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scoray [572]
3 years ago
8

When Anita planted a large bush in her garden, it was 5 feet tall. Now it is 40% taller. How tall is the bush now?

Mathematics
1 answer:
goblinko [34]3 years ago
7 0

Answer:

7 feet

Step-by-step explanation:

the new height of the bush can be represented in percentage form as 100% + 40% = 140% = 1.40

1.40 x 5 = 7 feet

Method 2

find 40% of 5 feet

0.4 x 5 = 2

Add 5 + 2 = 7 feet

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Which statements are true about the graph of the function f(x) = 6x – 4 + x2?
kaheart [24]
Write the function as
f(x) = x² + 6x - 4

Note that
x² + 6x = (x + 3)² - 9

Therefore
f(x) = (x  3)² - 9 - 4
      = (x + 3)² - 13

The vertex is at (-3, -13)., and the curve opens upward.
The axis of symmetry is x = -3.

Answer:
The vertex of the function is (-3, 13).
The graph increases over the interval (-3, -∞)


3 0
3 years ago
Please help me
Nata [24]

Answer:

1 1/2

Step-by-step explanation:

2 2/3 - 1 1/6 = ?

The LCD here is 6.  Convert 2 2/3 so that the denominator is 6:

2 2/3 = 2 4/6

Then subtract 1 1/6 from 2 4/6:  We get 1 3/6, or 1 1/2

5 0
3 years ago
An object is launched from a launching pad 144 ft. above the ground at a velocity of 128ft/sec. what is the maximum height reach
ollegr [7]

Answer:

18) a. h(x) = -16x² + vx + h(0) ⇒ h(x) = -16x² + 128x + 144

b. The maximum height = 400 feet

c. Attached graph

19) The rocket will reach the maximum height after 4 seconds

20) The rocket hits the ground after 9 seconds

Step-by-step explanation:

* Lets study the rule of motion for an object with constant acceleration

# The distance S = ut ± 1/2 at², where u is the initial velocity, t is the time

  and a is the acceleration of gravity

# The vertical distances h in x second is h(x) - h(0), where h(0)

   is the initial height of the object above the ground

∵ h(x) = vx + 1/2 ax², where h is the vrtical distance, v is the initial

  velocity, a is the acceleration of gravity (32 feet/second²) and x

  is the time

18)a.

∵ The value of a = -32 ft/sec² ⇒ negative because the direction

   of the motion

  is upward

∴ h(x) - h(0) = vx - (1/2)(32)(x²) ⇒ (1/2)(32) = 16

∴ h(x) = vx - 16x² + h(0)

∴ h(x) = -16x² + vx + h(0) ⇒ proved

* Find the height of the object after x seconds from the ground

∵ h(0) = 144 and v = 128 ft/sec

∴ h(x) = -16x² + 128x + 144

b.

* At the maximum height h'(x) = 0

∵ h'(x) = -32x + 128

∴ -32x + 128 = 0 ⇒ subtract 128 from both sides

∴ -32x = -128 ⇒ ÷ -32

∴ x = 4 seconds

- The time for the maximum height = 4 seconds

- Substitute this value of x in the equation of h(x)

∴ The maximum height = -16(4)² + 128(4) + 144 = 400 feet

c. Attached graph

19)

- The object will reach the maximum height after 4 seconds

20)

- When the rocket hits the ground h(x) = 0

∵ h(x) = -16x² + 128x + 144

∴ 0 = -16x² + 128x + 144 ⇒ divide the two sides by -16

∴ x² - 8x - 9 = 0 ⇒ use the factorization to find the value of x

∵ x² - 8x - 9 = 0

∴ (x - 9)( x + 1) = 0

∴ x - 9 = 0 OR x + 1 = 0

∴ x = 9 OR x = -1

- We will rejected -1 because there is no -ve value for the time

* The time for the object to hit the ground is 9 seconds

8 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B6%7D%20%20%2B%20%28%20%5Cfrac%7B4%7D%7B9%7D%20%29%20-%20%28%20-%202%29" id
Lady_Fox [76]

get a common denominator of 18

5/6 * 3/3 +4/9 * 2/2 - -2*18/18

15/18 +8/18 + 36/18

23/18 + 36/18

59/18

change to a mixed number

18 goes into 59 3 times with 5 left over

3 and 5 /18

6 0
3 years ago
What is the interval notation for y&lt;5?
Ilia_Sergeevich [38]

Hey there!☺

Answer: (-∞, 5)

Explanation:

You need to convert the inequality as an interval notation.

y as interval notation would be written like this:

(-∞, 5)

Hope this helps!

7 0
3 years ago
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