Aaron sprints 0. 45 kilometers. If he repeats this 12 times at practice, how many meters will he have sprinted by the end of practice?

Answer:

[tex]g(f(x))=25x^2-15x-7[/tex]

domain: (-∞,∞)

Step-by-step explanation:

g of f means plug the function f(x) in to x in the function g(x)

[tex]g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7[/tex]

since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)

Answer:

y=3x+4

Step-by-step explanation:

The original formula for slope-intercept is y=mx+b.

b is your y-intercept (where the line crosses the y-axis).

m is your slope which is 3/1 or just 3.

The number of visitors to the homepage of an online magazine in the year 2005 is 3527

An equation is an expression that shows the relationship between two or more number and variables.

Let y represent the total number of visitors x years since 2000. Hence:

y = 1100.74x - 1976.47

In the year 2005 (x = 5):

y = 1100.74(5) - 1976.47 = 3527.23

The number of visitors to the homepage of an online magazine in the year 2005 is 3527

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (1.6 \times 10 {}^{5} ) \sdot(2 .3 \times {10}^{1} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: (1.6 \times 2.3) \sdot(10 {}^{5} \times 10 {}^{1} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.68 \times 10 {}^{6} [/tex]

The value of Mario's car after 5 years is $8,249.

Deprecation is when the value of an asset declines with the passage of time as a result of wear and tear.

V = 15,999 − 1,550t

V = 15,999 − 1,550(5)

V = 15,999 - 7,750

V =$8,249

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The required equation based on the information given is y =0.433x + 24.493

It should be noted that one can simply copy and paste the data set into excel sheet

Then, use intercept and the slope formula to find slope and intercept. We will have

slope = SLOPE(y values, x values)

= 0.433

intercept = INTERCEPT(y values, x values)

= 24.493

Therefore, the required equation is y =0.433x + 24.493

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Answer:

a₃₂ = 131

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 7 and d = 4 , then

a₃₂ = 7 + (31 × 4) = 7 + 124 = 131

Answer:

2/3 (0,-3) is one possible answer.

Step-by-step explanation:

y  -1 = 2/3(x-6)  We want to get this into the slope intercept form of a line.  We want it to be in the form y = mx + b.  Let's clear the fraction first by multiplying the whole equation through by 3.

3(y - 1) = 3[2/3(x - 6)]

3y -3 = 2(x -6)

3y - 3 = 2x -12

3y = 2x - 9  Now divide all the way through by 3 to get

y = 2/3x - 3  

y = mx + b.  The m part is the slope.  In this equation the slope is 2/3

There are in infinite amount of points on a line.  I do not know if they give you a picture or if you are just to create your own.  I am going to create a point that have x = 0.  I get to pick the point.  I could pick any number.  0 is just usually really easy.  So, if I substitute 0 for x I will get:

y = 2/3(0) - 3

y = 1  so my point is (0,-3)

Now that I think about it, I do not think that I would start out clearing the fraction even though it works.  I think that I would do it like this"

y - 1 = 2/3(x - 6)  Distribute the 2/3 through (x - 4) to get

y-1 = 2/3x -4  I can make -6 a fraction by putting it over 1.  Now we have 2/3(-6/1)  multiply across to get  -12/3.  A positive times a negative is a negative.  -12 divided by 3 is -4.

y - 1 = 2/3x -4   now add 1 to both sides.

y = 2/3x -3

Answer:

151 19/27 in^3

Step-by-step explanation:

volume of cube is (side length)^3

(5 1/3)^3 = (16/3)^3 = 4096/27 = 151 19/27

Answer:

??

Step-by-step explanation:

Answer:

35%

Step-by-step explanation:

She is saving $0.70/$2.00 weekly.

To convert this into a percentage we covert it to decimal then multiply by 100 :

$0.70/$2.00 = 0.35

0.35 × 100 = 35%

Our final answer is 35%.

Hope this helped and have a good day

Part A

[tex]3x^2 -2x-1+9x+2x^2 -3=\boxed{5x^2 + 7x-4}[/tex]

Part B

[tex](5x^3 +4x^2 - x-3)-(5x^2 + 7x-4)=\boxed{5x^3 - x^2 - 8x+1}[/tex]

Part C

No, because although they provide examples for specific polynomials being closed under addition and subtraction, there is a loss of generality.

Counting numbers from 101 to 200, those with 6 as a digit are 19

Let's start by listing all the number between 101 and 200

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Now, let's count the numbers with 6 as a digit

= 19 numbers has 6 as a digit

Thus, counting numbers from 101 to 200, those with 6 as a digit are 19

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its the first one

a system can only be a function if there is only one value of y for each value of x. there cannot be two or more values of y for one single value of x in a function.

Answer:

x is 14

1st is 14

2nd is 20

Step-by-step explanation:

4/7 (x ) = (34 - x )(2/5)

4x/7 + 2x/5 = 34 x 2/5 = 68/5

34x/35 = 68/5

x = 14

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Answer:

the red curve is a hyperbola

Answer:

as x is approaching positive infinity, y approaches positive infinity

as x is approaching negative infinity, y is approaching negative infinity

If the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is: D. random.

A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly flipped or tossed by anybody.

This ultimately implies that, the outcome of flipping a fair coin is generally going to produce only one of two results and these include the following:

In this context, we can infer and logically conclude that if the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is considered as being random.

In conclusion, it is important to note that a fair coin is considered as being random when the distribution of heads and tails of a fair coin is very regular in a large number of flips.

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The completion of the tabs are:

You may calculate how many percentage points your findings will deviate from the actual population figure by using something called a margin of error.

In conclusion

In conclusion,

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The correct order to express cos3x in terms of cosx is; As shown in steps 1 to 9 below.

The steps to simplify the trigonometric identities cos 3x in terms of cos x are as follows;

Step 1; cos x = cos(2x + x)

Step 2; cos(2x) cosx - sin(2x) sinx

Step 3; 1 - 2sin^2x(cosx) -(2sinxcosx)sinx

Step 4; cosx - 2sin²x cosx - 2sin²x cosx

Step 5; cosx - 4sin²x cosx

Step 6; cosx( 1 - 4sin²x)

Step 7; cosx{1 - 4(1 - cos²x)}

Step 8; cosx{-3 + 4cos²x}

Step 9; 4cos³x - 3cosx

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The length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.

The area of a figure is the total space enclosed in two dimensions within its boundary.

The area of a rectangle is given as, area = length*width.

In the question, we are given that the area of a rectangle is represented by 25x³y⁶ and its width is represented by 10xy, and are asked to express the length of this rectangle in terms of x and y.

We know that the area of a rectangle is given as, area = length*width.

Substituting the known values in the equation, we get:

25x³y⁶ = length*10xy.

Rearranging this equation, we get:

length = 25x³y⁶/10xy = (5x²y⁵)/2 = 2.5x²y⁵.

Thus, the length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.

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Answer:

Step-by-step explanation:

The given relation can be used with the formula for the area of a triangle to give an equation for the altitude or base.

Let b represent the length of the base. Then the altitude (height) is (b+4). The area formula tells us the area is ...

  A = 1/2bh

Using given values, the equation becomes ...

  96 = 1/2b(b +4)

Simplifying the equation and multiplying by 2, we have ...

  192 = b² +4b

Adding (4/2)² = 4 will complete the square.

  196 = b² +4b +4 = (b +2)²

Taking the square root gives ...

  14 = b +2 . . . . . . we are not interested in the negative root

  12 = b . . . . . . . . subtract 2

  16 = b+4 . . . . . find the altitude

The base is 12 cm; the altitude is 16 cm.

Answer:

$0.45.

Step-by-step explanation:

Total amount of money held by all 5 children

= 5 * 0.50 = $2.50.

After 0.25 is lost the total = $2.25.

So the new average = 2.25 / 5

= $0.45.

Answer:

x² - 5x + 17 = [tex](2x)^{3x}[/tex]

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{2x}[/tex] (x² - 5x + 17) = 3x , then

x² - 5x + 17 = [tex](2x)^{3x}[/tex]

Simplification of the expression gives 2a + c = -24

4+4-3-4-2-5-1-8-9-0=a +c + a

First, let's add

[tex]8 -3 -4-2-5-1-8-9-0 = a+ c + a[/tex]

Then, let's substract

[tex]-24 = a + c + a[/tex]

[tex]-24 = 2a + c[/tex]

We then have,

[tex]2a + c = -24[/tex]

Thus, simplification of the expression gives 2a + c = -24

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The figure which is like a long oval can be decomposed to two semicircles and a rectangle so as to find the area.

Given a long oval and two lines are drawn where the sides are straight to form right angles.

We are required to find the way how we can decompose the composite figure to determine its area.

Area means the amount of space occupied by a two dimensional shape or object. The area of a figure can be decomposed to smaller figures so as to find the area.

The composed figure can be decomposed to two semicircles and a rectangle so as to find the area.

Hence the composite figure can be decomposed to two semicircles and a rectangle so as to find the area.

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Answer:

a

Step-by-step explanation:

The answers to the quadrilateral are ONM, NOM, and alternate interior angles.

Based on the SSS postulate, the two triangles △MLO and △ONM are congruent since three sides of △MLO are respectively equal to the three sides of △ONM.

Based on CPCTC, all of the corresponding angles of △MLO and △ONM are congruent as well since the two triangles are congruent, that is,  

∠LMO≅∠NOM and ∠NMO≅∠LOM.

Since the pair ∠LMO and ∠NOM as well as ∠NMO and ∠LOM are angles on the inner side of two lines but on opposite sides of the transversal MO, these pairs of angles are also alternate interior angles.

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Answer:    ONM

                 NOM

                alternate interior angles

Step-by-step explanation:  Complete the paragraph proof.

We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △

✔ ONM

. By CPCTC, ∠LMO ≅ ∠

✔ NOM

and ∠NMO ≅ ∠LOM. Both pairs of angles are also

✔ alternate interior angles

, based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.

By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.

An even number can be defined as a type of number which is divisible by two (2) without any remainder.

Since this 2-digit numbers are even and its digits are distinct, we can infer and logically deduce the following points:

By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.

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Using percentage of its total accounts the $50,000 is the amount to be uncollectible. The amount of $50,000 will be reported as an allowance for uncollectible accounts for the Year 2 on December 31 in the balance sheet.

According to the question,

Under the approach of the balance sheet, the ending balance of the allowance for the uncollectible accounts is the percentage (%) of the ending balance of the accounts receivable.

The amount of uncollectible accounts should reflect the aggregate needed ending balance of the allowance which amounts to $50,000.

Hence, using percentage of its total accounts the $50,000 is the amount to be uncollectible.

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