Y=-4x - 18 y=-10x-36
It’s system of equations PLS HELP ITS DUE TOMORROW

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.

Answer:

a

Step-by-step explanation:

all angles in a triangle is equal to 180 so

60+50=110 so p =70

80+30=110 so q =70

p=q

Answer:

p=q

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

There are 136 people on a train

34 are children

Therefore the percentage of people that are adults can be calculated as follows

= 136-34

= 102

= 102/136 × 100

= 0.75 × 100

= 75%

Hence 75% are adults

Answer:

57.5

Step-by-step explanation:

Recognize our numbers

3,5,34.50

Three uniform shirts sell for 34.50

34.50/3

=11.5

How much will five cost?

5x11.5

=57.5

Hope this helps!

Answer:

55.25

Step-by-step explanation:

1. First we need to work out the price of ONE shirt. To do that we divide the total price of 3 shirts by 3.

34.50 / 3 = 11.05

2. Now we know that the price of one shirt is $11.05p we can multiply that by 5 to get the price of 5 shirts.

11.05 * 5 = 55.25

= $55.25p

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:

In this question (t½) of C-14 is 5730 years, which means that after 5730 years half of the sample would have decayed and half would be left as it is. After 5730 years ( first half life) 70 /2 = 35 mg decays and 35 g remains left. After another 5730 years ( two half lives or 11460 years) 35 /2 = 17.5mg decays and 17.5 g remains left . After another 5730 years ( three half lives or 17190 years) 17.5 /2 = 8.75mg decays and 8.75g remains left. after three half lives or 17190 years, 8.75 g of C-14 will be left.

Step-by-step explanation:

Answer:

3√41

Step-by-step explanation:

The diagonal can be gotten using the pythagoras theorem

d² = l²+w²

d² = 12²+15²

d² = 144 + 225

d² = 369

d = √9*41

d = 3√41

Hence the diagonal is 3√41

Answer:

x = 5

Step-by-step explanation:

We have the algebraic expression and are asked to solve for x.

To solve, we need to isolate x.

2x + 22 = 4(x + 3)

Distribute :

2x + 22 = (4(x) + 4(3))

2x + 22 = 4x + 12

Subtract 12 from both sides :

2x + 10 = 4x

4x = 2x + 10

Subtract 2x from both sides :

2x = 10

Divide 2 from both sides to get x alone :

x = 5

Answer:

x = 5

Step-by-step explanation:

We have the algebraic expression and are asked to solve for x.

To solve, we need to isolate x.

2x + 22 = 4(x + 3)

Distribute :

2x + 22 = (4(x) + 4(3))

2x + 22 = 4x + 12

Subtract 12 from both sides :

2x + 10 = 4x

4x = 2x + 10

Subtract 2x from both sides :

2x = 10

Divide 2 from both sides to get x alone :

x = 5

Graph is on the picture.

hope ot helps.

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:

-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:

Answer B

Step-by-step explanation:

Write out f(x) and g(x) in a column; we will subtract g(x) from f(x):

f(x) = x^2  - 9          or f(x)   =   x^2           - 9

-g(x) = -(2 - x)          or -g(x) =           +x      -2

                                    ---------------------------------

                                      f(x) - g(x) = x^2 + x - 11   (Answer B)

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:

when the bases are different and the powers are same

Step-by-step explanation:

(a)²★(a)³=(a)²+³........

Answer:

Step-by-step explanation:

2x + 3x + 8 - 3x - 2 = 2x + 6

The first and third expressions.

Answer:

1 and 3

Step-by-step explanation:

This should be correct

Answer:

[tex]\displaystyle \frac{2(x + 3)}{5x - 2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{2x^2 + 16x + 30}{5x^2 + 13x - 6}[/tex]

Step 2: Simplify

Answer:

569870

Hope this helps you. Do mark me as brainly

Answer:

the answer is very big..... it is 575,876,495

Answer:

24 yw :)

Step-by-step explanation:

Answer:

168 hours

Step-by-step explanation:

Answer:

k= 2b/q

Step-by-step explanation:

see pic for explanation

Answer:

In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run. To find the slope of the line, pick two points on the line.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Substitute values and solve for r the equation of the time difference:

Raul's speed is 17 mph

Answer:

[tex] \huge \boxed{ \boxed{ \red{ \tt17 \: mph}}}[/tex]

Step-by-step explanation:

let's the speed of Raul be x

likewise

Miguel can drive 4 times as fast as Raul can ride his bicycle

therefore

4x

according to the question

[tex] \sf \frac{68}{4x}+3=\frac{68}{x}[/tex]

[tex] \implies \sf \frac{68 + 12x}{4x} = \frac{68}{x} [/tex]

[tex] \sf factor \: out \: 4 \: and \: reduce \: it : \\ \sf \implies \frac{4(17 + 3x)}{4x} = \frac{68}{x} \\ \\ \implies\sf \frac{17 + 3x}{x} = \frac{68}{x}[/tex]

[tex] \sf multipy \: both \: sides \: by \: x : \\ \sf \implies (\frac{17 +3 x}{x} )x = (\frac{68}{x} )x \\ \implies \sf 17 + 3x = 68[/tex]

[tex] \sf cancel \: 17 \: from \: both \: sides : \\ \implies \sf 17 - 17 + 3x = 68 - 17 \\ \implies \sf 3x = 51[/tex]

[tex] \sf divide \: both \: side s \: by \: 3 : \\ \sf \implies \frac{3x}{3} = \frac{51}{3} \\ \therefore x = 17[/tex]

Answer:

No

Step-by-step explanation:

Answer:

Its 5000

Step-by-step explanation 4883-3455=5000

-33

Hope this helps. :)))))

Answer:

26 units

Step-by-step explanation:

6+6+7+7 = 26 units