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8. EXERCISE Del Ray can run 20 1/2 miles in
2 1/4 hours. How many miles per hour can
he run?

Answer:

Please see below.

Step-by-step explanation:

f^-1 (x) essentially means the reverse.

We can substitute y for x in the equation and solve for y:

x = 4y -1

x+1 = 4y

y = (x+1)/4

so that is our answer for the first one:

f^-1(x) = (x+1)/4

We do the same trick for the second question:

x = 2y +1

x-1 = 2y

y = (x-1)/2

so the answer is f^-1(x) = (x+1)/2

The last question is slightly more complex, we can write is as:

x = 2y/(y-1)

x(y-1) = 2y

yx -x = 2y

yx = 2y + x

yx - 2y = x

y(x-2) = x

y = x/(x-2)

so the answer is x/(x-2)

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Answer:

w > 2

Steps:

w +2  > 4

w + 2 - 2 > 4 - 2

w > 2

Answer:

C

Step-by-step explanation:

Answer:

Adam's total cost: $9.20

Cindy's total cost: $9.20

Step-by-step explanation:

Since Adam and Cyndi's total bill costs $16, evenly splitting the cost means that each of them has to pay $8, not including the tip.

To find out the dollar value of their 15% tip, multiply $8 by 0.15:

$8 × 0.15 = $1.20.

Adam and Cindy will have to pay $8 (lunch cost) + $1.20 (tip) = $9.20 separately.    

This is one pathway to prove the identity.

Part 1

[tex]\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{1}{\tan(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\cot(\theta) = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)*\sin(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)(1-\cos(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\[/tex]

Part 2

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

Part 3

[tex]\frac{\sin^2(\theta)+\cos^2(\theta)-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)} \ \ {\checkmark}\\\\[/tex]

As the steps above show, the goal is to get both sides be the same identical expression. You should only work with one side to transform it into the other. In this case, the left side transforms while the right side stays fixed the entire time. The general rule is that you should convert the more complicated expression into a simpler form.

We use other previously established or proven trig identities to work through the steps. For example, I used the pythagorean identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex] in the second to last step. I broke the steps into three parts to hopefully make it more manageable.

750 (0.05) = 37.5

The commision rate turns into 0.05 times the sale price.

Answer:

Step-by-step explanation:

I don't do this question the same way as it is done in the classroom, but I will get you the right answer

Let the middle number = x

Let the smallest number = x - 2

Let the largest number = x + 2

x - 2 + x + x + 2 = 315             Combine like terms. The 2s cancel

3x = 315                                  Divide by 3

x = 105

So the middle number is 105

The smallest number is   103

The largest number is     107

Total                                  315

This method cuts out at least one step. It works best with an odd number of terms. If you have an even number, you have to use the more traditional method.

Step-by-step explanation:

Given,

ratio of HI, IJ , Jk = 2 : 1 : 2

let their value be

HI = 2x

IJ = x

JK = 2x

HK = 25

according to question,

HI + IJ + JK = Hk

now, after inserting the values we got,

→ 2x + x + 2x = 25

→ 5x = 25

→ x = 25/5 = 5

→ x = 5

therefore value of,

HI = 2x → 2×5 = 10

IJ = x → 5

JK = 2x → 2×5 = 10

Hence, value of JK is 10.

hope this answers helps you dear...take care and may u have a great day ahead!

Step-by-step explanation:

the total length of all lines is 100.

there are 2 times a d line, and 5 times an x line.

well, what we have here is an equation :

2d + 5x = 100

2d = 100 - 5x = 5×(20 - x)

d = 5/2 × (20 - x) = 50 - 5x/2

take whatever form fits best to what your teacher does in class.

Answer:

x = -4

Step-by-step explanation:

Step 1: Apply distributive property.

Step 2: Combine like terms.

Step 3: Subtract 8 from both sides.

Step 4: Divide both sides by 2.

Step 5: Check if solution is correct.

Therefore, x = -4.

Step-by-step explanation:

final position = (-56-17+29)m = -44m

44m below the sea level.

Answer:

Here is the answer 44

Step-by-step explanation:

56+17=73

73-29=44

Answer:

2/9

Step-by-step explanation:

Answer: 2/9

Step-by-step explanation:

First write as an improper fraction.

2 5/8 is equal to 21/8

Then re-write

7/12 divided by 21/8

Then multiply 7/12 by the reciprocal of 21/8 which is 8/21

The answer is 56/252

Simplify

The answer is 2/9

Answer:

4 3/28

Step-by-step explanation:

Hope this helps!

Answer:

[tex]4 \frac{3}{28}[/tex]

Step-by-step explanation:

First, let's turn these mixed fractions to regular fractions to make multiplying easier:

3 2/7 = 2/7 + 21/7 = 23/7

1 1/4 = 1/4 + 4/4 = 5/4

Then multiply:

[tex]\frac{23}{7}*\frac{5}{4} = \frac{( 23 * 5 ) }{(7*4)} =\frac{115}{28}[/tex]

This fraction cannot be simplified, so let's turn it into a mixed fractions:

[tex]\frac{115}{28} =4\frac{3}{28}[/tex]

Answer:

(E) 3

Step-by-step explanation: solve mo dapat pano mo malaman

pero I hope I helped

Answer:

x = 14

Step-by-step explanation:

Vertical angles are congruent , then

7x - 27 = 3x + 29 ( subtract 3x from both sides )

4x - 27 = 29 ( add 27 to both sides )

4x = 56 ( divide both sides by 4 )

x = 14

Answer:

m         =   cd³

Step-by-step explanation:

mass of        is proportional to          the diam

sphere                                                 cubed

Symbolically, this can be written as:

  m         =   cd³

Answer:

Step-by-step explanation:

As x approaches infinity, y approaches negative infinity

As x approaches negative infinity, y approaches infinity

Step-by-step explanation:

given,

30m of material cost = £210

so, cost of 1m material = 210/30 = £7

therefore, cost of 1m material is £7

now,

cost of 18m Material = 18 × 7 = 126

therefore, cost of 18m material is £126.

hope this answer helps you dear!

Answer: 126

Step-by-step explanation:

30 m of material cost 210

1 m of material cost [tex]\frac{210}{30}[/tex] Or 7

18 m of material cost 7 × 18 = 126

please give me a brainliest answer

Answer:

y = -1/4 -2

Step-by-step explanation:

Answer:

God

Step-by-step explanation:

Because I need points

Answer:

Step-by-step explanation:

The ratio of light times will be the ratio of distances:

 (light time to Neptune) / (light time to Mercury)

    = (Neptune distance)/(Mercury distance)

    = (27.93×10^8 mi)/(0.3598×10^8 mi) = 27.93/0.3598

    ≈ 77.6

Answer:

1) 5.091

2) 54.6731

3) 2.954

4) 0.17278

5) 68.031

Answer:

7 scarves

Step-by-step explanation:

you divide 28 by 4

Answer:

16

Step-by-step explanation:

Perimeter is the total length/ distance around the shape so 3+3=6   5+5=10   6+10=16

Answer:

disagree, its easy math, 10/3 =3.3 continued

Answer: y=2x+7

Step-by-step explanation:

The og equation to get to the equation is y=mx+b. M=slope & B=y intercept

Lets first pick 2 points to find the slope (the formula is y2-y1/x2-x1). After using the formal, I got my slope as 2. Now I could say y=2x+b. Now to find the y intercept, the x point should be 0 because these are on going lines (you could tell by the infinite arrows) meaning there is no starting point. I got my y intercept as 7. Now, I know that y=2x+7.

Answer:

Base-3 mi

Height-8 mi

Step-by-step explanation:

The area of a parallelogram is base*height.

Base*height=24

Now we just need to number that multiply to get 24. Those numbers can be 3 and 8 because 3*8=24.

The dimension of the parallelogram are 1 x 24, 2 x 12, 4 x 6, 8 x 3, and 24 x 1.

The opposite sides of the parallelogram are parallel and congruent. Let H be the height and W be the width of the parallelogram.

Then the area of the parallelogram will be

Area of the parallelogram = H × W square units

The area of the parallelogram is 24 square miles.

Then the dimension of the parallelogram is given as,

Area = 24

Area = 2 x 2 x 2 x 3

Area = 1 x 24, 2 x 12, 4 x 6, 8 x 3, 24, 1

The dimension of the parallelogram are 1 x 24, 2 x 12, 4 x 6, 8 x 3, and 24 x 1.

More about the area of the parallelogram link is given below.

https://brainly.com/question/16052466

#SPJ5

Answer:

if you learned derivative:

f'x=(x+3)(x-2)²+(x+5)(x-2)²+2(x+5)(x+3)(x-2)

  =4x³+12x²-26x-28=0

⇒x=2; =-0.84; =-4.16

⇒fx=0; =72.47; -36.97⇒fx contain (2;0); (-0.84;72.47); (-4.16;-36.97)

if x=0⇒f'x=-28<0⇒from -0.84 to 2, fx Decreasing

Step-by-step explanation:

Answer:

11v-w= -20t

Step-by-step explanation:

combine like terms

20t+11v=w

isolate variable

11v=w-20t

11v-w= -20t