Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).

1. x-int: (-2,0) , (5,0)
P (3,6)

The slope of the line that passes through (9, 1) and (-8, 2) is -1/17

If we have a linear equation or a segment that passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

In this case, we know that the two points are (9, 1) and (-8, 2), using the above formula we can find the slope to be:

slope = (2 - 1)/(-8 - 9)

slope = 1/-17 = -1/17

That is the slope of the line or segment that passes through the given points.

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Answer:x=10

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

Multiply the numbers

2⋅3x=[12(4x+20)]⋅22⋅3=[12(4+20)]⋅2

6x=[12(4x+20)]⋅26=[12(4+20)]⋅2

Combine multiplied terms into a single fraction

6x=[12(4x+20)]⋅26=[12(4+20)]⋅2

6x=[1(4x+20)2]⋅26=⎣⎡1(4+20)2⎦⎤⋅2

Multiply by 1

6x=[1(4x+20)2]⋅26=⎣⎡1(4+20)2⎦⎤⋅2

6x=[4x+20/2]⋅26=[4+20/2]⋅2

Re-order terms so constants are on the left

6x=4x+20/2⋅26=4+20/2⋅2

6x=2⋅4x+20/2

Cancel multiplied terms that are in the denominator

6x=2⋅4x+20/2

6x=4x+20

Subtract 4x from both sides

6x=4x+20

6−4=4+20−4

Simplify

6x-4x=4x+20-4x

2x=4x+20-4x

Combine like terms

2x=20

Divide both sides by the same factor

2x=20

2x/2=20/2

cancel 2 on both sides

20 divided by 2 is 10

so therefore,

x=10

Answer:

Step-by-step explanation:

Step-by-step explanation:

the highest exponent is 2, so, we expect to get 2 factors in x (as the multiplication of x×x = x²).

3 is a prime number, and the only factors to get 3 are 3 and 1

3 = 3×1

so, we expect to get factors that look like

(3x + a)(x + b)

when we do the multiplication, we get

3x² + 3bx + ax + ab = 3x² +(3b + a)x + ab

now we compare this to our original expression

3x² +(3b + a)x + ab = 3x² - 13x + 12

3b + a = -13

ab = 12

so, we know a and b must both be negative

(-×- = +, - - - = -).

the negative factors of 12 are

-12 × -1

-6 × -2

-4 × -3

which one of these pairs can make

3b + a = -13

be true ?

3×-12 + -1 = -37 no

3×-1 + -12 = -15 no

3×-6 + -2 = -20 no

3×-2 + -6 = -12 no

3×-4 + -3 = -15 no

3×-3 + -4 = -13 yes

so, our factors are

(3x - 4)(x - 3)

The minimum measurement is 12.85 and the maximum measurement is 12.94 that would be equal to 12.9.

What is rounding of decimal numbers?

Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up. The term "rounding decimals" describes the accurate rounding of decimal figures. To the nearest whole, tenth, or hundredth, we can round decimals.

Given, An ostrich egg has a width of 12.9 cm to the nearest tenth of a centimeter.

We have to find the minimum and maximum possible measurements.

If you're rounding to the nearest tenth of a centimeter, 12.85 centimeters is the smallest measurement that would equal 12.9 centimeters.

And 12.94 centimeters is the maximum measurement that would be equal to 12.9.

Therefore, the minimum measurement is 12.85 and the maximum measurement is 12.94.

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The parallel line has an equation of y = 2x + 3

The equation is given as

2y = 4x + 14

Make y the subject

2y = 4x + 14

Divide through by 2

y = 2x + 7

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = 2

This means that the slope of 2y = 4x + 14 is 2

The slopes of parallel lines are equal

This means that the slope of the other line is 2

i.e. m = 2

Recall that:

The equation of a line can be represented as

y = mx + c

Where

slope = m

So, we have

y = 2x + c

Assume any value for c

This gives

y = 2x + 3

Hence, the equation of the parallel line is y = 2x + 3

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Using front end estimation, the solutions to the given problems are;

1) 25.72

2) 137.521

3) 17.1

Front-end estimation is defined as a particular way of rounding numbers to estimate sums and differences.

The procedure for using front- end estimation, is to add or subtract only the numbers in the greatest place value. Thereafter, we add the decimals rounded to the nearest tenth.

1) 32.47 - 6.75

First of all, let's deal with the whole numbers part;

32 - 6 = 26

Next is to deal with the decimal part to get;

0.47 is approximately 0.5 while 0.75 is approximately 0.8. Thus;

0.5 - 0.8 = - 0.3

Thus, we have;

26 + (-0.3) = 25.70

Therefore, our given solution can be written as; 25.72

2) 118.234 + 19.287

First of all, let's deal with the whole numbers part;

118 + 19 = 137

Next is to deal with the decimal part to get;

0.234 is approximately 0.2 while 0.287 is approximately 0.3. Thus;

0.2 + 0.3 =0.5

Thus, we have;

137 + 0.5 = 137.5

Therefore, our given solution can be written as; 137.521

C)  17.9 - 0.8

First of all, let's deal with the whole numbers part;

17 - 0 = 17

Next is to deal with the decimal part to get;

0.9 - 0.8 = 0.1

Thus, we have;

17 + 0.1 = 17.1

Therefore, our given solution can be written as; 17.1

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The volume of the given rectangular box is given by 225 cubic inches.

We know that the volume of the rectangular box with length L and width W and height H is given by,

V = LWH

So given the length of rectangular box is = 12 1/2 inches = 25/2 inches

The width of rectangular box is = 4 1/2 inches = 9/2 inches

The height of box is = 4 inches

So the volume of the rectangular box = (25/2)*(9/2)*4 = 25*9 = 225 cubic inches.

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Answer:

Step-by-step explanation:

A = 75000(1 + (0.06 × 10)) = 120000

A = $120,000.00

B = 24000(1 + (0.07 × 0.75)) = 25260

B = $25,260.00

B=9 months

Answer:

Step-by-step explanation:

[tex]x[/tex] x 25/100=30

25/100[tex]x[/tex]=30

25[tex]x[/tex]=3000

[tex]x[/tex]=300/25

[tex]x[/tex]=120

Answer:

-5/3 or -1.67

Step-by-step explanation:

Answer:

-5/3

Step-by-step explanation:

Oh it's you again, I am just gonna copy paste my format from your previous question.

Use the slope formula: s=(y2-y1)/(x2-x1)

It doesn't matter the order.

Let's say -6 is x2 and 8 is y2; 3 is x1 and -7 is y1

Plug in the equation: s=[(8)-(-7)]/[(-6)-(3)]

Simplify and solve: s=[8+7]/[-9]

                               s = -15/9

                               s = -5/3

The average apple weight's 95% confidence interval is (119.14, 125.86).

According to one manufacturer, an apple weighs 120 grams on average with a 12-gram standard variation. According to statistics generated from a sample of 49 apples randomly selected from a shipment, the average weight per apple was 122. 5 grams.

Let, 

n = 49

x = 122.5 

σ = 12

To figure up and analyze a 95% confidence interval for the average apple weight; 

The formula for a 95% confidence interval is

(x ± 1.96*σ√n) 

(122.5 ± 1.96*12/√49)

(119.14, 125.86)

Consequently, a 95% confidence interval for the average apple weight is (119.14, 125.86).

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Answer: B^5

Step-by-step explanation: truss

Answer:

3√10 units

Step-by-step explanation:

[tex] \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \sqrt{10} = 5 \sqrt{10} [/tex]

[tex]3x + 2x = 5 \sqrt{10} [/tex]

[tex]5x = 5 \sqrt{10} [/tex]

[tex]x = \sqrt{10} [/tex]

So the length of the longer piece is 3√10 units.

Answer:

0.9*0.8=0.72

Step-by-step explanation:

there are 9 squares across the top and 8 square downward so the only equation similar to this is the first equation.

Answer: 0.9 x 0.8 = 0.72

Step-by-step explanation:

dark gray is 9 x 8, divide both numbers by 10, you get 0.9 x 0.8 = 0.72

By first subtraction b and then dividing by m, the solution of the linear equation for x is:

(y - b)/m = x

Here we have a linear equation that defines the variable y in terms of the variable x:

y = m*x + b

Where m and b are real numbers.

Now we want to find x in terms of the variable y, this means that we need to isolate the variable x.

if first we subtract b in both sides, we get:

y - b = m*x + b - b

y - b = m*x

If now we divide both sides by m, we get:

(y - b)/m = m*x/m

(y - b)/m = x

This is the linear equation solved for x.

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Answer:If you’re using imagine math it will be the the third one

Step-by-step explanation:

The range of the given relation is (-6, -3, 0, 3, 6).

Range:

Basically the set contains 2 elements in it, in which set contains all the second elements, on the other hand, is known as the range of the relation.

Given,

Here we have the relation (-5,6), (-3,3), (-1,0), (1,-3) and (3,-6)

Here we need to find the range of the relation.

According to the definition of the relation,

Range refers the y values of the coordinates,

So, based on this the value of the given coordinates are extracted as,

(-5, 6) => 6

(-3, 3) => 3

(-1, 0) => 0

(1, -3) => -3

(3, -6) => -6

Now we have arrange the range values from the smallest to largest,

Therefore, the range of the relation is (-6, -3, 0, 3, 6).

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Translation 1 unit up is the transformation which accomplish the graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Figure C is the result of a transformation on Figure B

We need to find which transformation is used for this.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

and  A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis

Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis.

The graph is just shifted slightly to right.

Figure B undergoes a translation of translation 1 unit up.

Hence translation 1 unit up is the transformation which accomplish the graph.

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Answer: 7 comic books would be left after putting them into groups of 8.

Step-by-step explanation: There will be 326 groups of comic books. 326 x 8 = 2,608 which means that there will be 7 comic books left after putting them all into groups of 8.

Using simple mathematical operations, we know that the lift will carry 1,120 more children than adults in a day.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

parentheses, exponents, multiplication, division, and PEMDAS.

So, to calculate how many more children the lift carries in a day:

The number of adults the lift can carry is 24.

The number of children the lift can carry is 40.

The lift carries people at full capacity 70 times.

Now, calculate as follows:

24 × 70 = 1,680

40 × 70 = 2,800

Difference:

2,800 - 1,680 = 1,120

Therefore, using simple mathematical operations, we know that the lift will carry 1,120 more children than adults in a day.

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Answer:

Step-by-step explanation:

To calculate the p-value, we have to follow the following steps:

To calculate the p-value, we need

p = sample proportion

p' = assumed population proportion in the null hypothesis

n = sample size

Example

Given, n =40, σ = 32.17 and X = 105.37. calculate p-value.

σₓ = σ/ √n

σₓ = 32.17 / √40

    = 5.0865

Now, by applying the test static formula, we get

t = (105.37 – 120) / 5.0865

t = -2.8762

Using the table, we find the value of P(t>-2.8762)

From the table, we get

P (t<-2.8762) = P(t>2.8762) = 0.003

If P(t>-2.8762) = 1- 0.003 = 0.997

P- value = 0.997 > 0.05

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she would have four seeds left because 6 seeds times six pots would equal 36 seeds so subtract 36 from forty to get four

Step-by-step explanation:

Answer:4

Step-by-step explanation:6x6=36+4=40

The cost is the cost per pound times the number of pounds minus the coupon.

If [tex]p[/tex] pounds are purchased, she will pay [tex]3.50p-3.25[/tex].

If 3 pounds are purchased, she will pay 3.50(3)-3.25=7.25.

Answer: x=30 degrees

Step-by-step explanation:

A triangle has 180 degrees, so:

90+x+20+x+10=180

90+2x+30=180

2x+30=90

2x=60

x=30

Answer:

a=5

a=2x-5

Step-by-step explanation:

hope it helps

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The width of the enlarged photo is 12 inches

The length of the original photo = 10 inches

The width of the original photo = 8 inches

The length of the enlarged photo = 15 inches

The width of the enlarged photo = x

Then the proportion of the length and width of the original and enlarged photo will be

10 / 8 = 15 / x

Cross multiply the terms

10x = 15 × 8

Multiply the terms in the equation
10x = 120

Divide both side of the equation by 10

10x / 10 = 120 / 10

x = 120 / 10

Divide the terms

x = 12 inches

Hence, the width of the enlarged photo is 12 inches

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Answer:

9:40

Step-by-step explanation:

Distance = rate x time

Let t = time

40 = 60t  Divide both sides by 60

[tex]\frac{40}{60}[/tex] = t  An hour would be 60 minutes so the number of minutes out of the total would be 40.