Calculate the difference between the average rates of change of Function B and Function A from x=2 to x=4.

The length of the bridge and the length the dog swam are 12.12 feet and 32.36 feet respectively

The problem forms a right angle triangle.

A right angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.

Therefore, the length of the bridge and the length the dog swam can be calculated as follows:

tan 68° = opposite / adjacent

tan 68° = 30 / x

cross multiply

x = 30 / tan 68

x = 12.12 ft

length of the bridge = 12.12 ft

The length the dog swim is as follows:

sin 68°= opposite / hypotenuse

sin 68° = 30 / h

h = 30 / sin 68

h = 32.3561767942

The distance the dog swimmed = 32.36 ft

learn more on right triangle here: brainly.com/question/22734914

Answer:

2

Step-by-step explanation:

3^2 = 9

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♪[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:f(x) = g(x)[/tex]

[tex]\qquad \sf  \dashrightarrow \:x + 2 = - {x}^{2} + 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + x + 2 - 4 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + x - 2 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 2x - x - 2 = 0 [/tex]

[tex]\qquad \sf  \dashrightarrow \:x(x + 2) - (x + 2) = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x + 2)(x - 1) = 0[/tex]

Hence, x = -2 or x = 1

Answer:

Step-by-step explanation:

i can't solve without seeing the prism

Answer:

[tex](\frac{2}{3})^{4}[/tex] written in simplest form is [tex]\frac{16}{81}[/tex]

Step-by-step explanation:

When taking a fraction to a certain power, you can rewrite the expression as the numerator taken to that power over the denominator to that power. In this case, the fraction is [tex]\frac{2}{3}[/tex] and the exponent is 4, so you can write the expression as [tex]\frac{2^{4}}{3^{4}}[/tex]. [tex]2^{4}[/tex] is 16, and [tex]3^{4}[/tex] is 81, so the fraction is [tex]\frac{16}{81}[/tex].

x           - inf            - 8              1/5              + inf

x+8                   -     0       +                +

5x-1                  -               -          0     +

result               +      0      -          ║     +

x+8/(5x-1) > 0 if x € ] -inf ; - 8[ U ] 1/5 ; + inf [

=> x < - 8 and x > 1/5

The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:

x ∈ (-∞, -8] ∪ [1/5, ∞)

We have,

To solve the inequality (x + 8)/(5x - 1) ≤ 0,

We can use the following steps:

Step 1:

Find the critical values of x where the expression (x + 8)/(5x - 1) is equal to zero or undefined.

The expression is undefined when the denominator is equal to zero:

5x - 1 = 0

x = 1/5

The expression is equal to zero when the numerator is equal to zero:

x + 8 = 0

x = -8

Therefore,

The critical values are x = -8 and x = 1/5.

Step 2:

Create a sign chart to determine the sign of the expression (x + 8)/(5x - 1) for each interval between the critical values.

On the interval (-∞, -8), the expression (x + 8)/(5x - 1) is negative if x + 8 is negative, which means x < -8.

On the interval (-8, 1/5), the expression (x + 8)/(5x - 1) is positive if both the numerator and denominator are negative, or if both are positive.

The numerator is negative on this interval, so the expression is positive if the denominator is negative, which means x < 1/5.

On the interval (1/5, ∞), the expression (x + 8)/(5x - 1) is negative if the numerator is negative and the denominator is positive, which means x > 1/5.

Step 3:

Write the solution in interval notation.

Therefore,

The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:

x ∈ (-∞, -8] ∪ [1/5, ∞)

Learn more about solutions to inequalities here:

https://brainly.com/question/22010462

#SPJ7

Answer:

681ft^2

Step-by-step explanation:

Start by finding the area of the whole thing with the missing triangle:

33 x 22 = 726

Then find the area of the triangle. You can do this by first finding out the side lengths of the triangle:

33 - 24 = 9 and 22 - 12 = 10

Then multiply both sides and divide by two because it is a triangle:

10 x 9 = 90       90/2 = 45

Then subtract the area of the triangle from the rectangle:

726 - 45 = 681

Answer:

pls give brainliest

Step-by-step explanation:

l  w +l x w=22 + 33 x 24 + 12=55 x 36 =1980

Answer:

2(m+8)

Step-by-step explanation:

5(m+2) -3(m-2)

= 5m+10-3m+6

= 2m+16

= 2(m+8)

Answer:

Step-by-step explanation:

[tex]\begin{aligned}& 5(m+2)-3(m-2) \\\\=& 5 m+5 \times 2-(3 m-6) \\\\=& 5 m+10-3 m+6 \\\\=&(5 m-3 m)+(10+6) \\\\=& 2 m+16\end{aligned}[/tex]

Answer:

3/12 + 239/12 = 20.16...

2309/23 + 32/32= 101.39

34/234 + 349/234=1.64

23/23-11/23= 0.52

57/78-32/78 = 0.32

Step-by-step explanation:

Just divide both sides first and then add, so it is easier to get your answer.

My answers are all rounded or repeated.

I hope this helps!

-No one

Answer/Step-by-step explanation:

3/12 + 239/12

3 + 239 = 242

242/12 = 20 1/6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Find common multiplier

2309/23 + 32/32

Add

2332/23

Mixed Fraction

101 9/23

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

34/234 + 349/234

23 + 349 = 383

383/234

Mixed Fraction

1 149/234

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

23/23-11/23

23 - 11 = 12

12/23

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

57/78 - 32/78

57 - 32 = 25

25/78

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~lenvy~

Answer:

a = 26

Step-by-step explanation:

29 + 33 + 27 + a + 19 + 17 + 10 / 7 = 23

135 + a / 7 = 23

135 + a = 161

a = 26

Answer: 20%

Step-by-step explanation: Add all the marbles together:5 + 8 + 6 +11= 30

Find the probability of orange: 6/30

Now divide 6 by 30= .2

Turn .2 into a decimal: 20%

Answer:

(4, 1 )

Step-by-step explanation:

x + 6y = 10 → (1)

x + 5y = 9 → (2)

subtract (2) from (1) term by term to eliminate x

0 + y = 1

y = 1

substitute y = 1 into either of the 2 equations and solve for x

substituting into (1)

x + 6(1) = 10

x + 6 = 10 ( subtract 6 from both sides )

x = 4

solution is (4, 1 )

Using the Pythagorean Theorem, it is found that the balloon rises 67.08 feet.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Researching this problem on the internet, it is found that the situation is modeled by a right triangle, in which the horizontal distance between the balloon and the student is of 60 ft, the vertical distance is of h, while the hypotenuse is of 90 ft, hence:

[tex]60^2 + h^2 = 90^2[/tex]

[tex]h = \sqrt{90^2 - 60^2}[/tex]

[tex]h = 67.08[/tex]

The balloon rises 67.08 feet.

More can be learned about the Pythagorean Theoremat https://brainly.com/question/26396675

Answer:

If B stands alone in the option,B is the answer.But if it doesn't,choose none or neither

Step-by-step explanation:

Mutually exclusive events are events that do not occur at the same time.On the venn diagram,mutually exclusive events do not overlap. Hence, B is a mutually exclusive event because W and T overlap. Since B doesn't stand alone in any option,the answer is none

Answer:

CD = 13.75

Step-by-step explanation:

Focus on only half of the rectangle as a triangle

We'll use pythagorean theorem to find the unknown side

[tex]10^{2} +CD^{2}=17^{2}\\CD^{2} = (17^{2} - 10^{2})\\CD^{2}=\sqrt{189} \\CD = 13.75[/tex]

Answer:

6 Hours

Step-by-step explanation:

No.of leaflets---no.of people---work hours

1000 ————. 4. - — — — — — — 5

1500 — — — —5 — — — — — ,— —?

If work increase, no.of people needed more

So, the required ratio is 1500/1000

If work men increase, no of hours decrease

So, the required ratio is 4/5

(1500/1000)× (4/5)×5 = 6

No.of hours required to distribute 1500 leaflets by 5 people = 6 hours

Answer:

Step-by-step explanation:

x = 5.4178

10000x = 54178.178

10x =              54.178              Subtract: that gets rid of the repeating decimal.

9990x  =        54124               Divide by 9990 on both sides

9990x/9990 = 54124/9990  The Greatest common divisor of these two is 2

x = 27062/ 4995

p/q = 27062 / 4995

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

We need to know two formulas before we start ~

Taking value of pi as 3.14

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:d = 7.4[/tex]

[tex]\qquad \sf  \dashrightarrow \:r = d \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 7.4 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 3.7 \: \: units[/tex]

[tex]\qquad \sf  \dashrightarrow \:area = 3.14 \times (3.7) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 42.9866 \approx43 \: \: unit {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 2.2 \: yd[/tex]

[tex]\qquad \sf  \dashrightarrow \: circumference = 2 \times 3.14 \times 2.2[/tex]

[tex]\qquad \sf  \dashrightarrow \: c =13.816 \: yd[/tex]

[tex]\qquad \sf  \dashrightarrow \:d = 5 \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:circumference = 3.14 \times 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:c = 15.7 \: \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:d = 6 \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:circumference = 3.14 \times 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:c =18 .84 \: \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 2.1 \: m[/tex]

[tex]\qquad \sf  \dashrightarrow \:area = 3.14 \times (2.1) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 3.14 \times 4.41[/tex]

[tex]\qquad \sf  \dashrightarrow \:a \approx13.85 \: \: m {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 1.3 \: mm[/tex]

[tex]\qquad \sf  \dashrightarrow \:c = 2 \times 3.14 \times 1.3[/tex]

[tex]\qquad \sf  \dashrightarrow \:c = 8.16 \: \: mm[/tex]

Answer:

Ok, to find MAD, you have to add up all of the decimals in the set, and then divide by how much decimals there are in the set.

Adding them all up...

The final result of the adding is 56.7

Now, we have to divide by how much decimals.

We now have. 56.7 / 6

Do the division.

56.7 / 6 ===> 9.45

No need to round, the final answer is 9.4

Answer: $284.20

Step-by-step explanation:

In the picture

Answer:

higher

Step-by-step explanation:

should be higher since 6 x 15 is 90, which is far away from 150

Answer:

should be higher

Step-by-step explanation:

because 6×15=90 and 90+19 is lower than 150

Answer:

10(x - 12)

Step-by-step explanation:

10(x - 12)

10x - 120 Distributive Property

Answer:

b=133 and c=47

Step-by-step explanation:

b+47=180

b=180-47=133

b=133

and

c=b+133=180

c=180-133=47

c=47

Answer:

-47

Step-by-step explanation:

you don't you use the calcaulator

Answer:

Here we will explain how to calculate one half of 80.

One half of 80 is simply one half times 80, which can be written as follows:

One/half x 80

Furthermore, you can convert "one" to "1" and "half" to "2" and then the equation and answer is:

1/2 x 80 = 40.00

Step-by-step explanation:

Hey there!

In order to find 1/5 of 80, we can just multiply 80 times 1/5:

[tex]\bold{\displaystyle\frac{1}{5} *80}[/tex]

80 can be written as follows:

[tex]\bold{\displaystyle\frac{1}{5} *\frac{80}{1}}[/tex]

In order to multiply fractions, just multiply the top of one fraction times the top of the other fraction; same with the bottom (also called the denominator)

[tex]\bold{\displaystyle\frac{80}{5}}[/tex]

Guess what? Now we can use mental maths to solve it :)

Hence, the answer is

[tex]\boxed{\boxed{\bold{16}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#ILoveLearning

:-)

Answer:

[tex] - 3 \frac{1}{6} \div ( - 1 \frac{4}{9} ) \\ \\ - \frac{19}{6} \div ( - \frac{13}{9} ) \\ \\ - \frac{19}{6} \times ( - \frac{9}{13} ) \\ \\ - \frac{19}{2} \times ( - \frac{3}{13} ) \\ \\ = \frac{57}{26} = 2 \frac{5}{26} = 2.1923[/tex]

Answer:

2 5/26

Step-by-step explanation:

1) convert 3 1/6 to improper fraction. Use this rule: a b/c = ac+b/c

- 3 * 6 + 1/ 6 ÷ -1 4/9

2) Simplify 3*6 to 18.

-18+1/6 ÷ -1 4/9

3) Simplify 18 + 1 to 19.

-19/6 ÷ -1 4/9

4) convert 1 4/9 to improper fraction. Use this rule: a b/c = ac+b/c

-19/6 ÷ -1*9+4/4

5) Simplify 1 * 9 to 9

-19/6 ÷ -9+4/9

6) Simplify 9 + 4 to 13.

-19/6 ÷ -13/9

7) Use this rule: a ÷ b/c = a × c/b

-19/6 × 9/-13

8) Use this rule: a × c/d = ac/bd

- 19*9/6*-13

9) Simplify 19 * 9to 171

-171/6*-13

10) Simplify 6 * -13 to -78

-171/-78

11) Move the negative sign to the left.

-(-171/78)

12) simplify 171/78 to 57/26

-(-57/26)

13) Remove parentheses.

57/26

14)  Convert to mixed fraction.

2 5/26