If f(x) = x/2 -2 and g(x) = 2x+ +x= 3, find (f + g)(x).

The equation your teacher has given you is an identity. We can prove this by transforming one side into the other. I'll transform the right hand side (RHS) into the left hand side (LHS).

This means I'll keep the LHS the same for each line. I'll only change the RHS. The goal is to get the same thing on both sides (I could go the other way around but I find this pathway is easier).

[tex]\tan^4(\theta)+\sec^2(\theta) = \sec^4(\theta)-\tan^2(\theta)\\\\\tan^4(\theta)+\sec^2(\theta) = \left(\sec^2(\theta)\right)^2-\tan^2(\theta)\\\\\tan^4(\theta)+\sec^2(\theta) = \left(\tan^2(\theta)+1\right)^2-\tan^2(\theta) \ \text{ ... see note 1}\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+2\tan^2(\theta)+1-\tan^2(\theta)\\\\[/tex]

[tex]\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\tan^2(\theta)+1\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\sec^2(\theta)-1+1 \ \text{ ... see note 2}\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\sec^2(\theta) \ \ \Large \checkmark\\\\[/tex]

So because we've arrived at the same thing on both sides, the original equation is an identity. It always true no matter what theta value you plug in, as long as theta is in the domain. So something like theta = pi/2 won't work because tan(pi/2) = undefined and sec(pi/2) = undefined. It's based on how cos(pi/2) = 0 and this value is in the denominator. Dividing by zero is undefined.

Consequently, this means all solutions to cos(theta) = 0 will be excluded from the domain. Everything else works.

Answer:

5/13

five blue marbles, but one blue removed  thus 5/13

Step-by-step explanation:

Answer:

C 5/13

Step-by-step explanation:

Answer:

Pressure is 80,000 pascals.

Step-by-step explanation:

Area:

[tex] = { \bf{ 30 \times {10}^{ - 4} \: {m}^{2} }}[/tex]

Pressure:

[tex]{ \bf{pressure = \frac{force}{area} }} \\ \\ { \tt{ = \frac{240}{30 \times {10}^{ - 4} } }} \\ = { \tt{80000 \: pascals}}[/tex]

Answer:

? ≈ 65°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{8}{19}[/tex] , then

? = [tex]cos^{-1}[/tex] ([tex]\frac{8}{19}[/tex] ) ≈ 65° ( to the nearest degree )

Answer:

An isometry preserves all the following except orientation .

does it give the answer choice or is it a blank space?

Answer:

63,70

Step-by-step explanation:

7 x 8 = 56

7 x 11 = 77

multiples of 7 and 9, 7 x 10

63 and 70

7×9 = 63

7×10 = 70

Answered by Gauthmath must click thanks and mark brainliest

Answer:

yes please, ask the question

Answer:

34

Step-by-step explanation:

x² = 30² + 16²

(pythagoras theorem)

x = Square root 30² + 16²

x = 34

Answer:

10.5 %

Step-by-step explanation:

Here .

let the Cost Price be 'x'

the..

by the question..

the marked price was fixed to make 30% profit

then..

the marked price will be

x+ 30% of x

= x + 30/100 × x

=x+ 0.3x

=1.3x

soo .. the marked price is 1.3x

now.. after allowing 15% discount..

the selling price will be

1.3x - 15% of 1.3x

= 1.3x - 0.195x

= 1.105x

thank you...

plzz mark me brainliest now

now..

profit made = 1.105x-x

= 0.105x

soo .

in percentage..

profit percent = profit/cp × 100%

= 0.105x/x × 100%

= 10.5 %

Answer:

X < -9

Step-by-step explanation:

5a +18 < -27

5a < -27 -18

5a < - 45

5a/5 < - 45/5

a < - 9

Answred by Gauthmath

Answer: -9

Step-by-step explanation:

5a+18 < -27

5a< -27-18

5a<-45

a< -45/5

a< -9

Answer:

8

Step-by-step explanation:

Make a ratio

2:9 = 11

In total there will be 11 cups of solution.

2:9 = 11

?:36 = ?

Divide

36 / 9 = 4

Now that you have found the scale factor, multiply

2 × 4 = 8

So, you will need 8 cups of shampoo concentrate.

Answer:

5.0645km

Step-by-step explanation:

For the first part of the journey where Vail skied 2 km north, 2 km west

displacement = √2² + (-2)²

displacement = √4+4

displacement = √8

displacement = 2√2 km

d1 = 2√2 km

For the second part of the journey where he skeid 1 km north, and 2 km west. How far was she from her starting point?

displacement = √1² + (-2)²

displacement = √1+4

displacement = √5

d2 = √5 km

Total displacement = d1 + d2

Total displacement = 2√2 + √5

Total displacement = 2(1.4142) + 2.2361

Total displacement = 2.8284+ 2.2361

Total displacement = 5.0645km

Hence she was 5.0645km from her starting point

1.

C. 5x + 4 - 2x is an algebraic expression

Answers:

[tex]a = 18\sqrt{2}[/tex]

[tex]b = 18[/tex]

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

Explanation:

For any 45-45-90 triangle, the two legs are the same length. We consider triangles like this to be isosceles. So we have b = 18 as the vertical leg because the horizontal leg is also 18 units long.

The hypotenuse of these types of triangles is always [tex]\sqrt{2}[/tex] times longer compared to the leg length. So the hypotenuse is [tex]a = 18\sqrt{2}[/tex]

As an alternative, you can use the pythagorean theorem to find the hypotenuse.

Answer:

Their speeds are;

5.83 mph and 17.49 mph

Step-by-step explanation:

We are told that they leave the park the same time.

Let the speed one car traveled be v

Since the other car is 3 times faster, then it means that, it's speed is 3v.

Now, after 6 hours they travel 140 miles.

We know that;

Speed = distance/time.

Thus;

(v + 3v) = 140/6

4v = 140/6

v = 140/24

v = 5.83 mph

Thus, second car's speed = 3v = 3 × 5.83 = 17.49 mph

Answer:

60

Step-by-step explanation:

Multiply length times width times height

Answer:

C or 104

Step-by-step explanation:

I assume this is surface area, and I don't know what kinda sadist person would make everyone learn in "Total Area," but it is what it is.

So, to find total area, we need to literally multiply every different number with the other.

(You should not do it the way I did, as I did it in the easiest and simpliest way to understand possible.)

Actually, you get the length, width, and height of a figure and do what is below pretty much.

You multiply the length by the width, the length by the height, and the width by the height (doesn't have to be in this order, this is just to make it easy to remember which ones you did.)

We multiply the

5 * 6

5 * 2

and then the

6 * 2

This accounts for every possible case, as multiplying 2 * 5 gives the same thing as the second expression anyways.

So we then solve these three expressions.

5 * 6 = 30

5 * 2 = 10

and then the

6 * 2 = 12

And we add them to get

30 + 10 + 12

= 52.

Then we multiply by 2, because there are two cases of each face of the shape.

You need to remember that there is 3 other faces on the shape you are looking at, it's just that the shape/figure is facing you in a way that you can't see them.

After multiplying by 2, we get

52 * 2

= 104, which is C.

TAKE A SCREENSHOT NOT A PICTURE AS WE DON'T NEED TO SEE SOME 420P MONITOR FROM 1987 THAT SHOWS EVERY PIXEL PLEASE AND THANK YOU :D

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Answer:

32 ounces

Step-by-step explanation:

Answer:

£510

Step-by-step explanation:

5% of 3400 is 170. SInce she gets that much money every year, after 3 years she'll have 3*170 = £510.

Answer: Simple Interest = PRT

P= 3400

R = 5% = 5/100

T = 3

=> 3400 × 5/100 × 3 = 510

=》3400 + 510 = 3910

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Let a² = x

a²-12a+36=0

or, (a-6)²=0

or, a-6=0

or, a = 6

Now a² = x, so x = 6² = 36

You want to pull out the square roots of each term since they are both perfect squares.

Factor using the difference of squares formula: a2-b2=(a+b)(a-b)

This formula allows the middle term to cancel out.

=x2 - 49

=(x + 7)(x - 7)

ANSWER: (x + 7)(x - 7)

Hope this helps! :)

Answer:

Step-by-step explanation:

-8z⁻² = -8/z²

Answer:

irrational

Step-by-step explanation:

Answer:

9. Hypotenuse = √(19.1²+11.3²) = √492.5 = 22.2 m²

10. Area = (34×40)/2 + (17²×π/2)

= 680 + 453.96

= 1133.96 cm²

Answered by GAUTHMATH

Answer:

You will need to order 3.75 cubic yards of topsoil.

Step-by-step explanation:

Since you want to put a 3 inch thick layer of topsoil for a new 15 ft by 26 ft garden, and the dirt store sells by the cubic yards, to determine how many cubic yards will you need to order given that the store only sells in increments of 1/4 cubic yards, the following calculation should be performed:

3 inches = 0.25 feet

15 x 26 = 390 x 0.25 = 97.5

1 cubic yard = 27 cubic feet

97.5 cubic feet = 3.61 cubic yards

3.75 = 1/4 x 15

Therefore, you will need to order 3.75 cubic yards of topsoil.

Answer:

Infenitely many solutions

Answer:

1)9-7+x

2+x

2)8-2x+5x

8+3x

3)-x+3x-9

2x-9

4)4x-4x-6

-6

you have to group the like terms

I hope this helps and sorry if they are wrong

Answer: 380.1

Step-by-step explanation:

The area of a circle is pi*r^2. So 11 times 11 is 121. Then multiply by pi. When multiplies by pi you get 380.132711084. rounded to the nearest tenth is 380.1.