what expressions are equivalent to 162x^4 - 144x^2 +32

Answer:

All Real Answers / Infinite Solutions

Step-by-step explanation:

Distribute: 5x-2x = 4x-x

Simplify: 3x=3x

Subtract 3x from each side: 0=0

Answer:

Median and IQR

Step-by-step explanation:

If we are to accurately compare two data sets, the best measure of central tendency is median and best measure of variability is the MAD.

The reason is that:

1. Median is not affected by outlier or extreme value. Due to this, if we use the mean, it can be misleading if there is any case of outlier(s) in the data sets.

2. The interquartile range (IQR) is the middle half of the data. It uses the concept of median to operate - think about the median value that splits the dataset in half. Similarly, you can divide the data into quarters. This also is not affected by outlier(s) or extreme value(s).

NB: When we say middle half or middle number, we assumed you have sorted the data sets either in ascending order or descending order. This will put the data sets in order of their sizes. E.g., 1 < 2 < 3, etc.

Answer:

Median and IQR

Step-by-step explanation:

Answer:

6 times 2 is 12, 6 times 4 is 24, 30 doesn't equal 36

Answer: [tex]A(t) = 2,675(1.003)^{120}[/tex]

[tex]A(t) = 4,170(1.04)[/tex]

[tex]A(t) = 5,750(1.0024)^{20}[/tex]

Step-by-step explanation:

The exponential growth equation is given by :-

[tex]y=Ab^x[/tex] , where A = initial value , x= time period , b= growth factor.

The growth factor should be greater than 1.

From all the given options , the equations that are exponential :

[tex]A(t) = 2,675(1.003)^{120}[/tex]  , here b= 1.003

[tex]A(t) = 4,170(1.04)[/tex] , here b= 1.04

[tex]A(t) = 3,500(0.997)^{4t}[/tex]  , here b=  0.997

[tex]A(t) = 5,750(1.0024)^{20}[/tex]  , here b= 1.0024

[tex]A(t) = 1,500(0.998)^{127}[/tex]  , here b= 0.998

[tex]A(t) = 2,950(0.999)[/tex] , here b= 0.999

From the above exponential equations , only first  , second and fourth equation has b>1.

So , the models that could represent a compound interest account that is growing exponentially. are :

[tex]A(t) = 2,675(1.003)^{120}[/tex]

[tex]A(t) = 4,170(1.04)[/tex]

[tex]A(t) = 5,750(1.0024)^{20}[/tex]

Answer:

367.25 dollars

Step-by-step explanation:

To calculate 35 percent of 565 you would first

35% is 197.75 the question says 35% off so you would have to take the 35% off the 565

(565-197.75 = 367.25)

Answer:

4×(x² - 4x + 2)

Step-by-step explanation:

4x2 - 16x + 8 = 4×x² - 4×4×x + 4×2 = 4×(x² - 4×x + 2)

Answer:

I'm assuming you meant 27 and not 2.7 sooo... 5/28 were pepperoni

Step-by-step explanation:

The given algebraic expression 9a1/2b14c3/2 appears to be a kind of factorization where a, b, c are variables raised to different powers. Unless values for these variables are provided, this expression can't be simplified further.

The expression 9a1/2b14c3/2 is considered as a form of factorization in mathematics where a, b, c denote variables, and the numbers 1/2, 14, 3/2 are their respective exponents. In other words, it's a product of the variables 'a', 'b', and 'c' raised to their respective powers. For instance, 'a' is under a square root (as signified by the power of 1/2), 'b' is raised to the power of 14, and 'c' is also under a square root but cubed (a power of 3/2).

Consequently, this expression doesn't seem to have a simpler or equivalent expression because the terms 'a', 'b', and 'c' are likely representing different entities, hence they can't be combined or simplified further. However, should there be values for 'a', 'b', and 'c', it's simply substituted into the expression and calculated accordingly.

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Answer:

He gained 31 yards minus 24 = which is 11 yards.

Step-by-step explanation:

If we gained 24 yards plus the 7 which is 31

So if he loss 20 yards that will be 11 yards left cause 31-24= 11

There's your answer. Hope this helps!

Answer:

2 2/5

Step-by-step explanation:

12 x 1/5 = 2 2/5

Answer:

That is math.

Answer:

When only solving for b you would multiple by the reciprocal of 1/18*b so you multiply 18 to both sides and b is equal to -108

Step-by-step explanation:

Answer:

  y = -10/3x -23

Step-by-step explanation:

The 2-point form of the equation of a line is useful for this.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Using your points, we have ...

  y = (-3 -7)/(-6 -(-9))(x -(-9)) +7

  y = (-10/3)(x +9) +7

  y = -10/3x -23 . . . . . . . simplify

The equation of the line passing through the points (-9,7) and (-6, -3) is y = -10/3x -14.

In mathematics, the equation of a line can be given as y = mx + c, where m is the slope of the line and c is the y-intercept. Firstly, we need to calculate the slope (m) which is (y2 - y1) / (x2 - x1). If we substitute the points (-9,7) and (-6, -3) we get (-3 - 7) / (-6 + 9) = -10 / 3, so m = -10/3. Next, to get the y-intercept (c) we can substitute the slope and one of the points into the equation: 7 = -(10/3)*(-9) + c, and we get c = -14. Therefore the equation of the line is y = -10/3x -14.

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Answer:

-75 ercent

Step-by-step explanation:

Step-by-step explanation:

Given,

The diameter of small pizza = 8 inches,

The diameter of medium pizza  = 10 inches and

The diameter of large pizza (d) = 11 inches

To find, the circumference of each size of pizza = ?

We know that,

The circumference of the circle = [tex]2\pi r= \pi d[/tex]

∴ The circumference of small size of pizza = 3.14 × 8 = 25.12 inches

The circumference of medium size of pizza = 3.14 × 10 = 31.4 inches

Also,

The circumference of large size of pizza = 3.14 × 12 = 37.68 inches

Thus, the circumference of small size, medium size and large size of pizzas are  25.12 inches, 31.4 inches and 37.68 inches.

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Answer: dividing

Step-by-step explanation:

Final answer:

To convert a fraction to a percent, divide the numerator by the denominator to get a decimal, multiply the decimal by 100, and then add the percent symbol (%).

Explanation:

To convert a fraction to a percent, you start by converting the fraction into a decimal. To do this, divide the numerator (the top number) by the denominator (the bottom number). Once you have the decimal, you multiply it by 100 to get the percent value. Finally, append the percent symbol (%) to the number.

Example:

For the fraction 3/4, first convert it to decimal:

Another way to convert fractions to percent is by finding an equivalent fraction that has 100 as its denominator. Then, simply use the numerator as the percent. If the fraction's denominator is not easily scalable to 100, it is easier to use the decimal method described previously.

Answer:

x-1=0 x=1

x+1=0 x= -1

x+5=0 x= -5

Step-by-step explanation:

Answer:

96 cubic feet

Step-by-step explanation:

Answer:

270 units³

Step-by-step explanation:

l×w×h = 10

lwh = 10

New Volume = (3l)×(3w)×(3h)

= 27×lwh

= 27×10

= 270 units³

Alternately,

Since the sides are increased in the same ratio,

The two prisms are similar figures

For similar figures,

volume1/volume2 = (side1/side2)³

New Volume/10 = (3/1)³ = 27

New Volume = 270 units³

Final answer:

The new volume of a rectangular prism, whose dimensions are tripled, is calculated by cubing the factor of increase (3) and multiplying it by the original volume. The new volume will be 270 cubic units.

Explanation:

If the original volume of a rectangular prism is 10 cubic units and the length, width, and height are all made three times as long, the new volume can be calculated using the principle that volume is proportional to the cube of the linear dimensions of the prism. This is often represented as V  imes L³ where V is volume and L is the linear dimension.

To find the new volume, you would multiply each dimension by 3 so the new length (L'), width (W'), and height (H') would be three times the original dimensions. The new volume would then be calculated as:

V' = L' times W' times H' = (3L) times (3W) times (3H)

Since the original volume (V = L  imes W  imes H) is given as 10 cubic units, and you've multiplied each dimension by 3, you would cube the factor of increase (3³ = 27) and multiply it by the original volume:

V' = 27  imes V = 27  imes 10 = 270 cubic units

Therefore, the new volume of the rectangular prism would be 270 cubic units.

(f-g)(x) = [tex]x^{2}[/tex] + 2x + 8

Step-by-step explanation:

Step 1:

Formula for (f-g) (x) = f(x) - g(x)

Step 2:

Substitute values of f(x) and g(x) in the formula and solve

(f-g)(x) = (2x + 1) - ([tex]x^{2} -7[/tex])

(f-g)(x) = 2x + 1 - [tex]x^{2}[/tex] + 7

          = 2x + 8 [tex]- x^{2}[/tex]

          = [tex]x^{2}[/tex] + 2x + 8

Final answer:

The division of 29r2 by 17 simplifies down to approximately 1.7059r^2, where r is a variable representing a real number.

Explanation:

The student is asking about a division of algebraic expressions, specifically 29r^2 divided by 17. The notation 29r^2 suggests that we have the variable r squared, multiplied by 29, and we need to divide this entire expression by 17. This is a straightforward division operation where each term in the numerator is divided by the denominator.

To find the solution, you divide 29 by 17 and keep r^2 (r squared) as part of the expression. Therefore, the simplified form of 29r^2 divided by 17 would be approximately 1.7059r^2, assuming that r represents a real number.

Answer:

a = 9√10

b=3√10

Step-by-step explanation:

see attached for reference for any right triangle

in our case

c is the hypotenuse

hence

c² = a² + b²

we are given that c = 30

also that a is 3 times as long as b or,

a = 3b    

substituting these into the pytharogrean formula.

c² = a² + b²

30² = (3b)² + b²

900 = 9b²+b²

10b² = 900

b² = 90

b = √90 = √9 √10 = 3√10

earlier we found that a = 3b,

hence

a = 3(3√10)

a = 9√10

Answer:

(a) P (U and V) = 0.

(b) P (U|V) = 0.

(c) P (U or V) = 0.83.

Step-by-step explanation:

Mutually exclusive events are those events that cannot occur at the same time. That is, if events A and B are mutually exclusive then,

                                         [tex]P (A\cap B) = 0[/tex]

Given:

Events U and V are mutually exclusive.

P (U) = 0.27 and P (V) = 0.56

(a)

As events U and V are mutually exclusive, the probability of their intersection will be 0.

That is,

[tex]P(U\ and\ V) = P (U\cap V) = 0[/tex]

Thus, the value of P (U and V) is 0.

(b)

The conditional probability of event B given A is:

[tex]P(B|A) =\frac{P(A\cap B)}{P(B)}[/tex]

Compute the value of P (U|V) as follows:

[tex]P(U|V) =\frac{P(U\cap V)}{P(V)}\\=\frac{0}{0.56}\\ =0[/tex]

Thus, the value of P (U|V) is 0.

(c)

The probability of the union of two events, say A and B, is

[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Compute the value of P (U or V) as follows:

[tex]P(U\ or\ V)=P(U\cup V)\\=P(U)+P(V)-P(U\cap V)\\=0.27+0.56-0\\=0.83[/tex]

Thus, the value of P (U or V) is 0.83.

The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.

Given :

A) P(U and V)

P(U and V) = P(U [tex]\cap[/tex] V) = 0

Because U and V are mutually exclusive events.

B) P(U|V)

[tex]\rm P(U|V) = \dfrac{P(U\cap V)}{P(V)}[/tex]

[tex]\rm P(U|V) = \dfrac{0}{0.56}[/tex]

P(U|V) = 0

C) P(U or V)

[tex]\rm P(U \;or\;V) = P(U\cup V)[/tex]

[tex]\rm P(U \;or\;V) = P(U)+P(V)-P(U\cap V)[/tex]

P(U or V) = 0.27 + 0.56 - 0

P(U or V) = 0.83

The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.

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Answer:

2 quarters and 5 dimes

Step-by-step explanation:

(2) 25 cent coins = 50 cents

(5) 10 cent coins = 50 cents

equals $1

Step-by-step explanation:

[tex]50 \geqslant 15x \\ \\ \implies \: \frac{50}{15} \geqslant x\\ \\ \implies \: \frac{10}{3} \geqslant x \\ \\ \therefore \: x \leqslant \frac{10}{3} \\ thus \: \{x \: | \: x \leqslant \frac{10}{3} \} \: is \: the \: correct \: \\ solution \: set.[/tex]

The correct solution set of 50 ≥ 15x is {x | x ≤ 10/3 }.\

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given that the expression;

50 ≥ 15x

We can add subtract the 15x - 50 of both sides,

⇒50 - 15x - 50  ≥  15x -15x - 50

⇒50 - 15x - 50 ≥  15x -15x - 50

⇒ - 15x  ≥ - 50

Now we multiply by -1 ,after this process inequality symbol must be reversed

⇒ 15x  ≤  50

Divide by 50 on both sides,

⇒ 15x / 50  ≤  50 / 50

⇒ 3x/10  ≤ 1

⇒ x  ≤  10 /3

Therefore, the solution set is {x | x ≤ 10/3 }

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Answer:

Ans: (-5, 5)

-5 < x < 5

Step-by-step explanation:

Standard form: f(x) = x^2 - 25 < 0.

First solve x^2 - 25 = 0 --> x = +- 5

Use the algebraic method to solve f(x) < 0. Between the 2 real roots (-5) and (5), f(x) < 0, as opposite in sign to a = 1.

Answer by open interval: (-5, 5)

First off, write the inequality as 2x>25

Divide both sides by 2 to get x>12.5

Hope this helped

Answer:

Step-by-step explanation:

Answer:

The Answer Is C

Step-by-step explanation:

I took the test

Answer:

Option C: (2, 1, 0)

Step-by-step explanation:

We are given a system of three equations. Usually, we eliminate a variable from the equations. Solve for the remaining two equations and determine the value of the third equation later.

Here, we are given the choices. So, we can readily substitute each option in the equations. The solution should satisfy all the three equations.

Option A: (3, 1, 0)

Equation (1): 3x + 3y + 6z = 9

⇒ 3(3) + 3(1) + 6(0) = 9 + 3 ≠ 9

Option A does not satisfy the first equation. So, it is eliminated.

Option B: (0, 1, 0)

Substituting in the first equation: 3x + 3y + 6z = 9

⇒ 3(0) + 3(1) + 6(0) = 3 ≠ 9

Option B does not satisfy as well. Hence, it is eliminated.

Option C: (2, 1, 0)

Substituting in 3x + 3y + 6z = 9

⇒ 3(2) + 3(1) + 6(0) = 9

It satisfies Equation 1. For this to be a solution, it should satisfy all the three equations. So, we check for equation 2 and 3.

Equation 2: x + 3y + 2z = 5

2 + 3(1) + 2(0) = 2 + 3 = 5

Equation 3: 3x + 12y + 12z = 18

3(2) + 12(1) + 12(0) = 6 + 12 = 18

Option C satisfies all the equations. So, it is the solution to the system.

On simple substitution, Option D can be eliminated as well.

Hence, the answer.

Answer:-16

Step-by-step explanation:

You want to isolate the variables (in this case it's m)

-80=5m

divide both sides by 5

-16=m

Answer:

B

Step-by-step explanation:

I just had the same paper last night