The values in the table represent a linear function. How does the value of y change in relation to a change in the value of x?

A) for every change in x by 3, y changes by 2
B) for every change in x by 2, y changes by 3
C) for every change in x by 3, y changes by -2
D) for every change in x by 2, y changes by -3

Answer:

544 words

Step-by-step explanation:

The number of 4 letter words can be constructed from ABCDE would be 5^4 = 625

The number of  4 letter words can be constructed using BCD would be 3^4 = 81

So the number of words that use at least one vowel would be  5^4 - 3^4  =  625-81 = 544

Since the histogram is not symmetric, the grades shown in the math class below are not normally distributed.

A histogram represents a normal distribution if it symmetric.

In this problem, we have that:

Since the percentages at the tails are different, the histogram is not symmetric, and  the grades shown in the math class below are not normally distributed.

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The permutation illustrates that if no one has been cast yet, the different ways that are there to cast Jean Valjean from the 22 men is 22.

The ways to cast Jean will be:

= 22!/(22 - 1)!

= 22!/21!

= 22

When Jean Valjean has already been cast, the different ways that are there to cast Inspector Javert from the remaining men will be:

= 21!/(21 - 1)!

= 21!/20!

= 21

When Jean Valjean and Inspector Javert have already been cast, the different ways that are there to cast Marius from the remaining men will be:

= 20!/(20 - 1)!

= 20!/19!

= 20

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Answer: 0.01225%

Step-by-step explanation:

[tex]\frac{8}{20} *\frac{8}{20} *\frac{8}{20} *\frac{7}{20} *\frac{7}{20} *\frac{5}{20} *\frac{5}{20} *\frac{5}{20} = \frac{49}{400000} =0.0001225=0.01225[/tex]%

The solution to the given graph is (-√5/2, √5/2)

Given the following quadratic graph f(x)=x²-1 and g(x) = -x² + 4

The solution will be the point of intersection of the two curves.

Equate the functions

x²-1 =  -x² + 4

Equate to zero

x²+x² - 1-  4 = 0

2x² -5 = 0

2x² = 5

x² = 5/2

x = ±√5/2

Hence the solution to the given graph is (-√5/2, √5/2)

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Answer:

-26730

Explanation:

To find the coefficient of [tex]x^7[/tex] in the expansion of [tex](3 -x)^{11}[/tex]

Use Binomial Expansion:

[tex](x+y)^n = \ ^n C_0 x^n + \ ^n C_1 x^{n-1} y + \ ^n C_2 x^{n-2}y^2 + ...+ \ ^n C_n y^n[/tex]

In this expansion,

[tex](3-x)^{11}[/tex]

The coefficient of [tex]x^7[/tex]

[tex]= 11C_{7} (3)^{11-7} (-x)^7[/tex]

[tex]= (330) (81) (-x^7)[/tex]

[tex]= -26730x^7[/tex]

Answer:

22.44 ft

Step-by-step explanation:

The radius is equal to half of the diameter or 1.75 ft (in this case).

The volume of a sphere is defined as the equation:

V = 4/3 * pi * radius ^ 3

V = 4/3 * 3.14 * 1.75 ^ 3

V = 4/3 * 3.14 * 5.36

V = 22.44 ft

Answer:

Length equals to 75 ft

Step-by-step explanation:

A=l x w           Area of a rectangle formula.

A/w=l              Solve for length

300=l x 4      

300=l x 4

4           4

300/4=l

75=l

Answer:

24

Step-by-step explanation:

7x4

Answer:

5

Step-by-step explanation:

f(x) = a(x-3)² - 2

When x = 4, y = 3, so:

3 = a(4-3)² - 2

5 = a

Vertical angles are congruent, so:

[tex]4x+50=150\\\\4x=100\\\\x=\boxed{25}[/tex]

Answer:

y=2x+3 and y=-2x-3

Step-by-step explanation:

First situation:

2x-y=3

making y subject

y=2x+3

Second situation:

2x+y=-3

making y subject

y=-2x-3

The equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have center of the circle(h, k) = (-7, -6)

The radius of the circle r = 2

The standard form of a circle:

(x - h)² + (y - k)² = r²

(x - (-7))² + (y - (-6))² = 2²

(x + 7)² + (y + 6)² = 4

Thus, the equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.

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Answer:

trust me its c i did the test on edge for me

Step-by-step explanation:

i did the test on edge

Answer:

$63.83

Step-by-step explanation:

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The equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100

The complete question is in the attached image

The given parameters are:

Area = 24

Legs = x and x + 2

The area of the triangle is calculated as:

Area = 0.5 * Base * Height

This gives

0.5 * x * (x + 2) = 24

So, we have:

0.5(x)(x + 2) = 24

Divide through by 0.5

(x)(x + 2) = 48

Expand

x^2 + 2x = 48

Subtract 48 from both side

x^2 + 2x - 48 = 0

Hence, the equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100

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Answer:

145 m/s

Step-by-step explanation:

v = u + 2at

v = 19 + 2(3)(21)

v = 19 + 126

v = 145

answer

V=145

Step-by-step explanation:

V=U+2at

v=19+2×3×21

v=19+126

v=145

Answer:

3  1/2  pints

Step-by-step explanation:

A pint is two cups

7 cups  /  2cups/pint =   7/2 pint = 3  1/2 pints

Answer:

Step-by-step explanation:

[tex]\frac{19}{x}[/tex] = tan 29°

x = [tex]\frac{19}{tan29^o}[/tex] ≈ 34.28

The restriction of the expression as given in the task content is; x +y = 0.

The expression in the task content is rational;

(1-x-y)/(x+y).

On this note, the restriction to the expression is the values which render the denominator of the expression equal to 0 and consequently the expression value to undefined.

Hence, the restriction is; x+y = 0.

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Answer:

[tex]\sqrt[10]{4}[/tex]

Step-by-step explanation:

Apply power to power rule on the exponents, [tex]\frac{2}{5}*\frac{1}{4} = \frac{1}{10}[/tex] when simplified

[tex]4^\frac{1}{10}[/tex] is also the same as [tex]\sqrt[10]{4}[/tex]

Answer:

[tex]\sqrt[10]{4}[/tex]

Step-by-step explanation:

We know that,

[tex](a^{x} )^y=a^x^y\\\sqrt{x} =x^{\frac{1}{2} } \\x^\frac{1}{y} =\sqrt[y]{x}[/tex]

By following those, let us solve the given expression.

[tex](4^\frac{2}{5} )^\frac{1}{4} \\\\4^\frac{2*1}{5*4} \\\\4^\frac{2}{20} \\\\4^\frac{1}{10}\\\\\sqrt[10]{4}[/tex]

The simplified form of the difference quotient of equation [tex]9x^2+5x-1[/tex] . in the form 9x + 9h + 5.

In question for equation [tex]9x^2+5x-1[/tex], simplified to difference quotient in the form of Ax+Bh+C where A, B, C are integers

equation is the relationship between variable and represented as  [tex]9x^2+5x-1[/tex]  is example of polynomial equation.

We know that,
for difference quotient
[tex]=\frac{f(x+h)-f(x)}{h} \\\frac{9(x+h)^2+5(x+h)-1-9x^2-5x+1}{h}\\\frac{9h^2+9hx+5h}{h}\\9x+9h+5[/tex]
While, compared with Ax+Bh+C
we have A=9, B=9, C=5.

Thus, The required value of difference Quotient in the form Ax+Bh+c where A, B and C is 9, 9 and 5 respectively

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 7+5y=-13 \end{gathered}$}[/tex]

Subtract 7 from both sides.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-13-7 \end{gathered}$}[/tex]

Subtract 7 from −13 to get −20.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-20 \end{gathered}$}[/tex]

Divide both sides by 5.

[tex]\large\displaystyle\text{$\begin{gathered}\sf y=\frac{-20}{5} \end{gathered}$}[/tex]

Divide −20 by 5 to get −4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf y=-4 \end{gathered}$} }\large\displaystyle\text{$\begin{gathered}\sf \ \ \to \ \ \ Answer \end{gathered}$}[/tex]

We let y = -4.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7+5\times-4=-13 \ \ \to \ \ [ Multiply] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7-20 \ \ \to \ \ [Subtract] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-13=-13 \ \ \to \ \ [ Equality \ holds ]} \end{gathered}$}[/tex]

Answer:

5y= -13-7

5y=-20

5y = -20

5 = 5

y = -4

Answer:

Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic.

Answer:

WHAT IS THE LINEAR EQUATION?

          y=2-3x     and y=x/3+2

WHY IS THAT THE LINEAR EQUATION

Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y

WHAT IS THE NONLINEAR EQUATION

Y = x(3x+2)

WHY IS THAT THE LINEAR EQUATION

A nonlinear function has more than one independent variable. The independent variable is x.

y= x(3x-2) is non linear equation.

y= x/3 + 2  is linear equation.

y= 3 -2x  is linear equation.

Linear equations are the equations of degree 1.

It is the equation for the straight line.

The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.

We know that the linear equation have highest degree 1.

First, y= x(3x-2)

y= 3x² -2x

Here, the highest degree is 2 which is non linear equation.

Now, y= x/3 + 2 have highest degree 1 which is linear equation.

and, y= 3 -2x have highest degree 1 which is linear equation.

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Answer:

full list of words from this list

factor anything that contributes causely to a result

multiply the number by which multiplicant is multiplied

multiply the number that is multiplied by a multiplier

project and refer that has been created by someone or some process

Answer: 154 m^3

Step-by-step explanation:

Volume = (5*2*7) + (3*7*4)

             = 70 + 84

             = 154 m^3

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Answer:

154 m^3

Step-by-step explanation:

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Answer:

  not equivalent; signs don't match

Step-by-step explanation:

Apparently, you want to compare the expressions ...

The distributive property allows you to eliminate parentheses by multiplying each term inside parentheses by the factor outside.

When we do that to the first expression, we get ...

  -0.5(3x +5) = (-0.5)(3x) +(-0.5)(5) = -1.5x -2.5

Note that the signs of the terms inside parentheses are the same, and the signs of the terms after removing parentheses are the same. (Both terms have their signs changed by the negative factor multiplying the parentheses.)

The expanded expression -1.5x -2.5 is not equivalent to -1.5x +2.5, which has terms of different signs.

Answer:

-1.

Step-by-step explanation:

1) according to the DeMoivre's theorem:

[tex]1*(cos\frac{ \pi}{6} +isin\frac{ \pi}{6})^{18}=1^{18}(cos(18*\frac{ \pi}{6})+isin(18*\frac{ \pi}{6}))=cos3\pi +isin3\pi =cos\pi +isin\pi ;[/tex]

2) if cos(π)=-1 and sin(π)=0, then cosπ+i*sin(π)=-1.