Given: f(x) = X2 - 3 and g(x)= x+1 The composite function g.f is
a) x² + 2x - 2
b) x² + 2x
c) x² - 2

Answer:

[tex] 6\sqrt{5} units [/tex]

Step-by-step Explanation:

The length of the wall = diagonal AC = distance between point A (-6, -2) and point C (6, 4).

Distance formula between two points on a graph (d) = [tex] \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

[tex] A(-6, -2) = (x_1, y_1) [/tex]

[tex] C(6, 4) = (x_2, y_2) [/tex]

[tex] d = \sqrt{(6 - (-6))^2 + (4 -(-2))^2} [/tex]

[tex] d = \sqrt{(6 + 6)^2 + (4 + 2)^2} [/tex]

[tex] d = \sqrt{(12)^2 + (6)^2} [/tex]

[tex] d = \sqrt{144 + 36} [/tex]

[tex] d = \sqrt{180} [/tex]

[tex] d = \sqrt{36*5} [/tex]

[tex] d = 6\sqrt{5} [/tex]

The length of the wall = [tex] 6\sqrt{5} units [/tex]

Answer:

10,500 cubic inches

Step-by-step explanation:

1. Find the new lengths after the scale factor

6 · 2.5 = 15

8 · 2.5 = 20

14 · 2.5 = 35

2. Solve for the volume (length · width · height

15 · 20 · 35 = 10500

The required volume of the prism after the scale factor is 2.5 is applied to the dimensions is 10,500 cubic inches. Option D is correct.

DImension for prism,
Length = 14
width = 8
Height = 6
Scale factor = 2.5
New volume to be determined.

The scale factor is defined as the ratio of modified change in length to the original length.

Applying scale factor 2.5 to the dimensions,
Length = 2.5 * 14 = 35
width = 8 * 2.5 = 20
Height = 6* 2.5 = 15

The new volume of the prism  = length * width *height
                                                    = 35 * 20 * 15
                                                    = 10, 500

Thus, The required volume of the prism after the scale factor is 2.5 is applied to the dimensions is 10,500 cubic inches. Option D is correct.

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Answer:

draw 2 lines and draw 2 circles in the lines with the edge touching the line

Step-by-step explanation:

In between two circles, there might be 0, 1, 2, 3, and 4 tangents are there.

"A tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.

1. When one circle is in between another and one circle does not touch the other one, then tangent is not possible.

2. When one circle is in between another and one circle touches the other one at a point inside the circle, then only one tangent is possible.

3. When one circle intersects the other one, then two tangents are possible.

4. When one circle touches the other one at a point outside, then three tangents are possible.

5. When one circle neither intersects the other one nor inside the other one, then four tangents are possible.

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Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan(x + y) = [tex]\frac{tanx+tany}{1-tanxtany}[/tex] , tan(x - y) = [tex]\frac{tanx-tany}{1+tanxtany}[/tex], tan [tex]\frac{\pi }{4}[/tex] = 1

tan2x = [tex]\frac{2tanx}{1-tan^2x}[/tex]

Consider the left side

tan([tex]\frac{\pi }{4}[/tex] + Θ ) - tan([tex]\frac{\pi }{4}[/tex] - Θ )

= [tex]\frac{tan\frac{\pi }{4}+tan0 }{1-tan\frac{\pi }{4}tan0 }[/tex] - [tex]\frac{tan\frac{\pi }{4}-tan0 }{1+tan\frac{\pi }{4}tan0 }[/tex]

= [tex]\frac{1+tan0}{1-tan0}[/tex] - [tex]\frac{1-tan0}{1+tan0}[/tex]

= [tex]\frac{(1+tan0)^2-(1-tan0)^2}{(1-tan0)(1+tan0)}[/tex]

= [tex]\frac{1+2tan0+tan^20-1+2tan0-tan^20}{1-tan^20}[/tex]

= [tex]\frac{4tan0}{1-tan^20}[/tex]

= 2 [tex]\frac{2tan0}{1-tan^20}[/tex]

= 2 tan2Θ = right side

Answer:

36

Step-by-step explanation:

There would be three on each edge. (Five, minus the two ends that have 3 sides painted.)

A cube has 12 edges.

12x3=36

Hey there! I'm happy to help!

In our problem, 100 is a certain percent of 80. When talking about percents, the word "is" means equals. Let's represent our certain percent with p and solve for it.

100=80p

Let's flip the equation around so p is on the left side.

80p=100

We divide both sides by 80.

p=1.25

As a percent, the increase is 125%.

Have a wonderful day!

Answer:

The answer is option 1.

Step-by-step explanation:

You have to apply Tangent Rule, tanθ = opposite/adjacent. Then, you have to substitute the following values into the formula :

[tex]tan(θ) = \frac{oppo.}{adj.} [/tex]

[tex]let \: θ = 25.7 \: , \: oppo. = h \: , \: adj. = 532[/tex]

[tex] \tan(25.7) = \frac{h}{532} [/tex]

[tex]532 \tan(25.7) = h[/tex]

[tex]h = 256 \: feet \: (3s.f)[/tex]

The value of height of tree is,

⇒ h = 256 feet

We have to given that,

A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° .

Hence, By given figure we get;

By using trigonometry formula, we get;

⇒ tan 25.7° = Opposite / Adjacent

⇒ tan 25.7° = h / 532

⇒ 0.4812 = h / 532

⇒ h = 0.4812 × 532

⇒ h = 256 feet

Therefore, The value of height of tree is,

⇒ h = 256 feet

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Answer:

3

Step-by-step explanation:

Basically we need to find out whats the remainder of 1425 when you divide by 9.

1425/9 = 158 R3

R3 is 3 marbles left, so the answer is 3.

Answer:

The y-intercept is 1/3.

Step-by-step explanation:

The equation given is in slope-intercept form. Recall that in slope-intercept form:

[tex]f(x)=mx+b[/tex]

m is the slope while b is the y-intercept.

Therefore, -2/9 would be the slope while 1/3 would be the y-intercept.

Answer:

The level of accuracy of the measurement ruler measurement tool is 1/16 of an inch

Step-by-step explanation:

The accuracy of a measurement tool is determined by the ability of the tool measure the accurate value of the  actual or standard measurement. The accuracy of a measurement tool depends on its ability to take small measurements

The parameter given includes;

The number of divisions on each 1/2 inch of the ruler = 8

Therefore, the smallest divisions on the ruler = (1/2) inch ÷ 8 = 1/16 inch

Therefore, the level of accuracy of the measurement ruler measurement tool = 1/16 of an inch.

A negative value would mean it is below sea level. A positive value would be above sea level.

-8 is 8 feet below sea level

+107 is 107 feet above sea level.

The answer Is:

The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.

Answer:

Step-by-step explanation:

The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.  

Answer:

x= 3 +√509/10

Or

x= 3 - √509/10

Step-by-step explanation:

Given:

5x2-3x = 25

Using completing the square method of solving quadratic equation

Step 1: Factor out the coefficient of the x^2 term.

5(x^2 - 3x/5) = 25

Step 2: Add a number that would complete the square inside the parenthesis and also add this to the other side of the equation.

Take (1/2) of (3/5)

1/2 × 3/5

= 3/10

Square 3/10

We have, 9/100

We have,

5(x^2 - 3x/5 + 9/100) = 25 + 9/100

Step 3: Simplify

x^2 - (3/5)x + 9/100 = 25 + 9/100

5(x^2 - 3x/5 + 9/100) = 5 + 9/20

Step 4:

factor the right side

(x - 3/10)^2 = 509/100

Take both roots

√ (x - 3/10)^2 = √509/100

x - 3/10 = ±√ [509/100]

x = [ 3 ±√509 ] / 10

x= 3+√509/10

Or

x= 3 - √509/10

Answer:

y > 9

Step-by-step explanation:

The range of a function is the interval of all possible y-values that make the function true.

Here, one way to figure this out is to look at a graph of the function (see attachment).

From the graph, we can see that y-values approach very closely the value 9 and then the line rises beyond 9 forever. Thus, we can conclude that the range for f(x) is y > 9.

~ an aesthetics lover

Answer:

15°

Step-by-step explanation:

The 165° and x forms a straight line or a supplementary angle. Supplementary angles add up to 180°. Therefore:

[tex]165+x=180[/tex]

Solve for x:

[tex]165+x=180\\x=15\textdegree[/tex]

Answer:

15 degress

165 and x lie on a 180 degress.

and 180 - 165 is 15.

Bye!

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

Answer:

D) 12

Step-by-step explanation:

the graphs slope is 3 using the rise over run method we have found this

now since we know the fifth x value gives a y value of 9 we can add 3 and have 12

Answer:

They should refinish 96 tables using method 1

They should refinish 82 tables using method 2

Step-by-step explanation:

Let

a = number of tables refinished using method 1

b = number of tables refinished using method 2

Time equation

a+2b=260 (1)

Cost equation

6a+5b=986 (2)

a+2b=260 (1)

6a+5b=986 (2)

Multiply (1) by 5 and (2) by 2

5a+10b=1,300 (3)

12a+10b=1,972 (4)

Subtract (3) from (4)

7a=672

Divide both sides by 7

a=96

Recall,

a+2b=260

96+2b=260

2b=260-96

2b=164

Divide both sides by 2

b=164/2

=82

They should refinish 96 tables using method 1

They should refinish 82 tables using method 2

Answer:

here you go

i hope i helped you

Step-by-step explanation:

Answer:

It would look like these shapes on the picture

Step-by-step explanation:

It is a shape with another one of it inside it, you should see it on the pictturres.

Hope this helped you

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Answer

72-30=42. The answer is 42

Step-by-step explanation:

to find the area of this, we first need to add are to the missing space, so we can make a rectangle. If we multiply the dimension of this new shape, we get 72. Now we need to find the are of the triangle-shaped space I added. To do this I must multiply the base by the height, and then divide it by 2, after multiplying the base with the height, which gave me 60, I divided it by 2 which gave me 30. Then I subtracted 30 from 72, therefore giving me 42

Answer:

42cm2

Step-by-step explanation:

You can divide the shape into two parts from the length at the top and the length at the bottom. Which means you have two shapes A and B.

Area of A which is a triangle= 1/2bh

                                              = 1/2*5(THIS IS THE BASE OF THE TRIANGLE)12

                                              = 30CM2

Area of b which is a rectangle= L*W

                                                 = 1(LENGTH) * 12(WIDTH)

                                                 = 12CM2

So to get the total area of the shape you add the area of shape a and b

THE ANSWER IS 42cm2

Answer:

The answer is (A); there is no solution.

Step-by-step explanation:

It doesn't require any calculations, really, just logic.  Look, 4n = 4n wil be equal because they are the same numbers multiplied by the same variable - no matter the variable's value.  However, if you subtract both values by different numbers, you won't get the same number:

Let's say n = 5

4n = 4n

= 4(5) = 4(5)

= 20 = 20

Now,

4n - 3 = 4n - 2

= 4(5) - 3 = 4(5) - 2

= 20 - 3 = 20 -2

= 17 ≠ 18

Hope this helps!  Tell me if I was wrong!

Answer:

It has no solution.

Step-by-step explanation:

If we try and solve it we end up with nonsense, so it has no solutions:

4n - 3 = 4n - 2

4n - 4n = - 2 + 3

0 = 1

-  which is, of course, absurd.

Also, just by looking at the equation we can see that  the term 4n  -3  cannot in any way be equal to 4n - 2.

Answer:

x = 78

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

Answer:

78 degrees

Step-by-step explanation:

According to vertical angles theorem (vertical angles, angles that are opposite to each other and formed by two intersecting straight lines, are congruent) 78 and x are congruent

Answer:

a ( 567 miles to unit)

b( looks like 2 units so i would say 1134 miles

Answ: the scale is

Step-bstep explanatio

Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.

So the answer is 166

Here is the calculation:

Cathy's basic pay for the fortnight is 7.2 × 70 = $504.

Her overtime pay for the week is (1.5 × 7.2) × 9 = $97.2.

Her weekend pay is (2 × 7.2) × 6 = $86.4.

Her total pay for the fortnight is 504 + 97.2 + 86.4 = $687.6.

Therefore, Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.

So the answer is 166

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Answer:

1/2 mile

Step-by-step explanation:

(1/8)*4 = 1/2 mile

Answer:

4/8 or 1/2

Step-by-step explanation:

becuase 4 times 1/8 is 4/8 which is 1/2

Answer:

14 yards²

Step-by-step explanation:

To find the area of this complex shape, we can break it down into two parts.

I've broken it down into the left shape (with side lengths of 2, 2, 4 and 4) and the right shape (with side lengths of 2, 2, 2 and 3).

Looking at the shape on the left, the width is 4 yards and the length is 2 yards. Multiplying these numbers will get the area for that shape.

[tex]2\cdot4=8[/tex] yards².

Now in the right shape, the length is 3 and the width is 2, so:

[tex]3\cdot2=6[/tex] yards².

Now we can add both of these to get the total area of the figure.

[tex]6+8=14[/tex] yards².

Hope this helped!

Answer:

14 yds^2

Step-by-step explanation:

We can split this into two rectangles

There is a vertical rectangle on the left, 4 yds by 2 yds

The area is 4*2 = 8 yd^2

There is a horizontal rectangle on the right  3 yds by 2 yds

The area is 3*2 = 6 yd ^2

Add the areas together

8+6 = 14

Answer:

230 liters

Step-by-step explanation:

1000 liters is 1 kiloliter

Multiplying by the conversion factor

.23 kiloliters * 1000 liter/ 1 kiloliter= 230 liters

Answer:

= 230litres

Step-by-step explanation:

know that

1000liters makes 1 kilometer

if 1000liters make 1kilometer then we will multiply 0.23 by 1000litres

that is,

0.23 x 1000

= 230litres

Answer:

y=3x+4

Step-by-step explanation:

x= the equal amount of books on 3 bookshelves

+4=the other 4 books on the fourth bookshelf

y=the total amount of books

Answer:

sqrt of (m-7) = n+3

m = (n+3)^2 + 7 or m= n^2 + 6n + 16

sqrt of (m)-7 = n+3

m = (n+10)^2 or m =n^2 + 20n + 100

Step-by-step explanation:

(2) move the constants to the other side, and square

or  (1) square and move constants

then you can solve for m

Answer:

[tex]n^2+6n+16[/tex]

Step-by-step explanation:

I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not  [tex]\sqrt{m} - 7 = n+3[/tex].

[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]

Hope this helped!

Answer:

a₁= -34

aₙ = 13n - 47

Step-by-step explanation:

This is an AP with the first term of -34 and the common difference of 13.

The nth term is:

This is the required formula.