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3 years ago

Plz help me with these three

Mathematics

1 answer:

umka2103 [35]3 years ago

4 0

1. + and - are inverses as well as × and ÷
2. They are equivalent because x equals -3 in each equation.
3. x-3=6 because x=9 in this equation whereas it equals 6 in all of the other ones

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Boyd grows only tomatoes and raspberries in his garden. Last year, he grew 140 pounds of tomatoes and 60 pounds of raspberries.

nadya68 [22]

Answer:

29%.

Step-by-step explanation:

We have been given that Boyd grew 140 pounds of tomatoes and 60 pounds of raspberries. This year, the production, by weight, of tomatoes declined by 20 percent, and the production, be weight, of raspberries declined by 50 percent.

First of all, we will find the weight of tomatoes and raspberries using the given information.

Since the production, by weight, of tomatoes declined by 20 percent, so this year production of tomatoes is 80% of 140 pounds.

$\frac{80}{100}\times 140=0.80\times 140=112$

Since the production, be weight, of raspberries declined by 50 percent, so this year production of raspberries is 50% of 30 pounds.

$\frac{50}{100}\times 60=0.50\times 60=30$

Total production this year: $112+30=142$ pounds.

Now, we will percent decrease formula.

$\text{Percent decrease}=\frac{\text{Initial value-Final value}}{\text{Initial value}}\times 100$

$\text{Percent decrease}=\frac{(140+60)-142}{140+60}\times 100$

$\text{Percent decrease}=\frac{(200)-142}{200}\times 100$

$\text{Percent decrease}=\frac{58}{200}\times 100$

$\text{Percent decrease}=0.29\times 100$

$\text{Percent decrease}=29$

Therefore, the total yield, by weight, of Boyd's garden declined by 29%.

5 0

3 years ago

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

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

Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the

fiasKO [112]

It’s B I did this question and got the same answer

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2 years ago

Therese filled a rectangular pool with water. The pool measured 214 yards long, 2 yards wide and 3 yards tall. If the pool was f

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Answer:

1284 yd^3

Step-by-step explanation:

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2 years ago

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Answer:

divisor

Step-by-step explanation:

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2 years ago

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