Slippery Slope
Two professional downhill skiers are going to begin a race. The skiers agree that Skier 1 is
slightly faster than Skier 2 so they decide that Skier 2 will get a 5 second head start to make the
race more competitive. Skier 1 skies at an average speed of 110 feet per second and Skier 2
skies at an average speed of 100 feet per second.
Who will win the race if the course is 5000 feet long?

Answer:

24.5

Step-by-step explanation:

Apply the pythagorean theorem:

35^2-25^2=c^2

1225-625=c^2

600=c^2

c=24.5

Answer:

Yes

Step-by-step explanation:

Janna runs at a steady pace of 7 minutes per mile. Is the relationship between the number of miles she ran and the distance she covered proportional -  Yes, this is proportional.

Answer:

The answer would be A. -42

Answer:06-16

Step-by-step explanation:

The student used the diameter in the calculation instead of the radius. The correct volume is 1155.5.

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The height of the board is an illustration of Pythagoras theorem

The ramp will rise 10.3 inches from the ground

The angle of elevation is given as:

[tex]\mathbf{\theta = 19^o}[/tex]

The length of the board is given as:

[tex]\mathbf{l = 30}[/tex]

The height h is calculated using the following tangent ratio

[tex]\mathbf{tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]

So, we have:

[tex]\mathbf{tan(19) = \frac{h}{l}}[/tex]

This gives

[tex]\mathbf{tan(19) = \frac{h}{30}}[/tex]

Make h the subject

[tex]\mathbf{h = 30 \times tan(19)}[/tex]

[tex]\mathbf{h = 10.3}[/tex]

Hence, the ramp will rise 10.3 inches from the ground

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Answer:

All of the above

Step-by-step explanation:

Answer:

All of the above

Step-by-step explanation:

Rational numbers that can be expressed as the fraction

It is a integer

a repeating non-terminating decimal

terminating decimal

-275[tex]\frac{1}{2}[/tex] --- this is a integer fraction -- rational

0 -- this is a whole number -- rational

56 --- natural number -- rational

34243.84 -- terminating decimal -- rational

-88/3 -- integer fraction -- rational

therefore all of the above are rational numbers

Answer:

-8f

Step-by-step explanation:

you will substitute in the numbers and multiply

Because f is a variable you write the -8 and attach the f to it

The value of function for given x value is -1.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=-(x+8)²-1.

Substitute x=-8 in the given function, we get

f(-8)=-(-8+8)²-1

= -0-1

= -1

Therefore, the value of function for given x value is -1.

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"Your question is incomplete, probably the complete question/missing part is:"

What is the value of f(x)=-(x+8)²-1, if x is -8?

Answer:

x2 + (y + 8)2 = 36

Step-by-step explanation:

:) took the test

The equations which represent circles that have a diameter of 12 units and a center that lies on the y-axis are x² + (y – 3)² = 36 and x² + (y + 8)² = 36.

Standard form of a circle is given by the equation,

(x - h)² + (y - k)² = r²

where, (h, k) is the center of the circle and r is the radius of the circle.

Given that,

A circle has a diameter of 12 units.

So radius = 12 / 2 = 6 units

Center of the circle lies on the Y axis.

So the x coordinate of the center of the circle will be 0.

So, in (h, k), h = 0

So the equation will be of the form,

(x - 0)² + (y - k)² = 6²

x² + (y - k)² = 36

Hence the options are x² + (y – 3)² = 36 and x² + (y + 8)² = 36.

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Answer:

C

Step-by-step explanation:

Slope of a line that goes trough the points (x1=9, y1=1) and (x2=17, y2=2)

m= (y2-y1)/(x2-x1) = (2-1) / (17-9) = 1/8

Answer:

Y^2/a = x

Step-by-step explanation:

Y = a sqr X

Square both sides

Y^2 = a * x

Divide a

Y^2/a = x

Answer:

[tex] x = \dfrac{y^2}{a^2} [/tex]

Step-by-step explanation:

[tex] y = a\sqrt{x} [/tex]

Square both sides.

[tex] (y)^2 = (a\sqrt{x})^2 [/tex]

[tex] y^2 = a^2(\sqrt{x})^2 [/tex]

[tex] y^2 = a^2x [/tex]

Divide both sides by a².

[tex] \dfrac{y^2}{a^2} = x [/tex]

Switch sides.

[tex] x = \dfrac{y^2}{a^2} [/tex]

Answer:

The answer is the second option

Step-by-step explanation:

All you have to do is replace x with the data given.

Example: f(x) = 3[tex]x^{2}[/tex] - 6

x = 0 => f(x) = 3 x [tex]0^{2}[/tex] - 6 = 3 x 0 - 6 = -6

x = 1 => f(x) = 3 x [tex]1^{2}[/tex] - 6 = 3 x 1 - 6 = 3 - 6 = -3

x = 2 => f(x) = 3 x [tex]2^{2}[/tex] - 6 = 3 x 4 - 6 = 12 - 6 =  6

Answer is (x - 2).

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Answer:

I can even see anything can you reupload your answer, please?

Step-by-step explanation:

Step-by-step explanation:

A number diminished by 6:

Sum of 5 and a number diminished by 6:

The square of the sum of five and a number diminished by 6:

Answer:

81

Step-by-step explanation:

Take half of the x-term coefficient, and square it.

Half of 18 is 9.

9² = 81

Answer: 81

Answer:

x = 7

Step-by-step explanation:

"six times a number is 21 less" = 6x + 21

"nine times the same number" = 9x

Equation: 6x + 21 = 9x

6x + 21 = 9x       [tex]\longmapsto[/tex]       Subtract 6x from both sides

21 = 3x               [tex]\longmapsto[/tex]       Divide both sides by 3

7 = x

x = 7

-Chetan K

Answer: The cost of renting a car from Company A be the same as renting a car from company B in 17.5 miles

Step-by-step explanation:

y=2.30x +15

y=1.90x +22

0.4x +7 Divide 0.4 from both sides

x=17.5

y=2.30(17.5)+15

y=40.25+15

y=40.25-15

y=25.25

Answer:

14 R3

Step-by-step explanation:

the closest multiple of 4 under 59 is 56. 56/4=14 and there is a remainder of 3 between 59 and 56

Answer: 14R3

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 x 2 = 8

there fore, it would take 8 $ to buy 5 slices excluding the delvry.

so, 8 x 2 = 16

16$ total

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Step-by-step explanation:

the slope of the line is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

the trick in such a situation is to find good points on the chart that are crossed by the line. and by "good" I mean points with round integer coordinates.

I see 2 such points :

(-2, 3) and (0, -3)

x changes by +2 (from -2 to 0)

y changes by -6 (from 3 to -3)

the slope is -6/+2 = -6/2 = -3

Answer:

2x  + 3 )(x   + 2 )

Step-by-step explanation:

2x² + 7x + 6          

Find two numbers multiplied together to get 6

and if you multiply one by 2, the answer is 7:

Tested:                                  

6 & 1  but 6 · 2 + 1 = 13 or 6 + 2 · 1  = 8 No

2 & 3  and 2 · 2 + 3 = 7    Yes

2x² = 2x  & x

 all signs are positive

   trinomial  factoring  (            )(            )

                                     (     +     )(      +    )

    2 and 3 are the numbers to use    (2x  + 3 )(x   + 2 )   or     (2x + 2) (x + 3)

The largest number goes with the 2x.

Therefore (2x  + 3 )(x   + 2 )

Check 2x(x + 2) + 3(x + 2)

              2x² + 4x + 3x + 6

              2x² + 7x + 6         checked                            

Answer:

11[tex]x[/tex]+6

Step-by-step explanation:

2[tex]x^{2}[/tex]= 4[tex]x[/tex] because 2 *2 = 4 + x = 4[tex]x[/tex]

since 7[tex]x[/tex] is a like term we add it to 4[tex]x[/tex] and it becomes : 11[tex]x[/tex]

Since 6 does not have a variable we do not add anything to it so, it stays the same and the simplified expression becomes : 11[tex]x[/tex] + 6

Answer:

y-intercept =3

x-intercept =3/2

slope =-2

Step-by-step explanation:

y=-2x+3

0=-2x+3

2x=3

x=3/2

Answer:

20

Step-by-step explanation:

[tex] \frac{20 \times 29}{29} = 20[/tex]

Answer:

20X29 devided by 9+20=84.4444444444

Answer:

A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F

B) [tex]f(x)=-0.4x+88[/tex]

Step-by-step explanation:

A)

In this problem, f(x) represents temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.

So we have:

x = minutes after the air conditioner started to cool the house

f(x) = temperature

Here we want to find what is the meaning of

[tex]f(30)=76[/tex]

Which implies that:

[tex]x=30[/tex], which means that 30 minutes have passed after the conditioner has started to cool the house

[tex]f(x)=76[/tex], which means that the temperature of the room at that time is 76°F

So, the interpretation of f(30) =76 is that:

"30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F"

B)

Here we want to write explicitly a function that tells us how the temperature inside the house varies as a function of x, the number of minutes passed after the air conditioner has turned on.

We know the following information:

- At time x = 0, the temperature inside the house is 88°F

- At time x = 30 min, the temperature inside the house is 76°F

We can assume that the temperature inside the house changes linearly with time; so, we can describe the temperature function with the equation of a line:

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

where

[tex]q[/tex] is the value of the temperature at x = 0, so q = 88

m is the rate of change of the temperature

The rate of change can be found by calculating the rate of change of the temperature with respect to the change in time; so we find:

[tex]m=\frac{76-88}{30-0} =-0.4[/tex]

which means that the temperature decreases by 0.4°F every minute. So, the function can be written as

[tex]f(x)=-0.4x+88[/tex]

Answer:

Graph Below:

Answer:

rachel is 10

Step-by-step explanation:

45/3=15

15-5=10

Answer : 10

Explanation : To find James you take 45 and divide by 3. To find Rachel you take 15-5=10

Answer:sadddddddddddddddddddddddddddddddddddddddddddddddddddd

Step-by-step explanation:

ddddddddddddddddddddddddddddddddddddddddddddddddddddddddd