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3 years ago

Please help me! For which I do not understand how to do this..

Mathematics

2 answers:

katovenus [111]3 years ago

6 0

What is the main question asking you about the number line?

SVEN [57.7K]3 years ago

6 0

Mark it between -1.5 and -1 & between 1 and 1.5

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If 4f(x)+f(5-x)=x2<br><br> What is f(x)?

aksik [14]

We are given that $4f(x)+f(5-x)=x^2$ .

Substitute x with 5-x, then the above equation becomes:

$4f(5-x)+f(5-(5-x))=(5-x)^2$ , that is

$4f(5-x)+f(x)=(5-x)^2$

So, we have the following system of equations:

i) $4f(x)+f(5-x)=x^2$
ii) $4f(5-x)+f(x)=(5-x)^2$

multiply the first equation by -4, so that we eliminate f(5-x)'s

i) $-16f(x)-4f(5-x)=-4x^2$
ii) $4f(5-x)+f(x)=(5-x)^2$

adding the 2 equations side by side we have:

$-15f(x)=-4x^2+(5-x)^2$

expanding the binomial, and collecting same terms we have:

$-15f(x)=-4x^2+(25-10x+x^2)$

$-15f(x)=-3x^2-10x+25$

dividing by -5:

$3f(x)=\frac{3}{5}x^2+2x-5$

dividing by 3:

$\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3}$

Answer: $\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3}$

6 0

3 years ago

The diameter of a circle is 5 inches. What is its circumference?

Natali5045456 [20]

Answer:

C≈15.71in

Step-by-step explanation:

Solve the equation for the diameter of the circle, d= C/π. In this example, "d = 12 / 3.14." or "The diameter is equal to twelve divided by 3.14." Divide the circumference by pi to get the answer. In this case, the diameter would be 3.82 inches.

Hope this helps!

5 0

3 years ago

Does the table represent a proportional or a nonproportional linear relationship?

fredd [130]

Answer:

nonproportional

Step-by-step explanation:

proportional would mean that the y intercept is 0 but it's 3

3 0

3 years ago

Element X is a radioactive isotope such that its mass decreases by 59% every day. If an experiment starts out with 390 grams of

miss Akunina [59]

Answer:

The function that represents the mass of the sample after t days is $A(t) = 390(0.41)^t$ .

The percentage rate of change per hour is of -2.46%.

Step-by-step explanation:

Exponential amount of decay:

The exponential amount of decay for an amount of a substance after t days is given by:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount, and r is the decay rate, as a decimal.

Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.

This means, respectively, that $r = 0.59, A(0) = 390$

$A(t) = A(0)(1-r)^t$

$A(t) = 390(1-0.59)^t$

$A(t) = 390(0.41)^t$

The function that represents the mass of the sample after t days is $A(t) = 390(0.41)^t$ .

Hourly rate of change:

Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So

-59%/24 = -2.46%

The percentage rate of change per hour is of -2.46%.

5 0

3 years ago

A sign company charges $28 per yard for each custom made banner. Ms. Gill orders two banners that are each 1 7/8 yards yards lon

Svetlanka [38]

Answer:

$896

Step-by-step explanation:

We are given that

Charge of 1 yard for each custom-made banner=$28

Length of 1 piece=15 yards

Length of another piece=2 yards

We have to find that how much money payed by Ms.Gill for all three banners.

According to question

Cost of 15 yards long banner=$420

Cost of 2 piece of 15 yards long banner==$840

Cost of 2 yards long banner==$56

Total cost of 3 piece of banners=840+56=$896

Hence, Ms gill pay for all three banners=$896

Your Welcome;)

8 0

3 years ago