If f(x)=x+2 and g(x)=x2+1 find:a. f(g(x)) b. g(f(x))

Answer:

Area = 180 cm^2

Step-by-step explanation:

See attached image.  The width of the rectangle, a , is the hypotenuse of a right triangle with legs 15 and 20.

Use the Pythagorean Theorem: leg^2 +leg^2 = hypotenuse^2

[tex]a^2=15^2+20^2\\\\a^2=225+400\\\\a^2=625\\\\a=\sqrt{625}=15[/tex]

The width, w, is one leg of a right triangle that has hypotenuse 20 and one leg 16.

[tex]w^2+16^2=20^2\\\\w^2+256=400\\\\w^2=144\\\\w=\sqrt{144}=12[/tex]

The rectangle has length 15 cm and width 12 cm so its area is 12 x 15 = 180 cm^2

Answer:

AREA RECTANGLE =300 cm²

Step-by-step explanation:

If 2 of the 3 vertices of a triangle match up with 2 of the 4 vertices of a rectangle,then the area of the triangle will be exactly half of the area of the rectangle

(Or the area of the rectangle  will be exactly double  of the area of the triangle)

  Area right triangle  = ½ × base × height.

A = 1/2(15X20)

A=1/2( 300)

Area triangle =150  

Area of rectangle is DOUBLE as the  area of triangle

AREA RECTANGLE = 300

Answer: Hope this helps you

1/2

Step-by-step explanation:

To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.

8x+2y = 4 ➨ 8x+2*0 = 4

Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:

8x = 4

Now I will divide both sides by 8, which isolates our x.

x = 1/2

The x-int is 1/2.

the correct options are:

Here we have the function:

[tex]F(x) = -\sqrt[3]{x}[/tex]

First, this is a cubic root, so its domain is the set of all real numbers (same for the range). And we know that the cubic root is an increasing function, so if we put a negative sign before it, we will have a decreasing function.

Then the correct options are:

The fourth option is incomplete, so we can't conclude if it is true or not, it would be true if it said:

"The function is a reflection over the x-axis of y = ∛x"

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Answer:

b, c, d

Step-by-step explanation:

Answer:

[tex]\circledast \ \ f\circ f\left( x\right) = x[/tex]

[tex]\circledast \ \ g\circ g\left( x\right) =4x - 21[/tex]

Step-by-step explanation:

[tex]f(x)=\frac{5}{2x}[/tex]

g(x) = 2x - 7

==============

[tex]f\circ f\left( x\right) =\frac{5}{2\left( f\left( x\right) \right) }[/tex]

             [tex]=\frac{5}{2\left( \frac{5}{2x} \right) }[/tex]

             [tex]=\frac{5}{\left( \frac{5}{x} \right) }[/tex]

             [tex]=5\times\frac{x}{5}[/tex]

             [tex]=x[/tex]

_____________

[tex]g\circ g\left( x\right) =2(g(x)) - 7[/tex]

            = 2(2x - 7) - 7

           = 4x - 14 - 7

           = 4x - 23

Answer: 462 square cm

Step-by-step explanation:

The area of the shaded region is the difference between the areas of the two rectangles.

Larger Rectangle: (42)(21)

Smaller Rectangle: (28)(15)

Area of shaded: (42)(21)-(28)(15)=462 square cm

Answer:

C) 20cm

Step-by-step explanation:

Perimeter is the distance around the edge of the shape.

8 + 7 + 5 = 20

Answer:

20 is answer

Step-by-step explanation:

as perimeter= sum of all side

= 8 +7+5=2ocm

B. none of these are correct

Answer:

3/2+1/2+17/2=21/2

Answer: 21/2 hours or 10 1/2 hours

Step-by-step explanation:

To find out the total number of hours needed for all activities scheduled for the day, simply add the needed hours for each activity.

You just need to add them because they have the same denominator.

3/2 for homework

1/2 for home chores

17/2 for sleep

[tex]\frac{3}{2} + \frac{1}{2} + \frac{17}{2} = \frac{21}{2}[/tex] hours

The normal distribution is also known as the Gaussian distribution. The correct option is B, while the approx z-score is 0.31.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Since the normal distribution is symmetrical about the mean. Therefore, the correct option is B, while the approx z-score is 0.31.

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Answer:

y = 2/5 x - 18/5

Step-by-step explanation:

y = mx + b

m = (y2 - y1)/(x2 - x1) = [-2 - (-6)]/[4 - (-6)] = 4/10 = 2/5

y = 2/5 x + b

-6 = (2/5)(-6) + b

-30 = -12 + 5b

5b = -18

b = -18/5

y = 2/5 x - 18/5

-0.8+1.875+100%

1.05+100%

0.1

Answer:

-10 and -2

Step-by-step explanation:

First, divide both sides by 4 to get |x+6| = 4
Then, Take the absolute vaule on both sides
x+6= 4 or -4
So, x could be 2 vaules
Your welcome!

4 | x + 6 | = 16

Divide both sides by 4.

[tex]\bf{\dfrac{4|x+6|}{4}=\dfrac{16}{4} }[/tex]

[tex]\bf{|x+6|=4 }[/tex]

Absolute value is solved.

[tex]\bf{|x+6|=4 }[/tex]

We know either x + 6 = 4 or x + 6 = -4.

x + 6 = 4 (Possibility 1)

x + 6 - 6 = 4 - 6 (Subtract 6 from both sides)

x=−2

x + 6 = -4 (Possibility 2)

x + 6 - 6 = -4 - 6 (Subtract 6 from both sides)

x=-10

Solution:

x=−2 or x=−10

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

the answer for the 2nd question is 1/4

Step-by-step explanation:

i took the test

The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).

Let's call the point that divides the line segment point P.

Point P divides the line segment into a ratio of 2:3

The ratio of 2:3 means we are dividing the line segment into 2+3=5 equal parts.

The horizontal distance between the two coordinates is 5.

The vertical distance between the two coordinates is 10.

Dividing both vertical and horizontal distance into five equal parts, we have a horizontal distance of 1 and a vertical distance of 2.

Every time we move one unit to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.

The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).

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Answer:

l & m intersect

2 & 3 are supplementary

1 & 3 are congruent

Step-by-step explanation:

The proof of expression"∡1 ≅ ∡3" is given below.

The complete flow chart is given in the attached image.

As per the provided diagram and the given information "Line l and line m intersect", the proof of the required statement can be done in the following steps.

Step 1:

Given: Line l and line m intersect.

Step 2:

∠1 is supplementary to ∠2

From the property of linear pair theorem.

Step 3:

∠2 is supplementary to ∠3

From the property of linear pair theorem.

Step 4:

As per the property of congruent supplements theorem,

∠1 ≅ ∠3

The complete chart is given below.

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Janelle rode the bus to the bus stop, talked with a friend, and then walked home ,  Option D is the correct answer.

The missing graph is attached with the answer.

A graph which shows change in distance with respect to time is called Time- Distance Graph.

It is used to calculate velocity.

As in the graph we it can be seen that , The distance is decreasing at a constant speed ,

then the distance becomes constant with time

and then again decreases but with a lower rate

This means

Janelle rode the bus to the bus stop (distance to time rate is high)

talked with a friend (distance is constant with time)

and then walked home. (distance to time rate is low)

Therefore Option D is the correct answer.

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Answer:

Janelle rode the bus to the bus stop, talked with a friend, and then walked home.

Step-by-step explanation:

Considering the hang time equation, it is found that Player 1 jumped 0.68 feet higher than Player 2.

The hang-time of the ball for a player of jump h is given by:

[tex]t = 2\left(\frac{2h}{32}\right)^{\frac{1}{2}}[/tex]

The expression can be simplified as:

[tex]t = 2\sqrt{\frac{h}{16}}[/tex]

For a player that has a hang time of 0.9s, the jump is found as follows:

[tex]0.9 = 2\sqrt{\frac{h}{16}}[/tex]

[tex]\sqrt{\frac{h}{16}} = \frac{0.9}{2}[/tex]

[tex](\sqrt{\frac{h}{16}})^2 = \left(\frac{0.9}{2}\right)^2[/tex]

[tex]h = 16\left(\frac{0.9}{2}\right)^2[/tex]

h = 3.24 feet.

For a player that has a hang time of 0.8s, the jump is found as follows:

[tex]0.8 = 2\sqrt{\frac{h}{16}}[/tex]

[tex]\sqrt{\frac{h}{16}} = \frac{0.8}{2}[/tex]

[tex](\sqrt{\frac{h}{16}})^2 = \left(\frac{0.8}{2}\right)^2[/tex]

[tex]h = 16\left(\frac{0.8}{2}\right)^2[/tex]

h = 2.56 feet.

The difference is given by:

3.24 - 2.56 = 0.68 feet.

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Answer:

4 kg

Step-by-step explanation:

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

Answer:

4 kg

Explanation:

Let the mass of tank be 't' and water 'w'

First equation :              (when it is 1/4 filled with water)

Second equation :        (when it is filled fully with water)

Insert second equation into first equation :

[tex]\rightarrow \sf t + \dfrac{1}{4} (10.4 - t) = 5.6[/tex]

[tex]\rightarrow \sf t - \dfrac{1}{4} t + 2.6 = 5.6[/tex]

[tex]\rightarrow \sf \dfrac{3}{4} t = 5.6 - 2.6[/tex]

[tex]\rightarrow \sf \dfrac{3}{4} t = 3[/tex]

[tex]\rightarrow \sf t = 4[/tex]

The tank weights 4 kg when it is empty.

Answer:

meight you gotta do better then that

Step-by-step explanation:

a picture is probably necessary

A percentage is a way to describe a part of a whole. The percentile ranking of Tina's sister is higher than her.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

A.)

The percentile ranking of Tine is,

Tina's Ranking = [1 - (54/300)] × 100% = 82%

Tina's soster Ranking = [1 - (23/175)] × 100% = 86.85%

Hence, the percentile ranking of Tina's sister is higher than her.

B.) It shows that you can succeed in the graduate examination if you exceed this value.

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Answer: [tex]f(x)=-(x-5)^{2}(x+2)[/tex]

Step-by-step explanation:

There is a double root at x=5 and a single root at x=-2, so we know f(x) is of the form [tex]f(x)=a(x-5)^{2}(x+2)[/tex] for some constant a.

To find a, we can substitute the coordinates of the y-intercept, (0, -50).

[tex]-50=a(0-5)^{2}(0+2)\\\\-50=50a\\\\a=-1[/tex]

So, [tex]f(x)=-(x-5)^{2}(x+2)[/tex]

Answer:

[tex]\frac{5pi}{6}[/tex]

Step-by-step explanation:

Answer:

[tex]x = \dfrac{\pi}{6}, \dfrac{5 \pi}{6}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\\implies x & = \sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{\pi}{6} \pm 2 \pi n, \dfrac{5 \pi}{6}\pm 2 \pi n\end{aligned}[/tex]

Therefore, the value of x in the interval [0, 2π) is:

[tex]x = \dfrac{\pi}{6}, \dfrac{\boxed{5} \pi}{\boxed{6}}[/tex]

Answer:

7754

Step-by-step explanation:

give brainiest, please. <3

Answer:

about 7,754 m

Step-by-step explanation:

101 * 70.2 = 7,090.2

7,090.2/0.9144 = 7,753.9

Answer:

A. $60.25

B. 76 miles

C. 216 miles

Step-by-step explanation:

x is miles

y is total amount spent

For A, 57 miles is the x value. Plug that in to x.

y= 46 + .25(57)

y= 60.25

For B, the total is the y. So plug 65 in for y.

65 = 46 + .25x   Subtract 46 from both sides

19 = .25x             Divide by .25

76 = x

For C, the maximum you can spend is $100. Plug that in for y.

100 = 46 + .25x   Subtract 46 from both sides

54 = .25x             Divide by .25

216 = x

The answer for part a is $60.25, for part b the answer is 76 miles, and for part c the answer is 216 miles.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation to represent the cost would be y=46+0.25x

x is the number of miles.

a) What is your cost if you travel 57 miles?

Plug x = 57 in the above equation:

y = 46 + 0.25(57)

y = $60.25

b) If your cost was $65.00, how many miles were you charged for traveling?

Plug y = 65 in the equation:

65 = 46 + 0.25x

x = 76 miles

c) Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?

Plug y = 100 in the equation:

100 = 46 + 0.25x

x = 216 miles

Thus, the answer for part a is $60.25, for part b the answer is 76 miles, and for part c the answer is 216 miles.

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Answer:

A ∩ (B U C) = {b , e , i}

Step-by-step explanation:

A = {b , e , g , i}

B = {a , b , e , f}

C = {a , e , i , j}

We note B U C ,The union of the two sets B and C

which is the set that contains all elements

that are in B or in C .

The easiest way to determine B U C :

Step1 : (write all the elements of B and C side by side)

B U C = {a , b , e , f , a , e , i , j}

Step2 : (delete the repeated elements)

B U C = {a , b , e , f , i , j}

FINDING A ∩ (B U C) :

it’s the set of elements that exist in both sets

A and B U C simultaneously:

A = {b , e , g , i}

B U C = {a , b , e , f , i , j}

Then

A ∩ (B U C) = {b , e , i}

The first term will be 4 and the common ratio will be 2. And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].

The complete question is attached below.

Let a be the first term and r be the common ratio. Then the geometric sequences will be

[tex]\rm a_n = a_{n -1} \cdot r[/tex]

The geometric sequence is given below.

4, 8, 16, 32, 64,................

Then the first term will be 4 and the common ratio will be 2.

And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].

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Answer:

y + 16 = 3(x + 5)

Step-by-step explanation:

When you write an equation in point-slope form, you only need two things: a point and a slope.

Given:

The standard point-slope equation is

y - y₁ = m(x - x₁)

Plug in what you know.

y - (-16) = 3(x - (-5))

Simplify.

y + 16 = 3(x + 5)

This is your equation.

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Answer: 7x+13

Step-by-step explanation:

7 is being multiplied by some number (x) and then the answer to that is added to 13.

The probability that a random passenger survived is 0.38

The probability that this passenger was in first class and survived is 0.153

The probability that the passenger in the first class survived is 0.620

The probability that the passenger that survived was in first class is 0.402

The probability that the passenger that survived was in third class is 0.362

The probability that a random passenger survived is 500 / 1317 = 0.38

The probability that this passenger was in first class and survived is 201 / 1317 = 0.153

The probability that the passenger in the first class survived is:  201 /324 = 0.620

The probability that the passenger that survived was in first class: 201/500 = 0.402

The probability that the passenger that survived was in third class is: 181 / 500 = 0.362

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