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den301095 [7]
2 years ago
6

Solve the system of equations by the substitution method. y = 5x + 6 y=9x+7.

Mathematics
1 answer:
joja [24]2 years ago
3 0

Answer:

(-1/4, 19/4)

Step-by-step explanation:

5x+6=9x+7

-4x=1

x= -1/4

y=5(-1/4) +6

y=19/4

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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
How can you tell that −10 and −20 are solutions to this inequality, but 10 is not? 3n − 40 < −5n + 8
pochemuha

Step-by-step explanation:

-10 or -20 satisfies the equation.

But when you substitute 10 in:

30-40<-50+8

-10<-42(wrong)

it's wrong

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3 years ago
A ream of paper contains 500 sheets of paper.Norm has 373 sheets of paper left from a ream.Express the protion of a norm has a f
Dima020 [189]
373/500
Divide both by 5:
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74.6%
0.746
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I have475 pounds of Apples to make1000 apple tarts how many pounds of apples are in each tart
olga nikolaevna [1]

Answer:

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Step-by-step explanation:

1000/475

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3 years ago
Consider right triangle △ABC below.
Zanzabum

Answer:

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Step-by-step explanation:

4 0
2 years ago
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