the volume of a cube depends on the length of its sides. this can be written in function notation as v(s). What is the best interpritation of v(3) = 27? A. A cube with the volume of 3 cubic feet has side lengths of 27 feet. B. 3 sides of the cube have a total length of 27 feet. C. 3 of these cubes will have a total volume of 27 cubic feet. D. A cube with side lengths of 3 feet has a volume of 27 cubic feet.

Answer:

5/2

Step-by-step explanation:

We take the ratio of a side of ABC over the same side on DEF

AB/ DE

35/14

Divide top and bottom by 7

5/2

Answer:C

Step-by-step explanation: substitute n=3 for all equations and see which equation accurately correlates to the graph for when x=3. When you do this you see that only option C is the correct equation

Answer:

C). [tex]a(n) = 7 + (n - 1) * 12[/tex]

Step-by-step explanation:

Plugin values into the equation.

Answer:

(6,-4)

Step-by-step explanation:

Reflecting over the x axis means flipping the point or line over it. Therefore the point's y value would the opposite from the beginning.

Answer:

Step-by-step explanation:

For any point reflected over the x-axis, the x-coordinate stays the same and the y-coordinate becomes negative.

6 stays the same

4 becomes -4.

Answer:

Water a tank can hold = 14 1/2 = 29/2

Volume of bucket 1 1/4 = 5/4

The expresson can be

29/2 / 5/4

No. of buckets used = 29/2 x 4/5

Answer:

b and e

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

3x - 2 = 16

3x = 16 + 2

3x = 18

x = 18/3

x = 6

Answer:

x=6

Step-by-step explanation:

3x-2=16

+2      +2

3x = 18

÷3    ÷3

x=6

Answer:

C.

Step-by-step explanation:

Explicit Formula: an = a1(r)^(n-1)

Our r = 1/4 because to get 64 down to 16 you need to divide by 4 or multiply by 1/4

Our a1 is the 1st term of the sequence, which is 64.

Plug it in: an = 64(1/4)^(n-1)

So our only viable option is C.

Answer:

Option C

Step-by-step explanation:

=> [tex]a_{n} = a_{1} * r^{(n-1)[/tex]

Where a1 = 64, r = 1/4

So,

=> [tex]a_{n} = 64 * (\frac{1}{4}) ^{n-1}[/tex]

Hey there! :)

Answer:

Option C.

Step-by-step explanation:

A perpendicular line to 2/3 will be the reciprocal and negative of this fraction. Therefore:

Slope of perpendicular line = -3/2.

Remember, the equation for solving for the slope is:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

We must find points that when plugged into this equation, equal to -3/2.

Plugging in the points in option A:

[tex]\frac{2}{3} \neq \frac{-3}{2}[/tex]

Option B:

[tex]\frac{3}{4} \neq \frac{-3}{2}[/tex]

Option C: This is the correct answer.

[tex]\frac{-3}{2} = \frac{-3}{2}[/tex]

Option D:

[tex]\frac{2}{10}\neq \frac{-3}{2}[/tex]

Answer:

5

Step-by-step explanation:

p(2) - q(2)

3 - (-2)

3 + 2

= 5

Answer: there a 3 feet to a yard a 36 inches to a yard( 12 inches to a foot) 1/3 of a yard is a foot hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

RHS means on the right hand side

And LHS means on the left hand side

So if x is one the right side of the expression ,it is on the RHS and if it is on the left side of the expression , it is on the LHS

Answer:

D

Step-by-step explanation:

3n - 5p + 2n = 10p

Add like terms.

5n - 5p = 10p

Add 5p to both sides.

5n = 10p + 5p

5n = 15p

Divide both sides by 5.

n = 15/5p

n = 3p

The solution of expression for n is,

⇒ n = 3p

We have to given that,

An expression to solve,

⇒ 3n - 5p + 2n = 10p

Now, We can solve the expression for n as,

⇒ 3n - 5p + 2n = 10p

Combine like terms,

⇒ 3n + 2n = 10p + 5p

⇒ 5n = 15p

Divide by 5 both side,

⇒ n = 15p/5

⇒ n = 3p

Therefore, The correct option is,

D. n = 3p

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Answer:

x=56 degrees interior angle of regular hexagon is 60 degrees

Step-by-step explanation:

The sum of the angles in a hexagon is 720.  So the size of an angle in a regular hexagon is 120 degrees.

angle BCA + angle x + angle DCE are equal to 180 degrees when added together.

We can use base angles theorem to find angle DCE : 180-32 = 148 148/2 = 74

Now we know that angle BCA + angle x = 180-74= 106 degrees. Since ABC is equilateral we alread know angle BCA is 60 degrees.  Now we can find x from doing 106-60 which equals 56 degrees.

x=56

Answer:

1) Side a = 9.55

2) Angle B = 51.36°

3) Angle C = 72.67°

Step-by-step explanation:

We would be solving the above questions using Law of Cosines

1) To find Side a using Law of cosines

a² = b² + c² - 2bc × Cos A

a = √(b² + c² - 2bc × Cos A)

a = unknown

b = 9

c = 11

Angle A = 56°

a = √(9² + 11² - 2 × 9 × 11 × Cos 56°

a = 9.55405

Approximately a = 9.55

2) To find Angle B

We would use the Law of Cosines as well

b² = a² + c² - 2ac × Cos B

Cos B = a² + c² - b²/2ac

B = arc cos ( a² + c² - b²/2ac)

a = 9.55

c = 11

b = 9

B = arc cos (9.55² + 11² - 9²/2 × 9.55× 11)

B = 51.36°

3) To find Angle C

We would use the Law of Cosines as well

c² = a² + b² - 2ac × Cos C

Cos C = a² + b² - c²/2ab

C= arc cos ( a² + b² - c²/2ab)

a = 9.55

b = 9

c = 11

C = arc cos (9.55² + 9² - 11²/2 × 9.55× 9)

C= 72.67°

Answer:

1a) 15, 7, x+5

1b) 7

2a) 18, 3r

Step-by-step explanation:

1a) Since Claire is 5 years older, she will always be her cousin's age plus 5

1b) Claire is 5 years older, so Claire's cousin is 5 years younger. So, Claire's cousin is Claire's age minus 5

2a) Diego will have the amount of Han's books times 3

Answer:

Clare Questions:

Cousin: 10, Clare: 15

Cousin: 2, Clare: 7

Cousin: x, Clare: x + 5

Cousin: 7, Clare: 12

Diego Questions:

Han: 6, Diego: 18

Han: can't tell if it is a 0 or n, Diego: 0 or 3n, respectively

Step-by-step explanation:

Since Clare is older than her cousin by 5, they will both age at the same rate, thus she will always be 5 years older.

example: if her cousin is 10, Clare will be 10 + 5 years older, therefore being 15.

Since DIego has 3 times as many books than Hans, it multiplies by 3.

example: if Han has 6 books, multiply 6 by 3 and you get Diegos amount, 18.

Answer:

one

Step-by-step explanation:

The maximum number of y intercepts a line can have is one

A line can only cross the y axis one time

A line can only cross the x axis one time

Otherwise it is not linear

Answer: $660

Step-by-step explanation:

If he saves $ 55 every month, he will have

55 x 12 = 660

Answer:8

Might I be right

Step-by-step explanation:

I think its 57.17 or about 52.2cubic inch

Answer:

The correct option is;

Choosing 4 neighborhoods at random and poll every home in those neighborhoods

Step-by-step explanation:

Given that the survey relate to how much money people are willing to spend on on concert tickets with the goal of being practical and unbiased, we have;

Required sampling = Random Sampling

The preferable type of random sampling is either;

1) Simple random sampling

Sampling a given percentage of the homes in the area randomly

2) Clustered random sampling

Completely polling entire population of randomly selected area

Given the practicability of sampling concert goers, since people may have different interests, a better representative sample will be to perform the clustered random sampling approach by choosing 4 neighborhoods at random and poll every home in those neighborhoods.

Answer: $641.51

Step-by-step explanation:

A = p (1+ r/n)^nt

A = 500 (1 + 0.025/4)^4*10

A = 641.51

The amount in an account where $500 in invested at 2.5% is $641.51.

Using this formula

A = p (1+ r/n)^nt

Where:

A=Amount

P= Principal=$500

R=Rate=2.5% or 0.025

n=4 (Quarterly)

T=Time=10 years

Let pug in the formula

A = $500(1 + 0.025/4)^4×10

A=$500(1.28302)

A =$641.51

Inconclusion the amount in an account where $500 in invested at 2.5% is $641.51.

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Answer:

[tex]a_{n} = -83/40[/tex]

Step-by-step explanation:

Given

[tex]a_{n} = -2 + 3/2 (n-1)[/tex]

In this problem to find 21st term we put 21 in place of n in the equation

[tex]a_{n} = -2 + 3/2 (21-1) = \\a_{n} = -2 + 3/2 (20)\\a_{n} = -2 + 3/40 = (-2*40 +3)/40 \\a_{n} = -83/40\\[/tex]

Thus, 21st term is -83/40.

Answer:

Kobe raised x + 24.55

Amari raised x

DJ raised 2x – 15.60

Answer:

it would be 3/5

Answer:

n = -15

Step-by-step explanation:

Given

Sum of Integers from 15 to 50 (inclusive) = Sum of integers from n to 50 (inclusive)

n < 15

Required

Find n

We can split the given parameters to 2

i. Sum of Integers from 15 to 50 (inclusive)

ii. Sum of integers from n to 50 (inclusive)

Solving for (i): Sum of Integers from 15 to 50 (inclusive)

We'll make use of sum of n terms of an arithmetic;

This is given as follows

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where n is the number of terms from 15 to 50

T1 is the first term; T1 = 15

Tn is the last term; Tn = 50

n is calculated using

[tex]n = T_n - T_1 + 1[/tex]

[tex]n = 50 - 15 + 1[/tex]

[tex]n = 36[/tex]

The formula becomes

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]S_n = \frac{36}{2}(15 + 50)[/tex]

[tex]S_n = \frac{36}{2}(65)[/tex]

[tex]S_n = 18(65)[/tex]

[tex]S_n = 1170[/tex]

Solving for (ii): Sum of integers from n to 50 (inclusive)

We'll also make use of the same formula used above

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where n is the number of terms from n to 50

T1 is the first term; T1 = n

Tn is the last term; Tn = 50

n is calculated using

[tex]n = T_n - T_1 + 1[/tex]

[tex]n = 50 - n + 1[/tex]

[tex]n = 50 + 1 - n[/tex]

[tex]n = 51 - n[/tex]

The formula becomes

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]S_n = \frac{51 - n}{2}(n + 50)[/tex]

Recall that the Sum of Integers from 15 to 50 (inclusive) = Sum of integers from n to 50 (inclusive);

This implies that

Sn (i) = Sn (ii)

As such; we have

[tex]S_n = \frac{51 - n}{2}(n + 50) = 1170[/tex]

[tex]\frac{51 - n}{2}(n + 50) = 1170[/tex]

Multiply both sides by 2

[tex]2 * \frac{51 - n}{2}(n + 50) = 1170 * 2[/tex]

[tex](51 - n)(n + 50) = 1170 * 2[/tex]

[tex](51 - n)(n + 50) = 2340[/tex]

Open Brackets

[tex]51(n + 50) - n(n + 50) = 2340[/tex]

[tex]51*n + 51 * 50 - n * n - n * 50 = 2340[/tex]

[tex]51n + 2550 - n^2 - 50n = 2340[/tex]

Reorder

[tex]-n^2 + 51n - 50n + 2550 = 2340[/tex]

[tex]-n^2 + n + 2550 = 2340[/tex]

Subtract 2340 from both sides

[tex]-n^2 + n + 2550 -2340 = 2340 -2340[/tex]

[tex]-n^2 + n + 210 = 0[/tex]

Multiply both sides by -1

[tex]-1(-n^2 + n + 210) = -1 * 0[/tex]

[tex]n^2 - n - 210 = 0[/tex]

At this point, we have a quadratic equation; as such, it'd be solved as follows:

[tex]n^2 - n - 210 = 0[/tex]

Expand

[tex]n^2 + 15n - 14n - 210 = 0[/tex]

Factorize

[tex]n(n + 15) - 14(n + 15) = 0[/tex]

[tex](n - 14)(n + 15) = 0[/tex]

Split the above expression

[tex](n - 14) = 0 \ or\ (n + 15) = 0[/tex]

[tex]n - 14 = 0 \ or\ n + 15 = 0[/tex]

[tex]n = 14\ or\ n = -15[/tex]

The question states that n < 15;

This means that we'll discard the value of n = 14

Hence, n = -15

Answer: C. (1, 4)

Step-by-step explanation:

The point where the two lines meet or intersect is the solution to the system of equations graphed. And in this case, the lines intersect at (1, 4).

I think its ƒ(x) = 1∕2(x – 2)2 + 1

The function that represents a parabola with vertex at (2,1) and y-intercept (0,3) is f(x) = - x² + 4x - 3.

What is general equations of parabola?

The general equation of a parabola is given by

⇒ y = a(x – h)² + k

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.

According to the question,

⇒ y = a(x – h)² + k

⇒ (h,k) = (2,1)

⇒  y = a(x – 2)² + 1

T find the value of a,

⇒ - 3 = 4a + 1

⇒ a =-1

⇒  y = -1(x – 2)² + 1

⇒ y = -(x² + 4 - 4x) + 1

⇒ y = -x² + 4x - 3

Hence the required function is y = -x² + 4x - 3.

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Answer:

Option 1: Domain of both functions are all real numbers.

Step-by-step explanation:

f(x) = 5x

Domain: All Real Numbers

Range: All Real Numbers

g(x) = 5

Domain: All Real Numbers

Range: y > 5

Answer: Option 1

Step-by-step explanation:

f(x) = 5x

Domain: All Real Numbers

Range: All Real Numbers

g(x) = 5

Domain: All Real Numbers

Range: y > 5

Answer:

Choices are not provided, but you can answer the question as follows: take the coordinates of quadrilateral WXYZ and apply:

W(xW, yW) -> W'(-xW, yW-2)

X(xX, yX) -> X'(-xX, yX-2)

Y(xY, yY) -> Y'(-xY, yY-2)

Z(xZ, yZ) -> Z'(-xZ, yZ-2)

For example, if point W is located at (1, 1), W' would be located at (-1, -1)

Step-by-step explanation:

Reflection over the y-axis transforms point (x, y) into (-x, y)

Translation down 2 units transforms point (x, y) into (x, y-2)

Answer:

The first choice hope this helps :)

Step-by-step explanation:

Answer:

1 - a/variable

2 - d/statistic

3 - b/population

4 - c/data

5 - e/parameter

6 - f/sample

I did comment asking if the two you'd already selected were definitely correct, but no answer was given, so I apologise if this is wrong. This is what I would put.

D is point lies between A and B.

Triangle △ABC has an altitude CD.
angles A and B are both acute.

Altitude is perpendicular bisector to side of triangle from opposite vertex of triangle.

Since △ABC
A and B are acute angles, and that altitude CD has one vertex at c and other is between A and B i.e. D

Thus, the required point of Altitude CD D lies between A and B.

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