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Answer: y - 2 = 2(x + 7)

Step-by-step explanation:

        Point-slope form is written as y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) where m is the slope and ( [tex]x_{1}[/tex], [tex]y_{1}[/tex]) are points on the line.

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

y - 2 = 2(x + 7)

Answer:

10 x 12 x 9 cm^2

= 1080 cm^2

Answer:

105

Step-by-step explanation:

a = 1/2(bh) + 1/2(bh)

a = 1/2(12)(10) + 1/2 (9)(10)

a= 1/2 (120) + 1/2(90)

a = 60 + 45

a = 105

Answer:

10000/p.

Step-by-step explanation:

r = pq/100

pq = 100r

q = 100r/p

As a percentage of r:

we have P = q * 100/r

P = 100r/p * 100/r

   = 10,000r / rp

   = 10000/p

Answer:

-1

Step-by-step explanation:

read warriors

by eren hunter.

Answer:

x=11

Step-by-step explanation:

let number =x

(8+3x)=41

group like terms

3x=41-8

3x=33

divide both side by the coefficient of x

3x/3=33/3

x=11

students voted= 195

Solution :

a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.

Jessica = 65 student

Sierra =  2 (Sixty-five students voted for Jessica.) = 2(65) = 130

Total number of students = NO of students voted for Jessica +NO of students voted for  Sierra

= 65+130

= 195

students voted= 195

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The value of the given equation the value of x : (3 , -10)

Definitions: A quadratic equation is a second-order polynomial equation in some kind of a single variable x ax2+bx+c=0. Because it is a second-order polynomial problem, the fundamental theorem of fundamental algebra guarantees therefore it has at least one solution.

the student haven't solved the equation properly he has not expanded the equation:

According to the given data:

The given equation is f(x) = (x - 3)² - 10

(x - 3)² - 10 = 0

this could be expand and write as:

x² + 9 -6x - 10 = 0

x² -6x -1 = 0

The vertex of an up-down facing parabola of the form y=ax^2+bx+c is Xv.

The parabola params are:

a=1, b=-6, c=-1

[tex]\:x_v=-\frac{b}{2a}[/tex]

[tex]x_v=-\frac{(-6)}{2 \cdot 1}[/tex]

Xv = 3

Putting x = 3 to get the value of y

we get:

y = -10

(3 , -10)

The value of the given equation the value of x : (3 , -10)

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Answer:

The highway is 21 km long.

Step-by-step explanation:

[tex]\frac{1 billboard}{1.5 km} =\frac{14 billboard}{x}[/tex]

x = 21 km

Answer:

x = 22.5

2x = 45

5x = 112.5

Step-by-step explanation:

The sum of all internal angles in a triangle is 180 degrees. This can be expressed as the following:

x + 5x + 2x = 180

Combine the like terms:

8x = 180

Divide both sides by 8 to find the value of x:

x = 180/8

Simplify:

x = 22.5

Multiply by 2 to get 2x:

2x = 22.5 * 2

2x = 45

Multiply by 5 to get 5x:

5x  = 22.5 * 5

5x = 112.5

Verify the answer is correct by taking all the obtained values and ensuring they sum to 180:

22.5 + 45 + 112.5 = 180

Dylan needs $ 21.45 for the purchase of both books and the magazine.

Addition refers to the basic operation of mathematics where we find the sum of two or moe numbers.

We are given that:

Dylan wants to buy two things:

1. she wants to buy a book for $ 16.95

2. she wants to buy a magazine for $ 4.50

So, the total money that she needs will be calculated by adding the prices of both the products.

So, by using addition, we get the total money required by Dylan as:

Total money = $ 16.95 + $ 4.50

Total money = $ 21.45

Therefore, we get that, Dylan needs $ 21.45 for the purchase of both books and the magazine.

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Answer:

the second piece of rope

Step-by-step explanation:

2.63 ≥ 2.5

2.085≤2.5

Answer:

a. -5; b. 4; c. -2.

Step-by-step explanation:

a) f(-3)=3*(-3)+4=-5;

b) f(3)=2*3-2=4;

c) f(0)=2*0-2=-2.

The cost of 94 training sessions is $1681.3.

62 training sessions for $1109

1 session = 1109/62

94 sessions = (1109/62) * 94

= $1681 .3

The cost of 94 training sessions is $1681.3.

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Answer:

54fhuuyfghhhrfbifgifd

Answer:

98

Step-by-step explanation:

The algebraic expression from the given statement is (a+b)/ab.

Given the statement is the quotient of the sum of a and b and the product of a and b.

In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.

In the given statement the sum of a and b means a+b.

And the product of a and b means ab.

Now, as it is given in the statement that the quotient of the sum of a and b and the product of a and b can be written as

(a+b)/ab.

Hence, the algebraic expression from the given statement "the quotient of the sum of a and b and the product of a and b" is (a+b)/ab.

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The value of the composite functions, (h ° f)(1) = 0.5.

Given the function, (h ° f)(1), this means h(f(1)) as a composition of functions.

Using the table given for the function, f(x), f(1) = -1.

This means that, to find (h ° f)(1) = h(f(1)), we would find the value of h(x) in the table where x = -1.

Thus, from the table for h(x), when x = -1, h(-1) = 0.5.

Therefore, the value of the composite functions, (h ° f)(1) = 0.5.

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Applying the definition of bisection, PR = RQ = 28.5 cm.

When a line segment bisects another line segment, it divides the line into two equal segments. This means the two resultant line segments formed have the same length.

The image below shows the bisection of segment PQ by segment ST at point R, which forms two equal segments, PR and RQ.

This means that the length of segments PR and RQ will be equal to each other.

Given that, PQ = 57 centimeters, therefore:

PR = RQ = 1/2(PQ)

PR = RQ = 1/2(57)

PR = RQ = 28.5 cm

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The speed and the course of the aircraft  is 27465 km/h.

A machine or vehicle can fly by obtaining support from the air, and this is how an airplane works. It uses either static lift, dynamic lift provided by an airfoil, or, in certain rare situations, the downward thrust from jet engines to counteract the pull of gravity.

From the figure, let us use cosine formula to calculate the resultant displacement.

B^2 = C^2 + A^2 - 2(A)(C) cosØ

Where C = 580km

A = 360 km

Ø = 153 degree

Substitute all the parameters into the formula

B^2 = 580^2 + 360^2 - 2(360)(580)cos153

B^2 = 466000 - ( - 372084.32 )

B^2 = 466000 + 372084.32

B^2 = 838084.32

Square root both sides

B = 915.5 km

You are told to use a scale of 1 cm to 50 km.

Therefore, B = 915.5/50 = 18.3 cm

The time given are: 09:23 and 09:25.

The time difference = 25 - 23 = 2 minute

Convert minutes to hours

2 minute = 2/60 = 1/30 hours

Speed = distance/time

Speed = 915.5 ÷ 1/30

Speed = 915.5 × 30

Speed = 27465 km/h

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Answer:

x=3 and y=

Step-by-step explanation:

Answer:

x=5 and y any number

Step-by-step explanation:

Based on the fact that m represents the number of months and w is the total number of spelling words, the equation that represents the relationship between m and w is w = 8m + 3

The first thing to find is the slope of the relationship. This can be found as:

= ( 51 - 43) / (6 - 5)

= 8 / 1

= 8

The y-intercept is:

w = 8m + c

43 = 8(5) + c

c = 43 - 40

c = 3

The equation to represent the relationship between m and w is:

w = 8m + 3

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Answer:

                  Equation: Y'=33.67+0.54*X'

Step-by-step explanation:

Given that

General regression line equation is:

Y'=a+b*X'

Therefore, the slope of the regression line is equal to the linear correlation coefficient times the difference between the standard deviations of y' and x'.

[tex]b = r\times\frac{S_y}{S_x}[/tex]

[tex]b = 0.5\times\frac{2.7}{2.5}[/tex]

b = 0.54

The mean of the lowered by the slope and mean of x is the intercept with axis y.

[tex]a = y'-b\times x'[/tex]

[tex]a = 68.5-0.54\times 64.5[/tex]

[tex]a = 33.67[/tex]

Now, putting the values of a and b in regression equation

So, we get

                  Y'=a+b*X'

Equation: Y'=33.67+0.54*X'

Answer:

                  Equation: Y'=33.67+0.54*X'

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Answer:

[tex]y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|}\cline{1-2} \phantom{\dfrac{1}{1}} x & y \\\cline{1-2} \phantom{\dfrac{1}{1}} -1 & 7 \\\cline{1-2} \phantom{\dfrac{1}{1}} 0 & \frac{7}{3}\\\cline{1-2} \phantom{\dfrac{1}{1}} 1 & \frac{7}{9}\\\cline{1-2} \phantom{\dfrac{1}{1}} 2 & \frac{7}{27}\\\cline{1-2} \phantom{\dfrac{1}{1}} 3 & \frac{7}{81}\\\cline{1-2}\end{array}[/tex]

Work out the first differences between the y-values:

[tex]7 \underset{-\frac{14}{3}}{\longrightarrow} \dfrac{7}{3} \underset{-\frac{14}{9}}{\longrightarrow} \dfrac{7}{9} \underset{-\frac{14}{27}}{\longrightarrow} \dfrac{7}{27} \underset{-\frac{14}{81}}{\longrightarrow} \dfrac{7}{81}[/tex]

As the first differences are not the same, it is not a linear function.

Work out the second differences:

[tex]-\dfrac{14}{3} \underset{+\frac{28}{9}}{\longrightarrow} -\dfrac{14}{9} \underset{+\frac{28}{27}}{\longrightarrow} -\dfrac{14}{27} \underset{+\frac{28}{81}}{\longrightarrow} -\dfrac{14}{81}[/tex]

As the second differences are not the same, it is not a quadratic function.

Work out if the second differences have a common ratio:

[tex]\implies \sf \dfrac{28}{27} \div \dfrac{28}{9}=\dfrac{1}{3}[/tex]

[tex]\implies \sf \dfrac{28}{81} \div \dfrac{28}{27}=\dfrac{1}{3}[/tex]

As the second differences have a common ratio of ¹/₃, the function is exponential with base ¹/₃.

General form of an exponential function:

[tex]y=a(b)^x[/tex]

where:

The y-intercept is the value of y when x = 0.

From inspection of the table, the y-intercept is ⁷/₃.

Therefore:

  [tex]a = \dfrac{7}{3}[/tex]

  [tex]b = \dfrac{1}{3}[/tex]

Substitute the found values of a and b into the formula to create an exponential function that models the given data:

[tex]\implies y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]

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Answer:

1215

Step-by-step explanation:

You have to multiply the smallest number with the largest number; then add the zero along with the numbers being multiplied; then add each number until you get the right answer

The interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).

We are given an expression that:

82 is less than a which is at least - 82.

This expression can also be written as:

- 82 < a and a > 82

where a is any variable that can take any value according to the expression.

This can also be written as:

- 82 < a < 82

In interval form, it will be written as:

( -82, 82)

"()" brackets are used as -82 and 82 are not included in the interval.

Therefore, we get that, the interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).

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Answer:

C. two-thirds raised to the fourteenth

Step-by-step explanation:

The final answer is -9, -30.75, -13

What is Quotient?

The number resulting from the division of one number by another.

In the given statement is:

What is the quotient for 81/-9

If we divide 81 by -9

The Quotient will be -9

And, come to the next :

-123 divide by -4

The quotient will be -30.75

And, 65 divided by (-5)

The Quotient will be -13

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By finding square numbers, we will get:

8 < √80 < 9

And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95

We want to approximate √80, now we need to find two consecutive square numbers such that one is smaller and the other is larger than 80.

We know that:

9*9 = 81

8*8 = 64

Then:

√81 = 9

√64 = 8

So we can see that:

√64 < √80 < √81

Then:

8 < √80 < 9

And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95

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