Translate this phrase into an algebraic expression.
The sum of 12 and twice Gail's savings
Use the variable g to represent Gail's savings.

Answer:

30 + 20 = 50

Step-by-step explanation:

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

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:

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:

Step-by-step explanation:

Divide 5.8/8

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:

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:

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.

Answer:

square root of 25 and square root of 16

Step-by-step explanation:

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: 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.

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:

  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

Answer:

After 12 years the investment will be worth $5145.

Step-by-step explanation:

The formula used for compounded interest is:

A = P(1+r/n)^nt

where,

A = future value

P = Principal Amount

r = interest rate

n = no of times interest is compounded

t = time

In the question given:

A=?

P = $2100

r = 7.75% or 0.0775

n = 1

t= 12

A= 2100*(1+0.0775/1)^1*12

A= 2100 *(1+0.0775)^12

A= 2100 *(1.0775)^12

A= 2100 * 2.45

A= 5145

So, after 12 years the investment will be worth $5145.

Answer:

33.33

Step-by-step explanation:

Answer:

1. f(x)=x+7

2. f(x)=1.2x

Step-by-step explanation:

1. If f(x+5)=x+12, then substitute

[tex]t=x+5\Rightarrow x=t-5[/tex]

Hence,

[tex]f(t)=(t-5)+12\\ \\f(t)=t+7[/tex]

Now change t into x:

[tex]f(x)=x+7[/tex]

2. If f(x-5)=1.2x-6, then substitute

[tex]t=x-5\Rightarrow x=t+5[/tex]

Hence,

[tex]f(t)=1.2(t+5)-6\\ \\f(t)=1.2t+6-6\\ \\f(t)=1.2t[/tex]

Now change t into x:

[tex]f(x)=1.2x[/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]  

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]

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:

[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]

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:

pretty sure the answer is 35%

Step-by-step explanation:

because thats what i got on my quiz and it was right

Answer:

a= -2

b= 3

Step-by-step explanation:

solving for a:

-6 times what equals 12?

-2

solving for b:

when multiplying two variables that have exponents you simply add the two exponents together. so to find b you want to subtract 2 from 5

Answer:

3n

Step-by-step explanation:

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:

D

Step-by-step explanation:

The best answer is D.

A number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.

Final answer:

The correct statement is that a number divisible by 10 is also divisible by 5 because 5 is a factor of 10. Any number ending in 0 can be divided by both 10 and 5 to yield whole numbers, confirming this relationship. So, option D is correct.

Explanation:

The statement that BEST explains the relationship between numbers divisible by 5 and 10 is 'a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10'. This is because any number that ends with a 0 is divisible by 10, and since 10 is made up of 2 and 5, that same number must also be divisible by 5. For example, take the number 30; it ends in a 0, so it is divisible by 10. When you divide 30 by 10, you get 3, which shows that 10 is a factor of 30. Now, if you take 30 and divide it by 5, you also get a whole number, which is 6 in this case. This further confirms that any number divisible by 10 will also be divisible by 5.

Answer:

  • 72 ft²

Step-by-step explanation:

The bottom side length of the triangle is the difference between the top base length and the bottom base length:

  13 ft - 5 ft = 8 ft

The vertical side length of the triangle is the same, because the triangle is an isosceles right triangle.

Since we know the base lengths and height of the trapezoid, we can use the usual formula for the area:

  A = (1/2)(b1 +b2)h

  = (1/2)(5 ft + 13 ft)(8 ft) = 72 ft²

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:

5.2 m

Step-by-step explanation:

5.2 m

To find the minimum depth of the water, we look at the minimum of the function h, given by the equation h = 2.5 sin 2π (t−4) /12.4 + 6.2. The minimum depth is -2.5 + 6.2 = 3.7m, but this option is not provided.

In this mathematics problem, we are given a sinusoidal function representing the depth of water, h, at a seaport over time, t. The equation is h = 2.5 sin 2π (t−4) /12.4 + 6.2.

To find the minimum depth of the water, we need to focus on the properties of the sine function, which varies from -1 to 1. Therefore, the minimum value of 2.5 * sin(2π(t−4)/12.4) is -2.5 when sin(x) = -1.

By adding 6.2 to the minimum value of the function (-2.5), we obtain -2.5 + 6.2 = 3.7, which is the minimum value of h. However, this option is not provided in the choices. There seems to be a mistake in the given problem or its options.

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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:

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