Richard and Gloria ran a 10-kilometer race. Gloria gave Richard a head start by letting him begin 2.2 kilometers in front of the start line. The distances of Richard and Gloria past the start line as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Whose time was faster, and by how much?


Richard’s Distance Past the Start Line
Time (minutes)
5
10
15
20
25
Distance (kilometers)
2.8
3.4
4.0
4.6
5.2

A graph titled Gloria's Distance Past the Start Line has time (minutes) on the x-axis and Distance (kilometers) on the y-axis. A line goes through points (5, 0.8), (10, 1.6), (15, 2.4), (20, 3.2) and (25, 4).
Gloria’s time was 0.5 minutes faster.
Richard’s time was 0.5 minutes faster.
Gloria’s time was 2.5 minutes faster.
Richard’s time was 2.5 minutes faster.

Answer:

Step-by-step explanation:

Given the function f(x) = tan (x)

From trigonometry identity, tan (x) = sin(x)/cos(x)

f(x) = sin(x)/cos(x)

Using the quotient rule to find the derivative of the function, we will have;

f'(x) = cos (x)cos (x) - sin (x)[-sin (x)]/ cos²x

f'(x) = cos²x - sin²x/ cos²x

Divide through by cos²x

f'(x) = cos²x/cos²x + sin²x/cos²x / cos²x/cos²x

f'(x) = 1 + sin²x/cos²x / 1

f'(x) = 1 + (sin²x/cos²x)

f'(x) = 1 + tan²x

From trig identity,  1 + tan²x = sec²x

Hence, f'(x) = sec²x

Hence the expression  f'(x)  in terms of the secant function is sec²x

f'(x) = 1/cos²x

For the function to be defined, it means that cos²x ≠ 0

cos²x ≠ 0

cos x ≠ 0

x ≠ cos⁻¹0

x ≠ 90⁰

Hence the value of x must not be equal to 90 for the function to be defined. x can be defined at when x = 0 since cos 0 = 1, the equation will  becomes f'(0) = 1/cos²0 = 1/1 = 1.

Hence the function is defined at 0≤x<90

Answer:

300m

Step-by-step explanation:

20 Times 15=300

Answer:

60/100 and .6

Step-by-step explanation:

Answer:

the 3/5 part of 6 3/5

Step-by-step explanation:

3/5 is equal to 3/10 because when you find the common denominator of 10, you multiply 3/5 by 2 and 3/10 by 1 because 10 is already 10. 3/5*2=6/10.

[tex]solution \: (a) \:: [/tex]

[tex] \frac{1}{7} x = 1[/tex]

[tex]x = 7[/tex]

[tex] solution \: (b) \:: \\ x \times \frac{1}{11} = 1[/tex]

[tex]x = 11[/tex]

[tex]solution \: (c) \:: [/tex]

[tex]1 \div \frac{1}{5} = x[/tex]

[tex]x = 5[/tex]

MN and QR

Hope it helps...

Answer:

dy/dx = (2t + 3t²) / (2t)

Step-by-step explanation:

y = t² + t³

dy/dt = 2t + 3t²

x = 5 +t²

dx/dt = 2t

dy/dx = (dy/dt) / (dx/dt)

dy/dx = (2t + 3t²) / (2t)

Answer:

y - 8 = 2

thats how you would write it so idk i guess pick c because its the closest

"8 less than y" ==> y-8

"is 2" ==> =2

therefore y-8=2

Answer:

x =(-1+√-15)/2=(-1+i√ 15 )/2= -0.5000+1.9365i

Step-by-step explanation:

I got two answers

Answer:

3 1/4

Step-by-step explanation:

Answer:

3 1/4

Step-by-step explanation:

im going to change the fractions to decimals

1/2 = 0.5

2 3/4 = 2.75

0.5 + 2.75 = 3.25

now im going to switch it back to fraction

3.25 = 3 1/4

Answer:

2/10, 1 1/4, 13/24, 11/24

Step-by-step explanation:

1. subtract the fractions

2. add the fractions

3. add the fractions

4. add the fractions

Given:

Annual interest rate = r⁡​%

Growth factor : x = 1 + r⁡​

The below function gives the amount in the account after 4 years when the growth factor is x⁡​ ⁣⁣.

[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]

To find:

The total amount in the account if the interest rate for the account is 3% each year and initial amount.

Solution:

Rate of interest = 3% = 0.03

Growth factor : x = 1 + ⁡0.03 = 1.03

We have,

[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]

Substitute x=1.03 in the given function, to find the total amount in the account if the interest rate for the account is 3% each year.

[tex]A(1.03)=800(1.03)^4+350(1.03)^3+500(1.03)^2+600(1.03)[/tex]

[tex]A(1.03)=800(1.12550881)+350(1.092727)+500(1.0609 )+618[/tex]

[tex]A(1.03)=900.407048+382.45445+530.45+618[/tex]

[tex]A(1.03)=2431.311498 [/tex]

[tex]A(1.03)\approx 2431.31 [/tex]

Therefore, the total amount in the account is 2431.31 if the interest rate for the account is 3% each year.

For initial amount the rate of interest is 0.

Growth factor : x = 1 + ⁡0 = 1

Substitute x=0 in the given function to find the initial amount.

[tex]A(1)=800(1)^4+350(1)^3+500(1)^2+600(1)[/tex]

[tex]A(1)=800+350+500+600[/tex]

[tex]A(1)=2250[/tex]

Therefore, 2250 was put into the account at the beginning.

Answer: 1/44

Step-by-step explanation:

Answer:

-3.5, -3, -1.5, -1, 2

Step-by-step explanation:

Answer:

-3.5, -3, -1.5, -1, 2

Step-by-step explanation:

negatives to positives

Answer:

A, the first one

Step-by-step explanation:

On the left side, the graph is going closer to 0, that explains the first coordinate 0. On the right side, the graph approaches positive infinity, so that explains the infinity. I hope this helps!

Step-by-step explanation:

y-8=7 y=15

|x-2|=15 has two solutions

17,-13

Answer:

answer

(x_2)- 8=7

2x=8-7

2x=1

that's the answer

Answer:

it is data that you can see or describe such as he is a boy

Step-by-step explanation:

Answer:

Transitive

Step-by-step explanation:

It's like a train. Since bc is equal to xy and xy is 8.Then the value of xy equals to bc.

Answer:

$5.60

Step-by-step explanation:

Each pound of strawberries costs $5.60.

To solve: $16.80 divided by 3

Answer:

60%

Step-by-step explanation:

all you need to do is multiply this by 100 (move two decimal places to the right).

0.6--> 60

60 percent

Answer: 60%

Explanation: .6 x 100 = 60

Answer:

[tex]-2\frac{-1}{2}[/tex]

Step-by-step explanation:

To distribute the -6, multiply every numerator by -6, this gets you

-6/4+12/3-30/6

To put these together, they all need to have a common denominator. We can make all of the denomiators 12 by multiplying the numerator by whatever we multiply the denominators by to get 12.

-18/12+48/12-60/12

This gets you -30/12

To make this a proper fraction, divide -30 by 12 and put the whole number to the left of the fraction (-2), making a mixed number. The remainder stays a fraction which is -6/12. This reduces down to -1/2. Put -2 and -1/2 together to get [tex]-2\frac{-1}{2}[/tex]

Answer:

4 2/3

Step-by-step explanation:

7/9 multiplied by 6/1 = 42/9

Simplify: 14/3

Turn it into a mixed number: 4 2/3

Answer:

Step-by-step explanation:

Team B=2.2*4.8= 10.56

Team C : 10.56 *1.5=15.84

[tex]f(x) = x + 2\\g(x) = x\\(g \circ f) = g(f(x)) = x + 2\\g \circ f)(3) = 3 + 2 = 5[/tex]

Answer:

1/15 per min

Step-by-step explanation:

3 times 5 equals 15 and so 1/15.

Try making a visual picture to see yourself.

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3, 5) and (7, -1)

The distance between them is

[tex]d = \sqrt{ ({ - 3 - 7})^{2} + ({5 + 1})^{2} } \\ = \sqrt{( { - 10})^{2} + {6}^{2} } \\ = \sqrt{100 + 36} \: \: \: \: \: \: \: \\ = \sqrt{136} \\ = 2 \sqrt{34} \\ = 11.66190378...[/tex]

We have the final answer as

Hope this helps you

Answer:

11 Squares are there in 11 squares

Answer:

11

Step-by-step explanation:

because take your question and realize you put, "How many squares are in the 11 squares?"

(Sry if wrong or information misunderstood!)