What is the volume of the rectangular prism with a length of 8 1/2centimeters, width of 9 1/3 centimeters and a height of 12 2/5 centimeters?

ANSWER

A. 1

D. 8

EXPLANATION

The vertical asymptote occurs at where the denominator of a rational function in its simplest form is equal to zero.

The rational function given is

[tex]p(x) = \frac{9}{(x - 1)(x - 8)} [/tex]

This rational function is in it's simplest form.

The vertical asymptotes occurs at

[tex](x - 1)(x - 8) = 0[/tex]

By the zero product principle, we must have either

[tex](x - 1) = 0 \: \: or \: \: (x - 8) = 0[/tex]

This implies that

[tex]x =1\: \: or \: \: x = 8[/tex]

Options A and D are correct.

It's not clear if this is a problem to solve or a problem to prove.  Let's see where it goes.

We note the cotangent half angle formula is

[tex]\cot x = \dfrac{ 1 + \cos 2x}{\sin 2x}[/tex]

The tangent and cotangent half angle is expressible in terms of the full angle without any ambiguity, so let's set b=a/4 so a=4b.  

It turns out to be true for all a (at least all a that don't make the any of the functions undefined).   So it's a problem to prove.

Here's the proof.  I actually did it from the bottom up, but it's better to present it this way as a proof.  

We start with the cosine double angle formula:

[tex]\cos 2b = 2\cos^2 b- 1[/tex]

Multipy both sides by sin b:

[tex]\sin b \cos 2b = 2 \sin b \cos^2 b - \sin b[/tex]

Sine double angle formula:

[tex]\sin b \cos 2b = \sin 2b \cos b- \sin b[/tex]

Add sin 2b to both sides:

[tex] \sin 2b+ \sin b\cos 2b = \sin 2b + \sin 2b \cos b - \sin b[/tex]

Divide by sin b sin 2b

[tex] \dfrac{1}{\sin b} + \dfrac{\cos 2b}{\sin 2b} = \dfrac{1 + \cos b}{\sin b} - \dfrac{1}{\sin 2b}[/tex]

Turn to cosecants and cotangents.  We use the cotangent half angle formula above.

[tex] \csc b + \cot 2b = \cot \frac b 2 - \csc 2b[/tex]

Substituting b=a/4:

[tex] \csc \frac a 4 + \cot \frac a 2 = \cot \frac a 8 - \csc \frac a 2 \quad\checkmark[/tex]

Answer:

$508.33

Step-by-step explanation:

If I bet $25 (And I win, of course), I will win:

If I win $61 per every $3 bet, then:

61/3 = x/25 ⇒ Solving for 'x':

61*25/3 = $508.33

Finally, if you bet $25 you will win $508.33.

Answer: FIrst option.

Step-by-step explanation:

We need to remember that a tangent is a line that touches a circle at one point. This point is the "Point of tangency".

We can observe in the figure that the line "s" touches the circle A at a point identified as "J" and it also touches the circle B at a point identified as "K". Therefore, we can make the following conclusion:

The point of tangency of line "s" to circle B is: The point K.

This matches with the first option.

Answer:

x=-4, x=1

Step-by-step explanation:

[tex]x=\frac{-(-6)+\sqrt{(-6)^{2}-4(-2) 8 } }{2(-2)} : -4\\x=\frac{-(-6)-\sqrt{(-6)^{2} -4(-2) 8} }{2(-2)} : 1\\[/tex]

Answer:

Step-by-step explanation:

[tex]\text{If}\ f(-x)=f(x)\ \text{then}\ f(x)\ \text{is an even function.}\\\\\text{If}\ f(-x)=-f(x)\ \text{then}\ f(x)\ \text{is an odd function.}[/tex]

======================================================

[tex]f(x)=-3x^4+7x^2\\\\f(-x)=-3(-x)^4+7(-x)^2=-3x^4+7x^2\\\\f(-x)=f(x)[/tex]

The function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) =  -3x⁴ + 7x²

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = -3x⁴ + 7x²

To check whether the function is odd or even, plug x → -x in the function:

f(-x) = -3(-x)⁴ + 7(-x)²

f(-x ) = -3x⁴ + 7x²

f(-x) = f(x)

The function is even.

Thus, the function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) =  -3x⁴ + 7x²

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Answer:

b = 2

Step-by-step explanation:

In order to find the value of b, we have to isolate b on one side of equation first

So,

[tex]3b+2(b-1)=8[/tex]

Multiplying 2 with b-1

[tex]3b+2b-2=8\\5b-2=8[/tex]

Adding 2 on both sides

[tex]5b-2+2=8+2\\5b=10[/tex]

Dividing by 5 on both sides

[tex]\frac{5b}{5}=\frac{10}{5} \\b=2[/tex]

So the value of b is 2 ..

ANSWER

The value of b is 2

EXPLANATION

The given linear equation in b is

[tex]3b + 2(b - 1) = 8[/tex]

We expand to get:

[tex]3b + 2b - 2= 8[/tex]

We now group similar terms to obtain:

[tex]3b + 2b = 8 + 2[/tex]

Combine the similar terms now to obtain:

[tex]5b = 10[/tex]

Divide both sides by 5 to get:

[tex]b = \frac{10}{5} [/tex]

This simplifies to:

[tex]b = 2[/tex]

The value of x is 75.2292.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

given: a right triangle with base 40 yard.

Also, angle of elevation 62° .

and one of the side is 'x'.

Using trigonometry

tan 62= x/40

1.88073= x/40

x= 40*1.88073

x= 75.2292

Hence, value of x is 75.2292.

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Answer:

C

Step-by-step explanation:

Given 2 secants intersect a circle from a point outside the circle, then

The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is

x(x + 10 + x) = 6(6 + 10 + x)

x(2x + 10) = 6(16 + x) ← distribute parenthesis on both sides

2x² + 10x = 96 + 6x ← subtract 96 + 6x from both sides

2x² + 4x - 96 = 0 ← in standard form

Divide through by 2

x² + 2x - 48 = 0 ← factor the left side

(x + 8)(x - 6) = 0

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

However x > 0 ⇒ x = 6 → C

Answer:

-4v + 2w = 7 is not a linear equation.

Step-by-step explanation:

A linear equation is one in the form:

y = mx + x

-4v + 2w = 7 is not a linear equation since it has v and w instead of y and x.

A linear equation is any equation in the form Ax + By = C, with the degree of each variable being 1 and the exponents strictly positive. Hence x^4 = y is not a linear equation because the exponent of x is 4.

In mathematics, a linear equation is any equation that can be written in the form Ax + By = C, where A, B, and C are constants, and x and y are variables. The degree of each variable in all the terms should be 1 and the exponents of the variables should be strictly positive integers. For example, an equation like ‘2x + 3y = 5’ would be considered linear. Looking at the provided options:

Therefore, the answer is x4 = y.

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Answer:it’s actually 3(x+2)

Step-by-step explanation:

Answer:

5 ft

Step-by-step explanation:

Let the height of the previous jump be represented by j.  Then 1.1j = 5.5 ft.

Dividing both sides by 1.1, we get j = 5 ft.  This was the height of the previous jump.

Answer:

5 ft

Step-by-step explanation:

The previous jumper jumped p

The new jumper jumped p*1.1 and that was 5.5 ft

1.1p = 5

Divide each side by 1.1

1.1p/1.1 = 5.5/1.1

p = 5

The previous jumper jumped 5 ft

Answer:

6/10 but can be reduced to 3/5

Step-by-step explanation:

take every number exept red add them toget her and theres your answer.

The probability that it is not red is 0.6.

Given: A bag contains 10 marbles.

Number of red marbles = 4

Number of blue marbles = 3

Number of white marbles = 2

Number of yellow marble = 1

A marble is drawn at random.

We have to find the probability that the marble is not red.

Hence, the marble can be blue, white and yellow.

∴ Apart from red marbles there are total of 6 marbles in the bag.

⇒ Total favorable outcomes = 6

⇒ Total number of outcomes = 10

Probability = (Total number of favorable outcomes) / (Total number of outcomes)

⇒ Probability = 6/10

⇒ Probability = 0.6

Therefore, the probability that it is not red is 0.6.

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Answer:

its A

Step-by-step explanation:

you do 28 x 66 :)

point N is at (3,2)

3units to the right and 3units up = x+3, y+3

3+3=6; 2+3=5

new coordinate: (6,5)

Answer:

f(x) = x²

Step-by-step explanation:

Answer:

a = -2 , b = -8

Step-by-step explanation:

* Lets talk about the solution of the linear equations

- There are three types of the solutions of the system of linear equations

# If the two lines intersect each other, then there is one solution

- The equations are ax+ by = c , dx + ey = f

# If the two lines parallel to each other, then there is no solution

- The equations are ax+ by = c , ax + by = d in its simplest form ,

  where a is the coefficient of x , b is the coefficient of y and

  c , d are the numerical terms

# If the two lines coincide (over each other), then there are infinite

   solutions

- The equations are ax+ by = c , ax + by = c in its simplest form, where

  a is the coefficient of x , b is the coefficient of y and c is the

  numerical term

* Lets solve the problem

∵ The system of equation is:

   ax - y = 8 ⇒ (1)

   2x + y = b ⇒ (2)

∵ The system create infinitely many solutions

∴ The lines are coincide

- The equations must be equal, then multiply equation(1) or (2) by -1 to

  make the coefficient of y in the two equations equal

∴ -ax + y = -8

∴ 2x + y = b

∵ Their coefficients of x are equal

∵ Their coefficients of y are equal

∵ Their numerical terms are equal

∵ The coefficient of x in equation (1) is -a and in equation (2) is 2

∴ -a = 2 ⇒ multiply both sides by -1

∴ a = 2

∵ The numerical term in equation (1) is -8 and in equation (2) is b

∴ b = -8

* The values for a and b will create infinitely many solutions are -2 , -8

Answer:

q = ± 5[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

q² - 125 = 0 ( add 125 to both sides )

q² = 125 ( take the square root of both sides )

q = ± [tex]\sqrt{125}[/tex]

  = ± [tex]\sqrt{25(5)}[/tex]

  = ± [tex]\sqrt{25}[/tex] × [tex]\sqrt{5}[/tex]

  = ± 5[tex]\sqrt{5}[/tex]

Answer:

Roots are [tex]q=5\sqrt{5},-5\sqrt{5}[/tex]

Step-by-step explanation:

Given : Function [tex]f(q)=q^2-125[/tex]

To find : Which are the roots of the quadratic function ?

Solution :

To find the roots equate the function to zero.

[tex]q^2-125=0[/tex]

Add 125 both side,

[tex]q^2=125[/tex]

Taking root both side,

[tex]q=\pm \sqrt{125}[/tex]

[tex]q=\pm \sqrt{5\times 5\times 5}[/tex]

[tex]q=\pm 5\sqrt{5}[/tex]

Therefore, roots are [tex]q=5\sqrt{5},-5\sqrt{5}[/tex]

Answer:

[tex] 10\sqrt{5} - 4 \sqrt{10} [/tex]

Step-by-step explanation:

[tex] \sqrt{5} (10 - 4 \sqrt{2} )[/tex]

Multiply

[tex] \sqrt{5} [/tex]

with each term within the bracket

[tex] = \sqrt{5} + \times 10 - \sqrt{5} \times 4 \sqrt{2} [/tex]

[tex] = 10 \sqrt{5} - 4 \sqrt{10} [/tex]

Answer:

The second option.

Step-by-step explanation:

4^2 × 4^8

(4 × 4)(4 × 4 × 4 × 4 × 4 × 4 × 4 × 4)  = 4^10

                    Or

4^2 × 4^8

=4^2+8

4^10

When solve an exponential with the same constant, you ga no problem. Just take one of those and and the exponent, you are good to go.

Please mark as brainliest.

Answer:

B

Step-by-step explanation:

The volume (V) of a pyramid is calculated as

V = [tex]\frac{1}{3}[/tex] area of base × height, hence

V= [tex]\frac{1}{3}[/tex] × 64 × 8 ≈ 170.7 ( to 1 dec. place )

For this case we have that by definition, the volume of a pyramid is given by:

[tex]V = \frac {1} {3} * A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

According to the data we have:

[tex]A_ {b} = 64mm ^ 2\\h = 8mm[/tex]

Substituting:

[tex]V = \frac {1} {3} * 64 * 8\\V = \frac {512} {3}\\V = 170.666666667[/tex]

If we round up we have that the volume is[tex]170.7 \ mm ^ 3[/tex]

Answer:

Option B

The golf course can provide water for approximately 89,610 families of four.

To find out how many families of four the golf course can provide water for, we need to compare the average water usage of the golf course with the average water usage of a family of four.

The golf course uses an average of 80 million gallons of water daily for irrigation.

To convert this to gallons per year, we multiply by 365:

80 million gallons/day * 365 days/year = 29.2 billion gallons/year.

Now, we divide the total water usage of the golf course by the water usage of one family of four:

29.2 billion gallons/year / 325,851 gallons/year = approximately 89,610 families of four.

The golf course can therefore provide water for approximately 89,610 families of four.

Answer:

Value of x is 37.

Step-by-step explanation:

Given:

line y and line z are parallel.

line x is traversal line.

To find: value of x.

∠( 3x + 4 )° and ∠ 115° are alternate interior angle in the given figure.

We know that Alternate interior angles of parallel lines are equal.

So,

3x + 4 = 115

3x = 115 - 4

3x = 111

x = 37

Therefore, Value of x is 37.

Two parallel lines are crossed by a transversal then the value of x is 37.

Given that line y and line z are parallel and line x is a traversal line.

To find that value of x.

We have ∠( 3x + 4 )° and ∠ 115° are alternate interior angles in the given figure.

We know that Alternate interior angles of parallel lines are equal So,

3x + 4 = 115

3x = 115 - 4

3x = 111

x = 37

Therefore, the Value of x is 37.

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Answer:

[tex]f(x) = 2 \times 2 + 3 \\ f(3) = 4 + 3 \\ 3f = 7 \\ f = \frac{7}{3} [/tex]

Answer:

The  answer is 15

Step-by-step explanation:

If ƒ (x ) = 2x 2 + 3, find ƒ (3).

2(3)^2 +3

6^2+3

= 15

Answer:

(8,2)

Please make sure I interpreted your system correctly below.

x+2y=12

-x=-y-6

Step-by-step explanation:

I assume the system is

x+2y=12

-x=-y-6

-----------

I'm going to multiply both sides of equation 2 by -1 giving me

x+2y=12

x=y+6

I'm now going to plug equation 2 into equation 1.

(y+6)+2y=12   I replaced x with y+6 in the first equation

y+6+2y=12

3y+6=12

3y=6

y=2

So

x=y+6

x=2+6

x=8

The solution is (8,2)

Answer:

The correct answer is : DCQ ( angle) = DCE (angle)

Answer:   DCQ=DCE

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

If they were similar corresponding sides would be in the same ratio.

Testing: 5/4 = 1.25

8/6 = 4/3 = 1.333...

They are not in the same ratio so  they are not similar.

Two figures are similar if their corresponding angles are congruent and their corresponding side lengths are proportional. We can determine if two figures are similar by comparing the ratios of their corresponding side lengths.

Determining whether two figures are similar involves a thorough examination of their corresponding angles and side lengths. Two figures are considered similar if their corresponding angles are congruent (equal) and their corresponding sides are in proportion, meaning that the ratios of the lengths of corresponding sides are the same throughout the figures.

First, we examine the angles. If all corresponding angles in the two figures are equal, then it's a strong indication of similarity. Similar figures have the same shape, and equal angles ensure that the shapes are the same when scaled up or down.

Next, we analyze the side lengths. For figures to be similar, the ratios of corresponding side lengths must be constant. This means that if you were to take any two sides from the first figure and divide their lengths, and then do the same for the corresponding sides in the second figure, the ratios should be equal.

In summary, similarity between two figures is established by the equality of corresponding angles and the constancy of ratios between corresponding side lengths. If both conditions are met, the figures are indeed similar, which means they have the same shape, and one can be obtained from the other through uniform scaling (enlarging or shrinking).

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Noreen can ship 632 boxes of candles

because 9480 divided by 15 is 632

Answer:

The x-value is between –1 and –2, and the y-value is between 3 and 4

Step-by-step explanation:

we have

y=-2x+1 ----> equation A

y=x+5 ----> equation B

Solve the system of equations by elimination

Multiply the equation B by 2 both sides

2y=2x+10 ----> equation C

Adds equation A and equation C

y=-2x+1

2y=2x+10

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

y+2y=1+10

3y=11

y=11/3

Find the value of x

y=x+5

11/3=x+5

x=(11/3)-5

x=-4/3

therefore

x=-1.33, y=3.67

The x-value is between –1 and –2, and the y-value is between 3 and 4

The x-value is between –1 and –2, and the y-value is between 3 and 4

Step-by-step explanation: