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erastova [34]
4 years ago
15

Distance between (5, -3) and (9, 2).

Mathematics
1 answer:
Mashutka [201]4 years ago
6 0

Step-by-step explanation:

Using distance formula:

√(5 - 9)² + (-3 - 2)²

√(-4)² + (-5)²

√16+25

√41

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A 5–foot string of lights will be attached to the top of a 4–foot pole for a holiday display. How many feet from the base of the
wel

Answer:

3

Step-by-step explanation:

The lights and pole form a right triangle. The question gives the hypotenuse as 5 and one side length as 4.

Use the Pythagorean theorem: a^2+b^2=c^2.

Plug in what you are given: 4^2+b^2=5^2

16+b^2=25

b^2=9

b = 3

Or you could recognize that it was a pythagorean triple: 3, 4, 5

5 0
4 years ago
Which equation is related to this equation? m*8=24 A. m=25\8 B. m=24*8 C. m=24-8 D. m=8\24
lozanna [386]

<span>Looking at the choices closely, you can find one relation or sameness with the given situation m*8=24. Isolating “m” gives you a new equation m=24/8 which is related to equation  m=25/8. It has same m value on the left of the equation and it contains 2 whole numbers and arithmetic operation (/) on the right of the equation.</span>

7 0
4 years ago
Read 2 more answers
Find the 7th term of the expansion of (3c + 2d)^9.
defon

Answer:

c

Step-by-step explanation:

Using Pascal's triangle, the expansion, although EXTREMELY lengthy, will help you find the 7th term.  I am going to type out the expansion only up til the 7th term (although there are actually 10 terms because we are raised to the power of 9).  If you would like to learn how to use Pascal's Triangle for binomial expansion, you will need to visit a good website that explains it because it's just too difficult to do it via this website.

The expasion is as follows (up to the 7th term):

1(3c)^{9} +9(3c)^{8}(2d)^{1} +36(3c)^{7}(2d)^{2} +84(3c)^6(2d)^3+126(3c)^5(2d)^4+126(3c)^4(2d)^5+84(3c)^3(2d)^6

That last term is the 7th term.  You find out its value by multiplying all the numbers together and adding on the c^3d^6.  Again those come from Pascal's triangle, and it's one of the coolest math things ever.  I encourage you to take the time to explore how it works.

5 0
3 years ago
Find the interest earned and the future value of an annuity with weekly payments of $400 for three years into an account that pa
qaws [65]

Answer:

the interest earned= 93.401

and the future value of an annuity= 493.401

Step-by-step explanation:

Given Data:

Interest rate= 7%

time,t = 3 years

weekly payment, P= 400

At the end of 3 years, final investment A= ?

n= 52 as it is weekly

As per the interest formula

A= P(1+r/n)^nt

Putting value in above equation

= 400\left(1+\frac{0.07}{52}\right)^{156}

= 493.401

Interest earned = A-P

                           = 493.401-400

                          = 93.401 !

7 0
3 years ago
(1 point) Let f be a periodic function of period 10 such that f(x)=x2 for −5≤x&lt;5. Then the Fourier series of f is
ehidna [41]

Answer:

The answer is "\frac{25}{3}".

Step-by-step explanation:

please find the complete question in the attached file.

a_0=\frac{1}{10}\int^{5}_{x=-5} x^2 dx\\

   =\frac{1}{10} (\frac{x^3}{3})^{5}_{-5}\\\\=\frac{1}{30}[5^3+5^3]\\\\=\frac{2}{30}(125)\\\\=\frac{1}{15} \times 125\\\\=\frac{25}{3}

7 0
3 years ago
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