\(f(x) = x {}^{2} + 12x + 36\)
Determine the value of f^-1 (225) in this situation.
A. 21 days

B. 9 days

C. 6 days

D. 15 days​

Answer:

≠

Step-by-step explanation:

4[6(2+3)] _____ 125 - 5 * 1

4[6(5)] _____ 125 - 5 * 1

4[30] _____ 125 - 5 * 1

120 _____ 125 - 5 * 1

120 _____ 125 - 6

120 _____ 119

120 ≠ 119

Answer:

119.9

Step-by-step explanation:

Using fundamental identities we found the trigonometric functions for the given conditions.

Given, `\(sin theta\)= -12/13 and sec theta > 0`To find:

Trigonometric functions for the given conditions. `sin theta, cos theta, tan theta, csc theta, sec theta, cot theta.`

We have, `sin theta = -12/13 and sec theta > 0`Now, using the Pythagorean identity,

we have, `sin^2 theta + cos^2 theta = 1`

putting the value of `sin theta` in above equation,

we get;`(-12/13)^2 + cos^2 theta = 1`or `144/169 + cos^2 theta = 1`or `cos^2 theta = 1 - 144/169`or `cos^2 theta = 25/169`Taking square root on both sides, we get;`

cos theta = sqrt(25/169)`As, `sec theta > 0`and `sec theta = 1/cos theta`, we get;`1/cos theta > 0`=>`cos theta > 0` (as cos theta is positive in first and fourth quadrant)

Now, `

tan theta = sin theta/cos theta = (-12/13)/(5/13) = -12/5`For `csc theta`, `csc theta = 1/sin theta = -13/12`For `sec theta`, `sec theta = 1/cos theta = 13/5`For `cot theta`, `cot theta = 1/tan theta = -5/12`Hence, `sin theta = -12/13, cos theta = 5/13, tan theta = -12/5, csc theta = -13/12, sec theta = 13/5 and cot theta = -5/12

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Partial Answer:

For #10 the solutions are 2 and 5

Step-by-step explanation:

Solutions for an equation can be x-intercepts, or where it touches the x or horizontal line. The equation in #10 touches the x line at 2 and 5.

Emira takes home approximately 97.60% of her gross pay after deductions.

We have,

To calculate the percentage of Emira's gross pay that she takes home after deductions, we need to subtract the total deductions from her gross pay and then divide that by her gross pay, and finally multiply by 100 to get the percentage.

Total deductions = FICA + Federal income tax + State income tax + Health insurance + Retirement savings

= $522.00 + $480.25 + $215.00 + $165.25 + $600.00

= $1982.50

Net pay (amount taken home)

= Gross pay - Total deductions

= $82,000 - $1982.50

= $80,017.50

Percentage of gross pay taken home = (Net pay / Gross pay) x 100

= ($80,017.50 / $82,000) x 100

≈ 97.60%

Therefore,

Emira takes home approximately 97.60% of her gross pay after deductions.

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Answer:70.99%

Step-by-step explanation:

Yearly income/12mnths

82,000/12=6833.3333 monthly pay

Deductions

6833.3333-1982.5= 4850.333

Net pay/gross pay

4850.3333/6833.3333=.70987

Answer 70.99

Answer:

22.32

Step-by-step explanation:

coat + 2 pairs of jeans + boots = 148

42.78 + 2j + 60.58 = 148

Combine like terms

103.36 + 2j = 148

Subtract 103.36 from each side

103.36 - 103.36 + 2j = 148-103.36

2j = 44.64

Divide by 2

2j/2 = 44.64/2

j =22.32

Answer:

$22.32

Step-by-step explanation:

42.78 (for the coat) + 60.58(for the boots) + 2j (for the two pairs of jeans) = 148(the total)

42.78 + 60.58+ 2j= 148

subtract the cost of the coat and the jeans

2j=44.64

divide by two

j=22.32

the jeans cost $22.32

Answer:

5 x 3 = 15, 15 x 4 = 60

60 x 1/3(basically just dividing by 3) = 20 in3

Answer:

H) 20

Step-by-step explanation:

Formula for the volume of a rectangular pyramid:

V = (whl)/3

Given:

w = 3

h = 4

l = 5

Work:

V = (whl)/3

V = (3 × 4 × 5)/3

V = (60)/3

V = 20

Answer:

Hope it helps.

Step-by-step explanation:

d

≈

11.98

cm

Answer:

  12 cm

Step-by-step explanation:

In terms of diameter, the volume of a sphere is ...

  V = π/6d³

Filling in the given volume and solving for d, we have ...

  900 cm³ = π/6·d³

  d³ = 5400/π cm³

  d = ∛(5400/π) cm ≈ 11.98 cm

The diameter is approximately 12 cm.

Answer:

1 feet

Step-by-step explanation:

15-14

Answer:

y=5x−z

Step-by-step explanation:

Step 1: Multiply both sides by y.

xy−5=yz

Step 2: Add -yz to both sides.

xy−5+−yz=yz+−yz

xy−yz−5=0

Step 3: Add 5 to both sides.

xy−yz−5+5=0+5

xy−yz=5

Step 4: Factor out variable y.

y(x−z)=5

Step 5: Divide both sides by x-z.

y(x−z)x−z=5x−z

y=5x−z

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer:

63-93=-30

-4-5=-9

-156-(-45)=-111

Step-by-step explanation:

63-93=-30

-4-5=-9

-156-(-45)=-156+45=-111

Hope this helps!

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The declaration states that the value of Arc EFC = 253°.

A measure is indeed a quantitative concept used to express how large a collection is. Each unique measure represents a different method for determining how large a collection is. It would initially appear that a set's cardinality is the only logical way to determine its number.

We can tell we are working with a circular that has 360 degrees because of the connection.

We can infer that we have it if we look at that file.

Arc EFC

Arc CD

Arc DE

And everything together give us 360,

Arc EFC + Arc CD + Arc DE = 360

If we examine the figure again, we can see that the central angle of an intercepted arc is identical to the arc's measure.

Arc CD is 90 degrees since the central angle is 90 degrees given

Arc DE is 17 degrees

Arc EFC + Arc CD + Arc DE = 360

If we input all the figures

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Therefore, Arc EFC = 253°

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The correct questions is:

Circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Answer:

\(f(x) = {x}^{2} - 5 \\ \\ g(x) = 4x - 4 \\ \\ find \: (f - g)x \\ \\ (f - g)(x) = ( {x}^{2} - 5)(4x - 4) \\ \\ = {x}^{2} - 4x + 4 \\ \\ (f - g)(x) = {x}^{2} - 4x - 1 \\ \\ (f - g)(5) = {(5)}^{2} - 4(5) - 1 \\ \\ = 4\)

The critical points of the function y = 49y - y³ are y = 7/√3 (local maximum) and y = -7/√3 (local minimum).

To find the critical points of the function y = f(x) = 49y - y³, we need to find the values of y where the derivative dy/dx is equal to zero or undefined.

To find where the derivative is undefined, we need to look for any values of y where the denominator of the derivative, dx/dy, is equal to zero. However, in this case, the derivative is given as dy/dx, so we first need to find the derivative with respect to y:

f(y) = 49y - y³

f'(y) = 49 - 3y²

Now, we can set f'(y) equal to zero and solve for y to find where the derivative is equal to zero:

49 - 3y² = 0

3y² = 49

y² = 49/3

y = ±(7/√3)

So the critical points of the function occur at y = 7/√3 and y = -7/√3.

To determine whether these critical points correspond to local maximum or minimum points, we need to use the second derivative test. Taking the second derivative of f(y), we get:

f''(y) = -6y

Plugging in y = 7/√3, we get:

f''(7/√3) = -6(7/√3) < 0

Therefore, y = 7/√3 corresponds to a local maximum.

Plugging in y = -7/√3, we get:

f''(-7/√3) = -6(-7/√3) > 0

Therefore, y = -7/√3 corresponds to a local minimum.

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The functions represented on the graph are (b)

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following intervals:

When the intervals are represented as inequalities, we have the following:

This means that the intervals of the graphs are x ≤ 2 and x > 2

From the list of options, we have the graph to be option (b

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Answer:

Short and simple: 625

Answer:

∠V = 32°

Step-by-step explanation:

VW = UV

⇒ Isosceles triangle. So, the angles opposite sides are equal.

∠W = ∠U

∴ ∠W = ∠U = 74°

 Sum of all angles of triangle = 180

74 + 74 + ∠V = 180

       148 + ∠V = 180

                ∠V = 180 - 148

∠V = 32°

Answer:

C (circumference) =2×π×r

we've got a 30-60-90 triangle

which means 9=d√3, d=5.19 exact inches

or ≈5.20 inches

d=2r, r=5.20÷2≈2.60 inches

C=2×3.14×2.60≈16.328

Answer:

V + 4 = 10

Step-by-step explanation:

V represents the video games she has (unknown to us), and the word problem says she adds 4 more.

Hope this helped!

As per the distance, the length of the curve y = 3x − 2 for −3 ≤ x ≤ 1 is 4√10.

To begin, let us recall that the arc length formula gives us a way to find the length of a curve in terms of the function that defines it. The formula is given by:

L = ∫aᵇ √[1 + (dy/dx)²] dx

where L is the length of the curve, a and b are the endpoints of the curve, and dy/dx is the derivative of the function that defines the curve with respect to x.

For the curve y = 3x − 2, we can find dy/dx by taking the derivative of the function with respect to x. This gives us:

dy/dx = 3

We can now substitute this into the arc length formula and integrate over the interval −3 ≤ x ≤ 1:

L = ∫−3¹ √[1 + (3)²] dx

L = ∫−3¹ √10 dx

L = √10 ∫−3¹ dx

L = √10 (1 - (-3))

L = √10 (4)

L = 4√10

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Answer:

see explanation

Step-by-step explanation:

(a)

The angle on the circumference is half the central angle , that is

∠ A = ∠ BOC ÷ 2 = 50° ÷ 2 = 25°

(b)

Δ AOC is isosceles ( OA = OC , radii of the same circle ) then the base angles are congruent , that is

∠ ACO = ∠ A = 25°

(c)

Δ BOC is isosceles ( OB = OC, radii of the same circle ) then the base angles are congruent, that is

∠ BCO = \(\frac{180-50}{2}\) = \(\frac{130}{2}\) = 65°

(d)

∠ ACO + ∠ BCO = 25° + 65° = 90° ( angle in a semicircle )

The scale factor between the two right-angled triangles is 2. The right triangle on the right is a scaled copy of the left one, with all sides doubled in length.

To find the scale factor, we can compare the lengths of the corresponding sides of the two triangles.

Let's label the sides of the left triangle as follows:

The length of the hypotenuse (the side opposite the right angle) is H.

The length of the shorter leg (adjacent to the smaller angle) is S.

Now, let's label the corresponding sides of the right triangle:

The length of the hypotenuse is 2H (twice the length of the hypotenuse in the left triangle).

The length of the shorter leg is 2S (twice the length of the corresponding side in the left triangle).

The scale factor is the ratio of the corresponding side lengths in the two triangles. In this case, we can choose to compare the lengths of the shorter legs, since they are both labeled S:

Scale factor = length of corresponding side in right triangle / length of corresponding side in left triangle

Scale factor = 2S / S

Scale factor = 2

Therefore, Between the two right-angled triangles, there is a scale ratio of 2. With all edges doubled in length, the right triangle on the right is a scaled replica of the left triangle.

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Answer:

7

Step-by-step explanation:

3*7+4=25

5*7-10=25

Answer:

7/40

Step-by-step explanation:

Dividing both the numerator and the denominator by 540, the new fraction is 7/40. (3780/540 = 7 and 21600/540 = 40)

hope this helps! <3

hope this helps you understand the concept

Using theorems related to inverse functions, the value of (F-1)(3) is :

(F-1)(3) = (2 - √30)/3^(1/3)

To find (F-1)(3), we first need to find the inverse of f(x).
To do this, we switch x and y in the equation f(x) = x^3 + 2x + 1:
x = y^3 + 2y + 1
Then we solve for y:
y^3 + 2y + 1 - x = 0

Using the cubic formula or factoring techniques, we can solve for y:

y = (-2 + √(4-4(1)(1-x^3)))/2(1)  OR  y = (-2 - √(4-4(1)(1-x^3)))/2(1)

Simplifying, we get:

y = (-1 + √(x^3 + 3))/x^(1/3)  OR  y = (-1 - √(x^3 + 3))/x^(1/3)

Thus, the inverse function of f(x) is:

F-1(x) = (-1 + √(x^3 + 3))/x^(1/3)  OR  F-1(x) = (-1 - √(x^3 + 3))/x^(1/3)

Now, to find (F-1)(3), we plug in x = 3 into the inverse function:

F-1(3) = (-1 + √(3^3 + 3))/3^(1/3)  OR  F-1(3) = (-1 - √(3^3 + 3))/3^(1/3)

Simplifying, we get:

F-1(3) = (2 + √30)/3^(1/3)  OR  F-1(3) = (2 - √30)/3^(1/3)

Therefore, (F-1)(3) = (2 + √30)/3^(1/3)  OR  (F-1)(3) = (2 - √30)/3^(1/3).

This solution involves the use of theorems related to inverse functions, including switching x and y in the original equation and solving for y, as well as the cubic formula or factoring techniques to solve for y.

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The sum of all edges of the regular quadrilateral Pyramid is approximately 66.68 cm.

The sum of all edges of a regular quadrilateral pyramid, we need to determine the number of edges in the pyramid and then calculate their total length.

A regular quadrilateral pyramid has a base that is a regular quadrilateral, meaning all sides of the base have the same length. Let's assume that each side of the base has a length of "a" cm.

The perimeter of the base is given as P = 30 cm, so each side of the base measures 30 cm divided by 4 (since there are four equal sides) which is 7.5 cm.

Now, let's consider the lateral face of the pyramid. A regular quadrilateral pyramid has four lateral faces, each of which is an isosceles triangle. The perimeter of a lateral face is given as 27.5 cm. Since there are three edges in each lateral face, the length of each edge is 27.5 cm divided by 3, which is approximately 9.17 cm.

Therefore, the sum of all the edges in the pyramid is calculated as follows:

Sum of edges = (4 × a) + (4 × 9.17)

Since we know that each side of the base (a) is 7.5 cm, we can substitute this value into the equation:

Sum of edges = (4 × 7.5) + (4 × 9.17)

            = 30 + 36.68

            = 66.68 cm

Hence, the sum of all edges of the regular quadrilateral pyramid is approximately 66.68 cm.

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