The area sector AOB is 20.25π ft squared. Find the exact area of the shaded region.

Answer:

A. [tex]x=6[/tex] or [tex]x=1[/tex]

Step-by-step explanation:

The given function is:

[tex]y=x^2-7x+6[/tex]

When y=0; we have:

[tex]x^2-7x+6=0[/tex]

[tex]x^2-6x-x+6=0[/tex]

Factor by grouping:

[tex]x(x-6)-1(x-6)=0[/tex]

[tex](x-6)(x-1)=0[/tex]

Either [tex](x-6)=0[/tex] or [tex](x-1)=0[/tex]

Either [tex]x=6[/tex] or [tex]x=1[/tex]

Since

[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]

we have

[tex]\csc(x)\sin(x)+\tan(x) = \dfrac{1}{\sin(x)}\cdot \sin(x)+\tan(x)=1+\tan(x)[/tex]

And since

[tex]\tan(x)=\dfrac{8}{15}[/tex]

we have

[tex]1+\tan(x) = 1-\dfrac{8}{15}=\dfrac{15}{15}-\dfrac{8}{15}=\dfrac{7}{15}[/tex]

The value of cscθ sinθ + tan θ is 7/15.

cscθ is the reciprocal of sinθ.

The expression is given by cscθ sinθ + tan θ.

We can simplify this expression before solving it.

Let the expression be y = cscθ sinθ + tan θ.

cscθ = 1/sinθ

y = sinθ * 1/sinθ + tan θ

y = 1 + tan θ

The value of tan θ is given as -8/15.

We can substitute this above:

y = 1 + tan θ

= 1 - 8/15

= (15-8)/15

= 7/15

The value of the expression cscθ sinθ+ tan θ is found to be 7/15.

Therefore, the value of cscθ sinθ + tan θ is 7/15.

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I assume one of the four options is the correct answer...

Remember that in order to determine if a function rule is correct, you should be able to plug an x value into the equation and get the corresponding y value as the answer.

The first option, f(x) = x + 1, is correct!

Answer:  The correct option is (A) f(x) = x + 1.

Step-by-step explanation: We are given to write a function rule for the following table :

x              -1           0           1             2

f(x)           0           1            2            3

From the given table, we see that

[tex]f(-1)=0=-1+1,\\\\f(0)=1=0+1,\\\\f(1)=2=1+1,\\\\f(2)=3=2+1.[/tex]

Therefore, the required function rule is given by

[tex]f(x)=x+1.[/tex]

Thus, option (A) is CORRECT.

Answer:

See below.

Step-by-step explanation:

If we translate h(x) to the left it will override  line d(x) because  the slope of both lines is the same. H(x) will need to move 4 units to the left to do this (because the slope =  2 = 8/4).

To represent the same function as d(x), the linear function h(x) with a slope of 2 should be translated 4 units to the left, resulting in the function h(x+4). This horizontal shift increases the value of y by 8 units, which equates to the vertical shift applied to create d(x).

To translate the linear function h(x) to result in the same function as d(x), which is h(x) translated 8 units up, we need to consider the properties of linear functions and translations. Since h(x) has a slope of 2, we can denote it as h(x) = 2x + b, where b is the y-intercept. When h(x) is translated 8 units up to become d(x), the new function is d(x) = h(x) + 8 = 2x + b + 8. To counteract this vertical shift with a horizontal translation and maintain the same function as d(x), we must shift h(x) in such a way that every x value for h(x) yields the same y-value for d(x) after the translation.

To achieve this, we would have to shift h(x) to the left by 4 units, resulting in the function h(x+4). This is because for every 1 unit increase in x, the value of h(x) increases by 2 units (the slope), so a shift of 4 units left would increase y by 8 units, which is the same effect as the vertical translation applied to obtain d(x). Thus, h(x+4) = 2(x+4) + b = 2x + 8 + b, which aligns with d(x). This explanation confirms that the properties of linear functions and translation mechanics allow us to equate d(x) with a horizontally translated version of h(x).

Answer:

[tex]\begin{array}{cccc}&\text{Watch basketball}&\text{Don't watch basketball}&\text{Total}\\\text{Watch soccer}&7&12&19\\\text{Don't watch soccer}&17&13&30\\\text{Total}&24&25&49\end{array}[/tex]

Step-by-step explanation:

From the diagram you can see that

So, you can fill the table in following way

[tex]\begin{array}{cccc}&\text{Watch basketball}&\text{Don't watch basketball}&\text{Total}\\\text{Watch soccer}&7&12&19\\\text{Don't watch soccer}&17&13&30\\\text{Total}&24&25&49\end{array}[/tex]

Answer:

dude was right but heres photo proof

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

y=mx+b

b= y-intercept

m=slope

m=-3

b=9

            [tex]\huge\boxed{Slope=-3,\;Y\;intercept=9.}[/tex]

___________________________________________________________

                                             [tex]\boxed{Explanation}[/tex]

y=mx+b.

m is always where the slope is located.

b is always where the y intercept is located.

Therefore, since -3 is located at m that is the slope and 9 is located at b so that is the y intercept.

ANSWER

[tex]log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) =\log 7[/tex]

EXPLANATION

The given logarithmic expression is:

[tex] log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]

We apply the product rule to the first two terms to get:

[tex]log( \frac{14}{3} \times \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]

We the apply the quotient rule:

[tex]log( \frac{14}{3} \times \frac{11}{5} \div \frac{22}{15} ) [/tex]

[tex]log( \frac{14}{3} \times \frac{11}{5} \times \frac{15}{22} ) [/tex]

We cancel out the common factors and simplify to obtain:

[tex]log( 7 ) [/tex]

Required Knowledge.

log(ab) =log(a) + log(b)

log(a/b) = log(a) -log(b)

SOLUTION

log(14/3) +log(11/5) -log(22/15)

=log((14/3)×(11/5)) -log(22/15)

=log(154/15) -log(22/15

=log( (154/15) ÷ (22/15) )

=log( (154/15) × (15/22) )

=log(154/22)

=log(77/11)

=log(7)

Hence 7 is your answer...

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

Step-by-step explanation:

multiply the top and bottom of the fraction by 15x

2*15x

=======

5*15x

30x

====

75x

Answer:

16.2

Step-by-step explanation:

A trick to remember for right triangles is SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Here, we have the side adjacent to the angle and the hypotenuse.  So we should use cosine.

cos 22° = 15 / x

x = 15 / cos 22°

x ≈ 16.2

Answer:

A set of parametric equations for the line y = 4x - 5 is;

x = t

y = 4t - 5

Step-by-step explanation:

To find a set of parametric equations for the line y = 4x - 5;

We can assign either variable x or y equal to the parameter t, in this case we can easily let x = t

We then substitute x = t in the original equation;

y = 4t - 5

Therefore, a set of parametric equations for the line y = 4x - 5 is;

x = t

y = 4t - 5

Answer:

90 because it’s a right angle and a right angle it 90 degrees

The two angles make up a right angle.

This means the two angles are complementary and need to equal 90 degrees.

X = 90 - 55.1 = 34.9

The coordinates after the reflection of the given graph are A'(1,-4), B'(2,-1), and C'(3,-3). The correct graph that shows the reflection is D).

Given :

The graph given has points -- (1,4), (2,1), and (3,3).

The following steps can be used in order to determine the correct figure that shows the reflection of the given graph:

Step 1 - According to the given graph. the points are A(1,4), B(2,1), and C(3,3).

Step 2 - According to the given data, take the reflection of the given graph.

Step 3 - So, after reflection about the x-axis, the points become A'(1,-4), B'(2,-1), and C'(3,-3).

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/1878272

Answer:

its 42%

Step-by-step explanation:

the answer above is wrong

The inflation rate in the car is 42%.

Inflation Rate (CPI, annual variation in %) Inflation refers to an overall increase in the Consumer Price Index (CPI), which is a weighted average of prices for different goods.

Sarah bought a car last year to drive back and forth to work after she spent $1,098 on gas this year she spent $1,562.

Based on the above information, the calculation is as follows:

[tex]\rm Inflation \ rate=\dfrac{1562-1098}{1098}\\\\ Inflation \ rate=\dfrac{464}{1098}\\\\ Inflation \ rate=0.42\\\\ Inflation \ rate=0.42 \times 100\\\\ Inflation \ rate= 42 \ percent[/tex]

Hence, the inflation rate of the car is 42%.

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Answer:

c

Step-by-step explanation:

11+17 x 7=130

x=130

130 is bigger than 120 but smaller than 180

Answer:

8800 yards

Step-by-step explanation:

1760 feet * 5  = 8800 yards

Answer:

8800

Step-by-step explanation:

I googled it

Answer:

See below

Step-by-step explanation:

In order to solve for the length of a cube, you must already know its width, depth, and volume. Then, arrange the problem as an equation:

Length x width x depth = volume

Next, solve the equation for the length. For example, If I have a cube with a width of 5ft, a depth of 5ft, and a volume of 50ft^3, I will solve for the length by arranging the values to fit the formula shown above:

L x 5 x 5 = 50

Then I'll multiply the values on the left:

25L = 50

And, finally, I will divide either side by 25, which leaves the answer:

L = 2ft

Hope this helps! Feel free to ask questions!

Answer:

294

Step-by-step explanation:

so three family's and 14$ a day so

14*3=42

then take 42 and times it by how many days so 7

so 42*7=294

Answer:

Option B

same-side interior angles

Step-by-step explanation:

Given in the question, two non parallel lines a and b.

The area between lines a and b is called the interior of the two lines.

Angles 4 and 5 are same-side interior angles.

Other options are wrong because:

The area which not between lines a and b is called the exterior

Corresponding angles are on same side of the traversal line.

Example

Angles 1 and 5

Alternate interior angles are in interior region but in opposite side of traversal line.

Example

Angles 3 and 5

Answer:

400

Step-by-step explanation:

The initial value of the investment is 100 *1 = $100

The final value of the investment after three months is 100 * 5 = $500

This means the value of the investment has increased from $100 to $500. The capital gain is the increase in the value of an investment;

500 - 100 = $400

Answer:

Final answer is [tex]\frac{5}{(x+1)}[/tex].

Step-by-step explanation:

Given expression is [tex]\frac{5\left(x-1\right)}{(x+1)(x-1)}[/tex] where x doesn’t equal 1 or -1. Now we need to find about which of the given choices is equal to the given rational expression. Choices are missing but we can still solve this problem.

[tex]\frac{5\left(x-1\right)}{(x+1)(x-1)}[/tex]

cancel out common factors from top and bottom.

[tex]=\frac{5}{(x+1)}[/tex]

Hence final answer is [tex]\frac{5}{(x+1)}[/tex].

Answer:

5/x+1

Step-by-step explanation:

(3,6) I think is the answer

Answer:

I believe it's (19,10)

Answer:

a. By Pythagorean Theorem: [tex]ET=\sqrt{113}[/tex]

b. By Distance Formula: [tex]ET=\sqrt{113}[/tex]

Step-by-step explanation:

The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).

The points have been plotted on the coordinate plane as shown in the attachment.

a. Using the Pythagoras Theorem;

[tex]ET^2=EC^2+CT^2[/tex]

We substitute the side lengths to obtain:

[tex]ET^2=7^2+8^2[/tex]

[tex]ET^2=49+64[/tex]

[tex]ET^2=113[/tex]

Take positive square root to obtain:

[tex]ET=\sqrt{113}[/tex]

b. The distance formula is given by:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The endpoints of ET are at E(-3,4) and T(4,-4).

Using the distance formula;

[tex]ET=\sqrt{(4--3)^2+(-4-4)^2}[/tex]

[tex]ET=\sqrt{(7)^2+(-8)^2}[/tex]

[tex]ET=\sqrt{49+64}[/tex]

[tex]ET=\sqrt{113}[/tex]

Answer:

120 miles

Step-by-step explanation:

we know that

The speed is equal to the distance divided by the time

Let

s------> the speed in mph

d-----> the distance in miles

t -----> the time in hours

s=d/t

solve for the distance

d=s*t

It will take Adam four hours to drive to Disney Park

s=x mph

t=4 h

substitute

d=4x -----> equation A

It will take Adam 2.5 times less time if driving 45 mph faster

so

s=(x+45) mph

t=4/2.5=1.6 h

substitute

d=1.6(x+45) -----> equation B

equate equation A and equation B

4x=1.6(x+45)

Solve for x

4x=1.6x+72

4x-1.6x=72

2.4x=72

x=30 mph

Find the distance d

d=4x -----> d=4(30)=120 miles

Answer:

120 miles

Step-by-step explanation:

The van needs 21 gallons of gas. Take 16/(320/420)

The van will need 21 gallons of gas to travel 420 miles, based on its fuel efficiency of 20 miles per gallon.

The student is asking how many gallons of gas a van needs to travel 420 miles, given that it travels 320 miles on 16 gallons of gas.

First, we calculate the van's fuel efficiency which is found by diving the miles traveled by the gallons of gas used. For the van in the question:

Fuel efficiency: 320 miles / 16 gallons = 20 miles per gallon (MPG)

Next, we can use this fuel efficiency to find out how many gallons will be needed for 420 miles. We divide the total miles by the MPG:

Gallons needed: 420 miles / 20 MPG = 21 gallons

Therefore, the van will need 21 gallons of gas to travel 420 miles.

Use substitution method

3a+9=54

3a+9-9=54-9

3a= 45

divide by 3

3a/3= 45/3

a= 15

Answer is a= 15

Answer:

a = 15

Step-by-step explanation:

3a + b = 54

3a + 9 = 54

3a + 9 - 9 = 54 - 9

3a = 45

3a divided by 3 = 45 divided by 3

a = 15

3 x 15 + 9 = 54

45 + 9 = 54

54 = 54

Answer:

15/p and -3

Step-by-step explanation:

4(px+1)=64

Distribute 4: 4px + 4=64

Subtract 4 from both sides : 4px+4-4=64-4

Divide by 4p: 4px/4p=60/4p

x=15/p

For this case we have to find the inverse of a function, follow the steps below:

Then, it is observed that of option 3:

[tex]f (x) = 4x[/tex]

Replace [tex]f (x)[/tex]with y:

[tex]y = 4x[/tex]

We exchange the variables:

[tex]x = 4y[/tex]

We solve for "y":

[tex]4y = x\\y = \frac {x} {4}[/tex]

Finally we change y by [tex]f ^ {- 1} (x):[/tex]

[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]

Answer:

The correct option is C

Answer:

It's the third choice.

Step-by-step explanation:

f(x) = y = 4x

x = 1/4 y

Change the y to x:

so the inverse g(x) = 1/4 x.

Answer:

B: 25%

Step-by-step explanation:

$90.00 - $67.50 = $22.5

$22.5 / $90 = 0.25 = 25%

Answer:

B: 25%

Answer:

25%

Step-by-step explanation:

The x-intercepts are: (-1,0) and (3,0).

The y-intercept is: (0,-9).

Hope this helps!