The expression below is a sum of cubes.

64x^3 + 125

A. True

B. False

Answer:

Negative Reciprocals

Step-by-step explanation:

Consider two slopes being perpendicular to each other:

[tex]\displaystyle \large{m_1\cdot m_2=-1}[/tex]

You will either receive:

[tex]\displaystyle \large{m_1=-\dfrac{1}{m_2}}[/tex]

or:

[tex]\displaystyle \large{m_2=-\dfrac{1}{m_1}}[/tex]

Say, you want to find perpendicular slope of 4. You have first slope as 4 and another as unknown which is assigned as m variable:

[tex]\displaystyle \large{4m=-1}\\\displaystyle \large{m=-\dfrac{1}{4}}[/tex]

Therefore, 4 and -1/4 are perpendicular to each other. See that one slope is positives while another is negative. If you have negative slope then the perpendicular slope is positive.

Hence, they are indeed reciprocal but also negative as well.

Answer:

cos θ = 4/5

Explanation given below in the image,

I hope my answer helps you.

Answer:

30.125

the answer is 30.125 so that is the answer of this question

Answer:

81

Step-by-step explanation:

[tex] {x}^{2} + 18x + {(( \frac{1}{2})(18)) }^{2} [/tex]

[tex] {x}^{2} + 18x + {9}^{2} [/tex]

[tex] {x}^{2} + 18x + 81[/tex]

[tex] {(x + 9)}^{2} [/tex]

Answer:

Step-by-step explanation:

In order to determine the correct answer, we need to confirm it first by making the solution below:Costs: $89.95 = New Lamp $239.99 = Comforter 6 3/5% = Sales Tax (convert this to decimal and we get 6.6%)  $351.72 = Total amount the Chang's paidLet's get the total costs first which is $329.946.6% of 329.94 is $21.78The total cost with the tax would be $351.72.Therefore, the Chang's paid the correct amount. The correct answer would be option D. The Chang's family paid the correct amount for their purchases.

Answer:

First space: 7

second space: 2

third space: -7

last space: -12

Step-by-step explanation:

To subtract, use "Add the opposite". In the problem the minus has aready been changed to adding, so you just change the second number (-7 in the first part or 7 in the second part) to their opposite sign. see image.

Answer: I.

Step-by-step explanation:

Capitalism is clearly not the answer. Capitalist governments such as America have their fingers into the economic trading.

Socialism and Communism sound plausible, but Communism is giving people money by their work, and Socialism is everything is owned by the public. Both still involve themselves in markets, so the answer is I

Answer:

d.

No economic system is free from government involvement.

Step-by-step explanation:

Answer:

NM = 17, LY = 5, m<NLY = 53.13 degrees, m<NMY = 28.07 degrees

Step-by-step explanation:

To solve for NM, you just use the Pythagorean theorem,

[tex]8^{2} + 15^{2} = x^{2}[/tex]

64 + 225 = [tex]x^{2}[/tex]

289 = [tex]x^{2}[/tex]

[tex]17 = x[/tex]

To solve for LY, you can use geometric mean,

[tex]\frac{10}{y} = \frac{15+y}{10}\\\\100 = 15y + y^{2} \\y^{2} +15y - 100 = 0\\(y+20)(y-5) = 0\\y= 5[/tex]

To solve for the other angles, use the inverse.

Sin-1, = 8/10

= 53.13

Other angle =

Tan-1 = 8/15

= 28.07

Hope this helps, I put a lot of time into this :)

GH is a tangent to the given circle.

A line that only touches a circle or an ellipse at one point is said to be tangential in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve.

As per the given diagram:

The line segments AB, AC, DC and EF are drawn in the diagram also a line GH is drawn in the diagram.

A line GH is drawn such that it's extending from both of its end towards infinity, and it touches the circle at only one point, which is G. This satisfies all the conditions for the line GH to be a tangent.

Hence, GH is a tangent to the given circle.

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Answer:

1/3

Step-by-step explanation:

This problem would be 1/2 x 2/3. The answer would be 1x2 over 2x3.

The value of a is equal to 3 and the value of b  is equal to 4.

A Complex Number is represented by z=a+bi, where:

a= real part

bi= imaginary number

b= imaginary part

i= [tex]\sqrt{-1}[/tex], therefore i²= -1

For solving this question, you should solve the product (-11 + 5i) * (1 – i). After that, you should compare the previous results with the result for expression ( (a + bi)* (2 + 3i) )-i. From this comparison, using the linear system you will find the variables a and b.

        (-11 + 5i) * (1 – i)=

        -11 +11i +5i -5i²

        -11 +16i -5i², as i²= -1 you can rewrite

        -11 +16i -5(-1)

        -11 +16i +5

         -6+16i

Then,

(-11 + 5i) * (1 – i)=  -6+16i

      ( (a + bi)* (2 + 3i) )-i

      (2a+3ai +2bi +3bi²) -i, as i²= -1 you can rewrite

      (2a+3ai +2bi +3b(-1)) -i

      (2a+3ai +2bi -3b) -i

     ( (2a-3b) + i(3a +2b) ) -i ,

For adding complex numbers, you must add or subtract the corresponding real and imaginary parts. Thus, you will have:

       (2a-3b) + i(3a +2b-1)

Then,

( (a + bi)* (2 + 3i) )-i=  (2a-3b) + i(3a +2b-1)

         For  (-11 + 5i) * (1 – i)=  -6+16i

                   real part = -6

                    imaginary part = 16

          For   ( (a + bi)* (2 + 3i) )-i=  (2a-3b) + i(3a +2b-1)

                   real part = 2a-3b

                    imaginary part = 3a +2b-1

                       2a-3b= -6

                       3a +2b-1=16, you can rewrite as 3a +2b=17.

Thus the system will be:

                             [tex]\begin{bmatrix}2a-3b=-6\\ 3a+2b=17\end{bmatrix}[/tex]

      2a-3b=-6    (1)

      3a+2b=17  (2)

     Multiplying equation 1 by 2 and equation 2 by 3, you can rewrite as:

      4a-6b= -12

      9a+6b=51  

    Sum the equations

     4a-6b+9a+6b= -12 +51

     13a= 39

        a=39/13=3

     Replacing the value of a=3 in equation 1, you can find b.

      2a-3b=-6    (1)

     2*3-3b= -6

     6 -3b = -6

        -3b = -6 -6

        -3b= -12

            b= -12/-3 = 4

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Smith's balloon is an algebraic expression

The expression that represents how many Balloons Smith has is p + 20

The given parameters are:

Small = p

Big = 20

Add the number of small and big ballons to get the total number of ballons

Total = Small + Big

This gives

Total = p + 20

Hence, the expression that represents how many Balloons Smith has is p + 20

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Answer:

SU=6

TU=6

ST=12

Step-by-step explanation:

SU and TU are equal because their hypotenuses are equal (10).

With this knowledge, you know that 2x+2=3x.

Subtracting 2x from both sides shows that x=2, so you can substitute that into the original line segment values in order to get 6 for both SU and TU. Double this to find the value of ST (12).

Answer:

0.72 meters

Step-by-step explanation:

by dividing 6.48 by 9, we get 0.72 meters

Answer:

here

Step-by-step explanation:

The mean amount of money Sadie saves each month is $10,724.29.

Mean is a measure of central tendency that is used to determine the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(10150 + 102211 + 10424 + 10769 + 11155 + 11477) / 7 =  $10,724.29.

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Answer:

Θ = 84°

Step-by-step explanation:

using the identity

cosx = sin(90 - x) , then

cos6° = sin(90 - 6)° = sin84°

that is Θ = 84°

Hope you enjoy  :)))))))

The interval contains all of the values in the range of the function 32 to 58 dollars.

The function is as follows:

p(x)  = 12 + 2x

where

He sells 10 to 23 candies per day.

Therefore,

x = 10 and x = 23

Hence,

p(10) = 12 + 2(10) = 12 + 20 = 32

p(23) = 12 + 2(23) = 12 + 46 = 58

Therefore, the interval contains all of the values in the range of the function 32 to 58 dollars.

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Answer:

x=16ft 2x+4=36

Step-by-step explanation:

perimeter o rectangle=2(l+b)

2(2x+4+x)=104

4x+8+2x=104

x=16ft,2x+4=36ft

The amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx. The probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z tables, the p-value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

Let we take:

X = The balance of a person’s bank account in Superior, WI

Then, by the given data, we have:

[tex]X \sim N(\mu = 580, \sigma = 125)[/tex]

Let the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents be X = x dollars. This is the money, below which lie 80% of Superior, WI residents, and so as their income, or values of X.

Symbolically, we have:

[tex]P(X < x) = 80\% = 0.8[/tex]

Converting X to standard normal variate Z, we have:

[tex]Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - 580}{125}\\[/tex]

Thus, the probability statement can be rewritten as:

[tex]P(X < x) =0.8\\P\left( Z < z = \dfrac{x -580}{125} \right) = 0.8[/tex]

From the z-tables, the value of Z for which the p-value comes out as between 0.84 and 0.85, let it be their average 0.845.

Thus, we get:

[tex]P(Z < z = 0.845) \approx 0.8[/tex]

Thus, we get:

[tex]z = \dfrac{x - 580}{125} \approx 0.8\\\\x \approx 0.8 \times 125 + 580 = 680[/tex]

Thus, the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx.

Now, for second question, we need:

The probability a random person from Superior has less than $400 or more than $1000 in their bank account.

So, income of a random person from Superior is a random value of X.

So, this probability is written as:

[tex]P(400 < X < 1000)[/tex]

Rewritting it, we get:

[tex]P(400 < X < 1000) = P(X < 1000) - P(X \leq 400)[/tex]

Converting X to Z (standard normal variate), we get:

[tex]P(400 < X < 1000) = P(X < 1000) - P(X \leq 400)\\\\P(400 < X < 1000) = P\left(Z < \dfrac{1000-580}{125} \right) - P\left(Z \leq \dfrac{400-580}{125} \right)\\\\P(400 < X < 1000) = P( Z \leq 3.36) - P(Z \leq -1.44)[/tex]

The p-value for Z = 3.36 is 0.9996

The p-value for Z = -1.44 is 0.0749

Thus, we get:

[tex]P(400 < X < 1000) = P( Z \leq 3.36) - P(Z \leq -1.44)\\\\P(400 < X < 1000) = 0.9996 - 0.0749 = 0.9247[/tex]

Thus, the probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

Thus, the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx. The probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

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Answer:

The warehouse has 31,250 cubic feet of space.

The air conditioner has to be at least 55 tons.

Answer:

687,500 for first blank

60 tons for second blank

Step-by-step explanation:

It is correct on edmentum

Answer:

range = 27

Step-by-step explanation:

the range is the difference between the largest and smallest values in the data set.

largest = 95 , smallest = 68

range = 95 - 68 = 27

Answer:

46

Step-by-step explanation:

Answer:

No, that is incorrect.

[tex]21 * 34 = 714\\20 * 35 = 700[/tex]

__________________________________________________________

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The correct factored form of the expression p³ - 125q³ is,

(p - 5q)(p² + 5pq + 25q²).

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

We know, a³ - b³ = (a - b)(a² + ab + b²).

Given, An expression p³ - 125q³.

= p³ - (5q)³.

= (p - 5q)(p² + p.5q + (5q)²).

= (p - 5q)(p² + 5pq + 25q²).

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Answer:

Investement P

Step-by-step explanation:

Answer:

The vertex of the graph is:

As this parabola opens upwards, the vertex is the minimum point.

From inspection of the graph, vertex = (-3, -1)

Equation of the graph

From inspection we can see that the x-intercepts are when
x = -4 and x = -2

[tex]\sf x = -4 \implies x+4=0[/tex]

[tex]\sf x = -2 \implies x+2=0[/tex]

Therefore:

[tex]\sf y=(x+4)(x+2)[/tex]

Expand:

[tex]\sf \implies y=x^2+6x+8[/tex]

Answer:

[tex]B)f(x) = {x}^{2} + 6x + 8[/tex]

Step-by-step explanation:

Let [tex] f(x)=x^2[/tex] be the parent function. With transformation of function, firstly,we know that,

algebraically

Clearly, The parabola is moved down by 1 unit thus, C is -1. Therefore our function transforms to

secondly, we know that,

algebraically,

in case,

Since the parabola is moved left by 3 unit, C is +3, and hence Our function eventually becomes

simplifying it yields:

[tex]\implies \boxed{f(x) = {x}^{2} + 6x + 8}[/tex]

Hence,B is our required answer

Answer:

1, 5

Step-by-step explanation:

I may be a little wrong but;

Multiply it by 3 and 4-

-12x+9y=-51

12x-16y=44

-7y=-7

y=1

x=5