what steps do you need to do to evaluate the following expression? Select two options. –5(–2) Drag 5 sets of –2 tiles to the window. Drag zero pairs to the window. Remove the 5 groups of –2 tiles. Remove 5 negative tiles from the window.

Answer:

( 1, - 1 )

Step-by-step explanation:

The time it will take the money to reach $8,838.51 is 14years

The formula for calculating compound interest is expressed as:

A = P(1+r)^t

where

P = $6,680

A = $8,838.51?

r = 2% = 0.02

Substitute and calculate the time 't"

8,838.51 = 6680(1+0.02)^t
1.3231 = 1.02^t

t = ln1.3231/ln1.02

t = 14years

Hence the time it will take the money to reach $8,838.51 is 14years

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Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1=[tex]\frac{1}{2} *PQ*RM[/tex]

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2=[tex]\frac{1}{2} *SR*PN[/tex]

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1=[tex]\frac{1}{2}*PQ*h[/tex]

S2=[tex]\frac{1}{2}*SR*h[/tex]

Adding them together, we get the area of the whole trapezoid:

S=S1+S2=[tex]\frac{1}{2} (PQ+SR)h,[/tex]

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> [tex]A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}[/tex]

Simplifying, we have

=>[tex]A= \frac{ah+2b_{1+C} }{2}[/tex]

Factoring we have,

=> [tex]A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2} \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}[/tex]

 But, [tex]a+ b_{1} + c[/tex]  is equal to [tex]b_{2}[/tex], the longer base of our trapezoid.

Hence, [tex]A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}[/tex]

We have discussed two ways by which we can derive area of a trapezoid.

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Answer:

angle ACB=45º

Step-by-step explanation:

angle 135º lies on a straight line

a straight line = 180º

thus, angle ACB= 180-135=45º

The company needs 41 labels on average, each minute.

The perimeter of a circle (circumference): 2 π radius

Replacing with the values given:

C = 2 (3.14) 2 = 12.56 cm

So, the area of one label is:

Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.

Now, the number of label be n

87.92 x n = 3612.64 cm2

n = 3612.64 / 87.92

n = 41.09

Hence, The company needs 41 labels on average, each minute.

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Both Amy and Laura increased their gas mileage in the first two weeks.

Option B is the correct answer.

The missing graph is attached with the answer.

A graph is a statistical way of showing data , it is used to show relation between the points.

A graph is useful in understanding the nature of a function.

From the data given in the question

The statements that can be concluded is , Option B

Both Amy and Laura increased their gas mileage in the first two weeks.

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Substitute [tex]y = \sqrt x[/tex], so that [tex]y^2 = x[/tex] and [tex]2y\,dy = dx[/tex]. Then the integral becomes

[tex]\displaystyle \int \frac{dx}{\sqrt{1 + \sqrt x}} = 2 \int \frac y{\sqrt{1+y}} \, dy[/tex]

Now substitute [tex]z=1+y[/tex], so [tex]dz=dy[/tex]. The integral transforms to

[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = 2 \int \frac{z-1}{\sqrt z} \, dz = 2 \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz[/tex]

The rest is trivial. By the power rule,

[tex]\displaystyle \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz = \frac23 z^{3/2} - 2z^{1/2} + C = \frac23 \sqrt z (z - 3) + C[/tex]

Put everything back in terms of [tex]y[/tex], then [tex]x[/tex] :

[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = \frac43 \sqrt{1+y} (y - 2) + C[/tex]

[tex]\displaystyle \int \frac{dx}{\sqrt{1+\sqrt x}} = \boxed{\frac43 \sqrt{1+\sqrt x} (\sqrt x - 2) + C}[/tex]

The value of the integral over limit is 20,  the average is 1.73

The signed area is shown in the graph attached.

A function is a mathematical statement used to find a relation between two variable.

To Evaluate the definite integral between

f(x) = 5 if 4≤x ≤9

f(x) = -1 if 9≤x≤14

[tex]\rm \int_{4}^{14}f(x) dx = \int_{4}^{9} 5 dx +\int_{9}^{14} (-1)dx\\\\\int_{4}^{14}f(x) dx = (5x)^{9}_{4} -(x)^{14}_{9}\\\\\int_{4}^{14}f(x) dx = 5*(9-4) - (14-9)\\\\\int_{4}^{14}f(x) dx = 20[/tex]

The average value of the interval is

= (5+5+5+5+5-1-1-1-1-1-1)/ 11 = 1.73

Therefore the average is 1.73.

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Answer:

Step-by-step explanation:

Answer:  31.792.5 cu. ft.   (choice B)

=================================================

Work Shown:

[tex]V = \pi*r^2*h\\\\V \approx 3.14*15^2*45\\\\V \approx 31,792.5 \text{ cubic feet}\\\\[/tex]

The result is approximate since [tex]\pi \approx 3.14[/tex] is approximate.

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

Radius (r) = 15 feet

Height (h) = 45 feet

Volume = ?

Taking π ≈ 3.14..

V = 3.14 × 15² × 45

V = 31,792.5 cu. feet

So, the cylindrical tank can hold upto 31,792.5 cu. feet of water..

The domain of the function is whole numbers from 0 to 10.

Given the graph of function represents the tickets sold vs cost. A movie theater sells up to 10 tickets at a time online. we have to find the domain of the graph.

As shown in the graph the number of tickets sold is 0 to 10 and also the number of tickets are always positive and a whole number. It can never be negative or in fraction form.

Hence, the value of x is a positive whole number. The domain of the function is the complete set of possible values of x. The domain of the function is whole numbers from 0 to 10.

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It will be 6 - 4.875 = 1.125 feet above the ground or 1.1 feet (rounded to the nearest tenth of a foot).

All you need to do is to replace t in the given equation with 1.5:

[tex]h=-16(1.5)^2+25(1.5)+6[/tex]

h=-4.875

The value is negative so we can assume that after 1.5 seconds the ball will be 4.875 feet lower than it was shot from.

The measurement of someone or something from head to foot or from base to top.

But we also know that it was shot from a height of 6 feet,

So it will be 6 - 4.875 = 1.125 feet above the ground or 1.1 feet (rounded to the nearest tenth of a foot).

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The solution to the equation 12x + 5x - 4 = 172x + 6 is D. No solution.

The information given is 12x + 5x - 4 = 172x + 6 and we are told to find the value of x.

12x + 5x - 4 = 172x + 6

Collect like terms

12x + 5x - 4 = 172x + 6

12x + 5x - 172x = 6 + 4

-155x = 10

x = 10/-155

x = -0.0645

Therefore, the correct option is no solution as the correct answer isn't given.

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Answer:

0.42 dollar per pint

2.36 pints per dollar

An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,

The total area of the billboard, A= x·y

The total printed area of the billboard, [tex]A_p=(x-2)(y-8)[/tex]

Given in problem that the area of the billboard is 3600 ft².

x·y = 3600

y = (3600)/x

Substituting the value of y in the equation of the total printed area of the billboard,

[tex]A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}[/tex]

Now, the value of x is needed to be minimum, therefore, differentiating the given function,

[tex]\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}[/tex]

Equate the differentiated function with 0,

[tex]0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.[/tex]

Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

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When decomposing into prime factors, it is when a number is taken out of its half, third, fifth and seventh, and it is also possible for the same number number.

         [tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{10692 }\\ \ 5346\\ \ 2673\\ \ \ \ 891\\ \ \ \ 297\\ \ \ \ \ 99\\ \ \ \ \ 33\\ \ \ \ \ 11\\ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 3\\ 3\\ 3\\ 3\\ 3\\ 11\\ \: \end{matrix} \end{gathered}$}[/tex]

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

The speed of the rabbit in miles per hour is 50.33 mi/h.

We know that the speed of the jackrabbit is:

1.35 km/min.

Now we need to use the relations:

1 hour = 60 minutes.

So, in one hour, the rabit runs 60 times the distance that it runs in one minute, then:

1.35 km/min = 60*(1.35 km/h) = 81km/h

Now we need to change kilometers for miles.

1km = 0.6214 mi

Then we can rewrite:

81km/h = 81*0.6214mi/h = 50.33 mi/h

The speed of the rabbit in miles per hour is 50.33 mi/h.

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The x axis is labeled as Number of days.

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

let x be the  number of days and y be money.

So, the equation is

y = -7x + 150.

Hence, the x axis is labeled as Number of days.

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The measure of angle OED is the measure of angle OBD. Then the correct option is C.

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Circle O is shown.

Line segment JE is a diameter and line segment OB is a radius.

A line is drawn from point J to point B to form a chord.

Tangents BD and ED intersect at point D outside the circle.

The radius and tangent are orthogonal to each other.

∠OED = ∠OBD = 90°

Then the correct option is C.

The complete question is given below.

Circle O is shown. Line segment J E is a diameter and line segment O B is a radius. A line is drawn from point J to point B to form a chord. Tangents B D and E D intersect at point D outside of the circle.

Use the diagram to complete the statements.

The measure of angle EJB is the measure of angle BOE.

The measure of angle BDE is the measure of angle BOE.

The measure of angle OED is the measure of angle OBD.

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Answer:

one-half, 180 minus, equal to

Step-by-step explanation:

The angles are: A =24.7° ; B = 40.6° ; C =114.7°.

The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.

Cosine Law

a² = b²+c²-2bc cos A

b² = c²+a² -2ca cos B

Sum of three angles of a triangle is 180°.

a = 34 ; b= 53; c = 74

Substituting the given values in the cosine law, we have

34² = 53² + 74² - 2*53 *74 * cos A

7844 cos A = 2809 + 5476 - 1156 = 7129

cos A = 7129/7844 = 0.9088

A = cos⁻¹ (0.9088) = 24.6600° = 24.7°

53² = 74² + 34² - 2 (74)(34) cos B

5032 cos B = 5476 + 1156 - 2809 = 3823

cos B = 3823/5032 = 0.7597

B = cos⁻¹ (0.7597) = 40.5622° = 40.6°

Also, A + B + C = 180°

24.7 + 40.6 + C =180

C =180 -  65.3 = 114.7°

Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°

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The incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

2ln(x) = In(3x) - [In(9) - 2ln(3)]

In(x²) = In(3x) - [In(9) - In(9)]

ln(x²) = ln(3x) - 0

ln(x²) = ln(3x/0)   (incorrect step)

ln(x²) = ln(3x)

x² = 3x  (correct step)

x² - 3x =0

x(x - 3) = 0

x = 0, 3

Thus, the incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

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Answer: Read attachment.

Step-by-step explanation: Attached below is my work. Hope it helps!

Answer:

The decrease in price is $61.92

The sale price is $196.08

Step-by-step explanation:

24% × 258 = 61.92

258 decrease 24% =

258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08

Answer:

(-3, -13)

(-1, -7)

(1, -1)

(3, 5)

(5, 11)

Step-by-step explanation:

Plug x into the equation y = 3x - 4 for each value of x to obtain the y value.

For example:

y = 3(3) - 4

y = 9 - 4

y = 5

Option D statement "A 12-gallon tank would cost $47.40 to fill completely" is true.

The whole of the independent variable's possible values makes up the domain of a function.

For the given data we need to find which of the given statements are true.

From option A:

The domain is {4, 8, 11, 15}.

The domain is all possible x values so this would be 0 to infinity as you can pay for more gallons not just to that certain set of numbers.

Therefore, option A is False.

From option B:

An 11-gallon tank would cost $44.00 to fill completely.

From the given table we can see that 11-gallon tank costs $43.45.

Therefore, option B is False.

From option C:

A 9.1-gallon fill-up would cost $35.49.

To find 9.1 gallons we need to find the cost of 1-gallon.

That is, 15.80/4 = $3.95 (Given in the table)

Now the cost of 9.1 gallon tank is $3.95 x 9.1 = $35.95 not $35.49

Therefore, option C is False.

From option D:

A 12-gallon tank would cost $47.40 to fill completely.

We found that 1 gallon is $3.95.

$3.95 x 12 = $47.40

Therefore, option D is True.

Hence, from the given statements option D is True.

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An equation is formed of two equal expressions. The number of infections in 6 weeks is 456.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The general equation of an exponential function is written as,

y = A(B)ˣ

Since the infection is increasing at a rate of 50%, therefore, the rate of growth will be,

B = 1.50

Substitute any value then we will get,

40 = A(1.50)⁰

A = 40

Thus, the exponential equation of the growth will be,

y = 40(1.50)ˣ

Now, the number of infections in 6 weeks will be,

y = 40(1.50)⁶

y = 455.625 ≈ 456

Hence, the number of infections in 6 weeks is 456.

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Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.

Triangle ABC and triangle RQP are similar based on side-angle-side criterion.

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

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.

Triangle ABC and triangle RQP are similar based on side-angle-side criterion.

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The point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.

Given that, Terry brings home $14 per hour he works. When he started this job, he had $40 in the bank.

We need to write and graph the equation that would represent how much money Terry has in the bank (y) after x hours of work.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, y=40+14x

Graph the line using the slope and y-intercept, or two points.

Slope: 14

y-intercept: (0, 40)

The coordinates to plot the graph are (0, 40), (1, 54), (2, 68) and (3, 82).

The graph for the given equation is given below.

Therefore, the point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.

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Answer:

  B.  2x = y; 2x +1.5y = 20

Step-by-step explanation:

The two given relations can be written as two equations, one for the numbers of fish, and one for their cost.

__

The number of goldfish (y) is twice the number of tetras (x), so one equation can be ...

  2x = y

The tetras (x) are $2 each, and the goldfish (y) are $1.50 each. Their total cost is the sum of products of the number of fish and the cost of each. That total is given as $20, so the other equation could be ...

  2x +1.5y = 20

Then the appropriate system of equations is ...

_____

Additional comment

The solution can be found by substituting for 2x to get ...

  y +1.5y = 20 . . . . . . substitute for 2x

  y = 20/2.5 = 8 . . . . divide by the coefficient of y

  x = y/2 = 4 . . . . . . . find the number of tetras

Rick bought 4 tetras and 8 goldfish.

__

The wording "twice as many goldfish as tetras" easily causes confusion. It is helpful to reword it as "goldfish were twice the number of tetras."