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Sholpan [36]
3 years ago
14

Evaluate the expressions

Mathematics
1 answer:
likoan [24]3 years ago
4 0
<h3>Answer:</h3>

1. x + 20

2. 0

3. 2x - 8

4. 95x + 10

5. -9x - 6

6. 4x + y - 5

7. -x + 6y + 5

8. x + y - 15

9. x + 4y + 4

<h3>Step-by-step explanation:</h3>

• When working with variables and numbers, you have to put the variables first (in alphabetical order) and then the numbers.

• To evaluate an algebraic expression, we find the value of the expression when the variable is replaced by a given number.

• To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

• When we are not given a number for the variable in the expression, we have to group like-terms.

  1. <u>Example:</u> 5x + 6 + 3x - 2 - y
  • 1st: group 5x and 3x (add the terms together) = 8x
  • 2nd: group 6 and -2 (add the terms together) = 4
  • 3rd: Since -y has no like-terms, we can't group it = -y
  • Fourth, put the terms in order (variables = alphabetical order and then numbers) = 8x - y + 4

1. 4x + 12 - 3x + 8

  • 4x - 3x = 1x = x
  • 12 + 8 = 20
  • x + 20

2. -8x + 1 + 2x - 1 + 6x

  • -8x + 2x + 6x = -8x + 8x = 0
  • 1 - 1 = 0
  • 0

3. 4x - 3 - 2x - 5

  • 4x - 2x = 2x
  • -3 - 5 = -8
  • 2x - 8

4. 100x + 5 - 5x + 5

  • 100x - 5x = 95x
  • 5 + 5 = 10
  • 95x + 10

5. -4x - 4 - 2 - 5x

  • -4x - 5x = -9x
  • -4 - 2 = -6
  • -9x - 6

6. 2x - 1 + 2x - 4 + y

  • 2x + 2x = 4x
  • -1 - 4 = -5
  • 4x + y - 5

7. 5y - x + 2y - y + 5

  • 5y + 2y - y = 5y + 1y = 6y
  • -x + 6y + 5

8. -15 + 3y - 3x - 2y + 4x

  • 3y - 2y = 1y = y
  • -3x + 4x = 1x = x
  • x + y - 15

9. 4 - 3y + 3x - 2x - y

  • -3y - y = 4y
  • 3x - 2x = 1x = x
  • x + 4y + 4

Hope I helped you, if I did can you please mark me the Brainliest?

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bagirrra123 [75]

For firework launched from height 100ft with initial velocity 150ft/sec, equation made is correct

(a) equation will be h(t) = -16t^2+150t+100

(b) Now we have to see when it will land. At land or ground level height h will be equal to 0. So simply plug 0 in h place in equation made in part (a)

0 = -16t^2 + 150t + 100

Now we have to solve this quadratic. We will use quadratic formula method to solve this equation.

t = \frac{-b \pm  \sqrt{b^2-4ac}}{2a}

a = -16, b = 150, c = 100.

Plugging these values in quadratic formula we get

t = \frac{-150 \pm  \sqrt{150^2-4(-16)(100)}}{2(-16)}

t = \frac{-150 \pm  \sqrt{22500+6400}}{-32}

t = \frac{-150 \pm  \sqrt{28900}}{-32}

t = \frac{-150+170}{-32}  = \frac{20}{-32} = -0.625

time cannot be negative so we will drop this answer

then t = \frac{-150-170}{-32}  = \frac{-320}{-32} = 10

So 10 seconds is the answer for this

(c) To make table simply plug various value for t like t =0, 2, 4, 6, 8 till 10. Plug values in equation mad in part (a) and find h value for each t as shown

For t =0 seconds, h = -16(0)^2+150(0)+100 = 100 feet

For t =2 seconds, h = -16(2)^2+150(2)+100 =336 feet

For t =4 seconds, h = -16(4)^2+150(4)+100 = 444 feet

For t =6 seconds, h = -16(6)^2+150(6)+100 = 424 feet

For t =8 seconds,h = -16(8)^2+150(8)+100 = 276 feet

For t =10 seconds, h = -16(10)^2+150(10)+100 = 0 feet

(d) Axis of symmetry is given by formula

x = \frac{-b}{2a}

t = \frac{-150}{2(-16)} =\frac{-150}{-32} = 4.6875

t = 4.6875 is axis of symmetry line

(e) x-coordinate of vertex is again given by formula

x = \frac{-b}{2a}

so t = 4.6875

then to find y coordinate we will plug this value of t as 4.6875 in equation made in part (a)

For t =4.6875, h = -16(4.6875)^2+150(4.6875)+100 = 451.563

so vertex is at (4.6875, 451.563)

(f) As the firework is launched so in starting time is t=0, we cannot have time before t=0 (negative values) practically. Also we cannnot have firework going down into the ground so we cannot have h value negative physically.

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