^2\\& = \dfrac{1}{2}(2+8)(4)+\dfrac{1}{2} \pi (1)^2\\& = 20+\dfrac{1}{2} \pi\\& = 21.6\: \sf units^2 \:(nearest\:tenth)\end{aligned}[/tex]

Area of the trapezium

Area of semicircle

Total area

Solving as exponents

[tex]\\ \rm\Rrightarrow 9^{(x-8)}=3^{(4x-12)}[/tex]

[tex]\\ \rm\Rrightarrow 3^{2(x-8)}=3^{2(x-6)}[/tex]

[tex]\\ \rm\Rrightarrow 2(x-8)=2(x-6)[/tex]

[tex]\\ \rm\Rrightarrow 2x-16=4x-12[/tex]

[tex]\\ \rm\Rrightarrow -2x=4[/tex]

[tex]\\ \rm\Rrightarrow x=-2[/tex]

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex]9^{x-8}=3^{4x-12}[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^{x-8}=3^{4x-12}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2(x-8)}=3^{4x-12}[/tex]

[tex]\implies 3^{2x-16}=3^{4x-12}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies 2x-16=4x-12[/tex]

Subtract 2x from both sides:

[tex]\implies 2x-16-2x=4x-12-2x[/tex]

[tex]\implies -16=2x-12[/tex]

Add 12 to both sides:

[tex]\implies -16+12=2x-12+12[/tex]

[tex]\implies -4=2x[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{-4}{2}=\dfrac{2x}{2}[/tex]

[tex]\implies x=-2[/tex]

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

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Given question:-}}}}[/tex]

             ❖ A number y increased by 5 is at least -21.

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

          ❖ First, if you come across the word "increased" it means we

    "increase" a number, or add something to that number, like

y increased by 5 [tex]\longmapsto[/tex] [tex]\sf{y+5}[/tex]

Now, we are also given that this expression is at least -21, which means it can't be -21; it can be -21 or it can be greater than -21.

So we have

[tex]\longmapsto\sf{y+5\geq -21}}[/tex]

Solving for y

[tex]\longmapsto\sf{y\geq -21-5}[/tex]

[tex]\longmapsto\sf{y\geq -26}[/tex]

So the values of y greater than or equal to -26 will make this inequality true.

 [tex]\rule{300}{1}[/tex]

Answer:

y >= - 26

Step-by-step explanation:

your equation at first looks like this

y + 5 >= -21

then you subtract 5 to both sides

y >= -26

Plotting the inequalities y ≤ 3x − 1 and y ≥ -x − 1 using the geogebra graphing tool, a possible solution to the system is (3, 1)

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the inequalities y ≤ 3x − 1 and y ≥ -x − 1

Plotting the inequalities y ≤ 3x − 1 and y ≥ -x − 1 using the geogebra graphing tool, a possible solution to the system is (3, 1)

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Answer:

22x-4

Step-by-step explanation:

2x(3+8)−4

Simplify  3+8 to 11.

2x×11−4

Simplify  2x times 11 to 22x.

22x−4

Answer:

Step-by-step explanation:

Answer:

What are the equivalent expressions?

Two expressions are said to be equivalent if they have the same value regardless of the value of the variable(s) in them.

Step-by-step explanation:

Answer:

24 and 16.

Step-by-step explanation:

They both are in between the sum of the two numbers.

Answer:

-32

Step-by-step explanation:

-2^2 is 4

-2^3 is -8

So 4•-8

=-32

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