the sum of the measures of two complementary angles is 90 degrees. find the measure of the angle labeled x

Please help ! I don’t understand :(

Elina [12.6K]

Answer:

A. The number quadrupled each week

Step-by-step explanation:

f(x)= 3(4)^x

As per the function, each week number increases 4 times

So the answer choice is A

7 0

2 years ago

How to differentiate ?

Bas_tet [7]

Use the power, product, and chain rules:

$y = x^2 (3x-1)^3$

• product rule

$\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}$

• power rule for the first term, and power/chain rules for the second term:

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}$

• power rule

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3$

Now simplify.

$\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}$

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

$\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) = \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)$

Differentiate both sides and you end up with the same derivative:

$\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2$

7 0

2 years ago

The product of a number and 12 is nomore than 15

allsm [11]

Answer:

As an equation, the product of a number and 12 is no more than 15 would be:

12n ≤ 15

N would represent the number.

≤ means less than or equal to, which is the same as "no more than".

5 0

3 years ago

In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard dev

Paha777 [63]

Answer:

0.3114

Option d is right

Step-by-step explanation:

Let X be the time spent on a treadmill in the health club

Given that research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 5.4 minutes

Also given that X is normal

the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

$= P(30$

round off to two decimals tog et

the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill is 0.31

Hence option d is right

3 0

3 years ago

An orange has 20 fewer calories

Andreyy89

Answer:

90 calories in a banana.

Step-by-step explanation:

O = B - 20 where O is the number calories in an orange and B is a that in banana.

Also 7B = 9O

From the above O = 7B / 9 so substituting in the first equation:

7B / 9 = B - 20

7B = 9B - 180

2B = 180

B = 90.

7 0

3 years ago