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sertanlavr [38]
4 years ago
13

Help me please justify each step 9x/4=-9 9x=-36 x=-4

Mathematics
2 answers:
Nesterboy [21]4 years ago
6 0

\dfrac{9x}{4}=-9\ \ \ |\text{Multiplication Property of Equality}\\\\4\cdot\dfrac{9x}{4}=4\cdot(-9)\\\\9x=-36\ \ \ \ |\text{Division Property of Equality}\\\\\dfrac{9x}{9}=\dfrac{-36}{9}\\\\x=-4

aleksandrvk [35]4 years ago
3 0

Answer:

The justification is mentioned below.

Step-by-step explanation:

Given equation,

\frac{9x}{4}=-9

Multiply both sides by 4 ( multiplicative property of equality ),

\frac{9x}{4}\times 4 = -9\times 4

9x=-36

Divide both sides by 9 ( division property of equality )

\frac{9x}{9}=\frac{-36}{9}

x=-4

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Since the question wants to know how many ingredients she used, All we have to do is add them.

So as the question says, she used 6/10 flour, 3 eggs, and 4/5 sugar.

Now we have two fractions in this scenario. Let's make them have the same denominator. Either we divide 6/10 by 2 or multiply 4/5 by 2. Let's multiply.

4/5 × 2 = 8/10

Now we have 6/10, 3, and 8/10

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3 + 6/10 = 3 and 6/10

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Simplify even further...

and your answer will be 4 and 2/5
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16 - 4 - 1

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The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f
Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

h(t)=-16t^{2}+25t+5

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

h(t)=-16(t^{2}-\frac{25}{16}t)+5

Complete the square

h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}

h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}

Rewrite as perfect squares

h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}

The vertex is the point (\frac{25}{32},\frac{945}{64})

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}

16(t-\frac{25}{32})^{2}=\frac{945}{64}

(t-\frac{25}{32})^{2}=\frac{945}{1,024}

square root both sides

(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}

t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}

the positive value is

t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec

8 0
3 years ago
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