Given the graph of g(x), describes the transformation of the parent function f(x)=2^x.

The area of the region that lies inside both curves r² = 2sin(2θ),  r = 1 is -0.1287 square units.

Since the curves are

We find their point of intersection.

So, r² = r²

2sin(2θ) = 1²

2sin(2θ) = 1

sin(2θ) = 1/2

2θ = sin⁻¹(1/2)

2θ = π/6

θ = π/12

So, we integrate the area from θ = 0 to θ = π/12

Now the area A of the region between two curves between θ = α to θ = β is

[tex]A = \int\limits^{\beta }_\alpha ({r^{2} - r^{'2} }) \, d\theta[/tex]

So, the area betwwen the curves r² = 2sin(2θ),  r = 1 between θ = 0 to θ = π/12 is

[tex]A = \int\limits^{\frac{\pi}{12} }_0 ({r^{2} - r^{'2} }) \, d\theta \\= \int\limits^{\frac{\pi}{12} }_0 ({2sin2\theta - 1^{2} }) \, d\theta\\= \int\limits^{\frac{\pi}{12} }_0 ({2sin2\theta - 1}) \, d\theta\\= \int\limits^{\frac{\pi}{12} }_0 {2sin2\theta}\, d\theta - \int\limits^{\frac{\pi}{12} }_0 {1} \, d\theta\\= [2(-cos2\theta)/2 - \theta]_{0}^{\frac{\pi}{12} } \\= [-cos2\theta - \theta]_{0}^{\frac{\pi}{12} } \\= -cos2\frac{\pi}{12} - \frac{\pi}{12} - ( -cos2(0) - 0)\\[/tex]

[tex]= -cos2(\frac{\pi}{12}) - \frac{\pi}{12} - ( -cos2(0) - 0)\\= -cos\frac{\pi}{6}- \frac{\pi}{12} - ( -cos0 - 0)\\= -cos\frac{\pi}{6}- \frac{\pi}{12} - ( -1)\\= -(\frac{\sqrt{3} }{2} ) - \frac{\pi}{12} + 1\\= -0.8660 - 0.2618 + 1\\= -1.1278 + 1\\= -0.1278[/tex]

So, the area of the region that lies inside both curves r² = 2sin(2θ),  r = 1 is -0.1287 square units.

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Answer:

1050 masks per person.

Step-by-step explanation:

1) Create an equation to find the total number of masks

2) Solve equation and divide total by 2 to get the number of masks that can be given to both Mark and Paula so that they have equal number.

1) Since Paula has 70% of the total masks, it can be represented as 0.7 * t where t is the variable representing the total number of masks. Mark on the other hand has the remaining number of masks out of 100% which is 30%. We can express that as 0.3. We multiply that by t because he has 30% of the masks. The final equation we have is 0.3t + 840 = 0.7t. 840 because Paula has 840 more masks than Mark.

2) Solve by subtracting 0.3t from both sides leaving you with 0.4t = 840. We divide both sides by 0.4 to get 2100. That is the total number of masks. If we divide that number by 2, we get 1050.

The area of the large rectangle by using the strategy is; 168cm².

The area of the rectangle can be determined by multiplying the length and width of the rectangle as follows;

Area = Length × width

Area = (10cm + 4cm) × (10cm × 2cm)

Area = (100+20+40+8)cm²

Area = 168 cm².

The strategy used above entails that the two binomials used to represent the length and width of the rectangle are multiplied according to binomial multiplication.

The strategy is that each term of the first binomials is used to multiply the terms in the second polynomial and the aggregate result of the multiplications is determined.

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Answer:

[tex]x^4-20x^3 +175x^2 -750x+1250[/tex]

Step-by-step explanation:

By the conjugate root theorem, 5+5i is also a root.

[tex]f(x)=a(x-5)^2 (x-5-5i)(x-5+5i) \\ \\

= a(x^2 - 10x+25)((x-5)^2 - (5i)^2) \\ \\

= a(x^2 - 10x+25)(x^2 - 10x+25+25) \\ \\

= a(x^2-10x+25)(x^2-10x+50) \\ \\

= a(x^4- 10x^3 + 50x^2 - 10x^3 + 100x^2 - 500x + 25x^2 - 250x+1250) \\ \\

= a(x^4-20x^3 +175x^2 -750x+1250) \\ \\ [/tex]

The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

The expression is given as:

(6x - 2)(6 x + 2).

The above expression is a difference of two squares.

And this is represented as

(a - b)(a + b)= a^2 - b^2

So, we have

(6x - 2)(6 x + 2) = (6x)^2 - 2^2

Evaluate

(6x - 2)(6 x + 2) = 36x^2 - 4

Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

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Complete question

What is the product?

(6x - 2)(6 x + 2).

Answer:

31

Step-by-step explanation:

Substitute -10 for x in b(x)=|x+41|, obtaining f(-10) = |-10 + 41|.  This result simplifies to f(-10) = |31| = 31

Answer:

here ya go :)

the black line is y=-2x-3

the lavender line is y=-x+6

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: 10x + 30 = 90[/tex]

[ according to given figure ]

[tex]\qquad \sf  \dashrightarrow \: 10x = 90 - 30[/tex]

[tex]\qquad \sf  \dashrightarrow \: 10x = 60[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 60 \div 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 6 \degree[/tex]

Correct choice is D

Using secant rule, the value of variable x in the diagram is 10.

A secant is a line that intersect a circle in two points.

Therefore, the following rule guides a secant.

(x + 32)32 = (20 + 28)28

Hence,

32x + 1024 = (48)28

32x + 1024 = 1344

32x = 1344 - 1024

32x = 320

divide both sides by 32

32x / 32 = 320 / 32

x = 10

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The area of the circle with the given circumference is: 42.25π in.².

Area = πr²

Circumference = 2πr.

Given the following:

Circumference of the circle = 13π in.

Find the radius (r):

2πr = 13π

Divide both sides by 2π

2πr/2π = 13π/2π

r = 13/2

r = 6.5

Area = πr² = π(6.5²) = 42.25π in.²

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[tex]order \: does \: not \:matter \\ sample \: space = 15 \: letters \\ no \: repetition\\ P(A) = 15C5 = 3003 \: ways[/tex]

Answer:

89.4 - 13.621 = 75.779

Explanation:

Subtract 13.621 from 89.4 to get 75.779.

El dinero que le falta a Maritza y su esposo para viajar es 330.

Para calcular el dinero que les falta debemos identificar la cifra total que les va a costar el viaje:

El valor total del viaje es s/3,130, entonces les faltarían s/330.

3,130 - 2,800 = 330

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Answer:

f(x)⁻¹ = (x - 11)²

Step-by-step explanation:

To find the inverse of the function, you need to (1) swap the places of the "x" and "y" variables and then (2) solve for "y". Remember, f(x) is another way of writing "y".

y = √x + 11                                        <----- Original equation

x = √y + 11                                        <----- Swap variables

x - 11 = √y                                         <----- Subtract 11 from both sides

(x - 11)² = (√y)²                                  <----- Square both sides

(x - 11)² = y                                        <----- Simplify

Another way of writing the output of an inverse function is with f(x)⁻¹.

answer:

x = - 9/2

y = -10

Step-by-step explanation:

make both equations look like y =

2x-3y=21 -> -3y= -2x+21 -> y = (-2x+21)/-3 -> y = 2/3x - 7

-6x + 2y = 7 -> 2y = 6x + 7 -> y = 3x + 7/2

now make the equations equal to each other (since they both equal y)

get x

2/3x - 7 = 3x + 7/2

-7 -7/2 = 3x - 2/3x

-14/2 -7/2 = 9/3x - 2/3x

-21/2 = 7/3x

(3/7) -21/2 = x

x = (3/7) -21/2

x = - 63/14

x = - 9/2

put it back in an equation to get y

y = 3x + 7/2

y = 3(-9/2) + 7/2

y = -27/2 + 7/2

y = -20/2

y = - 10

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Answer:

45° rotation clockwise

Step-by-step explanation:

When you plot these on the graph, the non prime ones are on quadrant 2 and when you plot the prime ones, it is on quadrant 1. This means that it is 45° to the right(clockwise)

⬇️red is prime blue is regular ⬇️

Volume of a cylinder: PI x radius^2 x height

= 3.14 x 5^2 x 10 = 785 m^3

Volume of a cone: pi x radius^2 x height/3

= 3.14 x 5^2 x 4/3 = 104.67 m^3

Total volume  = 785 + 104.67 = 889.67 M63

Answer: C. 889.67 M^3

Answer:

[tex]\textsf{C)}\quad \sf 889.67\: m^3[/tex]

Step-by-step explanation:

The given composite solid is made up of a cylinder and a cone.

To find the volume of the composite solid, find the volume of the cylinder and the volume of the cone, then add them together.

Volume of a cylinder:

[tex]\sf V=\pi r^2 h[/tex]

(where r is the radius and h is the height)

Given:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cylinder & = \sf \pi (5)^2(10)\\ & = \sf 250 \pi \:\:m^3 \end{aligned}[/tex]

Volume of a cone:

[tex]\sf V=\dfrac{1}{3} \pi r^2 h[/tex]

(where r is the radius and h is the height)

Given:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cone & = \sf \dfrac{1}{3} \pi (5)^2(4)\\ & = \sf \dfrac{100}{3}\pi \:\:m^3 \end{aligned}[/tex]

Therefore, the volume of the composite solid is:

[tex]\begin{aligned}\implies \sf Volume\:of\:composite\:solid & = \sf Cylinder\:volume+Cone\:volume\\ & = \sf 250\pi + \dfrac{100}{3}\pi \\ & = \sf \dfrac{850}{3} \pi \\ & = \sf \dfrac{850}{3} \times 3.14 \\ & = \sf 889.67\:m^3\:(2\:d.p.)\end{aligned}[/tex]

Using conditional probability, there is a 0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

For this problem, the events are given as follows:

The parameters are given as follows:

Hence the conditional probability is:

[tex]P(B|A) = \frac{0.33}{0.495} = 0.6667[/tex]

0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.

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Take the prime factorization of each factor in the product.

[tex]\dfrac{72 \times 78 \times 85 \times 90 \times98}{68 \times 84 \times 91 \times 108} \\\\ ~~~~~~~~ = \dfrac{(2^3\times3^2)\times(2\times3\times13)\times(5\times17)\times(2\times3^2\times5)\times(2\times7^2)}{(2^2\times17)\times(2^2\times3\times7)\times(7\times13)\times(2^2\times3^3)} \\\\ ~~~~~~~~ = \dfrac{2^6 \times 3^5 \times 5^2 \times 7^2 \times 13 \times 17}{2^6 \times 3^4 \times 7^2 \times 13 \times 17} \\\\ ~~~~~~~~ = 3 \times 5^2 = \boxed{75}[/tex]

Paul's rent budget is $750, given that his food budget of $225, is 30 percent of his rent budget.

Fractions are representation of quantities as a part of a certain quantity.

Written as a/b, read as a by b, and functions as a divided by b, represents a fraction showing a parts of b equal parts.

a is called the numerator, and b is called the denominator.

Percentages are modified fractions where the whole quantity is represented by 100.

To convert a fraction into percentages we multiply it by 100, while to convert percentages to fraction divided by 100.

In the question, we are given that Paul's budget for food is 30% of the budget he has for rent.

We are asked if his budget for food is $225, what is his budget for rent.

We assume Paul's budget for rent to be $x.

We know that Paul's food's budget is 30 percent of his rent.

Hence, Paul's food budget = 30% of x.

or, Paul's budget for food = 30/100 * x {To convert percentages to fraction divided by 100}

But, we know that Paul's food budget is $225. Thus, we can show that:

225 = 30/100 * x,

or, x = (225*100)/30 = 750.

Thus, Paul's rent budget is $750, given that his food budget of $225, is 30 percent of his rent budget.

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Answer:

a = 103°

b = 103°

c = 97°

d = 83°

e = 154°

Answer: About 830 dollars

Step-by-step explanation: find 15% off on 897 then find 7.5 percent of 897, then add them together.

Notice that

[tex]7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}[/tex]

[tex]12=2^2\times3[/tex], so

[tex]\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}[/tex]

Then taking the positive square root gives

[tex]\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}[/tex]

so [tex]\boxed{a=2}[/tex] and [tex]\boxed{b=1006}[/tex].

Answer:

IV 5

Step-by-step explanation:

you have to solve for x:

x-3<2

x-3+3<2+3

x=5

could you put the brainlyest Icon for me? I have 1500 points, but no brainlyest, so I can't move up the ranks.

Answer:

g(11) = 101

Step-by-step explanation:

g(r) = -20 + 11r

So in g(11), we just need to replace 'r' with '11'

g(11) = -20 + 11 (11)

--> g(11) = -20 + 121 = 101

--> g(11) = 101

Please comment down below if 8(11) wasn't a typo. I thought it was, so I replaced 8 with g. If that was intentional, I'll edit my answer as soon as possible.

Answer:

(-1,7)

Step-by-step explanation:

Use elimination, x = -1, y = 7

Answer:

(-1, 7)

Step-by-step explanation:

Elimination: Step 1

Write in standard form (you can have negatives)

(standard form= Ax+By=C)

Elimination: Step 2

Create(find) opposites

Elimination: Step 3

Add to cancel one variable

Elimination: Step 4

Solve for variable

Elimination: Step 5

Substitute into other equation to find other variable

In a linear system of equations, substitution results in one equation with one variable. The solution to a linear system is an ordered pair, not just a single value.

Problem:

Solve 2x+y=5;x+y=6

Steps:

I will solve your system by substitution.

(You can also solve this system by elimination.)

2x+y=5;x+y=6

Step: Solve 2x+y=5 for y:

2x+y+−2x=5+−2x(Add -2x to both sides)

y=−2x+5

Step: Substitute −2x+5 for yin x+y=6:

x+y=6

x+−2x+5=6

−x+5=6(Simplify both sides of the equation)

−x+5+−5=6+−5(Add -5 to both sides)

−x=1

-x/-1 = 1/-1 (Divide both sides by -1)

x=−1

Step: Substitute −1 for x in y=−2x+5:

y=−2x+5

y=(−2)(−1)+5

y=7(Simplify both sides of the equation)

Answer:

x=−1 and y=7

Answer:

Six years

Step-by-step explanation:

because it will divided the twoo digit and mutiple it self

Answer:

$4800

Step-by-step explanation:

Let's use the simple interest formula, P(1+rt), to find the final amount of the loan

10000(1+.12*4) = 14800, the final amount

14800 - 10000 = 4800 total in interest

Answer:

D

Step-by-step explanation:

I assume that for C and D, you meant e^x.

Since the function is defined at 0, eliminate A and B (since ln 0 is undefined)

Between C and D, we know that when x=0, e^x = 1. Since the y intercept of the graph is -3, this means the equation is y = e^x - 4.

Answer:24

Step-by-step explanation:

Answer:

Step-by-step explanation: