pls just solve its 7th grade not hard :)

Answer:

a) The initial height of the rock is of 48 feet.

b) It takes 1 seconds for the rock to reach maximum height.

c) The rock's maximum height is 50 feet.

d) It takes 6 seconds for the rock to land on the ground.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

The height of the ball after t seconds, in feet, is given by:

[tex]h(t) = -2t^2 + 4t + 48[/tex]

Which is a quadratic equation with [tex]a = -2, b = 4, c = 48[/tex]

a) What is the initial height?

This is [tex]h(0) = 48[/tex]. So the initial height of the rock is of 48 feet.

b) How many seconds does it take to reach the maximum height?

This is the value of t at the vertex. So

[tex]t_{v} = -\frac{b}{2a} = -\frac{4}{2(-2)} = 1[/tex]

It takes 1 seconds for the rock to reach maximum height.

c) What is the rock's maximum height?

This is the height of the ball after 1 second. So

[tex]h(1) = -2(1)^2 + 4(1) + 48 = 50[/tex]

The rock's maximum height is 50 feet.

d) How many seconds does it take to for the rock to land on the ground?

This is t for which [tex]h(t) = 0[/tex], so we solve the quadratic equation.

[tex]\bigtriangleup = (4)^2-4(-2)(48) = 400[/tex]

[tex]t_{1} = \frac{-4 + \sqrt{400}}{2*(-2)} = -4[/tex]

[tex]t_{2} = \frac{-4 - \sqrt{400}}{2*(-2)} = 6[/tex]

Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.

Step-by-step explanation:

3

[tex]3 \sqrt{xy { - }^{2} } [/tex]

Answer:

64 (1/2) n

ssssssssssssssssssssssssssssssssssssssssssssss

Answer:

12 12/42

Step-by-step explanation:

Answer:

12 17/42

Step-by-step explanation:

18/7+59/6       LCD=42

108/42+413/42

521/42

12 17/42

Answer:

center = (-12, 9)

radius = 5.92 (rounded)

Step-by-step explanation:

Answer:

The answer 8 inches

Hope this helps :)

Answer:

8 inches

Step-by-step explanation:

1 foot is 12 feet. 2/3 of 12 is 8.

Answer: (5, 11)

Step-by-step explanation:

y = 2x + 1

x + y = 16

Substitute 2x + 1 for y in 'x + y = 16'

x + y = 16

x + (2x + 1) = 16

3x + 1 = 16

Subtract both sides by 1

3x = 15

Divide both sides by 3

x = 5

Now to find y

Since we know what x is, we can use one of the equations and substitute 5 for x. I'll use both to show that you get the same answer.

Second equation:

x + y = 16

5 + y = 16

Subtract both sides by 5

y = 11

First equation:

y = 2x + 1

y = 2(5) + 1

y = 10 + 1

y = 11

The solution would be (5, 11)

Answer:

(5, 11) point form

x=5,y=11 equation form

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

2×3.7=7 is easy and less money

Answer:

the stem and leaf plot is invalid. please provide a diagram.

Answer:

56 ft square (Approx)

Step-by-step explanation:

Area of Rhombus= (1/2) * D1* D2 {D1 = 4.5; D2 = 5*5= 25}

= 1/2 * 4.5 * 25

= 56.25

= 56 ft square (Approx)

Answer:

22.5ft²

Step-by-step explanation:

4.5ft x 5ft = 22.5ft²

Answer:

These expressions are both correct because they are equivalent to each other.

5(4) + 7(4) = 20 + 28 = 48

(12 x 8)/2 = 96/2 = 48

Let me know if this helps!

Answer:The nail would be at the same height since trees grow at their tops.

Step-by-step explanation:

Answer:

speed of growth of tree = 5cm/year

Years after John Came = 10 years

5cm × 10= 50cm

The nail is 50cm higher

Step-by-step explanation:

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0.48p

Step-by-step explanation:

1.20÷10=0.12

0.12×4=0.48

put the wrong answer ignore this

Answer: the answer is D

The triangle GRS is not similar to the triangle ART because the ratio of the corresponding sides is not in the same proportion option (D) is correct.

It is defined as the law to prove that the two triangles have the same shape but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same propertions and the corresponding angles are congruent.

We have two triangles:

ΔGRS and ΔART in which:

GR = 36 units, SR = 45 units, AR = 15 units, and RT = 18 units

To check the similarity take the ratio of the corresponding sides.

[tex]\frac{36}{15} =\frac{45}{18}[/tex]   (after simplification)

[tex]\frac{12}{5} \neq \frac{15}{6}[/tex]  

As we can see the ratio of the corresponding sides is not in the same proportion.

Thus, the triangle GRS is not similar to the triangle ART because the ratio of the corresponding sides is not in the same proportion option (D) is correct.

Learn more about the similarity of triangles here:

https://brainly.com/question/8045819

Answer:

The rate is 6 for all of them

Step-by-step explanation:

The rate would be the price for one taco, so you divide the cost by the number of tacos you're getting.

Answers: Well 1 taco is 6$. 4 tacos is 24$. 5 tacos is 30$. 6 tacos is 36$.

Answer:

when the bases are different and the powers are same

Step-by-step explanation:

(a)²★(a)³=(a)²+³........

Answer:

22.5

Step-by-step explanation:

It is very important to use bidmas (the order of mathematical functions - standing for brackets, indices, division, multiplication, addition, subtraction) in this question. 15 + 6 x 7 - 12 divided by 2 can also be written as (15 + 6 × 7 - 12) ÷ 2. First, you should complete the multiplication to make (15 + 42 - 12) ÷ 2. Then, complete the addition which makes (57 - 12) ÷ 2. Afterwards, do the subtraction which makes it 45 ÷ 2. This is 22.5. I hope this helps!

Answer:

The stores profit was $757

Step-by-step explanation:

70 x 24.50=1715

they spent 1715 on 70 soccer balls.

They sold 40 of the soccer balls for 39.75 each.

so 40 x 39.75=1590

Then the the remainder of the soccer balls would be 30 since they only started with 70

so they sold 30 soccer balls for 29.50 each.

30 x 29.50= 882

So add 882+1590=2472

then take that number and subtract it from 1715

2472-1715=757 So in profit they made $757 dollars.

Answer:the distance is 8

( this isn’t college math if anything it’s the ending and or beginning of 6th)

Step-by-step explanation:

Answer:

-150

Step-by-step explanation:

x^2 - 7x^2 - 18x +42

3^2 - 7(3)^2 - 18(3) + 42

9 - 63 - 54 + 42

-54 -54 + 42

-108 + 42

-150

Answer:

k= 2b/q

Step-by-step explanation:

see pic for explanation

Answer:

1 [tex]3/8[/tex]

Step-by-step explanation:

Answer:

26 units

Step-by-step explanation:

6+6+7+7 = 26 units

Answer:

is this on shapes or multiple answer?

Step-by-step explanation:

like i was thinking 2 segments as parallel

Answer:

d. 108 °

Step-by-step explanation:

(2x + 3x) * 2 = 360

4x + 6x = 360

10x = 360

x = 36

Angle DAB = 3x = 36 * 3 = 108°

(Please heart and the answer if you find it helpful, it's a motivation for me to help more people)

Answer:

Cost of 1 article is Rs10