Solve the equation for the letter L: V = LWH

Answer:

It is rational

Step-by-step explanation:

The pi terms cancel out when you divide. This is due to the rule x/x = 1 where x is any number you want except x cannot be zero. So replace x with pi and we have pi/pi = 1

Therefore,

(3pi)/(2pi) = (3/2)*(pi/pi)

(3pi)/(2pi) = (3/2)*1 .... use the rule mentioned above

(3pi)/(2pi) = 3/2

we get a fraction or a ratio of two whole numbers, so this proves that the given expression is rational.

Answer:

q1 = 3x^2 + 6x + 16

Step-by-step explanation:

2 || 3    0     4    -  32

           6    12       32

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

     3    6    16         0

q(x) + r(x)/(x - 2)

r(x) = 0

q(x) = 3x^2 + 6x + 16

This does not factor down any further unless you have take complex number. The only real root isw

x = 2

Just in case you have done complex numbers

x2 = -1 + 2.0817i

x3 = -1 - 2.0817i

The simplification of the given expression is obtained as 1/216.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given expression is 6⁻³.

It can be simplified as below,

Rewrite the given expression as,

6⁻³ = ((6)⁻¹)³

Now, (6)⁻¹ = 1/6

⇒ 6⁻³ = (1/6)³

⇒ 1/6 × 1/6 × 1/6 = 1/216

Hence, the given expression can be simplified as 1/216.

To know more about exponents click on,

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Final answer:

Mr. Jimerson will earn $27.60 per hour after receiving a 15% raise on his original $24 per hour salary, resulting in a $3.60 increase per hour.

Explanation:

Mr. Jimerson earns $24 per hour working and qualifies for a 15% raise in salary. To calculate his new hourly salary after the raise, first determine the amount of the raise by finding 15% of his current hourly wage. Since 15% can be written as 0.15, we multiply his current wage by 0.15 to find the raise amount.

0.15 × $24 = $3.60

Next, add this raise amount to his original hourly wage to find his new salary:

$24 + $3.60 = $27.60 per hour

Therefore, Mr. Jimerson's salary after the raise will be $27.60 per hour.

Answer:

3x = t and it costs 15 dollars in total with x = 5.

Step-by-step explanation:

The 3 represents her friends and x represents the cost of one ticket. The variable t represents the total cost or tickets. If x equals 5, then it would be 15 because of 3x.  

Hope it helps :)

Answer:$52.50

Step-by-step explanation:

Hi There!

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

Remember to follow PEMDAS.

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Problem #1:

= (25 - 6.25) + (5 · 3)²

= (18.75) + (15)²

= 18.75 + 225

= 243.75

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

Problem #2:

= (8 + 3)² + 10 · (-4)

= (11²) + 10 · (-4)

= 121 + 10 · (-4)

= 121 + (-40)

= 81

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

Hope This Helps :)

Answer:

y = [tex]\frac{96}{5}[/tex]

Step-by-step explanation:

given that y and x are proportional then the equation relating them is

y = kx ← k is the constant of proportionality

to find k use the given condition y = 12 when x = 5

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{5}[/tex]

y = [tex]\frac{12}{5}[/tex] x ← equation of proportionality

when x = 8, then

y = [tex]\frac{12}{5}[/tex] × 8 = [tex]\frac{96}{5}[/tex]

Answer:

aproximatley 6 units

Step-by-step explanation:

Answer:

(4,2)

Step-by-step explanation:

Answer:

she would have to pay 42 dollars for 14 rides

so $3 for each ride 3* 14 is 42 or just add 3, 14 times

Answer:

2, 240

Step-by-step explanation:

In the table, the values should be

Year 1   725  

Year 2   579

Year 3   696

Since Year 4 sold 112% of the previous 3 years combined, we add 725+579+696=2000. We can find 112% by writing a proportion.

[tex]\frac{112}{100} =\frac{x}{2000}[/tex]

We solve through cross multiplication of numerator and denominator of the opposite fraction.

[tex]112(2000)=100(x)\\224000=100x\\2,240=x[/tex]

The idea is to pair up the terms, factor each sub-group, and then pull out the overall GCF to fully factor.

x^3+5x^2-6x-30

(x^3+5x^2)+(-6x-30)

x^2(x+5)+(-6x-30)

x^2(x+5)-6(x+5)

(x^2-6)(x+5)

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

Answer: (x^2-6)(x+5)

Answer:

3/8

Step-by-step explanation:

there are 6 outcomes with two heads and two tails, and 16 total outcomes. 6/16=3/8

The probability of getting the same number of heads and tails is 3/8

The sample space (S) is given as:

S = {HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT}

The outcomes (E) that the number of heads and tail are the same is

E = {HHTT HTHT HTTH THHT THTH TTHH}

The probability of getting the same number of heads and tails is then calculated as:

[tex]Pr = \frac{n(E)}{n(S)}[/tex]

So, we have:

[tex]Pr = \frac{6}{16}\\[/tex]

Simplify

[tex]Pr = \frac{3}{8}[/tex]

Hence, the probability of getting the same number of heads and tails is 3/8

Read more about probabilities at:

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Answer:

A) -56

Step-by-step explanation:

B) First, you have to ignore the plus sign, and recognize that the second negative number means you are subtracting that number.

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Answer:

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

Step-by-step explanation:

we are given

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

we can simplify left side and make it equal to right side

we can use trig identity

[tex]sin(3a)=3sin(a)-4sin^3(a)[/tex]

[tex]cos(3a)=4cos^3(a)-3cos(a)[/tex]

now, we can plug values

[tex]\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)} [/tex]

now, we can simplify

[tex]\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)} [/tex]

now, we can factor it

[tex]\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]

we can use trig identity

[tex]sin^2(a)+cos^2(a)=1[/tex]

[tex]\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]

we can cancel terms

[tex]=3-4(1-sin(a)cos(a))[/tex]

now, we can simplify it further

[tex]=3-4+4sin(a)cos(a))[/tex]

[tex]=-1+4sin(a)cos(a))[/tex]

[tex]=4sin(a)cos(a)-1[/tex]

[tex]=2\times 2sin(a)cos(a)-1[/tex]

now, we can use trig identity

[tex]2sin(a)cos(a)=sin(2a)[/tex]

we can replace it

[tex]=2sin(2a)-1[/tex]

so,

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

Answer:

To prove : sin(3a)-cos(3a)/sin(a)+cos(a) = 2sin(2a)-1                                      

Step-by-step explanation:

\frac{\sin3a-\cos3a}{\sin a+\cos a}=2\sin 2a-1\\\cos3a=4\cos^{3}a-3\cos a\\\sin 3a=3\sin a-4\sin ^{3}a\\substituting the value, we get\\L.H.S= \frac{3\sin a-4\sin ^{3}a-[4\cos ^{3}a-3\cos a]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4(\sin ^{3}a+4\cos ^{3}a)}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(\cos ^{2}a+\sin ^{2}a-\sin a\cos a)]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4+4\sin a\cos a]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)(-1+4\sin a\cos a)}{\sin a+\cos a}\\-1+4\sin a\cos a\\-1+2\sin 2a\\2\sin 2a-1=R.H.S

Since, sin(2a)= 2sin(a)cos(a)

2sin(2a)= 4sin(a)cos(a)

Answer:

Yes, x + 12

Step-by-step explanation:

Simplify the following:

3 x - 2 x + 12

Grouping like terms, 3 x - 2 x + 12 = (3 x - 2 x) + 12:

(3 x - 2 x) + 12

3 x - 2 x = x:

Answer: x + 12

Answer:

Yes, it is.

Step-by-step explanation:

3x + 12 - 2x =

Use the commutative property of addition to change the order of the addition.

= 12 + 3x - 2x

Use the distributive property of addition over multiplication in reverse (which is factoring).

= 12 + x(3 - 2)

Do the operation: 3 - 2 = 1

= 12 + x * 1

Simplify x * 1 to just x.

= 12 + x

Use the commutative property of addition.

= x + 12

There you have x + 12 from 3x + 12 - 2x by using properties and operations.

Answer:

Converse of triangle proportionality theorem

Step-by-step explanation:

We are given that in a triangle ABC, D and E are some points in AB and AC respectively.

D and E divide AB and AC such that

AD/DB =AE/DC

To prove that DE is parallel to third side BC>

This can be proved using converse of triangle proportionality theorem

REcollect the triangle proportionality theorem that

If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion

So converse is is a line intersects the other sides make proportional intercepts then the line is parallel to the third side.

Answer:

The answer is Converse of the Pythagorean theorem

Step-by-step explanation:

The calculation shows that 13 crates weigh 170 pounds less than 15 crates.

To find out how much less 13 crates of apples weigh than 15 crates of apples, we need to first determine the weight of the two different amounts of crates.

We know that one crate weighs 85 pounds.

So, for 15 crates, we multiply 15 by 85 to get the total weight:

= 15 crates x 85 pounds per crate = 1275 pounds

Next, we calculate the weight for 13 crates:

= 13 crates x 85 pounds per crate = 1105 pounds

Now, we subtract the weight of 13 crates from the weight of 15 crates:

= 1275 pounds - 1105 pounds = 170 pounds

Therefore, 13 crates of apples weigh 170 pounds less than 15 crates of apples.

Answer:

f(2) = 0

Step-by-step explanation:

Evaluate the function at x = 2.

f(x) = -3x^2 + 6x

f(2) = -3(2^2) + 6 * 2

f(2) = -3(4) + 12

f(2) = 0

Since you already know that two of the sides equal 10.8 mi which concludes to an isosceles triangle you'll add them which comes to 21.6 and lastly you just subtract 31 from 21.6 which is 9.4

Check out the attached image below. I've marked two red points on the line such that the points have whole number coordinates. This way I could compute the slope of this line to be -2/5

We move down 2 units (rise of -2) as shown by the blue arrows. Afterward, we move 5 units to the right as shown by the green arrows (which is the run). This gets us from the left red point to the right red point.

rise = -2, run = 5

slope = rise/run = -2/5

the original line shown has a slope of -2/5

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

Next we do two things to get the perpendicular slope.

Flip the fraction: -2/5 becomes -5/2

Flip the sign: -5/2 becomes +5/2 or simply 5/2

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

Final Answer: 5/2

Answer:

D) were laws passed by mainly Southern states to keep African Americans in a system of virtual slavery.

Step-by-step explanation:

The Black Codes were created by the Southern States and were extremely similar to slavery, in which the African Americans were not allowed many of their newly gotten rights, such as a right to education, voting, etc, and the African Americans had to endure a lot of codes that were created to make them feel inferior.

~

Answer:  D) were laws passed by mainly Southern states to keep African Americans in a system of virtual slavery.

To convert the slope-intercept form of a line, y = 6x - 4, to standard form, subtract 6x from both sides of the equation. The resulting standard form is -6x + y = -4.

You asked about writing the equation y = 6x - 4 in standard form. The standard form for the equation of a line in mathematics is usually given as Ax + By = C, where A, B, and C are constants, and A should ideally be a positive integer. To convert the given equation into standard form, we want to rearrange it so that both x and y are on the same side of the equation and the constant is on the other side.

Here are the steps to convert y = 6x - 4 to standard form:

Therefore, the standard form of the equation is -6x + y = -4.

See the attachment

Each of the points moves to 3 times the distance from A that it is currently.

For example, point B is 1 unit left and 2 units up from A. It moves to 3 units left and 6 units up from A.

Answer:

the segment that states the radius is AC.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You have to use Point Slope Form:

About Problem:

y - Y1 = m (x - X1)

y - -1 = -2/3 (x - -3)  ---- This is in Point Slope Form

If you want to solve it, & put it in Slope Intercept form, it would look like this:

y = mx + b

y = -2/3 - 2 --- This is in Slope intercept Form.... I might've solved it wrong... I'm not sure...

Really really sorry if I'm incorrect...

Answer:  The required equation of the line is [tex]2x+3y+9=0.[/tex]

Step-by-step explanation:  We are given to find the equation of a line that has a slope of [tex]-\dfrac{2}{3}[/tex] and passes through point (-3,-1).

SLOPE-INTERCEPT FORM :

The equation of a line having slope m and passing through the point (a, b) is given by

[tex]y-b=m(x-a).[/tex]

For the given line, we have

[tex]m=-\dfrac{2}{3},\\\\\\(a,b)=(-3,-1).[/tex]

Therefore, the equation of the line is given by

[tex]y-b=m(x-a)\\\\\Rightarrow y-(-1)=-\dfrac{2}{3}(x-(-3))\\\\\\\Rightarrow y+1=-\dfrac{2}{3}(x+3)\\\\\Rightarrow 3y+3=-2x-6\\\\\Rightarrow 2x+3y+9=0.[/tex]

Thus, the required equation of the line is [tex]2x+3y+9=0.[/tex]