Find the y-coordinate of the y-intercept of the polynomial function defined
below.

f(x) = 2(2x - 3) (5x + 5)

The equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

According to the question,

We have the following information:

y = 3x-1 and the point through which line is passing is (3,2)

We know that the slope of the given line (denoted by m) is 3.

Now, the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x')

In this case, we have x' = 3 and y' = 2.

y-2 = 3(x-3)

y-2 = 3x-9

Moving 2 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

y = 3x-9+2

y = 3x-7

Hence, the equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

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The materials travel faster on Belt One, considering the constants of the proportional relationships.

A proportional relationship is a linear function with intercept zero in which the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, according to the equation presented as follows:

y = kx

For each belt in this problem, the constant gives the velocity that the materials travel.

For Belt One, the relation is:

y = 157.1x.

Hence the velocity is of 157.1 inches per minute.

For Belt Two, the velocity is obtained as follows:

k = 125.6/2 = 62.8 inches per minute.

157.1 > 62.8, hence it travels faster on Belt One.

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The Linear inequality holds true for 21 ≥ x;

What is Linear Inequality?

The mathematical expression with unequal sides is known as inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to a symbol (), less than or equal to a symbol (), or not equal to a symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics. The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities.

In the given question, the given inequality given is:

-3(2x-11) ≥ 8x-9;

Solving the Inequality:

⇒-6x + 33 ≥ 8x - 9;

⇒33 + 9 ≥ 8x - 6x;

⇒ 42 ≥ 2x;

⇒ 21 ≥ x;

Hence,

The Linear inequality holds true for 21 ≥ x;

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The value of the function f(x) at x = -2 is ,  f(-2) = 1 , the correct option is (c) .

Function is defined as an expression that defines a relationship between one variable and another variable .

In the question ,

it is given that ,

the value of the function f(x) at different values of x is given ,

we have to find the value of the f(-2) , that is the value of the function f(x) at x = -2 .

from the table , we see that when x [tex]=[/tex] -2 , the value of f(x) is [tex]=[/tex] 1 ,

that means f(-2) [tex]=[/tex] 1 .

Therefore , The value of the function f(x) at x = -2 is ,  f(-2) = 1 , the correct option is (c) .

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Answer:

[tex] \huge{ \bold{ \orange{ - \frac{4}{3} }}}[/tex]

Step-by-step explanation:

The slope of a line passing through two points can be found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} \\ [/tex]

where

(x1, y1) and (x2, y2) are the points

From the question

The points are (4, 8) and (7, 4)

We have

[tex]m = \frac{4 - 8}{7 - 4} = - \frac{4}{3} \\ [/tex]

We have the final answer as

[tex] \bold{ - \frac{4}{3} }[/tex]

Hope this helps you

Answer: 15 cm

Step-by-step explanation:

just divide 60 by 4 and because a squar has 4 sides and that is it

The value of the angles that are intersected by BC are m/ABC is 35° and m/DBC is 43°

In the given figure the angle ∠ABD is intersected by the straight line BC such that two new angles are formed ,∠ABC and ∠ADC  .

Now from the properties of angles on a 2-dimensional plane we can see that :

m ∠ABC + m ∠ADC  = m ∠ABD

The values of the angles given are:

m ∠ABC = 5x - 5

m ∠ADC = 5x + 3

m ∠ABD = 78°

now we put these above values in the equation:

(5x - 5) + (5x + 3) = 78

or, 10 x - 2 = 78

or, 10 x = 80

or , x = 8

m ∠ABC = 5×8 - 5 = 35°

m ∠ADC = 5×8 + 3 = 43°

The value of the angles that are intersected by BC are m/ABC is 35° and m/DBC is 43° .

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The z-score for this amount of advertising time is z = -4.17 so option B is correct.

Given:

Average = 13 minutes

Standard deviation = 1.2 minutes.

Advertising time x = 8 minutes.

z = x - mean / standard deviation.

= 8 - 13/1.2

= -5/1.2

= -5/12/10

= -50/12

= -4.17.

Therefore the z-score for this amount of advertising time is z = -4.17 so option B is correct.

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The y-intercept is y = 3, and this is the initial height of the ball, and the maximum height is y = 19

The y-intercept is what we get when we evaluate in x = 0, then:

y = -0.25*x² + 4x + 3

replacing x by zero we get:

y = -0.25*0² + 4*0 + 3 = 3

The y-intercept is y = 3.

The maximum height is at the vertex, we know this because the leading coefficient is negative, which means that the parabola opens down.

The vertex is at:

x = -4/(2*-0.25) = 8

Evaluating there:

y = -0.25*8² + 4*8 + 3 = 19

that is the maximum height.

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Answer: x>-1

Step-by-step explanation:i just did that question

Answer:

Step-by-step explanation:

add 4 to -15 then divide that  by 11x the answer should be x=-1.

The sides and angles of the right triangle are as follows:

A right tangle triangle is a triangle that has on e of its angles as 90 degrees. The sides of a right triangle can be named based on the position of the angles.

The sides includes opposite side, adjacent side and hypotenuse side. The longest side of a right angle triangle is the hypotenuse side.

The sides of the right angle triangle can be found using trigonometric ratios as follows:

sin 85 = opposite / hypotenuse

sin 85 = a / 8

a = 8 sin 85

a = 7.96955758473

a = 8.0

cos 85 = adjacent / hypotenuse

cos 85 = b / 8

b = 8 cos 85

b = 0.69724594198

b = 0.7 units

Angle B = 180 - 90 - 85 = 5 degrees.

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The measure of <FEG= 61 and <HEG = 119.

The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.

when two lines in a plane intersect, one of the angles that are directly across from one another.

Given:

m< DEF= 119

Now, <DEF + <FEG= 180 (Linear Pair)

119+ <FEG = 180

<FEG = 180- 119

<FEG = 61

and, <DEF= <HEG = 119  (Vertical opposite angle)

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There are 15 crates and 35 boxes in the van when it is completely full.

Given,

Total number of crates and boxes=50

For every 7 crates the van can hold, there is room of 3 boxes.

let,

Number of crates =x

Number of boxes =y

As given,

Equation for total number of crates and boxes can be written as

[tex]x+y=50....i[/tex]

Space for 7 crates is equal to space for 3 boxes in van, it's equation can be written as

[tex]7x=3y\\\\x=\frac{3y}{7}[/tex].

Substituting 'x' in eq.[tex]i[/tex]

[tex]\frac{3y}{7}+y=50\\\\ \frac{3y+7y}{7}=50 \\\\10y=7*50\\\\10y=350\\\\y=\frac{350}{10}\\ \\y=35[/tex]

Substituting 'y' in eq.[tex]i[/tex]

[tex]x+35=50\\\\x=50-35\\\\x=15[/tex]

Thus, there are 15 crates and 35 boxes in the van when it is completely full.

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Answer:

27/256

Step-by-step explanation:

=(27)(1/4)(1)/(64)

=27/256

Answer: -1.631

Step-by-step explanation:

[tex]\log_{3} \frac{a}{3}=\log_{3} a-\log_{3} 3=-0.631-1=-1.631[/tex]

Answer:  Tommys dispacement 17 miles

Step-by-step explanation:

pyhagorean theorem

he went 15 up (leg 1)

and then right 8 (leg 2)

and Tommy's displacement is the hypotenuse

15^2+8^2=c^2

c^2 = 289

c = 17

Answer:

Step-by-step explanation:

Answer: 500 + 30 + 1 + 0.2 + 0.04 + 0.006

Answer:

Step-by-step explanation:

we cant see the problem or there answers

The additional number of days that is required to complete the rest of the work in mixed fraction is equal to 4 4/11 days.

First of all, we would determine the number of work left for Ann after two (2) working days:

In one (1) day, the amount of work that would be done by Ann alone is given by 1/10 days. Therefore, the amount of work that would be done by Ann alone in two (2) days is given by 2/10 or 1/5 days.

For the number of work left, we have:

Work left = 1 - 1/5

Work left = 4/5 days.

Similarly, the amount of work that would be done by Ben alone in one (1) day is given by 1/12 days.

Therefore, the combined work rate of both Ann and Ben is given by:

Combined work rate = 4/5 + 1/12

Combined work rate = 11/60

For the additional number of days required to complete the rest of the work, we have:

Additional days = 4/5 ÷ 11/60

Additional days = 4/5 × 60/11

Additional days = 4 × 12/11

Additional days = 48/11

Additional days = 4 4/11 days.

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The pressure at an altitude of 5000 m if The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases by about 11.5% is  58.08 kPa.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

The atmospheric pressure, P = 101 kPa,

For every 1000 meters, the pressure decreases by 11.5%,

So at the height of 5000 meter, the % decrease will be 5 × 11.5 = 57.5%,

Now let the 57.5% of 101 kPa be x then,

x = 57.5/100 × 101  kPa,

x = 58.08 kPa,

Therefore, the pressure at an altitude of 5000 m if The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases by about 11.5% is  58.08 kPa.

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If  each week it grow by 4% more than it did the previous week by  it grow in 9 week is  17.67cm.

Now let find the growth in 9 week

Growth in 9 week = 1.67cm × [( 1+ 0.04)^9 -1] ÷ [(1+0.04)-1]

Growth in 9 week = 1.67cm × [( 1.04)^9 -1] ÷ (1.04)-1]

Growth in 9 week = 1.67cm ×  [( 1.4233 -1) ÷ 0.04

Growth in 9 week = 1.67cm ×  [0.4233 ÷  0.04

Growth in 9 week = 1.67cm × 10.5825

Growth in 9 week = 17.67cm

Therefore 17.67cm is the 9 week growth.

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256 805 - 136.667 ≈ 256 668.333

The difference is approximately 256 668.333

The equation for the nth term of the arithmetic sequences are:

a_n = -11 + 4n and a_n = -10 + 2n where n is an positive integer.

What is the arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

The formula of nth term of an arithmetic sequence is a_n = a + (n-1) d

The arithmetic sequence is -7, -3, 1, ....

The first term is a = -7.

The common difference is d = (-3)-(-7) = 1 - (-3) = 4.

The nth term of an arithmetic sequence is

a_n = -7 + (n-1) 4

a_n = -7 + 4n -4

a_n = -11 + 4n

The arithmetic sequence is -8, -6, -4, ....

The first term is a = -8.

The common difference is d = (-6)-(-8) = -4 - (-6) = 2.

The nth term of an arithmetic sequence is

a_n = -8 + (n-1) 2

a_n = -8 + 2n - 2

a_n = -10 + 2n

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Answer: _______________________________

72

The earnings per hour be after working for 15 years is $11.4.

From the given table (2, 6.85), (4, 7.55), (6, 8.25).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)

1) Now, put (x1, y1)=(2, 6.85) and (x2, y2)=(4, 7.55) in slope formula, we get

m=(7.55-6.85)/(4-2)

= 0.7/2

= 0.35

Substitute m=0.35 and (x, y)=(2, 6.85) in y=mx+c, we get

6.85=0.35(2)+c

⇒ 6.85=0.7+c

⇒ c=6.85-0.7

⇒ c=6.15

Now, equation is y=0.35x+6.15

2). Put x=15 in the obtained equation, we get

y=0.35×15+6.15

⇒y=$11.4

3). Put y=9.65 in the obtained equation, we get

9.65=0.35x+6.15

⇒0.35x=9.65-6.15

⇒0.35x=3.5

⇒x=3.5/0.35

⇒x=10 years

Therefore, the earnings per hour be after working for 15 years is $11.4.

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Answer:

81 degrees

This is an acute angle since it’s less then 90 degrees

Step-by-step explanation:

All three angles of a triangle always equal 180 degrees

180-(78+31)

180-109

81 degrees

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Answer:

Red paint  = 12.5 gallons

Blue paint = 7.5 gallons

Step-by-step explanation:

The given ratio of red paint to blue paint is:

Let x be the number of gallons of purple paint.

Therefore, the expression for each color of paint needed per x gallons of purple paint is:

[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8}x$}[/tex]

[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}x$}[/tex]

To calculate the number of gallons of red and blue paint needed to make 20 gallons of purple paint, substitute x = 20 into the found expressions:

[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8} \times 20=\dfrac{100}{8}=12.5$}[/tex]

[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}\times 20=\dfrac{60}{8}=7.5$}[/tex]

Therefore, the number of gallons of paint that should be used are: