Directions: Solve for x.
1.

Step-by-step explanation:

To find the composite function, it says

[tex](f \: o \: g)(x)[/tex]

means we put the function g(x) into f(x) so that means it looks like

[tex]( \sqrt{x}) {}^{2} - 4[/tex]

Which equal

[tex]x - 4[/tex]

So that expression above is the answer.

To find the range we must find the range of the inner function ,(g(x) and then see which parts it corresponds of f(x).

The range of a g(x) which is a radical function is all real numbers.

The range of a f(x) which is a quadratic function is all real numbers greater than or equal to -4.

This means for our function to work we can use any numbers as long as it greater than -4.

So we would represent that as x is all real numbers as long as x is greater than or equal to -4

In interval notation this would be

[-4,+ infintiy)

Answer:

799 feet

Step-by-step explanation:

We solve using the Trigonometric function of Tangent.

tan theta = Opposite /Adjacent

From the above question, we have the height of the surveyor = 5.5 feet

theta = Angle of elevation = 65°

Adjacent = 370 feet

Let Opposite = height + height of spider rock

tan 65° = h - 5.5 /370 feet

Cross Multiply

tan 65° × 370 feet = h - 5.5

793.46756059 feet = h - 5.5

h = 793.46756059 feet + 5.5

h = 798.96756059 feet

Approximately = 799 feet

The height of the Spider rock = 799 feet

Answer:

[tex] f'(x) = \frac{sin( \frac{1}{x}) }{ {x}^{2} } [/tex]

Step-by-step explanation:

Please see the attached picture for the full solution.

• Differentiate cosine

• Then multiply it with the derivative of the term inside the bracket

Answer:

155

Step-by-step explanation:

Answer:

2*x^(3/8)

Step-by-step explanation:

Answer:

2*x^(3/8)

Step-by-step explanation:

khan

Answer: 30 meters.

Step-by-step explanation:

Since the scale used by Bruce in the drawing that she made is:

1 milimeter = 10 meters

If the restaurant kitchen is 3 milimeters long in the drawing, the length of the actual kitchen will then be:

1/3 = 10/x

Cross multiply

1 × x = 3 × 10

x = 30

Therefore, the actual length is 30 meters.

Answer:

380 cubic inches

Step-by-step explanation:

The basic formula is length x width x height, so it's pretty simple, you just do 4 x 19 x 5! The order doesn't matter as long as it's just the length worth and height

I, sometimes do length x width, then use the answer for that and multiply it by the height (So that I can break it down)

Answer:

I think that it would be [tex]28^{2}[/tex] cm

Step-by-step explanation:

8 x 7 = 56

56/2 = 28

Answer:

the answer is 9

check the picture for workings

Answer:

Unitary cost= $1.75

Step-by-step explanation:

Giving the following information:

He spent $21 on 12 single-scoop ice cream cones.

To calculate the unitary cost, we need to use the following formula:

Total cost= number of units*unitary cost

Unitary cost= total cost / number of units

Unitary cost= 21 / 12

Unitary cost= $1.75

Answer:

y = -1/2 x + 25

The relationship is linear, but it takes some doing.

Step-by-step explanation:

Remark

This is a very interesting problem. I've never seen one quite like it. There is probably a much better way of solving it, but I did not discover it.  

You have to introduce another variable which I labeled as z.

Let time = x

Let distance = y

Let the step away from the starting point = z   which will be the same for x and y. So 18 and 16 the step away from the start is 3.

So as the time increases, the distance decreases.  What we are going to do sort of resembles a parametric relationship.

t starts with 10

x = 10 + 4*(z - 1)   and increases by 4 with each step

d starts with 20 and decreases by 2 with each step

y = 20 - (z - 1)*2

Now solve for z in each of the forgoing equations.

x = 10 + 4z - 4

x = 6 + 4z

x - 6 = 4z

(x - 6)/4 = z

y = 20 - 2z + 2

y = 22 - 2z

y - 22 = - 2z

(y - 22)/-2 = z                    

Since the zs must be kept the same, the left sides are equated

(x - 6)/4 = (y - 22)/-2               Cross multiply

-2(x - 6) = 4(y - 22)                 Remove the brackets.

-2x + 12 = 4y - 88                   add 88 to both sides.

-2x + 100 = 4y                        Switch the sides

4y = - 2x + 100                       Divide by 4

y = -1/2 x  + 25

Now for sure you have to try this.

Let x = 14

y = -1/2 * 14 + 25

y = -7 + 25

y =  18

Try another one

Let x = 22

y = -1/2 * 22 + 25

y = - 11 + 25

y = 14

Those two at least check.

Answer:

x =  47 degrees.

Step-by-step explanation:

The angles in a triangle add up to 180 degrees, therefore:

x + 43 + 90 = 180

x = 180 - 43 - 90

x = 180 - 133

= 47 degrees.

Answer:

23°

Step-by-step explanation:

For this scenario say point G is the center point,

If we look to the left, we see angle FGE has a value of 23

and in this case angle CGD is a congruent angle to FGE therefore the two angles must be the same

so therefore angle CGD should be 23 degrees

Answer:

-6/7 -rational and real

3120- natural, whole,integers, rational,real

5.123456...- rational and real

√2- real

0 - whole, integers, rational real

Answer:

31

Step-by-step explanation:

a + (n-1)d  where a = first term;  n = which number we want;  d = common difference.

=> 4 + (10 - 1)3

=> 4 + (9)*3

=> 4 + 27

=> 31

Answer:

q= 49.5

Step-by-step explanation:

[tex] \frac{33}{q} = \frac{8}{12} [/tex]

Cross multiply:

8q= 33(12)

8q= 396

Divide by 8 on both sides:

q= 396 ÷8

q= 49.5

Answer:

Step-by-step explanation:

hello :

27 ×32 = 3x×2y

means : 27 ×32 = 6xy

xy= (27 ×32)/6

xy = 144

but : 144 =12² = (4×3)²=(2²×3)²

144=2^4 ×3²

so : xy = 2^4 ×3²

if  x and y the integere numbers so x and y are the divisors of 144

1  , 144,  2 ,72 , 4 , 36 , 8  18 , 3 , 48  , 6  , 24 , 9 , 16 , 12

Answer:

it's correct

Step-by-step explanation:

Answer:

y = 6

Step-by-step explanation:

(y + 6) × y = 72

y = negative number²

When negative numbers are squared they become positive.

y = 6

Check

(6 + 6) × 6 = 72

12 × 6 = 72

Complete Question

Luke has a cylinder with a radius of 5 inches and a height of 6 inches. What is the volume of his cylinder in cubic inches?

Answer:

471.24 cubic inches

Step-by-step explanation:

The formula for the volume of a cylinder =

πr²h

r = Radius = 5 in

h = Height = 6 in

Hence,

Volume = π × (5 in)² × 6 in

= 471.24 cubic inches

Therefore, the volume of his cylinder in cubic inches = 471.24 cubic inches

Answer:

52

Step-by-step explanation:

Answer:

The common difference is 4 or C on your test

Step-by-step explanation:

-17+4= -13

-13+4= -9

And so on...

Answer:I think the answer is x=27

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

Given

[tex]\frac{y}{3}[/tex] + [tex]\frac{y+3}{5}[/tex]

The common denominator is 15 ( the LCM of 3 and 5 )

Multiply numerator/ denominator of first fraction by 5

Multiply the numerator/ denominator of second fraction by 3

= [tex]\frac{5y}{15}[/tex] + [tex]\frac{3y+9}{15}[/tex] ← add numerators , leaving denominator of 15

= [tex]\frac{5y+3y+9}{15}[/tex]

= [tex]\frac{8y+9}{15}[/tex]

(b)

Given

[tex]\frac{3x}{8}[/tex] - [tex]\frac{x+5}{4}[/tex]

The common denominator is 8 ( the LCM of 8 and 4 )

Multiply numerator/ denominator of second fraction by 2

= [tex]\frac{3x}{8}[/tex] - [tex]\frac{2(x+5)}{8}[/tex] ← simplify numerators leaving denominator of 8

= [tex]\frac{3x-2x-10}{8}[/tex]

= [tex]\frac{x-10}{8}[/tex]

Answer:

a) (8y + 9)/15.

b) (5x + 10)/8.

Step-by-step explanation:

(a)  y/3 + (y + 3)/5

     The LCD of 3 and 5  is 15 so we have:

     5y/15 + 3(y + 3)/15

      = (5y + 3(y + 3)) / 15

     = (5y + 3y + 9)/15

     = (8y + 9)/15.

b)  3x/8 + (x + 5)/4

     The LCD of 4 and 8  is 8 so we have:

     3x/8 + 2(x + 5)/8

      = (3x + 2x + 10) / 8

      = (5x + 10)/8.