The length of the base of a rectangular prism is 8 inches. The width of the prism is 4 1 2 inches, and the height is 3 1 2 inches. What is the volume of the prism? A) 84 in3 B) 92 1 2 in3 C) 104 in3 D) 126 in3

Answer: 10x+13x+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

7x^2 + 3x^2 = 10x^2

-2x + 15x = 13x

9 - 4 = 5

Put these together. Don't do any more than putting them together in a string.

Answer: 10x^2 + 13x + 5

Answer:

a= 3 b=6 c= 5

Step-by-step explanation:

For this case we have the following expression:

[tex]3 ^ {\frac {6} {5}}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [c] {a ^ b} = a ^ {\frac {b} {c}}[/tex]

Then according to the given expression we have the following:

[tex]a = 3\\b = 6\\c = 5[/tex]

Answer:

[tex]a = 3\\b = 6\\c = 5[/tex]

Answer:

56.5 inches

Step-by-step explanation:

We are given the area of a circle and we are to find the circumference of the same circle.

We know that the area of a circle is given by [tex]\pi r^2[/tex] so equating the given value to get.

[tex]\pi r^2=254.47[/tex]

[tex]r^2=\frac{254.47}{\pi }[/tex]

[tex]r=\sqrt{81.00}[/tex]

r = 9 inches

Since we now know the radius of the circle so we can find its circumference.

Circumference of circle = [tex]2\pi r[/tex] = [tex]2\pi (9)[/tex] = 56.5 inches

Answer: 56.54 in

Step-by-step explanation:

The area can be calculated with this formula:

[tex]A=\pi r^2[/tex]

Where r is the radius

And the circumference can be calculated with this formula:

[tex]C=2\pi r[/tex]

 Where r is the radius

Solve for the radius from  [tex]A=\pi r^2[/tex]. Then, tha radius is:

[tex]r=\sqrt{\frac{A}{\pi }}=\sqrt{\frac{254.47in^2}{\pi }} =9in[/tex]

Then, the circumference is:

 [tex]C=2\pi (9in)=56.54in[/tex]

Answer:

3a-7

Step-by-step explanation:

2(2a-5)-(a-3)

Distribute the 2

2*2a -2*5 - (a-3)

4a -10 - (a-3)

Distribute the minus sign

4a-10 -a +3

Combine like terms

4a-a -10+3

3a-7

(X-2)^2 +(y-5)^2 = 256

Answer:

1) g(x) ----> y-intercept -3

2) h(x) ----> y-intercept -1

3) f(x) ----> y-intercept 2

Step-by-step explanation:

we know that

The y-intercept or initial value, is the value of y when the value of x is equal to zero

Calculate the y-intercept of each exponential function

case 1) A function g, has a growth factor of 2 and a value of 1, and passes through the point (1,-2)

The exponential function is equal to

[tex]g(x)=1(2)^{x}+c[/tex]

Find the value of c

For x=1, g(x)=-2

substitute

[tex]-2=(2)^{1}+c[/tex]

[tex]-2=2+c[/tex]

[tex]c=-4[/tex]

so

[tex]g(x)=(2)^{x}-4[/tex]

Find the y-intercept

For x=0

[tex]g(0)=(2)^{0}-4[/tex]

[tex]g(0)=-3[/tex]

case 2) Observing the table

For x=0

f(0)=2

therefore

The y-intercept of f(x) is 2

case 3) Observing the graph

For x=0

h(0)=-1

therefore

The y-intercept of h(x) is -1

Order the functions from least to greatest y-intercept

1) g(x) ----> y-intercept -3

2) h(x) ----> y-intercept -1

3) f(x) ----> y-intercept 2

Final answer:

To find the y-intercept of an exponential function, evaluate it at x = 0. The constant term in the function represents the y-intercept. Order the functions by comparing these constant terms from least to greatest.

Explanation:

To find the y-intercept of an exponential function, we need to evaluate the function when x is equal to zero. The exponential function is usually given in the form f(x) =[tex]ab^x[/tex], where a is the y-intercept. This is because any number (except zero) raised to the power of zero is 1, so[tex]b^0[/tex] will always be 1, leaving us with f(0) = a.

After finding the y-intercept for each function, order them from least to greatest to complete the task. For example, if we have functions such as f(x) = [tex]2(3)^x, g(x) = 5(2)^x[/tex], and h(x) = [tex]-1(4)^x,[/tex] their y-intercepts would be 2, 5, and -1 respectively. Ordered from least to greatest, the functions by their y-intercepts would be h(x), f(x), g(x).

2x^2+10x-3x-15= 2x^2+7x-15

Answer:

2x^2+10x-3x-15= 2x^2+7x-15

Step-by-step explanation:

Answer:

C.15+25y

Step-by-step explanation:

5(3+5y) solved via distribution is 15+25y

Happy to help :D

C. Because 5(3+5y) is the same as 5x3 plus 5x5y which is 15 + 25y

Answer:

Step-by-step explanation:

n, n + 1, n + 2 - three consecutive integers

The equation:

138 - n = (n + 1) + (n + 2)

138 - n = n + 1 + n + 2                 combile like terms

138 - n = 2n + 3           subtract 138 from both sides

-n = 2n - 135               subtract 2n from both sides

-3n = -135            divide both sides by (-3)

n = 45

n + 1 = 46

n + 2 = 47

The three consecutive integers in question are 45, 46, and 47. This was solved by setting up and solving a simple algebraic equation.

Let the three consecutive integers be x, x+1, and x+2. According to the problem, the sum of the second and third integers is equal to 138 minus the first one. This can be written mathematically as:

x + (x + 1) + (x + 2) = 138

Solving this equation gives:

3x + 3 = 138
3x = 135
x = 45

Hence, the three consecutive integers are 45, 46, 47.

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Answer:

no

Step-by-step explanation:

there is not one point that is very distant from all of the other ones

no there is not an outlier :)

Answer:

Step-by-step explanation:

12 seconds for 28 claps

1 second for (28/12) claps

? claps for 1.75 mins?

1.75 minutes = 105 seconds (1.75×60 = 105)

105 seconds for (28/12)×105 claps

= 245 claps

Answer:

Your friends can clap their hands 245 times in 1.75 minutes.

Step-by-step explanation:

First of all, you should know how many seconds represents 1.75 minutes, because the amount of applause your friends can make is in that measure of time.  In order to make this conversion, a simple rule of three is made, knowing that 1 minutes is 60 seconds:

If 1 minute is 60 seconds, how many seconds are 1.75 minutes?

[tex]\frac{1.75minutes*60seconds}{1minute} =105 seconds[/tex]

Knowing that your friend can clap his hands 28 times in 12 seconds and knowing that 1.75 minutes is 105 seconds, you can perform a rule of three again:

If they can clap their hands 28 times in 12 seconds, how many applause can they make in 105 seconds?

[tex]\frac{105seconds*28applause}{12} =245 applause[/tex]

Then your friends can clap their hands 245 times in 105 seconds, which is 1.75 minutes.

Answer:

(0,0), (0,9), (9,0)

Step-by-step explanation:

The matrix corresponding vertices are:

(0,0)

(0,3)

(3,0)

Rosa scales by 3T, so we need to multiply each point by 3.

(3*0, 3*0)

(0*3, 3*3)

(3*3, 0*3)

=

(0,0)

(0,9)

(9,0)

last answer choice is right.

Answer:

[tex]\large\boxed{(0,\ 0),\ (0,\ 9),\ (9,\ 0)}[/tex]

Step-by-step explanation:

[tex]n\cdot\left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right] =\left[\begin{array}{ccc}(n)(a)&(n)(b)&(n)(c)\\(n)(d)&(n)(e)&(n)(f)\end{array}\right] \\\\============================[/tex]

[tex]\text{We have:}\\\\T=\left[\begin{array}{ccc}0&0&3\\0&3&0\end{array}\right] \Rightarrow\text{vertex}\ (0,\ 0),\ (0,\ 3),\ (3,\ 0)\\\\-----------------------------\\\\3T=\left[\begin{array}{ccc}(3)(0)&(3)(0)&(3)(3)\\(3)(0)&(3)(3)&(3)(0)\end{array}\right] =\left[\begin{array}{ccc}0&0&9\\0&9&0\end{array}\right] \\\\\text{new vertex:}\ (0,\ 0),\ (0,\ 9),\ (9,\ 0)[/tex]

Answer:

log(2)

Step-by-step explanation:

property of logs says

Log(60) - Log(30) = Log(60/30) = Log (2)

Answer:

1.20

Step-by-step explanation:

properties of log

log x - log y = logx/logy

Answer:

28.26 cm²

Step-by-step explanation:

It's not the point O, but the circle O.

The area of a circle is given by the formula A = π r²

We already have r (3cm)... so we can plug it directly into the equation:

A = π r² = π 3² = 9π = 28.26 cm²

Answer:

A = 28.27

Step-by-step explanation:

A = π r^2

A = π 3^2

A= π (9)

A = 28.27433

No he should have multiplied 5,700 by 0.05

Answer:

The correct option is B) No, he should have multiplied $5,790 by 0.05.

Step-by-step explanation:

Consider the provided information.

He is paid $14.00 per hour, plus 5% commission. He worked 8 hours and sold 6 computers today for a total of $5,790.

Now find his total earning as shown:

$14 × 8 = $112

It is given that he sold 6 computers for a total of $5,790 and he gets a commission of 5% of total sale.

5% = [tex]\frac{5}{100}=0.05[/tex]

Now multiply 0.05 with $5,790

$5,790 × 0.05 = $289.5

Hence, the total income is $112+$289.5=$401.5

To calculate his pay, Henry multiplies 14 × 8, then adds the product to 5,790, then multiplies the sum by 0.05.

Henry's calculation is incorrect as he needs to multiply 5,790 with 0.05 and then he need to add the product of 14 × 8

Therefore, the correct option is B) No, he should have multiplied $5,790 by 0.05.

Answer:

[tex]\large\boxed{\sqrt{20}-\sqrt{80}=-2\sqrt5}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{20}=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=2\sqrt5\\\\\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5\\\\\sqrt{20}-\sqrt{80}=2\sqrt5-4\sqrt5=(2-4)\sqrt5=-2\sqrt5[/tex]

Answer:

The answer is 18.2.

Hope this helps!

Answer: 18.2

Step-by-step explanation:

you would round to 18.2 because with 5 and above, you give it a shove, 4 and below let it go

ANSWER

B. 81

EXPLANATION

The given expression is:

[tex] {3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } [/tex]

Recall that:

[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]

We simplify the expression using the properties of exponents to obtain:

[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11}{5} - - \frac{9}{5} } [/tex]

We simplify the exponents to get;

[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11 + 9}{5}} [/tex]

[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{20}{5}} [/tex]

[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{4} [/tex]

[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = 81[/tex]

The correct answer is B. 81

Answer:

32768^1

Step-by-step explanation:

Solved the equation and added the first power.

Combine Like Terms:

2/3m+-4/5-3/5m

=(2/3m+-3/5m)+(-4/5)

=1/15m+-4/5

Answer:

-1/5m-4/5

Step-by-step explanation:

Answer:

(7x-5)(7x+5)

Step-by-step explanation:

Answer:

(7x + 5)(7x - 5)

Step-by-step explanation:

49x² - 25 ← is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

49x² = (7x)² ⇒ a = 7x

25 = 5² ⇒ b = 5

49x² - 25

= (7x)² - 5² = (7x + 5)(7x - 5)

Answer:

f(x) =  3(x + 2)(x - 1)(x + 3)

Step-by-step explanation:

A logical first step would be to factor 3 out of all four terms:

f(x) = 3x^3+12x^2+3x-18 = 3(x^3 + 4x^2 + x - 6)

Roots of this x^3 + 4x^2 + x - 6 could be factors of 6:  {±1, ±2, ±3, ±6}.

I would use synthetic division here to determine which, if any, of these possibilities are actually roots of x^3 + 4x^2 + x - 6.  Let's try x = 1 and see whether the remainder of this synth. div. is 0, which would indicate that 1 is indeed a root of x^3 + 4x^2 + x - 6:

1    /    1    4    1    -6

                1    5    6

    ------------------------

          1     5    6    0

Yes, 1 is a root of x^3 + 4x^2 + x - 6, and so (x - 1) is a factor of x^3 + 4x^2 + x - 6.

Look at the coefficients of the quotient, which are   1, 5 and 6.

This represents the quadratic 1x² + 5x + 6, whose factors are (x + 2) and

(x + 3).

Thus, the given polynomial in factored form is:

f(x) = 3x^3+12x^2+3x-18 = 3(x + 2)(x - 1)(x + 3)

Answer:

3(x + 2)(x - 1)(x + 3)

Step-by-step explanation:

apex

Answer:

B). graph of increasing exponential function going through point (0, 3)

Step-by-step explanation:

Given function is [tex]f\left(x\right)=3\left(1.5\right)^x[/tex]

Now we need to find about which of the given choices best describes the given function. Where given choices are:

A). graph of increasing exponential function going through point 0, 2

B). graph of increasing exponential function going through point 0, 3

C). graph of increasing exponential function going through point 0, 1

D). graph of increasing exponential function going through point 0, 4

plug x=0 into given function

[tex]f\left(x\right)=3\left(1.5\right)^x[/tex]

[tex]f\left(0\right)=3\left(1.5\right)^0=3(1)=3[/tex]

Hence graph passes through point (0,3).

growth factor 1.5 is greater than 1 so that means it is increasing function.

Hence correct choice is:

B). graph of increasing exponential function going through point (0, 3)

Answer: Your answer is c

Step-by-step explanation:  The first thing you can do is add the two equations together to cancel out x

5x-2y=3

-5x+4y=9

added them together will get us 2y=12, from here divide 2 and get y=6

Plug 6 into the first equation and solve for x.

5x-2(6)=3

5x-12=3, add 13 to the other side

5x=15, divide 5 and get the answer

x=3

Step-by-step explanation:

[tex]r>-11\qquad\text{change the signs}\\\\\boxed{-r<11}\qquad\text{multiply both sides by 3}\\\\\boxed{-3r<33}\\\\r>-11\qquad\text{multiply both sides by 3}\\\\\boxed{3r>-33}[/tex]

Answer:

A

C

D

Step-by-step explanation:

Answer:pies 9 :p

Step-by-step explanation:

36÷4=9

Answer:

(4,-2)

Step-by-step explanation:

plug in and simplify;

y+2=-3(x-4)

-2+2=-3(x-4)

0=-3x+12

3x=12

x=4

The missing value in the solution of the equation is ( 4 , -2)

An equation is a mathematical statement that consists of two algebraic expression equated by an equal sign.

The given equation is

y +2 = -3 (x-4)

The value of x at y = -2 ,

Substituting the value of y in the equation

-2 + 2 = -3 ( x -4)

0 = -3x +12

-12 = -3x

x = 4

The value of x is 4

Therefore the missing value in the solution of the equation is ( 4 , -2)

To know more about Equation

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Answer:

The pepperoni and peppers are mixed up

Step-by-step explanation:

Answer:

The mistake my friend made was that pepperoni and peppers are mixed up, pepperoni is suppose to be 20% while peppers is supposed to be 14%

Step-by-step explanation:

Given that 4000 students

Pepperoni = 800

Sausage = 1,000

Mushrooms = 1,200

Peppers = 560

Onions = 240

Other = 200

To find the degree of each on the circle graph, we have:

Pepperoni = 800/4,000 * 100 = 20%

Sausage = 1,000/4,000 * 100 = 25%

Mushrooms = 1,200/4,000 * 100 = 30%

Peppers = 560/4,000 * 100 = 14%

Onions = 240/4,000 * 100 = 6%

Other = 200/4,000 * 100 = 5%

The mistake my friend made is that pepperoni and peppers are mixed up, pepperoni is suppose to be 20% while peppers is supposed to be 14%

____________________________________________________

Answer:

Your answer would be $34.

____________________________________________________

Step-by-step explanation:

In order to get the mean cost that she wants from the gift, we would need to get the numbers that we already had, and have another set of row with the amount of gifts she needs with the mean she wants.

Here is how it should look like:

$25  $14  $33  $19    x

$25  $25  $25  $25 $25

We are trying to find the number for "x"

Therefore, we would need to use the process of adding, then subtracting after.

Lets add:

[tex]25+14+33+19=91\\\\25+25+25+25+25=125[/tex]

What we would do now is subtract the numbers in order to get the price that Tonya wants from her gift, if she buys another gift.

[tex]125-91=34[/tex]

Tonya should spend $34 on her last gift.

$34 should be your FINAL answer

____________________________________________________

Answer:

63,960 possibilities in total.

Step-by-step explanation:

For the first number, you can choose from 41 different numbers, so there are 41 possibilities.

For the second number, you cannot choose the same as the first one, so you are now limited to 40 possibilities.

For the third number, you are down to 39 possibilities since you cannot pick the same as the first two ones.

So, you have 41 * 40 * 39 = 63,960 possibilities in total.

Picking a new combination is easy... remembering it is the hard part :-)

If you want to calculate it from a formula standpoint, the base formula would be:

[tex]P(n,r) = \frac{n!}{(n-r)!} = \frac{41!}{(41-3)!} = 63960[/tex]

Where n is the total numbers possible and r is the quantity of numbers you have to pick.