why do we have to learn math

Answer:

1.d

2.b

3.c

4.d

5.c

Step-by-step explanation:

1. f(x) + g(x) = x - 11.

2. f(x) - g(x) = - 3x + 9.

3. f.g = 30x² + 28x - 6, all real numbers.

4. f/g = x + 4, all real numbers, x ≠ 4.

5. It doesn't matter which discount is applied first the result is the same.

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

1. f(x) = - 5x - 4 and g(x) = 6x - 7.

Therefore, f(x) + g(x) = - 5x - 4 + 6x - 7.

f(x) + g(x) = x - 11.

2. f(x) = 3x + 2 and g(x) = 6x - 7.

Therefore, f(x) - g(x) = 3x + 2 - (6x - 7).

f(x) - g(x) = 3x + 2 - 6x + 7.

f(x) - g(x) = - 3x + 9.

3. f(x) = 5x + 3 and g(x) = 6x - 2.

Therefore, f.g = f(x)×g(x) = f(x).g(x).

f.g = (-5x + 3)(6x - 2).

f.g = -30x² + 10x + 18x - 6.

f.g = 30x² + 28x - 6.

The domain is all real numbers no restrictions.

4. f(x) = x² - 16 and g(x) = x + 4.

Therefore, f/g = f(x)/g(x).

f/g = (x² - 16)/(x + 4)(x - 4).

f/g = (x + 4)(x - 4)/(x - 4).

f/g = x + 4.

The domain of f/g is all real numbers except x ≠ 4.

5. Let, The original amount be 100.

25% off on 100 is 75 and 10% off again is 75 - 7.5 = 67.5.

Again, 10% off on 100 is 90 and 25% off on 90 is 90×0.75 = 67.5.

So, Both way is the same.

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Answer:

[tex]\sin B=\displaystyle\frac{b}{c}[/tex]

Step-by-step explanation:

Hi there!

This is the sine ratio:

[tex]\sin\theta=\displaystyle\frac{opposite}{hypotenuse}[/tex] where "opposite" is the side opposite the angle, "hypotenuse" is the hypotenuse of the right triangle and theta is the angle.

To find sin B, we must identify which sides of the triangle are the opposite side and the hypotenuse.

The side opposite to angle B would be b.

The hypotenuse is the side opposite the right angle, and that would be c.

[tex]\sin B=\displaystyle\frac{b}{c}[/tex]

I hope this helps!

Answer:

The choice second

[tex] \sin( B) = \frac{b}{c} [/tex]

Step-by-step explanation:

sin B = opposite/hypotenuse

4 granola bars is $9.00 12 granola bars is $27.00 24 granola bars is $54.00

Answer:A

Step-by-step explanation:

The solution is in the file below

Answer:

200

Step-by-step explanation:

Let the number = x

[tex]One-fifth \ of \ a \ number = \dfrac{1}{5}x\\\\\\5 \ more \ than \dfrac{1}{5}x =\dfrac{1}{5}x+5\\\\\\one-fourth \ of \ the \ same \ number = \dfrac{1}{4}x\\\\\\5 \ less \ than \dfrac{1}{4}x=\dfrac{1}{4}x-5\\\\\\\\\dfrac{1}{5}x+5=\dfrac{1}{4}x-5\\\\\\\dfrac{1}{5}x=\dfrac{1}{4}x-5-5\\\\\\\dfrac{1}{5}x-\dfrac{1}{4}x=-10\\\\\\\dfrac{4}{20}x-\dfrac{5}{20}x=-10\\\\\\\dfrac{-1}{20}x=-10\\\\\\x= -10*\dfrac{20}{(-1)}\\\\\\x=200[/tex]

Answer:

[tex]15^4[/tex]

Step-by-step explanation:

Given the following question:

[tex]15\times15\times15\times15[/tex]

In order to find the exponent of the given expression we count how many times the number is being multiplied by itself, that number would then be the exponent.

[tex]15\times15\times15\times15[/tex]
They're four 15's
[tex]15^4[/tex]

To prove the answer:
[tex]15\times15\times15\times15=50625[/tex]
[tex]15^4=50625[/tex]
[tex]15^4[/tex]

Hope this helps.

Answer: 12

Step-by-step explanation:

Distribute the 9(x-11) first. If you distribute it, it becomes 9x-99

9x-99=9

Add 99 to both sides

9x=108

Divide by 9 on both sides

X=12

The associated z score for filling to 10.98 oz. is -1.16.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

where x is the raw score, μ is the mean and σ is the standard deviation.

Given that μ = 12.01, σ = 0.89, hence:

For x = 10.98:

z = (10.98 - 12.01)/0.89 = -1.16

The associated z score for filling to 10.98 oz. is -1.16.

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Answer:

infinite solutions

Step-by-step explanation:

y = 2x + 6

when x = 0,  y = (2 x 0) + 6 = 6  ⇒  (0, 6)

when y = 0,  0 = 2x + 6  ⇒  x = 3  ⇒ (3, 0)

Plot the two points and draw a line through them

3y = 6x + 18

divide everything by 3  ⇒  y = 2x + 6

Therefore, y = 2x + 6 equals 3y = 6x + 18

So the lines overlap (produce the same graph)

Therefore, the system will have infinite solutions

Answer: 6

Step-by-step explanation:

Since the 3 semicircles are identical, we know that each semicircle has a diameter of 4, meaning they each have a radius of 2.

We can use the fact that (arc length of semicircle) = (pi)(r) to get the arc length of each to be 2pi.

Meaning 2pi + 2pi + 2pi = 6pi.

The cοmplete equatiοn fοr h(x) is h(x)=4

An expοnential functiοn is a mathematical functiοn οf the fοrm f(x) = a^x, where a is a cοnstant and x is the variable. The cοnstant a is called the base οf the expοnential functiοn, and it is typically a pοsitive real number. When a is greater than 1, the functiοn represents expοnential grοwth, while when a is between 0 and 1, the functiοn represents expοnential decay.

Expοnential functiοns have sοme special prοperties, such as the fact that the rate οf change οf the functiοn is prοpοrtiοnal tο its value. In οther wοrds, the larger the value οf the functiοn, the faster it grοws οr decays. Expοnential functiοns alsο have a hοrizοntal asymptοte at y = 0 when a is between 0 and 1, and nο hοrizοntal asymptοte when a is greater than 1.

Expοnential functiοns are widely used in mathematics, science, ecοnοmics, and engineering tο mοdel phenοmena that exhibit expοnential grοwth οr decay, such as pοpulatiοn grοwth, radiοactive decay, and cοmpοund interest. They are alsο used in prοbability theοry tο mοdel the distributiοn οf randοm variables, such as the expοnential distributiοn.

Tο cοmplete the equatiοn fοr h(x), we need tο find the values οf a and b in the expοnential functiοn that cοrrespοnd tο the given table οf values:

x | h(x)

0 | 10

1  | 10

2 | 10

3 | 4

4 | 4

5 | 4

Since the value of h(x) is constant (equal to 10) for x = 0, 1, and 2, we know that  [tex]b^0 = b^1 = b^2 = 1[/tex], which implies that b = 1.

Substituting b = 1 into the exponential function, we have:

[tex]h(x) = a * 1^x = a[/tex]

To find the value of a, we can use any of the given values of h(x) for which x > 2. For example, when x = 3, we have:

h(3) = 4 = a

Therefore, the complete equation for h(x) is:

[tex]h(x) = 4 * 1^x = 4[/tex]

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Answer:

8 7/8 is the correct answer

Step-by-step explanation:

hope this helps

[tex]x - 2 \frac{5}{8} = 6 \frac{1}{4} [/tex]

[tex]x - \frac{21}{8} = \frac{25}{4} [/tex]

[tex]x = \frac{50}{8} + \frac{21}{8} [/tex]

[tex]x = \frac{71}{8} [/tex]

[tex]x = 8 \frac{7}{8} [/tex]

[tex] \huge \boxed{ \tt positive}[/tex]

[tex] \\ \\ [/tex]

[tex] \longrightarrow \sf \dfrac{ - 11}{ - 3} [/tex]

[tex] \\ \\ [/tex]

[tex] \longrightarrow \sf \dfrac{ \cancel- 11}{ \cancel - 3} [/tex]

[tex] \\ \\ [/tex]

[tex] \longrightarrow \sf \dfrac{ 11}{ 3} [/tex]

Answer:

a) 82

b) 144

c) 75

d) 150

e) 241

f) 80

Step-by-step explanation:

There is a total of 360 degrees in a circle. To find the missing angles, you just have to add all of the other angles and subtract them from 360.

Answer:

ok so first we know that 1/3 of a hour is 20 minutes since

60*1/3=20

so every 20 minutes 1/15 of the lawn is mowed then we need to just multiply 20 by 15

20*15=300

300 minutes or 5 hours

Hope This Helps!!!

Answer:

5 Hour

Step-by-step explanation:

For 1/15 of lawn it takes = 1/3

So, for entire lawn it will take = 1/3 * 15 = 5

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[RevyBreeze]

Answer: 180 miles x 3 hours = 540

540/2 = 270

270 is the average speed

Step-by-step explanation:

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

Work Shown:

AC/QS = BC/RS

4/10 = m/15

4*15 = 10*m

60 = 10m

10m = 60

m = 60/10

m = 6

The first equation is possible because the triangles are similar. The horizontal sides AC and QS form the ratio AC/QS. This is equal to the ratio of the diagonal sides BC/RS since similar triangles have their sides in proportion.

After the equation is set up, we cross multiply and then solve for m.

Hey there!

6/11 = c/11

6(77) = c(11)

6(77) = 11(c)

462 = 11c

We got the new equation above because we had to CROSS MULTIPLY.

11c = 462

DIVIDE 11 to BOTH SIDES

11c/11 = 462/11

CANCEL out: 6/6 because it give you 1

KEEP: 462/11 because it help solve for the c-value

NEW EQUATION: c = 462/11

SIMPLIFY IT!

c = 42

Therefore, your answer is: c = 42

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:24 degrees

Step-by-step explanation:

94+41 = 135 degrees

180 - 135 = 45 degrees

111 + 45 = 156 degrees

180 - 156 = x = 24 degrees

Hope I could help :)

Please Mark brainliest

Answer:

Step-by-step explanation:

One angle is shared and the sum of interior angles is 180:

Answer:

No

Step-by-step explanation:

Simplify : Distribute

4(4b+5c)

16b+20c

Hence, 4(4b+5c) equal to 16b+20c.

Answer:

The answer is -19 because 127 - -6 will equal 133 and divided by -7 will equal the answer -19.

Answer:

-17.28

Step-by-step explanation:

-7x +6= 127

-7x = 127-6

-7x= 121

x= -17.28

Answer:

The speed of the wind is 40mph, the speed of the plane in still air is 360mph

Step-by-step explanation:

distance = speed * time

Both legs of the trip are 800 miles, let 'x' represent the speed of the plane in still air and 'w' represent the speed of the wind, then 'x+w' represents the speed with the wind and 'x-w' represents the speed into the wind

800 = (x-w)2.5

800 = (x+w)2

Rewrite equations:

800=−2.5w+2.5x;800=2w+2x

Steps: Solve 800=−2.5w+2.5x for w:

800=−2.5w+2.5x

800+2.5w=−2.5w+2.5x+2.5w(Add 2.5w to both sides)

2.5w+800=2.5x

2.5w+800+−800=2.5x+−800(Add -800 to both sides)

2.5w=2.5x−800

2.5w/2.5 = 2.5x - 800 / 2.5 (Divide both sides by 2.5)

w=x−320

Step: Substitute x−320 for w in 800=2w+2x:

800=2w+2x

800=2(x−320)+2x

800=4x−640(Simplify both sides of the equation)

800+−4x=4x−640+−4x(Add -4x to both sides)

−4x+800=−640

−4x+800+−800=−640+−800(Add -800 to both sides)

−4x=−1440

-4x/-4 = -1440/-4 (Divide both sides by -4)

x=360

Step: Substitute 360 for x in w=x−320:

w=x−320

w=360−320

w=40(Simplify both sides of the equation)

solving this system we have:

w=40

x=360

Therefore, the speed of the wind is 40mph, the speed of the plain in still air is 360mph

Answer:

y = [tex]\frac{9}{2}[/tex][tex]\sqrt{2}[/tex]

x = 9

Step-by-step explanation:

this triangle is isosceles because the base angles are each 45°

the ratio of sides in a 45-45-90° triangle are 1 : 1 : [tex]\sqrt{2}[/tex]

so 'y' is going to also be [tex]\frac{9}{2}[/tex][tex]\sqrt{2}[/tex]

'x' will be [tex]\sqrt{2}[/tex] multiplied by  [tex]\frac{9}{2}[/tex][tex]\sqrt{2}[/tex] which will be:

[tex]\frac{(9x2)}{2}[/tex] = 9

Answer:

by posting a question :)

Step-by-step explanation:

Answer:

Um, you didn't provide anything for me to answer so i don't really know what to provide for you.

Step-by-step explanation:

1. Observe problem

I think 200ft and 125 ft are both sides, so:

sqrt(200^2+125^2) is 25sqrt{89}

which is

235.84952