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3 years ago

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Mathematics

1 answer:

wlad13 [49]3 years ago

5 0

Answer:

y DOES NOT vary directly with x

Step-by-step explanation:

If variation is direct, the ratio of y to x is a constant. Here, we have ...

11/7 ≠ 13/8

so variation is not direct.

___

It appears that y = 2x-3, rather than y = kx for some k. The added constant (-3) means variation is not direct.

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Austin purchase 2/3 of a pound of yum yum treats. If yum yum treats are $6.00 per pound how much does Austin pay

Oksi-84 [34.3K]

1. The information given in the problem above, is:

- Austin purchases 2/3 of a pound of yum yum treats.
- Yum yum treats are $6.00 per pound (1 pound=$6.00).

2. Keeping this on mind you have: If 1 pound of yum yum treats is $6.00, how much is 2/3 of a pound?

1 pound------------$6.00
2/3 of a pound----x

x=(2/3)(6.00)/1
x=(2/3)(6.00)
x=12/3
x=$4.00

Therefore: How much does Austin pay?

The answer is: Austin pays $4.00.

5 0

3 years ago

A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the

serious [3.7K]

Answer:

The equation is $A=6000e^{-0.23t}$ at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it decays by using t=3 hours and A=3000. This means $A_0=6000$ in this context.

$A=A_0e^{rt}\\3000=6000e^{r(3)}$

$0.5=e^{(24.5)r}$

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 3.

We solve with a calculator $\frac{ln0.5}{3} =r\\-0.23=r$

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is $A=6000e^{-0.23t}$

5 0

3 years ago

Two young sumo wrestlers decided to go on a special diet to gain weight rapidly. They each gained weight at a constant rate. The

Radda [10]

Answer: the first wrestler gains more at the beginning, the second wrestler gains more faster

Step-by-step explanation:

5 0

3 years ago

Solve the simultaneous equation y-2x+1=0 and 4x^2+3y^2-2xy=7

Lapatulllka [165]

The first equation is $y-2x+1=0$

$y=2x-1$ (Equation 1)

The second equation is $4x^{2}+3y^{2}-2xy=7$ (Equation 2)

Putting the value of x from equation 1 in equation 2.

we get,

$4x^{2}+3(2x-1)^{2}-2x(2x-1)=7$

$4x^{2}+3(4x^{2}+1-4x)-4x^{2}+2x=7$

by simplifying the given equation,

$12x^{2}-10x-4=0$

$6x^{2}-5x-2=0$

Using discriminant formula,

$D=b^{2}-4ac$

$D=25-4 \times 6 \times -2 = 73$

Now the formula for solution 'x' of quadratic equation is given by:

$x=\frac{-b+\sqrt{D}}{2a} and x=\frac{-b-\sqrt{D}}{2a}$

$x=\frac{5+\sqrt{73}}{12} and x=\frac{5-\sqrt{73}}{12}$

Hence, these are the required solutions.

8 0

3 years ago

Compare 2x+8>18 and 2x+8 greaterthan or equal to 18

Sergio039 [100]

2x + 8 > 18 2x+ 8 ≥ 18
2x > 18 -8     2x ≥ 18 - 8
2x > 10    2x ≥ 10
x > 10/2 x ≥ 10/2
x>5 x ≥ 5

   The answer that combines both inequality is x ≥ 5

6 0

3 years ago