For 11, we can subtract x from both sides for the first equation to get y=8-x, making the slope -1 for both equations and therefore making it parallel.

For 13, we can solve for y in the first equation by subtracting 14 from both sides and therefore getting 2x-14=y. For the next one, we can subtract 4x from both sides to get 10-4x=2y. Dividing both sides by 2, we get 10-2x=y. Since for the equations to be parallel they must be the same and for perpendicular they must be -1/(slope), this fits neither.

Using those two explanations, I implore you to solve the other two on your own!

3 0

3 years ago

A population of insects grows exponentially, as shown in the table. Suppose the increase in population continues at the same rat

oksano4ka [1.4K]

Answer-

The insect population at the end of week 11 is 1730.

Solution-

A population of insects grows exponentially.

The general form of exponential function is,

$y=ab^x$

Where,

a, b are constants.

Putting the data given in the table, in the the equation in order to get the values of a, b

At (0, 20)

$\Rightarrow 20=ab^0$

$\Rightarrow a\cdot (1)=20$

$\Rightarrow a=20$

Now the exponential function becomes,

$y=20b^x$

At (1, 30)

$\Rightarrow 30=20b^1$

$\Rightarrow 20b=30$

$\Rightarrow b=\dfrac{30}{20}$

$\Rightarrow b=\dfrac{3}{2}$

Now the equation becomes,

$y=20(\frac{3}{2})^x$

For calculating the number of insects at the end of the 11th week, putting x=11, so

$y=20(\frac{3}{2})^{11}$

$=1729.95 \approx 1730$

8 0

4 years ago

Read 2 more answers

Cassie has test grades of 71, 78 and 83 on the first three tests in her

Neporo4naja [7]

Answer:

x ≥ 88

Step-by-step explanation:

In order to have at least an average of 80 after 4 tests, the sum of her scores must be at least 80 * 4 = 320 so we can write the following inequality:

71 + 78 + 83 + x ≥ 320

232 + x ≥ 320

x ≥ 88

3 0

3 years ago

Read 2 more answers

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