please help asap!! Show work 2 and 3

Answer:

-0.04 = decrease of 4%

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]

Given interval:

Therefore:

Given values:

Substitute the values into the formula:

[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(1940)-f(1920)}{1940-1920}\\\\&=\dfrac{45.3-46.1}{1940-1920}\\\\&=\dfrac{-0.8}{20}\\\\&=-0.04\end{aligned}[/tex]

Therefore, the average rate of change was -0.04 which is a decrease of 4%.

The equation of the line that represents the graph will be y = - 1.6x + 3.4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

From the graph, the two points are (-1, 5) and (4, -3). Then the equation of the line is given as,

(y - 5) = [(- 3 - 5) / (4 + 1)](x + 1)

y - 5 = - 1.6(x + 1)

y = - 1.6x - 1.6 + 5

y = - 1.6x + 3.4

The equation of the line that represents the graph will be y = - 1.6x + 3.4.

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Answer:

reciprocal

Step-by-step explanation:

Reciprocal just means to turn it upside down.

The surface area of the given cuboid excluding the bases is; 28 square units

The formula for surface area of a cuboid is;

SA = 2lw + 2lh + 2hw.

We are given;

Length; l = 2 in

Width; w = 1.5 in

Height; h = 4 in

Now, since we are to exclude the bases, it means that;

SA = 2(lh + hw)

= 2((2 * 4) + (4*1.5))

= 2 * 14

= 28 square units

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Using the concept of proportion and substitution with the total money to be divided given, The answer is Carl gets $480, Stacy gets $720, and Peter gets $240.

Proportion refers to the relationship between two or more quantities or values, often represented as a ratio or fraction. It can also refer to the relative size or scale of something in relation to something else. In mathematics, a proportion is an equation that states that two ratios are equal. For example, "the ratio of apples to oranges is 2:3" can be written as the proportion "2/3 = x/y," where x and y represent the number of apples and oranges. In statistics, a proportion is a measure of the frequency with which an event occurs, often expressed as a decimal or percentage.

The substitution method is a technique used to solve systems of equations, which are sets of two or more equations containing multiple variables. The basic idea behind the substitution method is to solve for one variable in terms of the others in one equation, and then substitute that expression into the other equations. This can be done by isolating one variable by adding or subtracting other variables from both sides of the equation, and then using the resulting equation to express that variable as a function of the others. Once one variable is expressed in this way, it can be substituted into the other equations, allowing us to solve for the other variables.

S = 3P (Stacy gets three times as much as Peter)

P = C/2 (Peter gets half the amount that Carl gets)

C + S + P = 1200

We can substitute the first equation into the second one to get:

S = 3(C/2)

Now we can substitute the second equation into the first one to get:

C + 3(C/2) + C/2 = 1200

We can simplify this equation by multiplying out the 3(C/2) term and combining like terms to get:

5C/2 = 1200

Now we can solve for C by multiplying both sides by 2/5:

C = 480

Now that we know C = $480, we can use the earlier equations to find S and P:

S = 3P = 3(480/2) = $720

P = C/2 = 480/2 = $240

So Carl gets $480, Stacy gets $720, and Peter gets $240.

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The  company´s revenue function can be written as 0.36x ² + 815.04x + 11,340.

It was recorded that the demand d for a company's product at cost x is predicted by the function d(x)=0.36x + 810.

We also told that  price p that the company can charge for the product is given by p(x) = x+14.

The Revenue can be computed as [ price × quantity]

where p(x) = x+14

And d(x) = 0.36x + 810

Then if we inpued to the formula , we have

=[ (x + 14) * (0.36x + 810)]

then if we open the bracket we have:

0.36x² + 810x + 5.04x + 11,340

Then we can make some simplification as:

= 0.36x ² + 815.04x + 11,340

Therefore, the Company's revenue  wilol be  0.36x ² + 815.04x + 11,340

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Answer:

--------------------------------

Initial area is 2400 km².

Decrease rate is 8.5% per year.

The area after 8 years will be:

The area of the forest after 8 years will be 1,179 km².

The forest decreases exponentially each year. Each year, the forest would decline by 8.5% each year.

The exponential equation that would be used to determine the area of the forest in 8 years is:

Area of the forest = initial area x (1 - percent decrease/100)^number of years

Area of the forest = 2,400 x (1 - 8.5%/100)^8

Area of the forest = 2,400 x (91.5/100)^8

Area of the forest = 2,400 x 0.915^8

Area of the forest = 1,179 km²

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Answer: If you're on the test, the answer should be B

Step-by-step explanation:

Answer:

[tex]\left(\frac{\pi}{4}, 0 \right), \left(\frac{3\pi}{4}, 0 \right), \left(\frac{5\pi}{4}, 0 \right), \left(\frac{7\pi}{4}, 0 \right)[/tex]

Step-by-step explanation:

The [tex]x[/tex]-intercepts are when [tex]y=0[/tex].

[tex]0 \leq x \leq 2\pi \implies 0 \leq 2x \leq 4\pi \\ \\ \cos 2x=0 \implies 2x=\frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2} \\ \\ \implies x=\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} \\ \\ \therefore \left(\frac{\pi}{4}, 0 \right), \left(\frac{3\pi}{4}, 0 \right), \left(\frac{5\pi}{4}, 0 \right), \left(\frac{7\pi}{4}, 0 \right)[/tex]

The sum of the sequence ∑₀⁵⁰⁰(2i - 312) is 94500

The sum of a sequence is the sum of terms of the sequence.

Given the sum ∑₀⁵⁰⁰(2i - 312).

To evaluate the sum, we expand the brackets.

So, we have that

∑₀⁵⁰⁰(2i - 312) = ∑₀⁵⁰⁰2i -  ∑₀⁵⁰⁰312

= 2∑₀⁵⁰⁰i -  ∑₀⁵⁰⁰312

Now, ∑₀⁵⁰⁰i is the sum of natural numbers

So, ∑₀⁵⁰⁰i = n(n + 1)/2 where n = 500

Also, ∑₀⁵⁰⁰312 = 312n where n = 500

Thus substituting these into the equation for the sum, we have that

∑₀⁵⁰⁰(2i - 312) = 2∑₀⁵⁰⁰i -  ∑₀⁵⁰⁰312

= 2n(n + 1)/2 - 312n

Given that n = 500, substituting n = 500 into the equation, we have that

∑₀⁵⁰⁰(2i - 312) = n(n + 1) - 312n

= 500(500 + 1) - 312 × 500

= 500(501) - 312 × 500

= 250500 - 156000

= 94500

So, the sum is 94500

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Answer:

Step-by-step explanation:

All triangle's angles have a sum of 180 degrees.

56 + 61 = 117

180 - 117 = 63

x = 63

The area of the shape Illustrated will be 202 square inches.

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

We can break this shape down into two rectangles, one with the dimensions of 13in by 4in and the other by 15in and 10in. Now we can find the area of both shapes by multiplying the sides together so the 13in by 4in shape has the area of 52 square inches and the 15in by 10in shape has the area of 150 square inches.

Now, add the two areas together and the total area of the whole shape:

= 150 + 52

= 202 square inches

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The values of m in the graph of y = mx²-5x-2 have no x-intercepts are

m< 25/8.

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

Given a function y = mx²-5x-2 for not having the x-intercepts means that at any value of m function can not have the value zero or in other words function would not have any roots.

Thus for not having any root b² - 4ac < 0

For our function

a = m

b = -5

c = -2

substituting the values in the general formula

(-5)² - 4 * m * -2 < 0

25 + 8m< 0

m < 25/ 8

Therefore, The values of m are m 25/8 on the graph of y = mx2-5x-2, which has no x-intercepts.

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Answer:

-2\x^2-1

Step-by-step explanation:

1.To find the total distance Julia has traveled, you can use the Pythagorean theorem. The distance she traveled in the x-direction (west) is 10 km and the distance in the y-direction (south) is 15 km. The total distance traveled is the square root of (10^2 + 15^2) = 17.67 km.

2.In a right angle triangle, the side opposite the 90 angle is the hypotenuse. The side opposite the 250 angle is the side that is opposite to the angle and not the hypotenuse. Using the sine function of trigonometry, the opposite side can be calculated as: opposite = 15 cm * sin 250 = 12.08 cm. Rounded to nearest centimeter, the length of the side opposite the 250 angle is 12 cm.

3.The ladder forms a right triangle with the house and the ground. To find the length of the ladder, you can use the Pythagorean theorem. The ladder's length is the square root of (12^2 + 12^2) = 16.97m. Rounded to the nearest whole number, the ladder is approximately 17 meters long.

4.To find the length of the line Mark drew, you can use the Pythagorean theorem. The length of the line is the square root of (20^2 + 25^2) = 29.89 ft.

5.To find the length of the diagonal of the screen, you can use the Pythagorean theorem. The diagonal length is the square root of (13^2 + 12^2) = 16.97cm. Rounded to the nearest whole number, the size of the screen is 17 cm.

6.To find the length of the ramp, you can use the tangent function of trigonometry. The length of the ramp is: 15m / tan 550 = 18.24m. Rounded to nearest whole number, the length of the ramp is 18m.

7.To find the height of the building you can use the Pythagorean theorem. The height of the building is the square root of (185^2 - 90^2) = 129.49m. Rounded to nearest whole number, the height of the building is 129m.

8.To find the length of the ramp, you can use the tangent function of trigonometry. The length of the ramp is: 10m / tan 320 = 16.6m. Rounded to nearest whole number, the length of the ramp is 17m.

9.To find the distance from point B to C, you can use the information given. The distance from point A to point B is 15 feet, and the distance from point A to point C is 10 feet. If you subtract the distance from A to B from the distance from A to C, you get 10 - 15 = -5 feet. This distance is not possible as it is negative, therefore the answer is not valid.

10.To find the height on the building where the mini-stick touched, you can use the tangent function of trigonometry. The height is 9 inches * tan 430 = 16.24 inches. Rounded to nearest whole number, the height on the building where the mini-stick touched is 16 inches.

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Answer:

To find the median marks, we need to arrange the marks in ascending order and find the middle value.

0-20: 42 students

21-30: 38 students

31-40: 120 students

41-50: 84 students

51-60: 48 students

61-70: 36 students

71-80: 32 students

Since there are a total of 450 students, the median will be the value at the 225th position if we arrange the marks in ascending order. The value at the 225th position will be the lower value of the interval that the 225th student falls in.

The students in the intervals 0-20, 21-30, and 31-40 account for 42+38+120 = 200 students, which means that the 25th student falls in the 41-50 interval. Therefore, the median marks are 41.5.

To find the percentage of failures, we need to count the number of students who scored below 35 marks and divide it by the total number of students, and multiply the result by 100 to express it as a percentage. The number of students who scored below 35 marks is 42+38 = 80. The percentage of failures is 80/450 * 100 = 17.78%.

Answer: -2x + 3y > 7

Step-by-step explanation:

x coordinate is -2

y coordinate is 3

> is the left side

Besides that answer is the only one that makes sense if you only look at the x and y coordinate

Width is 50 on each side and length.

Find the dimensions of the field if the length ?

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Answer: Yes

Step-by-step explanation:

In the similar quadrilaterals shown, the value of x is 18.3.

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

Given two quadrilaterals whose all four angles are the same. In this condition ratio of their side are equal

Thus,

22 / 18 = x / 15

x = 18.33

Therefore, the value of the x in the given similar quadrilaterals is 18.3.

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Answer:

-5a

Step-by-step explanation:

Think of it as 5-10 since both of them have "a"

5-10=-5

-5a

Answer:

-5a

Step-by-step explanation:

Algebra are algebraic expressions that can be used as variables and is subjected to BODMAS rule just like numerical expressions.

Example: 5b + 9b = 14b

Given from the question:

5a - 10a = -5a

Answer:

[tex](a-b)^3 = (a-b)^(a-b)^2\\\\=(a-b)(a^2 - 2ab +b^2)\\\\= a(a^2 -2ab +b^2) -b(a^2 - 2ab +b^2)\\\\= a^3 -2a^2b -ab^2 -a^2b + 2ab^2 -b^3\\\\= a^3 - 3a^2b + 3ab^2 -b^3[/tex]

Step-by-step explanation:

I am not sure if you wanted it in exactly 4 steps, But this is the way to do it.

If in exactly 4 steps, omit the third step. Then we would get:

[tex](a-b)^3 = (a-b)^(a-b)^2\\\\=(a-b)(a^2 - 2ab +b^2)\\\\= a^3 -2a^2b -ab^2 -a^2b + 2ab^2 -b^3\\\\= a^3 - 3a^2b + 3ab^2 -b^3[/tex]

Hope that helps ya

Answer:

I'm going sit on a computer with me to work and get some milk for a bacon for the blue cup next time I'm in level 12 with all my heart broken bones so I'm going sit on it all the night and get back on it all night so I'm going sit on my couch with the milk to make it can't be gk for a bit

The solution of |2x - 1|= 5  are x=-2 and x=3.

Two or more expressions with an Equal sign is called as Equation.

The given equation is |2x - 1| = 5

2x-1=+5

Add 1 on both sides

2x=6

Divide both sides by 2

x=3

Now take 2x-1=-5

Add 1 on both sides

2x=-4

x=-2

The solution of |2x - 1|= 5  are x=-2 and x=3.

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The probability of not landing on that colour or the complement is 3/4.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, the probability of landing on a certain colour is p, we are asked to write an expression for the probability of not landing on that colour or the complement, and also suppose the probability of p is 1/4.

We know that, p(not an event) = 1 - p(E)

Therefore, the if the probability of landing on a certain colour is p, then the probability of not landing on that colour = 1 - p

Also,

If the probability of p is 1/4,

Then, p(not an event) = 1 - 1/4 = 3/4

Hence, the required expression is p(not an event) = 1 - p(E)

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Answer:

10.12

Step-by-step explanation:

100%+6.5%=106.5%

106.5% divided by 100=1.065

155.75 multiplied by 1.065=165.87375..

165.87375-155.75=10.12375

which equals 10.12

4q² + 8q +4 = (4q+4)(q+1) = 4(q+1)²

Given, 4q² + 8q +4

Factorization of the given equation takes place as follows:

the equation is a function of q

or f(q) = 4q² + 8q +4

we can write 8q = 4q + 4q

f(q) = 4q² + 4q+ 4q +4

now we can take (q+1) as common

f(q) = 4q(q+1) + 4(q+1)

or f(q) = (4q+4)(q+1) = 4(q+1)²

4q² + 8q +4 = (4q+4)(q+1) = 4(q+1)²

Therefore, the factors of 4q² + 8q +4 are (4q+4)(q+1) or 4(q+1)².

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Answer: 4 (q + 1)²



Step-by-step explanation:

I did the attached solution through middle term breaking meothod, but you could apply the whole square formula as well and get the same answer. i.e (a + b)² = a² + 2ab + b²

hope that helps...

The inequality that best represents the purchase made by Gabriela, given the number of hand soaps and lotions purchased, is x + y > 12

Gabriela bought more than 12 bottles of hand soaps and lotions which simply means that the total number of these items that Gabriela bought as more than  12 bottles when added together.

The inequality would therefore be:

Number of hand soaps + Number of lotions > 12

Assuming the number of hand soaps is x and the number of lotions is y, the inequality would be:

x + y > 12

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