1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the equation?

2) A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 4 more of the twenties. The total value of the money is $305.00. Find the number of twenty-dollar bills. What is the equation?

Answer:

10 cm

Step-by-step explanation:

Answer:

10 cm

Step-by-step explanation:

Since, the volume of a cuboid is,

V = l × w × h,

Where,

l = length,

w = width,

h = height,

∵ The shape of the aquarium must be cuboid,

We have, l = 20 cm, w = 12 cm, V = 2400 cm³,

By substituting the values,

2400 = 20 × 12 × h

2400 = 240h

[tex]\implies h = \frac{2400}{240}=10[/tex]

Hence, the height of the water in Nemo's aquarium would be 10 cm.

Answer: see below

Step-by-step explanation:

30 - 60 - 90 triangles have angles in the triangle measuring 30, 60, and 90 degrees. A 30 - 60 - 90 triangle also has special side ratios according to a side's location in the triangle.

The side across from the 30 degree angle is represented by x.

The side across from the 60 degree angle is represented by x[tex]\sqrt{3}[/tex].

The side across from the 90 degree angle is represented by 2x.

45 - 45 - 90 triangles have angles in the triangle measuring 45, 45, and 90 degrees. A 45 - 45 - 90 triangle has special side ratios similar to the 30 - 60 - 90 triangle.

The side across from either of the 45 degree angles is represented by x.

The side across from the 90 degree angle is represented by x[tex]\sqrt{2}[/tex].

These ratios can be used to find missing sides. If you know that a triangle is one of these special triangles and you also know one of its side lengths, you can plug the known length in for x in the proper place.

EX: you have a 30 - 60 - 90 triangle with a side length of 2 across from the 30 degree angle. You then know that the side across from 60 is 2[tex]\sqrt{3}[/tex] and the side across from 90 is 4.

Answer:

increasing the radius makes the circle larger.  (Answer B)

Step-by-step explanation:

The formula for the area of a circle is A = πr².  Hence, Area of a Circle depends solely on the variable r and the constant of proportionality π.

Thus, increasing the radius makes the circle larger.

Answer:

3n

Step-by-step explanation:

The first step is to combine like terms, 35 and 11 are both integers without variables, so we can combine.

24+3x= 23

Now we subtract 24 from 23 to isolate 3x, and we get -1.

3x=-1

To solve we just need to divide -1 by 3.

Answer: -1/3

The value of x after solving the equation will be equal to -1/3

The expression is defined as the relationship between the numbers and variables and are arranged in the form of an equation.

The first step is to combine like terms, 35 and 11 are both integers without variables, so we can combine.

24+3x= 23

Now we subtract 24 from 23 to isolate 3x, and we get -1.

3x=-1

To solve we just need to divide -1 by 3.

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Answer:

The water bill increases by about $19 for every additional resident in the home

Step-by-step explanation:

This is because times x shows that it is to each and every person and it is increasing.

Answer:

The answer is C. The water bill increases by about $19 for every additional resident in the home.

Step-by-step explanation:

The equation above consists of y as the dependent variable, x as the independent variable, 19.485 as the slope, and 86.912 as the constant. The constant represent the fixed water bill. The x variable represents the additional water usage.

Answer:

[tex]36\ liters\ of\ soil[/tex]

Step-by-step explanation:

we know that

The ratio of soil, manure and leaf mould is [tex]3:1:2[/tex]

That means

For every 6 liters of the compost, he use 3 liters of soil

so by proportion

Find how many liters of soil does he use for 72 liters of compost

[tex]\frac{3}{6}=\frac{x}{72}\\ \\x=3*72/6\\ \\x=36\ liters\ of\ soil[/tex]

For this case we have that the volume of the cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

h: It is the height of the cylinder

A: It is the radius of the cylinder

We have to, according to the given data:

[tex]h = 7\\r = 6[/tex]

Substituting:

[tex]V = \pi * (6) ^ 2 * 7\\V = \pi * 36 * 7\\V = 252 \pi[/tex]

ANswer:

Option A

[tex]252 \pi \ units ^ 3[/tex]

the answer is 252π option A

Answer:

Well there are 6 toppings. For one person to select sausage, it is  \frac{1}{6} . For two people, multiply them together and the probability is  \frac{1}{36}

Answer:

We apply the chain rule, along with the quotient rule, to find d ... 3. (4 pts) A particle moves on a line so that its coordinate at time t is y ... (10 pts) A cylindrical tank with radius 5 m is being filled with water at a rate of ... h/(t) = V /(t)/25π m2. ... cup has the shape of a cone with height 10 cm and radius 3 cm (at.

Step-by-step explanation:

Answer:

V = 392.7 m3

Step-by-step explanation:

To find the volume of the cone, first calculate the hieght and the radius.

To find the length of the radius, equate the given area to the formula for the area of a circle and solve for r.

πr2=25π

Divide both sides by π.

r2=25

Take the positive square root of both sides.

r=5 m

It is given that the height of the cone equal to three times the radius. So, use the radius to find the height.

h=3r

Substitute 5 for r.

h=3⋅5

Simplify.

h=15 m

To find the volume of the cone, use the formula for the volume of a cone.

V=13πr2h

Substitute 5 for r and 15 for h.

V=13⋅π⋅52⋅15

Simplify.

V=125π

Use a calculator to approximate.

V≈392.7 m3

Therefore, the volume of the cone is about 392.7 m3.

I believe it’s the second option 2^2x+6=2^6

Answer:

[tex]\large\boxed{2^{2x+6}=2^6}[/tex]

Step-by-step explanation:

[tex]4^{x+3}=64\\\\4^{x+3}=4^3\\\\(2^2)^{x+3}=(2^2)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+3)}=2^{(2)(3)}\\\\2^{2x+6}=2^6[/tex]

Answer:

Part 2) [tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex] or [tex]P=22.36\ units[/tex]

Part 4) [tex]P=[19+\sqrt{17}]\ units[/tex] or [tex]P=23.12\ units[/tex]

Part 6) [tex]A=36\ units^{2}[/tex]

Part 8) [tex]A=16\ units^{2}[/tex]

Part 10) [tex]A=6.05\ units^{2}[/tex]  

Step-by-step explanation:

we know that

The formula to calculate the distance between two points is equal to  

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]  

Part 2) we have the rectangle ABCD

[tex]A(-4,-4),B(-2,0),C(4,-3),D(2,-7)[/tex]

Remember that in a rectangle opposite sides are congruent

step 1

Find the distance AB

[tex]A(-4,-4),B(-2,0)[/tex]

substitute in the formula

[tex]AB=\sqrt{(0+4)^{2}+(-2+4)^{2}}[/tex]  

[tex]AB=\sqrt{(4)^{2}+(2)^{2}}[/tex]  

[tex]AB=\sqrt{20}\ units[/tex]  

step 2

Find the distance BC

[tex]B(-2,0),C(4,-3)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-3-0)^{2}+(4+2)^{2}}[/tex]  

[tex]BC=\sqrt{(-3)^{2}+(6)^{2}}[/tex]  

[tex]BC=\sqrt{45}\ units[/tex]  

step 3

Find the perimeter

The perimeter is equal to

[tex]P=2[AB+BC][/tex]

substitute

[tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex]

or

[tex]P=22.36\ units[/tex]

Part 4) we have the quadrilateral ABCD

[tex]A(-2,-3),B(1,1),C(7,1),D(6,-3)[/tex]

step 1

Find the distance AB

[tex]A(-2,-3),B(1,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1+3)^{2}+(1+2)^{2}}[/tex]  

[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]  

[tex]AB=5\ units[/tex]  

step 2

Find the distance BC

[tex]B(1,1),C(7,1)[/tex]

substitute in the formula

[tex]BC=\sqrt{(1-1)^{2}+(7-1)^{2}}[/tex]  

[tex]BC=\sqrt{(0)^{2}+(6)^{2}}[/tex]  

[tex]BC=6\ units[/tex]  

step 3

Find the distance CD

[tex]C(7,1),D(6,-3)[/tex]

substitute in the formula

[tex]CD=\sqrt{(-3-1)^{2}+(6-7)^{2}}[/tex]  

[tex]CD=\sqrt{(-4)^{2}+(-1)^{2}}[/tex]  

[tex]CD=\sqrt{17}\ units[/tex]  

step 4

Find the distance AD

[tex]A(-2,-3),D(6,-3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(-3+3)^{2}+(6+2)^{2}}[/tex]  

[tex]AD=\sqrt{(0)^{2}+(8)^{2}}[/tex]  

[tex]AD=8\ units[/tex]  

step 5

Find the perimeter

The perimeter is equal to

[tex]P=AB+BC+CD+AD[/tex]

substitute

[tex]P=[5+6+\sqrt{17}+8]\ units[/tex]

[tex]P=[19+\sqrt{17}]\ units[/tex]

or

[tex]P=23.12\ units[/tex]

Part 6) Calculate the area of rectangle ABCD

[tex]A(-1,5),B(3,5),C(3,-4),D(-1,-4)[/tex]

Remember that in a rectangle opposite sides are congruent

step 1

Find the distance AB

[tex]A(-1,5),B(3,5)[/tex]

substitute in the formula

[tex]AB=\sqrt{(5-5)^{2}+(3+1)^{2}}[/tex]  

[tex]AB=\sqrt{(0)^{2}+(4)^{2}}[/tex]  

[tex]AB=4\ units[/tex]  

step 2

Find the distance BC

[tex]B(3,5),C(3,-4)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-4-5)^{2}+(3-3)^{2}}[/tex]  

[tex]BC=\sqrt{(-9)^{2}+(0)^{2}}[/tex]  

[tex]BC=9\ units[/tex]  

step 3

Find the area

The area is equal to

[tex]A=[AB*BC][/tex]

substitute

[tex]A=[4*9]=36\ units^{2}[/tex]

Part 8) Calculate the area of right triangle ABC

[tex]A(-3,3),B(-3,-1),C(5,-1)[/tex]

step 1

Find the distance AB

[tex]A(-3,3),B(-3,-1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(-1-3)^{2}+(-3+3)^{2}}[/tex]  

[tex]AB=\sqrt{(-4)^{2}+(0)^{2}}[/tex]  

[tex]AB=4\ units[/tex]  

step 2

Find the distance BC

[tex]B(-3,-1),C(5,-1)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-1+1)^{2}+(5+3)^{2}}[/tex]  

[tex]BC=\sqrt{(0)^{2}+(8)^{2}}[/tex]  

[tex]BC=8\ units[/tex]  

step 3

Find the distance AC

[tex]A(-3,3),C(5,-1)[/tex]

substitute in the formula

[tex]AC=\sqrt{(-1-3)^{2}+(5+3)^{2}}[/tex]  

[tex]AC=\sqrt{(-4)^{2}+(8)^{2}}[/tex]  

[tex]AC=\sqrt{80}\ units[/tex] -----> is the hypotenuse

step 4

Find the area

The area is equal to

[tex]A=(1/2)AB*BC[/tex]

substitute

[tex]A=(1/2)(4*8)=16\ units^{2}[/tex]

Part 10) Calculate the area of triangle ABC

[tex]A(3,0),B(1,8),C(2,10)[/tex]

step 1

Find the distance AB

[tex]A(3,0),B(1,8)[/tex]

substitute in the formula

[tex]AB=\sqrt{(8-0)^{2}+(1-3)^{2}}[/tex]  

[tex]AB=\sqrt{(8)^{2}+(-2)^{2}}[/tex]  

[tex]AB=\sqrt{68}\ units[/tex]  

step 2

Find the distance BC

[tex]B(1,8),C(2,10)[/tex]

substitute in the formula

[tex]BC=\sqrt{(10-8)^{2}+(2-1)^{2}}[/tex]  

[tex]BC=\sqrt{(2)^{2}+(1)^{2}}[/tex]  

[tex]BC=\sqrt{5}\ units[/tex]  

step 3

Find the distance AC

[tex]A(3,0),C(2,10)[/tex]

substitute in the formula

[tex]AC=\sqrt{(10-0)^{2}+(2-3)^{2}}[/tex]  

[tex]AC=\sqrt{(10)^{2}+(-1)^{2}}[/tex]  

[tex]AC=\sqrt{101}\ units[/tex]  

step 4

we know that  

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  

a,b,c be the lengths of the sides of a triangle.  

The area is given by:  

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]  

where  

p is half the perimeter  

p=[tex]\frac{a+b+c}{2}[/tex]  

we have  

[tex]a=AB=\sqrt{68}=8.25\ units[/tex]  

[tex]b=BC=\sqrt{5}=2.24\ units[/tex]  

[tex]c=AC=\sqrt{101}=10.05\ units[/tex]  

p=[tex]\frac{8.25+2.24+10.05}{2}=10.27\ units[/tex]  

Find the area

[tex]A=\sqrt{10.27*(10.27-8.25)(10.27-2.24)(10.27-10.05)}[/tex]  

[tex]A=\sqrt{10.27*(2.02)(8.03)(0.22)}[/tex]  

[tex]A=6.05\ units^{2}[/tex]  

Let point Q = (4,y)

√[ (4-0)^2 + (y-0)^2 ] = √[ (6-0)^2 + (0-0)^2 ]

Square both side

(4-0)^2 + (y-0)^2 = (6-0)^2 + (0-0)^2

4^2 + y^2 = 6^2

16 + y^2 = 36

y^2 = 36-16

y^2 = 20

y= √20

y= 2√5

Answer:

2√5

Step-by-step explanation:

On the graphic, you see point Q is roughly between 4 and 4.5 units on the Y-axis.

So, all we have to do is find a value similar to that in the answer choices.  So, let's look at the values:

2√5:  2 * 2.23 = 4.46... that's pretty much what we're looking for.

4√2: 4 * 1.41 = 6.4.  Way too big.

2√13: 2 * 3.6 = 7.2, way too big.

8√2: We know that will necessary be way bigger than 4.5, so let's not even evaluate it.

Answer:

30 + 20 = 50

Step-by-step explanation:

I think the answer would be 50? Wouldn’t it

Answer:

around %114.98

Answer:

Answer (a):

distance traveled per revolution = 1.5 feet

Answer (b):

slope = 1.5 feet per revolution

Step-by-step explanation:

We have been given a graph which shows number of revolutions v/s distance traveled in feet.

Answer (a):

Now we need to find about how far does Miguel travel per revolution. That means find distance traveled in 1 revolution.

From graph we see that 10 revolution corresponds to 15 feet.

then 1 revolution = 15/10 = 1.5 feet

hence final answer is 1.5 feet.

Answer (b):

slope means [change in y-value] / [change in x-value]

From graph we see that 10 revolution corresponds to 15 feet.

then slope = 15/10 = 1.5 feet per revolution

Answer a is 1.5 and so is b

Answer:

Events C and D are  mutually exclusive.

P(C ∩ D) = 0

Step-by-step explanation:

We notice that event C is even numbers and Event D is odd number.  We cannot roll a die and have both events occur at the same time.  That means they are mutually exclusive.  Either one event occurs or the other occurs.

P(C ∩ D) = 0  This means the events do not intersect (overlap).  Or are mutually exclusive.

Answer:

leading coefficient is 1

degree is 9

Leading coefficient: 1

Degree: 9

Answer:

x = 13.7

Step-by-step explanation:

Sin = Opp./Hypo.

so

Sin (17) = x / 47

x = sin (17) * 47

x = 0.2924 * 47

x = 13.7

The total number of buckets of fish walruses were fed each day is

A = 35/3 buckets or 11 2/3 buckets

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 total number of buckets of fish walruses were fed each day be = A

Now , the equation will be

The number of buckets of fish dolphins were fed each day = 2 1/3 buckets

The value 2 1/3 = 7/3 buckets

And ,

The number of buckets of fish walruses were fed each day = 5 x number of buckets of fish dolphins were fed each day

Substituting the values in the equation , we get

The number of buckets of fish walruses were fed each day = 5 x 7/3

The number of buckets of fish walruses were fed each day = 35/3 buckets

Number of buckets of fish walruses were fed each day = 11 2/3 buckets

Therefore , the value of A is 11 2/3 buckets

Hence , The total number of buckets of fish walruses were fed each day is

A = 35/3 buckets or 11 2/3 buckets

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Final answer:

To determine how much fish the walruses are fed, multiply the 2 1/3 buckets of fish fed to dolphins by 5. The calculation gives us an answer of 11 2/3 buckets of fish fed to walruses each day.

Explanation:

The dolphins at the sea aquarium are fed 2 1/3 buckets of fish each day. To find out how much the walruses are fed, we have to multiply the quantity of fish fed to dolphins by 5, since walruses are fed 5 times as much.

First, convert 2 1/3 to an improper fraction: 2 1/3 = 7/3.
Now, multiply 7/3 by 5 to get the walruses' daily fish intake in buckets.
7/3 × 5 = 35/3.

35/3 is an improper fraction, and when converted to a mixed number, it equals 11 2/3 buckets of fish per day.

Hence, the walruses at the sea aquarium are fed 11 2/3 buckets of fish each day.

Answer:

Shift to the right 3 units.

Answer:

Shift to the right 3 units

Step-by-step explanation:

Translations are a type of rigid transformation of functions, in which the position of the graph of a function is modified. The general form of the graph of a function moves up, down, left, or right.

Vertical translations:

Let:

[tex]a >0[/tex]

[tex]y=f(x)+a[/tex]  shifts the graph [tex]a[/tex] units up

[tex]y=f(x)-a[/tex] shifts the graph [tex]a[/tex] units down

Horizontal translations:

Let:

[tex]b>0[/tex]

[tex]y=f(x+a)[/tex] shifts the graph [tex]b[/tex] units to the left.

[tex]y=f(x-a)[/tex] shifts the graph [tex]b[/tex] units to the right.

Using the previous information we can conclude that the function:

[tex]f(x-3)[/tex]

Is a Horizontal translation in which the graph was shifted [tex]b=3[/tex] units to the right.

[tex]f(x-3)=(x-3)^3[/tex]

I leave you the graphs, so you can corroborate the answer easily.

Answer:

Option B

[tex]g(x) = -6x^2[/tex]

Step-by-step explanation:

If the graph of the function [tex]g(x)=cf(x)[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

In this problem we have the function [tex]f(x)=x^2[/tex]  

We now that this function  is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis

Then  [tex]|c| =6 >0[/tex]  and [tex]c=-6<0[/tex]

Therefore the graph of [tex]g(x)[/tex] is [tex]g(x) = -6f(x)[/tex]

[tex]g(x) = -6x^2[/tex]

Answer:

$6.54 per pound

Step-by-step explanation:

we know that

To find the unit price divide the total cost by the total pounds

so

[tex]\frac{4.36}{(2/3)}=\frac{4.36*3}{2}=\$6.54\ per\ pound[/tex]

The cross section is A. Hexagon, a 6-sided figure.

Answer:

Hexagon

Step-by-step explanation:

A polygon are plane figure with more than 3sides e.g Pentagon , hexagon, heptagon etc.

Based on the diagram the cross section of the solid contains a six sided plane figure known as a hexagon.

An hexagon is a polygon with six equal sides and angles.

Answer:

Step-by-step explanation:

Given are some properties of triangles and we have to check whether they are correct

i) Only two of three angle bisectors of the internal angles of a triangle are concurrent.

This is incorrect since all three angle bisectors concur at incentre

ii) The circumcenter of a triangle is the point where the perpendicular bisectors of the sides meet.

-- correct because the meeting point is equidistant from all three vertices

iii) Given any three non-collinear points, there exists exactly one circle that passes through the points.

-- correct because any three points determine a circle

iv) Given any three non-collinear points, there exists exactly one circle that passes through the points.

-- Correct

v) The incenter of a triangle is the point where the angle bisectors meet.

-- Correct and the centre is equidistant from the sides of the triangle

Statements 2, 3, and 5 are correct.

Analyze each statement to determine which are correct:

Answer:

  Eighty percent of the recipes in a cookbook require salt.

Step-by-step explanation:

The above statistic describes the entire population of recipes in the cookbook. It is not projecting anything about the population based on a sample.

Answer:

The radius of the cylinder is [tex]11.5\ in[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]V=2,908.33\ in^{3}[/tex]

[tex]h=7\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute the values and solve for r

[tex]2,908.33=(3.14)r^{2}(7)[/tex]

[tex]r^{2}=2,908.33/[(3.14)(7)][/tex]

[tex]r=11.5\ in[/tex]

Answer:

The answer is 5

Step-by-step explanation:

Got it right on edg :)

The value of 3 - (-2) is 5. In math, value can mean different things that are closely related. Generally, a mathematical value can be any specific mathematical thing.

To calculate the value of 3 - (-2), we need to understand that subtracting a negative number is equivalent to adding its positive counterpart.

So one can say that

3 - (-2)

Then Rewrite the double negative as addition:

3 + 2

So add the numbers:

3 + 2 = 5

Therefore, the value of 3 - (-2) is 5.

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Answer:

* Domain: all reals except multiples of 2π

* Range: (-∞ , -2] ∪ [2 , ∞)

Step-by-step explanation:

* Lets revise the period, the domain and the range of csc(x)

- The period of csc(x) is 2π

- To find the period of csc(x) use 2π / coefficient of x

- The domain of csc(x) is all x ≠ nπ

- The range is y ≤ -1 , y ≥ 1

* Lets revise the vertical and the horizontal stretch and compress

- A vertical stretching is the stretching of the graph away from

the x-axis

• if k > 1, the graph of y = k•f(x) is the graph of f(x) vertically

 stretched by multiplying each of its y-coordinates by k.

- A vertical compression is the squeezing of the graph toward

 the x-axis.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

  by multiplying each of its y-coordinates by k.

- A horizontal stretching is the stretching of the graph away from

 the y-axis

• if 0 < k < 1 (a fraction), the graph is f (x) horizontally stretched by

 dividing each of its x-coordinates by k.

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

• if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally

 compressed by dividing each of its x-coordinates by k

∵ f(x) = 2csc(x/2)

- The coefficient of x is 1/2

∵ The period of x = 2π

∴ The period of x/2 = 2π/1/2 = 4π

∵ The domain of csc(x) is all x ≠ nπ

∴ The domain of csc(x/2) is all x ≠ n2π

∵ f(x) = 2csc(x/2)

∵ csc(x/2) multiplying by 2

- That means every y-coefficient multiplying by 2

∵ The range of csc(x/2) is y ≤ -1 and y ≥ 1

∴ The rang of f(x) = 2csc(x/2) is y ≤ -1(2) and y ≥ 1(2)

∴ The rang of f(x) = 2csc(x/2) is y ≤ -2 and y ≥ 2

* Domain: all reals except multiples of 2π

* Range: (-∞ , -2] ∪ [2 , ∞)

* Look to the graph attached

- The red is y = csc(x)

- The blue is f(x) = 2csc(x/2)

Answer:

  160 in³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base and h is the height. Filling in the given numbers, you have ...

  V = (20 in²)(8 in) = 160 in³

The volume of the prism is 160 cubic inches.

Final answer:

The volume of a right pentagonal prism can be found by multiplying the base area by the height of the prism. In this case, the volume is 160 cubic inches.

Explanation:

To find the volume of a right pentagonal prism, we need to multiply the area of the base by the height of the prism. In this case, the area of the base is 20 square inches and the altitude (height) is 8 inches. So, the volume can be found by multiplying 20 by 8.

Volume = Base Area x Height

Volume = 20 square inches x 8 inches = 160 cubic inches

Therefore, the volume of prism is 160 cubic inchinches