Determine the independent variable and dependent variable in the situation
The independent variable is the <em><u>"</u></em><em><u>amount of water the plant receives</u></em><em><u>"</u></em>, and the dependent variable is the <u><em>"</em><em>height of the plant</em><em>"</em><em>.</em></u>
- An independent variable is a the variable which causes a change.
- A dependent variable is the result or effect of a change.
Therefore, the independent variable from the phenomena is <em><u>"amount of water"</u></em> and the dependent variable is the <u><em>"</em><em>height of the plant</em><em>"</em><em>.</em></u>
Read more:
brainly.com/question/23700645
To solve for x, we will begin by using the distributive property
6x - 2(x + 4) = 12
6x - 2x - 8 = 12
(always remember to sort your negatives!)
Add like terms
4x - 8 = 12
Add 8 to both sides
4x = 20
Divide both sides by 4
x = 5
Answer:
The rocket's maximum height will be 1424 feet.
It will reach that height in 4 seconds.
It will reach the ground in 8 seconds.
Step-by-step explanation:
One easy way to find the peak is to find the derivative and solve for zero:
h(t) = -16t² + 128t + 1680
To find the derivative of each term in that format, you simply multiply the coefficient by the exponent, and reduce the exponent by one. In the case of terms with no variable, they disappear. That gives us:
h'(t) = -32t + 128
This derivative describes the rate of change of h with respect to t, so to find the peak, we simply need to solve it for zero:
0 = -32t + 128
32t = 128
t = 4
So the maximum height occurs when t = 4. Let's plug it in to the original equation:
h(t) = -16t² + 128t + 1680
h(4) = -256 + 512 + 1680
h(4) = 1424
So the rocket's maxiumum height is 1424 feet.
And we've already answered the second question, it happens at 4 seconds.
Also, the amount of time going up will be the same as the amount of time going down, which means that it will reach the ground in twice that time, or 8 seconds.
Answer:
She sold 5.775 kilograms of pears at the farmer's market.
Step-by-step explanation:
Let's first determine the information that the question gives us, and what we need to find.
Given:
The farmer sold 7.7 kilograms of apples and pears
1/4 of the weight is apples
The rest of the weight is pears
Find:
Kilograms of pears that the farmer sold
Start by finding the fraction of the whole weight that was pears...
Now, find 3/4 of 7.7...
She sold 5.775 kilograms of pears at the farmer's market.
Answer:
64 carnations and 16 roses.
Step-by-step explanation:
The events committee buys 80 flowers
The flowers are a combination of carnations and roses.
Each carnation costs $0.50 and each rose costs $2.50
The committee spends a total of $72
<u>Solution:</u>
<u />
Let there be (c) carnations and (r) roses.
So,
c + r = 80 flowers
and $0.50c + $2.50 = $72
This forms a simultaneous equation:
c + r = 80 ... (i)
0.5c + 2.5r = 72 ... (ii)
Multiplying equation (i) by 0.5 and equation (ii) by 1 gives;
0.5c + 0.5r = 40 ... (i)
0.5c + 2.5r = 72 ... (ii)
Subtracting (i) from (ii) gives;
0c + 2r = 32
2r = 32
r = 32 ÷ 2 = 16
Therefore, there are 16 roses
and 80 - 16 = 64 carnations
