Given that f(x) = x^2 + 6x – 2, g(x) = x – 7, and h(x) = x + 4
find each function. (f + g)(x)

Answer:

h^-1(x) = (5x - 6)/2

Step-by-step explanation:

To find the inverse of h(x) = (2x + 6)/5, we need to solve for 'x':

y = (2x + 6)/5 ⇒ 5y = 2x + 6 ⇒ 5y - 6 = 2x ⇒ x = (5y - 6)/2

Therefore, h^-1(x) = (5x - 6)/2

Answer:

(5x-6)/2

Step-by-step explanation:

h(x) = (2x + 6)/5

y =  (2x + 6)/5

To find the inverse, exchange x and y

x = (2y+6) /5

Then solve for y

Multiply each side by 5

5x = (2y+6)/5*5

5x = 2y+6

Subtract 6 from each side

5x-6 = 2y+6-6

5x-6 = 2y

Divide by 2

(5x-6)/2 = 2y/2

The inverse is

(5x-6)/2

Answer:

Sin x = a / b.

Step-by-step explanation:

The opposite side =a and the adjacent side = 4 (because tan x = a/4.

Cos x = 4/b so the hypotenuse = b ( because  Cos = adjacent /hypotenuse.

So sin x = opposite /hypotenuse = a / b.

Answer:

sin x° = a divided by b is the answer

Step-by-step explanation:

I got 100% on the test!

Answer:

[tex]-3x-6 < -33[/tex]  and [tex]-3x-6 \geq -6[/tex]

Step-by-step explanation:

we have

[tex]-33 > -3x-6 \geq -6[/tex]

we know that

Compound inequality can be divided into two inequalities

so

[tex]-33 > -3x-6[/tex]

rewrite

[tex]-3x-6 < -33[/tex]

and

[tex]-3x-6 \geq -6[/tex]

therefore

An equivalent form of the compound inequality is

[tex]-3x-6 < -33[/tex]  and [tex]-3x-6 \geq -6[/tex]

Answer:

Check attachment for the included diagram

The last option is the correct otpiton 98.5m

Step-by-step explanation:

We know that side 1= 65m

Side 2 =55m

Then, the angle between the two sides are not given, let call the third angle X

We know the other two opposite angles and which are 40° and 30°.

Applying sum of angle in as triangle

The sum of angle in a triangle is 180°

Then,

X+30+40 =180

X+ 70 =180

X=180-70

X=110°

So, using cosine rule

c² = a²+b²-2abCosX

c² = 65²+55²-2•65•55Cos110

c² = 4225+3025-(-2445.44)

NOTE: -×-=+

c² = 4225+3025+2445.44

c² = 9695.44

c=√9695.44

c=98.465

To the nearest ten

c= 98.5m

The last option is the correct answer

Answer:

The distance between the two landmarks is 98.5m

Step-by-step explanation:

I've attached an image to depict where toby is standing, the landmark and the angles.

To get the distance between the 2 landmarks, we will make use of cosine rule which is given as;

c² = a² + b² − 2ab cos(C)

Where, a and b are the two given lamdmarks.

c = the distance between the landmarks

C is the angle opposite the distance between the landmarks i.e the angle at the point at where toby is standing

Now, we are not given the angle C. But we can calculate it from knowing that sum of angles in a triangle is equal to 180.since we know 2 angles, thus, C = 180 - (40 + 30) = 110°

Now, we can solve for c by plugging in the relevant values ;

c² = 55² + 65² - (2*55*65*Cos110)

c² = 4225 + 3025 -7150(-0.342)

c² = 9695.3

c=√9695.3

c=98.46m ≈ 96.5m

Answer:

The answer is D: 5,000

Step-by-step explanation:

That is the easiest question to solve. Good luck!

The number of earthworms he have if his square of compost has a side length that is five times longer is 5000.

The first step is to determine the number of earthworms in a compost with a side length of 1.

1000 / 4 = 250

Number of earthworms with side length five time longer : (4 x 5) x 250 = 5000

To learn more about multiplication, please check: https://brainly.com/question/13814687

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Answer:

  y = -1/2x +5

Step-by-step explanation:

Slope-intercept form is ...

  y = mx + b

Matching this to the equation you have, you see that ...

  m = -2/4 = -1/2

  b = 5

The equation is already in slope-intercept form. The fraction that is the slope can be reduced, but that is not essential to the form.

Answer:

Option A

Step-by-step explanation:

This is because whenever you have a negative exponent, you put it to the reciporical value of it.  If you have two same exponenet bases, you add them up.

Please mark for Brainliest!! :D Thanks!!

For more questions or more information, please comment below!

The option (A) is correct after using the properties of the integer exponent.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an expression:

[tex]\rm =\dfrac{\left(10a^{-8}b^{-2}\right)}{4a^3b^5}[/tex]

[tex]\rm =\dfrac{5a^{-8}b^{-2}}{2a^3b^5}[/tex]

[tex]= \rm \dfrac{5b^{-2}}{2a^{11}b^5}[/tex]

[tex]\rm =\dfrac{5}{2a^{11}b^7}[/tex]

Thus, the option (A) is correct after using the properties of the integer exponent.

Learn more about the integer exponent here:

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Step-by-step explanation:

[tex]m\angle2+m\angle3=m\angle5\ and\ m\angle2=25,\ then\ 25+m\angle3=m\anlg5[/tex]

Insert 25 instead of m<2 into the equation

Answer:

25 + m∠3 = m∠5

Step-by-step explanation:

Substitution property of equality states that,

If a + b = c and b = e ⇒ a + e = c

Given,

[tex]m\angle 2 + m\angle 3 = m\angle 5[/tex] and [tex]m\angle 2 = 25[/tex]

By substituting the value of m∠2 in first equation,

[tex]25 + m\angle 3 = m\angle 5[/tex]

Hence, the missing terms is '25 + m∠3'

0.85 and strong positive correlation

Good Luck!

Answer:

0.85 & Strong Positive Correlation

Step-by-step explanation:

On EDGE 2023

The square had a side length of 3x+13.

Because the perimeter is 12x+52, you have to divide that by each of the four sides.

Answer:

Ava was in charge of clearing a 16 mile ratius along the parks sidewalk, after she finished, she was ordered to get the exact number of feet in each mile, she knew she cleared 84480 feet, how can she find a, the exact number of one mile?

Step-by-step explanation:

Ava had to clear 84480 feet, after she finished she had to find out the exact number of feet in a mile, she knew she had 5280 feet in a mile, so you have to divide 5280 to 84480

Answer:

{Vanilla, strawberries, sprinkles}

Step-by-step explanation:

If you're trying to find c then the answer is all things that are not in C that are in the other sets

Using the given sets, C' consists of vanilla, strawberries, sprinkles

What C' means is that we are to list all items that are not in set C but are in set A and set B.

To learn more about sets, please check: https://brainly.com/question/12843263

Answer:

23%

Step-by-step explanation:

There are 4 male and 3 female freshmen. Thus the total number of freshmen is 7.

On the other hand, we have 14 male students and 16 female students. Thus the total number of students is 30.

If a student is selected at random, the probability that the student is a freshman is;

( 7/30) * 100 = 23.33%

Answer:A

Step-by-step explanation:

Answer:

X=5

Step-by-step explanation:

1: 90 plus 50 because there is a 90 degree angle

2: 8x=140 and then you divide by 8

3: x=5 I hope I helped you and I hope you have a wonderful day

Answer:

X=5

Step-by-step explanation:

8x+50=90

    8x=40

        x=5

Answer:

Step-by-step explanation:

The zeros are the x-values where the graph crosses the x-axis (y=0; That's why it is called a "zero.") The graph crosses y=0 at x=1 and x=3.

A factor of the polynomial is zero at each zero. Hence the factorization is ...

  y = (x -1)(x -3)

The first factor is zero at x=1; the second factor is zero at x=3.

Answer:

(1, -5); (4, 3)

Step-by-step explanation:

We generally orient maps with north at the top. This problem presumes that orientation along with a grid having units of 1 mile. "Town Center" is taken to be the origin of the grid. As is usually the case, left/right coordinates are indicated first in an ordered pair, with up/down coordinates being indicated second.

Then the warehouse location 8 miles south and 3 miles west of Town Center is considered to have coordinates of (-3, -8). Movement 3 miles north and 4 miles east is considered to be translation by (4, 3). This translation vector is the answer to the second part of the problem.

The answer to the first part of the problem is the sum of the starting position and the translation:

(-3, -8) +(4, 3) = (1, -5)

The truck's final position is (1, -5). The translation vector to get it there is (4, 3).

Answer:

This does represent an exponential function , because his savings increase by a constant rate

Step-by-step explanation:

Let

x -----> the number of weeks

y ----> the amount saved

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

r is the rate of change

where

[tex]a=\$6[/tex]

[tex]r=100\%=100/100=1[/tex] ---- because he doubles the amount each week

[tex]b=1+r[/tex] ----> [tex]b=1+1=2[/tex]

substitute

[tex]y=6(2)^{x}[/tex]

therefore

This does represent an exponential function , because his savings increase by a constant rate

Answer:

1/6

Step-by-step explanation:

I guess we are to assume each is equally likely.  There a 6 possible outcomes and one D so the answer is 1/6

Answer:

  C.  bal(156)

Step-by-step explanation:

In 13 years, there are ...

  13 × 12 = 156 . . . months.

So, the balance after the 156th payment is desired. The bal(156) function of a TI-84 graphing calculator will give that value.

Answer:

bal (156) is the right APEX answer. hope this helps!!

Answer:

D

Step-by-step explanation:

both angles have 2 straight lines that intersect in the middle, this is called vertical angles which means, according to the law, that each angle is equal to the other so 10x + 10 = 110. Therefore the answer is D

Answer:

D 10x+10 = 110

Step-by-step explanation:

10x +10 and 110 are  vertical angles   and vertical angles are equal

10x+10 = 110

Answer:

  $3355.20

Step-by-step explanation:

The formula for simple interest is ...

  i = Prt

where P is the principal amount, r is the annual rate, and t is the number of years. Fill in the given values and do the arithmetic.

  i = 12,000×0.0699×4 = 3355.20

Paul owes $3355.20 in interest.

Answer:

a. 12sqrt(3) cm.                                     b. 72sqrt(3) cm squared

Step-by-step explanation:

a. I hope you see this a 30-60-90 triangle

The short side is opposite to 30

The long leg is opposite to 60

The hypotenuse, the longest side, is opposite 90.

So you are given short side which is 12 cm.

The long leg (the height in this case) is short side times square root of 3 so your height is 12sqrt(3) cm.

b. The area of a triangle is .5*base*height.

You have both the base and height now so plug them in:

.5(12)(12sqrt(3)) cm squared

6(12)sqrt(3)  cm squared

72sqrt(3) cm squared

Answer:

f(x) = 4|x|

Step-by-step explanation:

the graph of f(x) = |x|, looks like a "V"

if we want to make the graph "narrower", what we are doing is really trying to make the slope steeper (i.e more vertical) so that the opening of graph at the top of the "V" becomes smaller.

in order the make the slope steeper, we have to multiply the x-term of the function (in this case |x|) by any factor that is greater than 1. (multiplying by factors smaller than 1 will make the slope more gentle and hence making the "V" wider).

The only choice that shows the original function multiplied by a number that is greater than 1 is f(x) = 4|x|

Answer:

D

Step-by-step explanation:

B) The estimated animal population in 2050, given the same percent increase from 1950 to 2000, will be approximately 8,100.

The percent increase from 1950 to 2000 =  (New Population - Original Population) / Original Population x 100%

In this case, it is:

(7200 - 6400) / 6400 x 100%

= 12.5%

The population in 2050 under the same percent increase, we apply this percentage to the population in 2000:

7200 x (1 + 12.5/100) = 7200 x 1.125 = 8100

The expected population in 2050 is 8,100.

Thus, the correct answer is B) 8,100.

To calculate the percent increase over 50 years, we first find the absolute increase from 1950 to 2000, and then determine the percent increase relative to the initial value in 1950.

Next, we apply that percent increase to the population in 2000 to predict the population in 2050.

Calculate the Absolute Increase

The increase in the animal population from 1950 to 2000 is:

[tex]\[7200 - 6400 = 800.\][/tex]

Calculate the Percent Increase

To find the percent increase over the period from 1950 to 2000, use the following formula:

[tex]\[ \frac{{\text{increase}}}{{\text{initial value}}} \times 100 = \frac{{800}}{{6400}} \times 100 = 12.5\%. \][/tex]

Thus, the population increased by 12.5% over 50 years.

Apply the Percent Increase to Predict the 2050 Population

Given the 12.5% increase, the expected increase in population from 2000 to 2050 would be 12.5% of 7200:

[tex]\[ 0.125 \times 7200 = 900. \][/tex]

Thus, the predicted population in 2050 is:

7200 + 900 = 8100.

Question :

In 1950, scientists estimated a certain animal population in a particular geographical area to be 6,400. In 2000, the population had risen to 7,200. If the animal population experiences the same percent increase over the next 50 years, what will the approximate population be?

A) 8,000

B) 8,100

C) 8.400

D) 8.600

Answer:

The cloud is at height 977 feet to the nearest foot

Step-by-step explanation:

* Lets explain how to solve this problem

- You place a bright searchlight directly below the cloud and shine the

  beam straight up to measure the height of the cloud

- You measure the angle of elevation of the cloud from a point 120 feet

 away from the base of the searchlight

- The measure of the angle of elevation is 83°

- Lets consider the the height of the cloud and the distance between

 the base of the searchlight and the point of the angle of elevation

 (120 feet) are the legs of a right triangle

∴ We have a right triangle the height of the cloud is the opposite

  side to the angle of elevation (83°)

∵ The distance between the base of the searchlight and the point

  of the angle of elevation (120 feet) is the adjacent side of the

  angle of elevation (83°)

- By using the trigonometry function tan Ф

∵ Ф is the angle of elevation

∴ Ф = 83°

∵ tan Ф = opposite /adjacent

∵ The side opposite is h (height of the cloud)

∵ The adjacent side to Ф is 120 feet

∴ tan 83° = h/120 ⇒ by using cross multiplication

∴ h = 120 × tan 83° = 977.322 ≅ 977 feet

* The cloud is at height 977 feet

Using trigonometry, specifically the tangent function, with the angle of elevation at 83° and the distance from the searchlight being 120 feet, the cloud's height is calculated to be approximately 1142 feet when rounded to the nearest foot.

To calculate the height of the cloud, we will use trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite side (the height of the cloud) and the adjacent side (distance from searchlight to observation point). The formula is as follows: tan(angle) = opposite/adjacent.

Given the angle of elevation is 83° and the distance (adjacent) is 120 feet, we apply the formula:

We use a calculator to find the tangent of 83°, and then multiply that by 120 feet to get the height.

height = 120 feet * tan(83°) ≈ 120 feet * 9.51436

The height is approximately 1141.7 feet. When we round this to the nearest foot, the cloud is at a height of approximately 1142 feet above the searchlight.

Explanation:

A triangle can be formed for b=3 and B=15° as long as side c is between 3 and 3/sin(15°) ≈ 11.59 inches in length. The limit for side c on the high end is that it is opposite a right angle. The limit for side c on the other end is that it is opposite a linear angle.

For the given length of side c, there are two possible triangles with b=3 and B=15°. (See attached.)

_____

For the given values of b and c, the largest possible value of B is the angle that puts side c opposite a right angle: B ≤ arcsin(3/7) ≈ 25.3769°

Answer:

A

Step-by-step explanation:

The angle on the right side of the triangle is 10° ( alternate angle )

Since the triangle is right with hypotenuse x use the sine ratio to solve for x

sin10° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{200}{x}[/tex]

Multiply both sides by x

x × sin10° = 200 ( divide both sides by sin10° )

x = [tex]\frac{200}{sin10}[/tex] ≈ 1, 151.8 m

Answer:

The correct answer is first option

1151.8 m

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin ?  = Opposite side/Hypotenuse

Cos ? = Adjacent side/Hypotenuse

Tan ? = Opposite side/Adjacent side

To find the value of x

From the figure we can see a right angled triangle.

We can write,

Sin 10 = opposite side/Hypotenuse

 = 200/x

x = 200 * Sin 10

 =  200 / 0.1736

 = 1151.8

The correct answer is first option

1151.8 m

Answer:

864 units²

Step-by-step explanation:

Area of each sloped side,

= 1/2 x base x height

= 1/2 x 16 x 19 = 152 units²

There are 4 sloped sides, so area of all sloped sides = 4 x 152 = 608 units²

Area of base = Length x Width = 16 x 16 = 256 units²

Total surf. area = area of all sloped sides + area of base

= 608 + 256

= 864 units²

Answer:

I know this is a late answer but it's A. 864 units²

Step-by-step explanation:

Have a great day!

1. The four subintervals are [0, 2], [2, 3], [3, 7], and [7, 8]. We construct trapezoids with "heights" equal to the lengths of each subinterval - 2, 1, 4, and 1, respectively - and the average of the corresponding "bases" equal to the average of the values of [tex]R(t)[/tex] at the endpoints of each subinterval. The sum is then

[tex]\dfrac{R(0)+R(2)}2(2-0)+\dfrac{R(2)+R(3)}2(3-2)+\dfrac{R(3)+R(7)}2(7-3)+\dfrac{R(7)+R(8)}2(7-8)=\boxed{24.83}[/tex]

which is measured in units of gallons, hence representing the amount of water that flows into the tank.

2. Since [tex]R[/tex] is differentiable, the mean value theorem holds on any subinterval of its domain. Then for any interval [tex][a,b][/tex], it guarantees the existence of some [tex]c\in(a,b)[/tex] such that

[tex]\dfrac{R(b)-R(a)}{b-a)=R'(c)[/tex]

Computing the difference quotient over each subinterval above gives values of 0.275, 0.3, 0.3, and 0.26. But just because these values are non-zero doesn't guarantee that there is definitely no such [tex]c[/tex] for which [tex]R'(c)=0[/tex]. I would chalk this up to not having enough information.

3. [tex]R(t)[/tex] gives the rate of water flow, and [tex]R(t)\approx W(t)[/tex], so that the average rate of water flow over [0, 8] is the average value of [tex]W(t)[/tex], given by the integral

[tex]R_{\rm avg}=\displaystyle\frac1{8-0}\int_0^8\ln(t^2+7)\,\mathrm dt[/tex]

If doing this by hand, you can integrate by parts, setting

[tex]u=\ln(t^2+7)\implies\mathrm du=\dfrac{2t}{t^2+7}\,\mathrm dt[/tex]

[tex]\mathrm dv=\mathrm dt\implies v=t[/tex]

[tex]R_{\rm avg}=\displaystyle\frac18\left(t\ln(t^2+7)\bigg|_{t=0}^{t=8}-\int_0^8\frac{2t^2}{t^2+7}\,\mathrm dt\right)[/tex]

For the remaining integral, consider the trigonometric substitution [tex]t=\sqrt 7\tan s[/tex], so that [tex]\mathrm dt=\sqrt 7\sec^2s\,\mathrm ds[/tex]. Then

[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}\frac{7\tan^2s}{7\tan^2s+7}\sec^2s\,\mathrm ds[/tex]

[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}\tan^2s\,\mathrm ds[/tex]

[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}(\sec^2s-1)\,\mathrm ds[/tex]

[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\left(\tan s-s\right)\bigg|_{s=0}^{s=\tan^{-1}(8/\sqrt7)}[/tex]

[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\left(\tan\left(\tan^{-1}\frac8{\sqrt7}\right)-\tan^{-1}\frac8{\sqrt7}\right)[/tex]

[tex]\boxed{R_{\rm avg}=\displaystyle\ln71-2+\frac{\sqrt7}4\tan^{-1}\frac8{\sqrt7}}[/tex]

or approximately 3.0904, measured in gallons per hour (because this is the average value of [tex]R[/tex]).

4. By the fundamental theorem of calculus,

[tex]g'(x)=f(x)[/tex]

and [tex]g(x)[/tex] is increasing whenever [tex]g'(x)=f(x)>0[/tex]. This happens over the interval (-2, 3), since [tex]f(x)=3[/tex] on [-2, 0), and [tex]-x+3>0[/tex] on [0, 3).

5. First, by additivity of the definite integral,

[tex]\displaystyle\int_{-2}^xf(t)\,\mathrm dt=\int_{-2}^0f(t)\,\mathrm dt+\int_0^xf(t)\,\mathrm dt[/tex]

Over the interval [-2, 0), we have [tex]f(x)=3[/tex], and over the interval [0, 6], [tex]f(x)=-x+3[/tex]. So the integral above is

[tex]\displaystyle\int_{-2}^03\,\mathrm dt+\int_0^x(-t+3)\,\mathrm dt=3t\bigg|_{t=-2}^{t=0}+\left(-\dfrac{t^2}2+3t\right)\bigg|_{t=0}^{t=x}=\boxed{6+3x-\dfrac{x^2}2}[/tex]