The width of a rectangle is 32 inches shorter than twice its length. The area of the rectangle is 72 square inches. What is the length of the rectangle?

Answer:

Step-by-step explanation:

Givens

sin(theta) = - 8/17

cos(theta)= 15/17

Tan(theta) = ?

Comment

Without using the Pythagorean Theorem, you could simply use tan(theta) = Sin(theta) / cos(theta)

Tan(theta) = sin(theta) / cos(theta)

Tan(theta) =[tex]\dfrac{\dfrac{-8}{17} }{\dfrac{15}{17} }[/tex]

Now turn  the bottom fraction upside down and multiply.

Tan(theta) = [tex]\dfrac{-8}{17}*\dfrac{17}{15} = \dfrac{-8}{15}[/tex]

Answer Tan(theta) = -8/15

Answer:

C = 3

Step-by-step explanation:

By using the distributive property, we multiply 1 and 6c inside the brackets by -2. This gives us 3 -2 - 12c = -35. Next, we subtract 2 from 3, giving us 1 - 12c = -35. We will now subtract 1 from both sides, leaving us with -12c = -36, or simply 12c = 36. Finally, we divide by 12, giving us C = 3. I hope this helps!

Answer:

the volume is about 84.8 in³

Step-by-step explanation:

Let b be the base of the cone

and h be the height of the cone

Formula :

Consider the cone with base b and height h

The volume = (1/3)×b×h

………………………………………………………

In our example:

b = 3.14×3^2 = 28.26

h = 9

Therefore

The volume = (1÷3)×(28.26)×9 = 84.78

Answer: [tex]a+b+\sqrt{a^{2}+b^{2}}[/tex]

Step-by-step explanation:

The distance from (0,b) to (0,0) is b.

The distance from (0,a) to (0,0) is a.

Using the Pythagorean theorem, the distance from (0,b) to (a,0) is [tex]\sqrt{a^{2}+b^{2}}[/tex]

So, the perimeter is [tex]\boxed{a+b+\sqrt{a^{2}+b^{2}}}[/tex]

Answer:

A. true

Step-by-step explanation:

"f(x) = ... " is the classic way of writing a function.

The other root is 1 and the value of the coefficient q is 12.

A quadratic equation is a second-order polynomial equation in a single variable x. ax²+bx+c=0. with a ≠ 0 .

Given:

x²-13x+q=0

when x= 12

So, 12²-13*12+q=0

144-156+q=0

-12+q=0

q=12

Now, x²-13x+12=0

x²-12x-x+12=0

x(x-12) - 1(x-12)=0

(x-1)(x-12)=0

x=1, 12

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Answer:

33 blocks

Step-by-step explanation:

Given the length , breath and height for small block  6cm, 4cm, and 2cm an d for large 2m = 200cm, 4cm and 2cm.

volume is given by  

             V = Length x breath x height

Volume of small block = 6 x 4 x 2 = 48 cm^3

Volume of big block = 200 x 4 x 2 = 1600 cm^

No of blocks = Volume of big block/ volume of small block

                     = 1600/48

                     = 33.33

Therefore no of blocks formed = 33

Answer:

Step-by-step explanation:

(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.

(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.

(3) By definition, all angles of a regular polygon are congruent.

(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.

(5) This is true. (See statement (1)).

Answer:

Options B, C, E

Step-by-step explanation:

Answer:

He multiplied the denominators incorrectly

Step-by-step explanation:

we know that

The volume of a rectangular prism is given by the formula

V=LWH

we have

L=3/4 ft

W=5/1 ft

H=1/2

substitute

V=(3/4)(5/1)(1/2)= 3x5x1=    15

                           ₋₋₋₋₋₋₋₋    ₋₋₋₋ ft³

                           4x1x2=    8

therefore

He multiplied the denominators incorrectly

Answer: $5.99 is the answer hope this helps!

The probability that Hope performs any of the activities each day of the week can be expressed in the tree diagram.

A tree diagram is a term for a graphical tool that shows the possible outcomes of an experiment. To build a tree diagram, start by putting a branch for each of the possibilities.

The tree diagram of Hope's activities must include all the days of the week and on each day there must be three branches for each of the possible activities that she is going to do (play tennis, swim or play soccer).

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Step-by-step explanation:

I hope this helps!!!!!

Using the figure given, The one equation that matches with the diagram is 3x=30-6.  The diagram that matches the equation circled is given in the image attached.

From the above, we can see that the equation that matches with the diagram are:

Note that for 3(x+6)=30

3x +  18 = 30

3x = 30-18

3x = 12

x = 12/3

x = 4

Then fixing x into the equation =

3(x+6)=30

3(4+6)=30

Therefore , 12 + 18 will give us 30 and the answer is straight forward. The same applies for 30=3x+6 and 6+3x=30 as the answer is straight forward.

But the one equation that does not matches with the diagram is 3x=30-6 because its output is not straight forward.

3x =30-6

3x = 24

x = 24/3

x = 8

Fixing 8 into the equation

3x = 30-6

3(8) = 24

=24 is the  answer and not 30

Therefore, Using the figure given, The one equation that matches with the diagram is 3x=30-6.

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Answer:

the answer to a is 70

the answer to b is 55

the answer to c is 15

(f+g)(x)  

= f(x) + g(x)

= 4x^2 +5x -3 + 4x^3 -3x^2 +5

= 4x^3+x^2+5x+2

By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.

We know that the average temperature is given by the equation:

f(x)=31cos(0.0055πx)+88

And it is in Fahrenheit degrees.

To get the lowest average temperature, we just need to find the minimum of the above function.

Remember that the minimum of the cosine function is:

cos(x) = -1

Then the lowest value of the above function is:

f(x₀) = 31*(-1) + 88 = 57

From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.

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Answer:

it’s C, 5.2

hope i helped

ur wlcm :)

correct me if im wrong

Answer:

Transitive

If x = 2y and 2y = 8, then x = 4.

Answer:

4/7=12/21

18/20=9/10

6/5=30/25

81/90=9/10

Step-by-step explanation:

12 / 21  will be equal to 4/7 and is denoted in the simplest form.

A fraction that possesses the same value as another fraction regardless of how it's denominators and numeric components could be different is said to be equivalent.

12 / 21 can be simplified with the help of 3. This will result in 4/7.

18/20 can be simplified with the help of 2. This will result in a 9/10.

30/25 can be simplified with the help of 5. This will result in 6/5.

81/90 can be simplified with the help of 9. This will result in a 9/10.

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Answer:

2

Step-by-step explanation:

4 halves=2

1 half=0.5

2 halves=1

3 halves=1.5

4 halves=2

Answer: 2556

Step-by-step explanation:

Let the amount of the deposit be x dollars

The amount of simple interest earned can be represented by the formula PRT/100

Where,

P is the amount of deposit

R is the annual rate of interest

T is the time in years

Therefore,

P=x

R=6

T=150/360 = 15/36 = 5/12

So,

Simple interest = x(6)(5)/1200

63.90 = 30x/1200

63.90= x/40

x= 63.90×40

x=2556

Therefore, amount deposited = 2556

Using it's formula, it is found that the mean of the discrete random variable is given by:

B. 30.47.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Hence, considering the table, the mean of the discrete distribution is:

E(X) = 23 x 0.16 + 25 x 0.09 + 26 x 0.18 + 31 x 0.12 + 34 x 0.24 + 38 x 0.21 = 30.47.

Hence option B is correct.

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The solution to x^2 - 4x = 5 is x = -1 or 5

The equation is given as:

x^2 - 4x = 5

Take the coefficient of x

k = -4

Divide by 2

k/2 = -2

Square both sides

(k/2)^2 = 4

Add this value to the sides of the equation

x^2 - 4x + 4= 5 + 4

Express as a difference of two squares

(x - 2)^2 = 9

Take the square root of both sides

x - 2 = ±3

Add 2 to both sides

x = 2 ± 3

Evaluate

x = -1 or 5

Hence, the solution to x^2 - 4x = 5 is x = -1 or 5

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Answer:

51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.

Answer:

Exact form: -3/2

Decimal Form: -1.5

Step-by-step explanation:

Hello there!

We need to find out the slope of the given two coordinates/points, that are:

Solution:

We'll need to use the formulae that is used to find out the slope,that is:

[tex] \pink{\star}\boxed{\rm \: Slope = \cfrac{y_2 -y_1}{x_2 - x_1}} \pink{\star}[/tex]

According to this question,here:

So substitute them accordingly:

[tex] \rm \: m = \cfrac{ - 6 -( 6)}{8 - 0} [/tex]

Simplify using PEMDAS rule.

[tex] \rm \: m = \cfrac{ - 12}{8} [/tex]

-12/8 could be canceled.

[tex] \rm \: m = \cfrac{ - 6}{4} [/tex]

-6/4 could also be canceled.

[tex] \boxed{ \rm \: m = \cfrac{ - 3}{2} \: or \: - \cfrac{3}{2} }[/tex]

Or it could be represented as decimal:

[tex] \boxed{ \rm \: m = - 1.5}[/tex]

Hence , the slope m will be -3/2 or -1.5

[tex] \rule{225pt}{2pt}[/tex]