Identify the vertex of the function, f(x) = 3(x

. In the 2012 Olympics, Usain Bolt ran the 100m dash in 9.63 seconds. Jim Hines won the 1968 Olympic gold with a time of 9.95 se

Nimfa-mama [501]

Answer:

A. 3.2% faster

B. 3.3% slower

C. 103.3%

Step-by-step explanation:

In order to find this out, we need to take the differences and divide them by the comparative time. So, in the first one, we take the difference (.32) and divide it by Hines time.

.32/9.63 = 3.2%

In the second, we take the difference and divide by Bolt's time.

.32/9.95 = 3.3%

And finally, in the last one, we take Hines' time and divide by Bolt's.

9.95/9.63 = 103.3%

3 1

3 years ago

Write the equation of a line perpendicular to 9x−4y=−5 that passes through the point (−9,3).

Oksana_A [137]

Answer:

4x + 9y = - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

9x - 4y = - 5 ( subtract 9x from both sides )

- 4y = - 9x - 5 ( divide terms by - 4 )

y = $\frac{9}{4}$ x + $\frac{5}{4}$ ← in slope- intercept form

with slope m = $\frac{9}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{9}{4} }$ = - $\frac{4}{9}$ , then

y = - $\frac{4}{9}$ x + c ← is the partial equation

To find c substitute (- 9, 3 ) into the partial equation

3 = 4 + c ⇒ c = 3 - 4 = - 1

y = - $\frac{4}{9}$ x - 1 ( multiply through by 9 to clear the fraction )

9y = - 4x - 9 ( add 4x to both sides )

4x + 9y = - 9 ← equation in standard form

3 0

2 years ago

Explain the distance formula then use it to calculate the distance between A(1, 1)and B(7, -7)

lbvjy [14]

The <u>Distance Formula</u> = $\sqrt{( X_{2} - X_{1}) ^{2}+( Y_{2} - Y_{1}) ^{2}}$
A(1,1) ⇒ the first 1 is $X_{1}$ & the second 1 is $Y_{1}$ .
B(7,-7) ⇒ the first 7 is $X_{2}$ & the second is -7 is $Y_{2}$ .
Now all you have to do is SUBSTITUTE the variables into the distance formula to get: $\sqrt{(7-1) ^{2}+(-7-1) ^{2}}$ .
After you plug that formula into your graphing calculator (or solve it manually & mentally), you should end up with the answer 10, therefore d=10.

4 0

3 years ago

Figure ABC is reflected about the x-axis to obtain figure A′B′C′: Triangle ABC is located on the coordinate plane with vertex A

zavuch27 [327]

Answer:

Figure ABC is congruent to figure A’B’C’.

Step-by-step explanation:

All the other answers doesn't make sense

5 0

3 years ago

ive students came for after-school tutoring. Priya’s teacher assigned each of them the same number of problems to complete. Then

tensa zangetsu [6.8K]

Answer:

The equation for the situation is:

$5y+2=27$

where $y$ represents the number of questions initially assigned to each student by the teacher.

On solving, we find that 5 questions were originally assigned to each student by the teacher.

Step-by-step explanation:

Question:

Five students came for after-school tutoring. Priya’s teacher assigned each of them the same number of problems to complete. Then she assigned 2 more problems to one of the students. 27 problems were assigned in all. Use y as the variable. Write an equation for the situation. Then, find the number of problems originally assigned to each by the teacher.

Given:

Total number of students = 5

Total problems assigned = 27

To find the number of problems originally assigned by the teacher.

Solution:

Let the number of problems originally assigned by the teacher to each student be = $y$

If each student is assigned $y$ questions initially.

Then, 5 students was initially assigned = $5y$ questions