7. If F(x) = f(g(x)), where f(-2) = 8, f'(-2) = 4, f'(5) = 3, g(5)=-2, gʻ(5) = 6.. Find F'(5)
​

The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

More can be learned about least common denominator at https://brainly.com/question/19249494

#SPJ1

Answer:

total of 25 students playing football

Step-by-step explanation:

only Football = 2

Football/Baseball = 14

Football/Tennis = 3

All = 6

Add them all: 2 + 14 + 3 + 6

Answer:

25

Step-by-step explanation:

Total number of students that play football = 3 + 2 + 6 + 14 = 25

Answer:

282.74

Step-by-step explanation:

A=2πrh+2πr2=2·π·5·4+2·π·52≈282.74334

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Learn more about inequality here:

https://brainly.com/question/25944814

#SPJ1

Answer:

Step-by-step explanation:

Transformation involves changing the position of a shape in the coordinate.

See attachment for the image of the triangle

Assume the triangle is triangle ABC.

The coordinates of ABC are:

\(\mathbf{A = (-1,-4)}\)

\(\mathbf{B = (-2,-7)}\)

\(\mathbf{C = (5,-6)}\)

The transformation rule is given as:

\(\mathbf{(x,y) \to (x -5,y+6)}\)

So, we have:

\(\mathbf{A' = (-1 -5,-4+6)}\)

\(\mathbf{A' = (-6,2)}\)

\(\mathbf{B' = (-2 -5,-7+6)}\)

\(\mathbf{B' = (-7,-1)}\)

\(\mathbf{C' = (5 -5,-6+6)}\)

\(\mathbf{C' = (0,0)}\)

So, the coordinates of the new triangle would be:

\(\mathbf{A' = (-6,2)}\)

\(\mathbf{B' = (-7,-1)}\)

\(\mathbf{C' = (0,0)}\)

See attachment for the image of ABC

Read more about transformations at:

https://brainly.com/question/12463306

Answer:

(5/8)/(1/2)=10/8=5/4

Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

x = 11

Step-by-step explanation:

3x+1 = 2x+12 (subtract 2x from both sides)

x+1 = 12 (subtract 1 from both sides)

x = 11

So x is equal to 11

Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation:

Answer:

\(w^{22}\)

Step-by-step explanation:

\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)

Answer:

24 and 1/2

Step-by-step explanation:

20 + 10 - 5 and 1/2 = 24 and 1/2

Answer:

x = \(\frac{13}6}\) = 2 \(\frac{1}{6}\)

Step-by-step explanation:

34.2 = 13.4 + 9.6x

20.8 = 9.6x

x = 20.8 / 9.6

x = \(\frac{13}6}\)

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

The angle is 16 degrees or 164 degrees.

Any triangle that is not a right triangle is said to be oblique. There are two types of triangles: acute triangles, in which all three angles are less than right angles, and obtuse triangles (one of the three angles is greater than a right angle). Actually, right triangles could equally well be included in the category of "oblique triangles" for trigonometric purposes. In that case, studying oblique triangles is basically studying all triangles.

Given, the area of an oblique triangle which is going to be used as an area of the formula backward to find a missing measure.

We know two side lengths of the triangular region 60 ft and 1 20 ft

Area = 1000-square-foot

A= 1/2*60*120=1000

A=3600=1000

Dividing both sides with 3600,

We get an angle of 16 degrees.

But it is also possible that the area will be the same. If we use this in supplementary angle as well we get,

180-16 = 164 degrees.

To know more about triangles visit: brainly.com/question/2773823

#SPJ4

When constructing a perpendicular bisector of a segment, you should make arcs with the same radius from each endpoint as D. this makes the arcs parallel to the segment

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90-degree angle.

A line segment known as a perpendicular bisector divides a straight line segment into two congruent or equal segments. At the exact midpoint of the line segment, they divide it. The arcs with the same radius from each endpoint is important as this makes the arcs parallel.

Learn more about segment on:

https://brainly.com/question/2437195

#SPJ1

Answer:yes

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

scale factor=md/od

=0.5/2

0.25

Answer:

-----------------------

Triangular faces have a base of 7 cm and height of 9 cm.

The area of one face is:

The area of one of the triangular faces in this square pyramid is

1.5 square cm

The area of a triangular face in the figure displaying net of square pyramid is achieved by using the formula for re of triangle

The formula for area of triangle is given by

= 1/2 base * height

= 1/2 * 7 * 9

= 1/2 * 63

= 31.5 square cm

We can therefore say that the e area of one of the triangular faces in this square  pyramid is 31.5 square cm

Learn more about area of a triangle at

https://brainly.com/question/17335144

#SPJ1

Answer:

4x + 3 = 59

x = 14

Step-by-step explanation:

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this here by stating the following:

4x + 3 = 59

Solve for (x), use inverse oeprations:

4x + 3= 59

4x = 56

x = 14

Answer:

Relationship : Vertical angle

Step-by-step explanation:

(4x + 3) = 59

4x = 59 - 3

4x = 56

x = 56/4

x = 14

\(\rightarrow\sf((p(x) {x}^{2} + 2x + 4)( {x}^{2} + 2x + 4)) \\ = \sf {ax}^{2} + bx + c \\ = \sf(p(x) {x}^{2} {x}^{2} + p(x) {x}^{2} (2x) + p(x) {x}^{2} \times 4 + 2x \times {x}^{2} + 2x(2x) + 2x \times 4 + {4x}^{2} + 4(2x) + 4 \times 4) \\ = \sf( {x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16) \\ \rightarrow \large\boxed{\sf\red{{{x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16}}}\)

\(\large\boxed{\sf{\red{{x}^{4} p(x) + {2x}^{3} p(x) + {4x}^{2} p(x) + {2x}^{3} + {8x}^{2} + 16x + 16}}}\)

\(\color{red}{==========================}\)

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ

✍︎ꕥᴋɪᴍ ᴀʀᴀꕥ

Answer: 26/3 or 8 2/3

Step-by-step explanation:

In the addition or subtraction of fraction, first, you have to convert all of them into improper fraction if they are mixed; then, you need to find the LCD (Least Common Denominator).

Converting fraction:

5 3/4=23/4

2 11/12=35/12

Finding LCD:

4 and 12 is 12

Converting fraction into common denominator:

23/4=69/12

35/12=35/12

Solve:

 5 3/4 + 2 11/12

=69/12 + 35/12

=104/12

The probability that a randomly chosen child has a height of less than 33.3 inches when mean height is 56.8 inches and standard deviation is 9.4 inches will be 98%.

As per the question statement, in the country of United States, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.8 inches and standard deviation of 9.4 inches. We are supposed to find the probability that a randomly chosen child has a height of less than 33.3 inches.

z = (X - μ) / σ, where X is the data data, μ = mean, σ = standard deviation

z = (66.09 - 56.8) / 9.4

z = 0.988 or 98%

So, the probability that a randomly chosen child has a height of less than 33.3 inches when mean height is 56.8 inches and standard deviation is 9.4 inches will be 98%.

To learn more about probability, click on the link given below:

https://brainly.com/question/12402189

#SPJ1

Answer:

The area of the shaded region is 36.

Step-by-step explanation:

First, let's find the area of the rectangle as a whole, which will be 5*10 = 50. How did we get 50? The right side is 5 (from 2+3), and the top is 10 (3+7). Multiplying those numbers together will give you the area.

Now, the problem asks to find the shaded region. Let's solve for the area of the non-shaded region: (7*2) = 14.

Now, we can subtract the whole rectangle area minus the non-shaded region to find the shaded region:

50 - 14 = 36

Answer:

21.5≤μ≤25.2

Step-by-step explanation:

The formula for calculating confidence interval is expressed as;

CI = xbar±(z*s/√n)

xbar is the mean = 23.7

s is the standard deviation= 16.3

n is the sample size = 438

z is the z score at 95% confidence level

z = 1.96

Substitute into the formula

CI = 23.7±(1.96×16.3/√438)

CI = 23.7±(1.96×16.3/20.93)

CI = 23.7±(1.96×0.77788)

CI = 23.7±1.5264

CI = (23.7-1.5264, 23.7+1.5264)

CI = (21.4736, 25.2264)

The confidence interval to the nearest tenth is 21.5≤μ≤25.2

Answer:

Step-by-step explanation:

..........................

To analyse the influence of exercise on reaction time, the researchers equation might have utilised the average change in reaction time for the group as a whole or looked at individual changes in reaction time.

In several trials, regular exercise has been proven to enhance reaction time. It is feasible that running two laps around a track will improve reaction time for the students in this study.

In this study, the response variable is the reaction time of 15 randomly selected students before and after running two laps on a track. The researchers measured reaction time using an online game, which was most likely a timed task that required participants to respond fast to a stimuli. To analyse the influence of exercise on reaction time, the researchers might have utilised the average change in reaction time for the group as a whole or looked at individual changes in reaction time.

To know more about exercise visit:

https://brainly.com/question/13128077

#SPJ1