Find expressions for the possible dimensions of the rectangular prism.
V=5y3 = 37y2 + 14y
The possible dimensions of the rectangular prism are
(Use a comma to separate answers as needed.)

[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} \stackrel{\textit{half of diameter}}{r=6~\hfill }\\ h=7 \end{cases}\implies SA=\pi (6)\sqrt{6^2+7^2}+\pi 6^2 \\\\\\ SA=6\pi \sqrt{85}+36\pi \implies SA=6\pi (\sqrt{85}+6)\implies SA\approx 286.88[/tex]

Answer:

-5x

Step-by-step explanation:

Answer:

-5x

Step-by-step explanation:

-4x-x --------------> factor out the x

= (-4-1) x

= -5x

Answer:

first off, welcome to brainly, second, your answer is 14.4

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

In a mapping diagram, a relation that is a function can have two arrows coming from the same input value

false

Answer: False.

Step-by-step explanation:

By definition, a relation is a function if each input value has only one output value.

Knowing this, we can say that in a mapping diagram, a function will never have two arrows coming from the same input value.

 In other words, if in a mapping diagram a relation has two arrows coming from the same input value, this means that this input value has two output values, and according to the definition mentioned above, this relation cannot be a function.

Therefore, the statement "In a mapping diagram, a relation that is a function can have two arrows coming from the same input value", is FALSE.

Answer:

Slope of JK = -4/5

Step-by-step explanation:

We know that GHJK is a parallelogram. If GHJK is a parallelogram then the sides of parallelogram will be:

GH, HJ, JK, GK

Hence the opposite sides will be:

GH and JK

HJ and GK

We know that opposite sides of parallelogram are parallel to each other and the slopes of parallel lines is equal.

So the slope of GH and JK will be equal.

And slopes of HJ and GK will be equal.

As we are given the slope of GH which is -4/5, the slope of JK will also be -4/5 because both lines are parallel.

ANSWER

See explanation

EXPLANATION

If we can simplify the first fraction to obtain the second fraction, then the two fractions are equivalent pairs

EQUIVALENT PAIRS

[tex] \frac{32}{4} \: and \: \frac{8}{1} [/tex]

[tex]\frac{36}{6} \: and \: \frac{6}{1} [/tex]

[tex]\frac{35}{7} \: and \: \frac{5}{1} [/tex]

NOT EQUIVALENT PAIRS

[tex]\frac{18}{3} \: and \: \frac{9}{1} [/tex]

[tex]\frac{20}{5} \: and \: \frac{3}{1} [/tex]

[tex]\frac{100}{10} \: and \: \frac{5}{1} [/tex]

Answer:

Equivalent pairs

32/4 and 8/1

36/6 and 6/1

35/7 and 5/1

Not Equivalent pairs

18/3 and 9/1

20/5 and 3/1

100/10 and 5/1

Step-by-step explanation:

Equivalent pairs: Those pairs that are different fractions but represent the same number.

1. 18/3 and 9/1

18/3 can be simplified into 6/1

so, 18/3 and 9/1 are not equivalent pairs

2. 32/4 and 8/1

32/4 can be simplified into 8/1

so, 32/4 and 8/1 are equivalent pairs

3. 36/6 and 6/1

36/6 can be simplified into 6/1

so, 36/6 and 6/1 are equivalent pairs

4. 20/5 and 3/1

20/5 can be simplified into 4/1

so, 20/5 and 3/1 are not equivalent pairs

5. 35/7 and 5/1

35/7 can be simplified into 5/1

so, 35/7 and 5/1 are equivalent pairs

6. 100/10 and 5/1

100/10 can be simplified into 10/1

so, 100/10 and 5/1 are not equivalent pairs

The range is given by: largest number in the data set - smallest number in the data set.

In our case, the largest value is 9 and the smallest value is 6.9. Therefor:

Range = 9 - 6.9 = 2.1

Thus, you have correctly identified the answer as the second choice (2.1). It is easy to get confused with much larger data sets but always keep in mind that the range is simply the largest value minus the smallest value. This makes sense since 'range' refers to the spread in something, for example if you were testing your vocal range you would find the highest note you could sing and the lowest note - this is the same here, we are just finding the range of a data set instead.

Answer:

The correct answer is second option

2.1

Step-by-step explanation:

Points to remember

Range of a data set

The range of a data set means that, the difference between the highest and lowest value of the data set.

To find the range of data set

It is given that, a data set

7.7, 8.4, 9, 8, 6.9

Highest value = 9 and lowest value = 6.9

Range = Highest value - lowest value

 = 9 - 6.9 = 2.1

Therefore the correct answer is second option

Answer:

Step-by-step explanation:

64

There are 8 numbers on the spinner.

The first spinner could be 1 of 8 and the second spin could also be 1 of 8.

To find the total outcomes, multiply the number of outcomes of each spin by each other.

Spin 1 : 8 out comes

Spin 2: 8 outcomes

Total outcomes = 8 x 8 = 64

The answer is D. 64

the assumption being that the endpoints are two continuous points in the pentagon, Check picture below.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-1)]^2+[3-4]^2}\implies d=\sqrt{(2+1)^2+(3-4)^2} \\\\\\ d=\sqrt{9+1}\implies d=\sqrt{10}~\hfill \stackrel{\stackrel{~\hfill \stackrel{\textit{5 sides}}{}}{\textit{perimeter of the pentagon}}}{5\sqrt{10}}[/tex]

Answer:

x = -1, 1, -5 , 5.

Step-by-step explanation:

x4 – 26x2 + 25 = 0

Factoring:

(x^2 - 25)(x^2 - 1) = 0

So x^2 - 25 = 0 gives x^2 = 25 and x = +/- 5.

x^2 - 1  gives  x^2 = 1 and x = +/- 1.

Follow below steps:

To solve the equation x4 − 26x2 + 25 = 0, we can use substitution to simplify the equation. Let's set u = x2, which turns our equation into a quadratic form: u2 − 26u + 25 = 0.

Now, we apply the quadratic formula where a = 1, b = -26, and c = 25 to find the values of u. The quadratic formula is u = (-b ± √(b2 - 4ac))/(2a). Substituting the values, we get the roots for u which are u = 25 and u = 1.

Now we substitute back for x by setting x2 = u, which gives us two separate equations to solve: x2 = 25 and x2 = 1. Solving these, we find the solutions for x to be x = 5, x = -5, x = 1, and x = -1.

Answer:

96

Step-by-step explanation:

If m - n = 2, then 4m - 4n = 4(m - n) = 4(2).

Then (4x + 2y)(4m - 4n) equals (4x + 2y)(8), or 8(4x + 2y).

But we are told that 2x + y = 6.  Multiplying all terms by 2, we get

4x + 2y = 12.  Substituting 12 for 4x + 2y, we get our final answer:

(4x + 2y)(4m - 4n) equals (4x + 2y)(8), or 8(4x + 2y), or 8(12) = 96

Answer:

96

Step-by-step explanation:

(4x + 2y)(4m - 4n) = ?

We have an equation

2x+y =6

Multiply it by 2

2(2x+y) = 2*6

Distribute

4x+2y = 12

Substitute 12 in for 4x+2y into the original problem

12(4m - 4n) = ?

We have an equation

m-n = 2

Multiply this by 4

4(m-n) = 4*2

Distribute

4m-4n = 8

Substitute 8 in for 4m -4n in 12(4m - 4n) = ?

12 * 8 = ?

96

For this case we have that if two lines are perpendicular, then the product of their slopes is -1.

If we have the following equation of the line:

[tex]y = -4x + 9[/tex]

The slope is [tex]m_ {1} = - 4[/tex]

Then yes:

[tex]m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- 4}\\m_ {2} = \frac {1} {4}[/tex]

The equation of the new line will be:

[tex]y = \frac {1} {4} x + b[/tex]

We substitute the point to find "b":

[tex]5 = \frac {1} {4} (4) + b\\5 = 1 + b\\b = 5-1\\b = 4[/tex]

Finally, the equation is:

[tex]y = \frac {1} {4} x + 4[/tex]

Answer:

[tex]y = \frac {1} {4} x + 4[/tex]

Answer:

(5, 8)

Step-by-step explanation:

f(x) + 4 is the graph of f(x) translated 4 units vertically up

given (5, 4) is a point on f(x), then the coordinates of the corresponding point

x- coordinate remains unchanged and add 4 to the y- coordinate

The corresponding point on f(x) + 4 is (5, 4 + 4) = (5, 8)

XW represents the altitude.

The correct answer is an option (C)

"It is a line segment that joins a vertex of triangle to the mid-point of the side that is opposite to that vertex."

"It is the perpendicular drawn from the vertex of the triangle to the opposite side."

"A line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. "

"A line drawn from the vertex of a triangle to its opposite side such that it divides the angle into two equal or congruent angles."

for given question,

XW is altitude of triangle XYZ.

Therefore the correct answer is an option (C)

Learn more about the altitude of triangle here:

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Answer:

-56

Step-by-step explanation:

Simplify the following:

-4 (9 + 5)

9 + 5 = 14:

-414

-4×14 = -56:

Answer:  -56

Answer:

b

Step-by-step explanation:

Given

a cos2x

b

2sinxcosx = sin2x

c

2cos²x - 1 = cos2x

d

1 - 2sin²x = cos2x

b is the expression not equal to the others

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

Note

cos2x = cos²x - sin²x = cos²x - (1 - cos²x) = 2cos²x - 1

cos2x = (1 - sin²x) - sin²x = 1 - 2sin²x

Answer:

Complex numbers are numbers in which the real component and the imaginary part of the number are both represented. The numbers in standard form will be a + bi, where a is the real part and bi is the imaginary part. An example of a complex number would be 3 +5i. 3 is the real part, and 5i is the imaginary part.

Step-by-step explanation:

Hope this helps!

The complex number 3cis210 can be written in standard form as - (3√3/2)i - (3/2).

The complex number 3cis210 can be written in standard form as:

3cis210 = 3(cos(210°) + i sin(210°))
Using the trigonometric identities cos(210°) = -√3/2 and sin(210°) = -1/2, we can simplify:

3cis210 = 3(-√3/2 + i(-1/2))

Therefore, the complex number 3cis210 in standard form is - (3√3/2)i - (3/2).

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The complete Question is given below:

Write as a complex number in standard form 3cis210

The volume of a cone increases by a factor of 27 when its height is multiplied by 3, as the volume of a cone scales with the cube of its linear dimensions.

The question asks how many times larger the volume of a cone becomes if its height is multiplied by 3. The volume of a cone is given by the formula V = ([tex]\frac{1}{3}[/tex]1/3)πr²h, where r is the radius and h is the height. If you multiply the height by 3, the volume will increase by a factor of 3 since volume scales with the third power of the linear dimensions. Therefore, the new volume would be 3³, or 27 times the original volume. This result can also be demonstrated by the mathematical expression Vnew = ([tex]\frac{1}{3}[/tex])πr²(3h) = 27Voriginal.

Answer: Third option.

Step-by-step explanation:

When you divide fractions you can multiply the first fraction by the reciprocal of the second fraction.

To find the reciprocal of the fraction, you need to flip it. Then the original denominator will be the new numerator and the original numerator will be the new denominator.

Then, the reciprocal of the fraction [tex]\frac{1}{3}[/tex] is:

 [tex]\frac{3}{1}=3[/tex]

Therefore, you can find the quotient of [tex]8[/tex]÷[tex]\frac{1}{3}[/tex]  by multiplying [tex]8[/tex] by [tex]3[/tex]:

[tex]8[/tex]÷[tex]\frac{1}{3}=8*3=24[/tex]

When dividing fractions these are the steps you will take:

1. The first number in the expression stays the same (if it is a whole number then you may just place a one in the denominator and keep the numerator as the whole number like so)

[tex]\frac{8}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex]

2. Change the division sign into a multiplication sign

[tex]\frac{8}{1}[/tex] × [tex]\frac{1}{3}[/tex]

3. Take the reciprocal (switch the places of numerator and denominator) of the second number in the expression

[tex]\frac{8}{1}[/tex] × [tex]\frac{3}{1}[/tex]

4. Multiply across

[tex]\frac{8*3}{1*1}[/tex]

As you can see to find the quotient of [tex]\frac{8}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex] you must multiply 8 by 3 (C)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

81

Step-by-step explanation:

Given

x² - 18x = 29

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 9)x + (- 9)² = 29 + (- 9)²

x² + 2(- 9)x + 81 = 29 + 81

(x - 9)² = 110

Answer:

81

Step-by-step explanation:

Answer:

B. (2/3) x (2/3) x (2/3)

C. 8/27

D. 2^3 /3^3

Step-by-step explanation:

You need to know the following property

[tex]\LARGE \left(\frac{a}{b} \right)^c = \frac{a^c}{b^c}[/tex]

Exponent also means you're multiplying the same number for an 'n' number of times.

For example, 2^3 = 2 * 2 * 2

we multiply it by itself 3 times since 3 is the exponent.

x^y

x is the base, y is the exponent

we read it as x to the power of y

If the exponent is 2, we say it as x squared

If the exponent is 3, we say it as x cubed

The exponential expression (2/3)^3 is equivalent to options B: (2/3) x (2/3) x (2/3), C: 8/27, and D: 2^3 /3^3, because they all result in the same value.

The exponential expression (2/3)^3 can be interpreted as multiplying 2/3 by itself three times. Here's how it works:

(2/3) x (2/3) x (2/3) = 8/27. In other words, 2 cubed (2^3 = 8) divided by 3 cubed (3^3 = 27), which equals 8/27.

So, the equivalent expressions among the given options are:

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[tex]x+y-3z=8\\x=-y+3z+8[/tex]

Answer: 5/2

Step-by-step explanation:

Cross multiply

18 = 8x - 2

20 = 8x

20/8 reduces to 5/2

Answer:

x = 5/2

Step-by-step explanation:

Step 1: Cross multiply

18 = 8x - 2

Step 2: Use the Addition Property of Equality

20 = 8x

Step 3: Use the Division Division Property of Equality

20/8 = x

Step 4: Simplify

5/2 = x

Answer:

The height of the tower is 150 ft

Step-by-step explanation:

Let the height of the tower be H feet.

The corresponding sides will then be in the same proportion.

The ratio of the shadows will be in the same proportion as the ratio of the heights.

[tex]\frac{H}{10}=\frac{120}{8}[/tex]

We multiply both sides by 10 to get:

[tex]\frac{H}{10}\times 10=\frac{120}{8}\times 10[/tex]

[tex]H=150[/tex]

Therefore, the height of the tower is 150 ft

Answer:

Height of the tower = 150 foot

Step-by-step explanation:

We need to find height of the tower with 120-foot shadow.

We have a 10-foot  street sign casts a shadow of 8 feet.

[tex]\texttt{Ratio of height to shadow height =}\frac{10}{8}=\frac{5}{4}[/tex]

We have

       [tex]\frac{\texttt{Height of tower}}{\texttt{Shadow height of tower}}=\frac{5}{4}\\\\\frac{\texttt{Height of tower}}{120}=\frac{5}{4}\\\\\texttt{Height of tower}=\frac{5}{4}\times 120=150feet[/tex]

Height of the tower = 150 foot

Answer:

It is A

Step-by-step explanation:

2x + y = 5

y + 3 = 2x

From equation 2:

y = 2x - 3

Substituting in the first equation:

2x + 2x - 3 = 5.

Answer:

2x + 2x - 3 = 5.

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

It is just common sense. The top numbers have to be smaller than the top numbers

Answer:

14 inch

Step-by-step explanation:

formula for circumference:

2(pi)r @ (pi)d

*where: r = radius

d= diameter

pi used = 22/7

22/7 x d = 44

d= 44/ (22/7)

=14