Select the x-coordinate of the vertex of the parabola defined by the function f(x) = -7x^2 + 3x + 1.

Answers

Answer 1

Answer: $f(x) = -7x^2 + 3x + 1 \n \na=-7, \ b=3 , \ c=1 \n \n vertex(h, k) \ is \ given \ by: \n \n h = (-b)/(2a ) , \ \ k = c-(b^2)/(4a) \n \nh=(-3)/(2\cdot (-7))=(-3)/(-14)=(3)/(14)$

$k = 1-( 3^2)/(4 \cdot (-7)) =1-(9)/(-28)=1+(9)/(28)=1(9)/(28)=(37)/(28)\n \n \n Answer : \ Vertex =((3)/(14), (37)/(28))$

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The distance from Earth to the Moon is approximately 240,000 mi.. The speed of light is 3.00 * 10^8 m/s. How long does it take for light to travel from Earth to the Moon and back again?. Please Show work.

Answers

First we have to convert miles to meters:
1 mile ≈ 1,609.34 m
Time of traveling one way:
$t = (240,000 * 1,609.34m)/(3.00*10^(8)m/s ) = \n = (8*10 ^(4) *1,609.34s)/(10 ^(8) ) = (8*1,609.34 s)/(10,000)$ = 1.28 s
From Earth to the Moon and back time is: 2 · 1.28 s = 2.56 s

True or False:No Explanations Needed

If two figures are similar then they are congruent.

If the ratios of the length of corresponding sides of the two triangles are equal then the triangles are congruent

if triangles are similar then the have the same shape

if two triangles are congruent then each pair of corresponding angles are congruent

if two angles of one triangle are congruent to corresponding angles of another triangle then the triangles are similar

Answers

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true
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the answer is true to all of them.

9 miles is approximately equal to 16km. How many km are equal to 63 miles? How many miles are equal to 48km?

Answers

The correct answer is 27 miles!

16 x 7 =112 so 63 miles would equal 112 km
48km equals 21.8258172

What is the average of four tenths and five thousandths?

Answers

four tenths is expressed as .4
five thousandths is expressed as .005
the sum of these is .405 and divided by 2 (there are two numbers we added), we get .2025, that is the average

$((4)/(10)+(5)/(1000)):2 = ((400)/(1000)+(5)/(1000))*(1)/(2) =\n \n=(405)/(1000)*(1)/(2)=(405)/(2000)=(81)/(400)= .2025$

Rise over run please?????????

Answers

Answer:

1/3

Step-by-step explanation:

up 1 right 3

M= rise/run M= 1/3

Rise 1 run 3

45 students were asked if they have visited Canada, Mexico or the USA

Answers

Answer:

THERE YA GO BUDDY!!

Step-by-step explanation:

To work out the probability that both randomly chosen students have only visited Mexico, we need to consider the number of students who have visited Mexico and subtract those who have also visited other countries.

From the given information:

- 11 students have visited Canada

- 2 students have visited Canada and Mexico (but not the USA)

- 3 students have visited Mexico and the USA

- 1 student has visited all three countries

- 6 out of the 19 students who have visited the USA have also visited at least one of the other countries.

We can calculate the number of students who have only visited Mexico as follows:

Total students who have visited Mexico = Total students who have visited Mexico and the USA - Students who have visited all three countries - Students who have visited Canada and Mexico (but not the USA)

= 3 - 1 - 2

= 0

Since there are no students who have only visited Mexico, the probability that both randomly chosen students have only visited Mexico is 0.

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