MATHEMATICS HIGH SCHOOL

The formula for height, in feet of a projectile under the influence of gravity is given by h=-16t^2+vt+s, where t is the time in seconds, v is the upward velocity at the start, and s is the starting height. Marvin throws a baseball straight up into the air at 70 feet per second. The ball leaves his hand at a height of 5 feet. When does the ball reach a height of 75 feet?

Answers

Answer 1

Answer:

1.55s

Step-by-step explanation:

The height equation of the projectile is given as;

h = -16t^2 + vt + s .......1

where;

t is the time in seconds,

v is the upward velocity at the start,

s is the starting height.

Given;

v = 70 ft/s

s = 5 ft

Substituting the values equation 1 becomes;

h = -16t^2 + 70t + 5

For the ball to reach 75 ft, h = 0

75 = -16t^2 + 70t + 5

-16t^2 + 70t + 5 - 75 = 0

-16t^2 + 70t - 70 = 0

solving the quadratic equation;

Time t = 2.83 s and t = 1.55s

Therefore, the ball will first reach 75 ft after 1.55 seconds.

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answer and enjoy the points :D

Answers

Answer:59

Step-by-step explanation:

The GDP is $11,465.2 billion. The population is 249,793,675. Find the per capita GDP.

Answers

Answer: $ 45898.68

Step-by-step explanation:

Given: Population = $249,793,675$

GDP = $11,465.2 billion

Since we know that 1 billion = 1,000,000,000

Therefore, GDP = $11,465,200,000,000

Also, the per capita GDP is calculated by :-

$\text{per capita GDP}=\frac{\text{GDP}}{\text{Population}}\n\n=(11,465,200,000,000)/(249,793,675)\n\n=45898.6801808\approx\$45898.68$

Hence, the per capita GDP = $ 45898.68

it would be 45898.68 $ for the capital gdp

Suppose △FMN≅△HQR . Which congruency statements are true? Select each correct answer. NF¯¯¯¯¯¯≅HQ¯¯¯¯¯¯ MN¯¯¯¯¯¯¯≅QR¯¯¯¯¯ ∠M≅∠Q ∠R≅∠F ∠N≅∠M QH¯¯¯¯¯¯≅MF¯¯¯¯¯¯

Answers

Answer: $\overline{MN}\cong\overline{QR}$

$\angle{M}\cong\angle{Q}$

$\overline{MF}\cong\overline{QH}$

Step-by-step explanation:

We know that if two triangles are congruent , then the corresponding angles and sides are congruent by CPCTC.

Given: $\triangle {FMN}\cong\triangle{HQR}$

Therefore , the corresponding angles and sides of $\triangle {FMN}\text{ and }\triangle{HQR}$ are congruent.

∠F corresponds ∠H

∠M corresponds ∠Q

∠N corresponds ∠R

⇒ ∠F ≅ ∠H

∠M ≅ ∠Q

∠N ≅ ∠R

$\overline{MF}\cong\overline{QH}\n\overline{MN}\cong\overline{QR}\n\overlien{FN}\cong\overline{HR}$

So , from the given options, the true congruency statements are :-

$\overline{MN}\cong\overline{QR}$

$\angle{M}\cong\angle{Q}$

$\overline{MF}\cong\overline{QH}$

△FMN ≅ △HQR
so
MF ≅ QH
MN ≅ QR
NF ≅ RH
and
∠F ≅ ∠H
∠M ≅ ∠Q
∠N ≅ ∠R

Answer
MN ≅ QR
∠M ≅ ∠Q
QH ≅ MF

(3/4)(12x-8)-5x how do I solve this?

Answers

$(3)/(4)*(12x-8)-5x=(3(12x-8))/(4)-5x=(36x-24)/(4)-5x=(36x-24)/(4)-5x=$
$=9x-6-5x=4x-6$

Answer:

4-6x

Step-by-step explanation

Simplify 15 + 6(x + 1).

Answers

15 + 6(x + 1)

First, expand to get rid of parentheses.
$15 + 6x + 6$
Second, simplify. Keep your 6x and add 15 + 6.
$6x + 21$

Answer: 6x + 21

first you use the distrbutive property and multiply 6 by x and 6 by 1 then you get 15 + 6x + 6 now add 15 and 6 together and you get 21 + 6x as your answer

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Answers

38000 rounded to two significant figures

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