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Answer:

[tex]\displaystyle A = \frac{32}{3}[/tex]

General Formulas and Concepts:

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                                   [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                        [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                             [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                           [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                                       [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Curve: x³ + 2x² - 3x

Interval: [-3, 1]

Step 2: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

2x-25<89

x<57

Step-by-step explanation:

2x-25<89

2x<89+25

2x<114

Divide by 2...

x<57

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Answer:

Subtraction property ; x = 3.25

Division property ; - 6

multiplication property ; - 125

Addition property ; 13

Step-by-step explanation:

A.)

x + 3.75 = 7

Using the subtraction property : subtract 3.75 from both sides

x + 3.75 - 3.75 = 7 - 3.75

x = 3.25

B. )

–3b = 18

According to the division property :

Divide both sides by - 3

-3b / - 3 = 18 / - 3

b = - 6

C.)

m/5 = - 25

Using the multiplication property :

m/5 * 5 = - 25 * 5

m = - 125

D.)

m – 4 = 9

Using the addition property :

Add 4 to both sides :

m - 4 + 4 = 9 + 4

m = 13

Answer:

A. Subtraction property ; x = 3.25

B. Division property ; - 6

C. multiplication property ; - 125

D. Addition property ; 13

Step-by-step explanation:

Answer:

(in image attached)

Step-by-step explanation:

A.

Left: 6×-3

Right: -3×-2

Bottom: 6×-2

B.

48÷6 = 8

-42÷6 = -7

-56÷8 = -7

-56÷-7= 8

Area = l ×b

[tex]a = l \times b \\ a = 11 \times 9 \\ a = 99[/tex]

Answer:

7

Step-by-step explanation:

Here we have the hypotonouse and an angle

we are looking for the side opposite to the angle

this means we should use SOH

sin(26)=(x/16)

16*sin(26)=x

x=7.01393

which is closest to 7

Answer:

She's, "HOT"!

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

6 is x so this is the answer

Answer:

320m

Step-by-step explanation:

that is the procedure above

Answer:

B

Step-by-step explanation:

Line crosses y-axis at 2.

Slope = [tex]\frac{-1}{5}[/tex]

For each 1 square the line rises/falls it moves to the right/left 5 squares.

Negative slope lines are downhill left to right.  

The correct graph to represent the line y = -1/5 x + 2 will be;

⇒ Graph 2

What is Equation of line?

The equation of line with slope m and y intercept at point b is given as;

y = mx + b

Given that;

The equation of line is;

⇒ y = - 1/5 x + 2

Now,

The standard form of the equation of line with slope m and y intercept at point b is given as;

y = mx + b

By comparing we get;

Slope (m) = - 1/5

In the second figure;

Let two points on the graph (0, 2) and (5 , 1).

So, Slope is defined as;

m = (1 - 2) / (5 - 0)

m = - 1 / 5

And, Clearly the y - intercept is at point 2.

Therefore,

Graph 2 shows the correct graph to represent the line y = -1/5 x + 2.

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Answer:

34.64 cm

Step-by-step explanation:

sin 60 = [tex]\frac{x}{40}[/tex]

sin 60 (40) = x

34.64 = x

equilateral triangles have 60° angles.

sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]

hypotenuse is 40. All sides are 40.

x = opposite or height of triangle.

Answer:  B) y = -x+ 5

Step-by-step explanation:

If the x-value in the solution (x, y) is 2, then the y-value is:

[tex]y=\frac{1}{2} (2)+2 = \frac{2}{2} +2=1+2=3[/tex]

So the solution coordinate is (2, 3).

Test each of the answer choices to see if whether the y-value is 3 when the x-value is 2. If it's true, then it could be the other equation in the system.

A) y = -2x + 4

[tex]y = -2x + 4\\\y = -2(2) + 4 = -4 + 4 = 0[/tex]

B) y = -x+ 5

[tex]y = -x+ 5\\y = -(2) + 5 = 5 - 2 =3[/tex]

C) y = 2x

[tex]y=2x\\y=2(2)=4[/tex]

D) y = 2x + 1

[tex]y = 2x + 1\\y=2(2)+1=4+1=5[/tex]

Answer:

<A = <B

=> 8x - 8 = 5x + 25

<=> 3x = 33

<=> x = 11

with x = 11 => mB = 5.11 + 25 = 55 + 25 = 80⁰

Answer:

x=11

B=80

Step-by-step explanation:

8x-8=5x+25

3x=33

x=11

B=5(11)+25

B=80

Answer:

perimeter of a square is l+l+l+l

16+16+16+16=64

Answer:

4√2 cm

Step-by-step explanation:

Perimeter of square = 4a = 16cm

a = 16 / 4

a = 4 cm

Length of each side = 4 cm

Diagonal^2 = side^2 + side^2

= 4^2 + 4^2

= 16 + 16

Diagonal^2 = 32

Diagonal = 4√2 cm

Answer:

biggafigure a

mnn

Step-by-step explanation:

Answer:

60x24

Step-by-step explanation:

60x24=1224

Answer: [tex]\$125,971.2[/tex]

Step-by-step explanation:

Given

Principal amount [tex]P=\$100,000[/tex]

Rate of interest [tex]r=8\%[/tex]

Time period [tex]t=3\ yr[/tex]

Amount in compound interest is given by

[tex]\Rightarrow A=P\left(1+r\%\right)^t\\\Rightarrow A=100,000(1+0.08)^3\\\Rightarrow A=\$125,971.2[/tex]

Thus, the amount accruing for loan is [tex]\$125,971.2[/tex]

Given:

Divide 73.85 by 4.1.

To find:

The first step when applying properties of operations to divide 73.85 by 4.1.

Solution:

We have,

Divide 73.85 by 4.1 [tex]=\dfrac{73.83}{4.1}[/tex]

Here, the dividend is 73.83 and divisor is 4.1.

First, we have to remove the decimals.

In numerator we have to digits after decimal and in denominator we have 1 digit after decimal.

So, multiply the divisor and dividend by 100 to remove the decimal.

Therefore, the first step is "Multiply the divisor and dividend by 100".

Answer:

B

Step-by-step explanation:

What is the first step when applying properties of operations to divide 73.85 by 4.1?

Answer:

Step-by-step explanation:

The formula for this is

14(20) = 25x and

280 =25x so

x = 11.2

Given:

The expression is:

[tex]2x^3+mx^2+nx+c[/tex]

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

[tex]m+n=-6[/tex]

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

[tex]P(x)=2x^3+mx^2+nx+c[/tex]

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

[tex]P(2)=P(-1)[/tex]              ...(i)

Substituting [tex]x=-1[/tex] in the given polynomial.

[tex]P(-1)=2(-1)^3+m(-1)^2+n(-1)+c[/tex]

[tex]P(-1)=-2+m-n+c[/tex]

Substituting [tex]x=2[/tex] in the given polynomial.

[tex]P(2)=2(2)^3+m(2)^2+n(2)+c[/tex]

[tex]P(2)=2(8)+m(4)+2n+c[/tex]

[tex]P(2)=16+4m+2n+c[/tex]

Now, substitute the values of P(2) and P(-1) in (i), we get

[tex]16+4m+2n+c=-2+m-n+c[/tex]

[tex]16+4m+2n+c+2-m+n-c=0[/tex]

[tex]18+3m+3n=0[/tex]

[tex]3m+3n=-18[/tex]

Divide both sides by 3.

[tex]\dfrac{3m+3n}{3}=\dfrac{-18}{3}[/tex]

[tex]m+n=-6[/tex]

Hence proved.

Answer:

D

Step-by-step explanation:

5(x-5)=353 + x

the first 5 is all his tests, in the parenthesis x is the average score, and -5 is the 5 points lower mentioned in the problem.

Answer:

B

Step-by-step explanation:

We are given that Markus scored 85, 92, 82, and 94 on his first four tests and x on his fifth.

We know that his score on the fifth test is five points lower than the average of all five tests.

To find the average, we add up all the values and divide by the number of values there are. Therefore, the average of all five tests is:

[tex]\displaystyle \frac{85+92+82+94+x}{5}[/tex]

Simplify:

[tex]\displaystyle =\frac{353+x}{5}[/tex]

His test score x is five points lower than the average. Hence:

[tex]\displaystyle x=\left(\frac{353+x}{5}\right)-5[/tex]

Rewrite. We can add five to both sides:

[tex]\displaystyle x+5=\frac{353+x}{5}[/tex]

And multiply both sides by five. Hence:

[tex]\displaystyle 5(x+5)=353+x[/tex]

Thus, our answer is B.

Notes:

By solving the equation, we see that x = 82. So, Markus scored 82 points on his fifth test.

If that is true, then his average score of all fives tests will be:

[tex]\displaystyle \frac{85+92+82+94+82}{5}=87[/tex]

82 is indeed five points fewer than 87, so our answer is correct and matches the given information.

Answer:

Step-by-step explanation:

The area is:

We can find the area,

→ 2(3.5 × 2)+ (7 × 2) + 2(1.8 × 2)

→ 14 + 14 + 7.2

→ 35.2 cm²

Thus, the area is 35.2 cm².

Answer:

c = 24

Step-by-step explanation:

Answer:

the fourth option

Step-by-step explanation:

1/2x - 2y > -6

1/2x + 6 > y

or

y < 1/2x + 6

so, the solution is all the y values smaller (= below) the line function.

and because it is "<" and not "<=" the line itself is not included

Given:

The exponential function is:

[tex]R(x)=(5.3)^x[/tex]

To find:

The domain of the given exponential function.

Solution:

We know that the general form of an exponential function is:

[tex]f(x)=ab^x[/tex]

Where, a is the initial value and b is growth/decay factor.

This function is defined for all real values of x, so the domain of these type of functions is the set of all real number.

We have,

[tex]R(x)=(5.3)^x[/tex]

Here, a is 1 and b is 5.3. This function is defined for all real values of x

Therefore, the domain of these type of functions is the set of all real number or it can be written as [tex](-\infty,\infty)[/tex].

The substitution method is used in elimination to find the solution to the equation.

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The given equation in the problem is;

Equation P: a - b = 9

Equation Q: a+b=5

The value obtained from the equation P is;

a - b = 9

a=b+9

Substitute the value in the equation Q;

a+b=5

b+9+b=5

2b=9-5

b=2

The value of a is;

a-b=9

a-2=9

a=9+2

a=11

Hence the value of a and b will be 11 and 2.

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Answer:

y axis then translate x+1,y+1

Answer:

2nd option

Step-by-step explanation:

[tex]\frac{7\pi }{12}[/tex] is an angle in the second quadrant

Thus to find the reference angle, subtract from π , that is

r = π - θ