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3 years ago

Ax + By = -C solve for x

Mathematics

2 answers:

Elanso [62]3 years ago

6 0

Isolate the variable x
[Subtract both sides by -By]
Ax = -By - C
[Then Divide both sides by A to isolate x]
x= (By-C)/A

RoseWind [281]3 years ago

3 0

Answer:

C=−Ax−By

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

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Use binomial expansion to solve each exercise. (a) Find the coefficient of xy19 in (3x − 2y) 20.(b) Give a formula for the coeff

pishuonlain [190]

9514 1404 393

Answer:

(a) -29,884,416

(b) C(n,(n -k)/2) . . . where C(n,k) = n!/(k!(n-k)!) and k ∈ ℕ

Step-by-step explanation:

(a) The coefficient of the k-th term of the expansion is ...

C(20,k)(3x)^(20-k)(-2y)^k

For k=19, this is ...

19(3x)(-2y)^19 = -29,884,416xy^19

The coefficient of the term is -29,884,416.

(b) The p-th term of the expansion of (x +1/x)^n is ...

C(n,p)(x^(n-p)(1/x)^p = C(n,p)(x^(n-2p))

For some exponent k of x, the value of p will be ...

k = n -2p

p = (n -k)/2

Then the coefficient of x^k will be C(n, (n-k)/2), where C(n, x) = n!/(x!(n-x)!).

You will notice that there will only be a term x^k for k having the same parity as n.

5 0

3 years ago

1) In Math class Mike and Karen are looking at two numbers: 152 and 33 +. 53.

vladimir2022 [97]

Answer:

Mike is right. 152 is larger than 33 + 53/

Step-by-step explanation:

First we need to add 53 + 33 to see if it will equal up ro 152. So 53 + 33 = 86.

86 is less than 152, so Mike is correct and Karen is wrong, as usual.

7 0

3 years ago

What is the domain for the function ?

Fynjy0 [20]

( - ∞, ∞ )

f(x) is defined for all real values of x

8 0

3 years ago

A recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, w

charle [14.2K]

Answer:

90% confidence interval for the mean time per week spent listening to the radio is $11.5 \pm 1.676 \times \frac{9.2}{\sqrt{51} }$ .

Step-by-step explanation:

We are given that a recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours.

Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average amount of time spent listening to music = 11.5

s = sample standard deviation = 9.2 hours

n = sample of students = 51

$\mu$ = population mean per week spent listening to the radio

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.676 < $t_5_0$ < 1.676) = 0.90 {As the critical value of t at 50 degree of

freedom are -1.676 & 1.676 with P = 5%}

P(-1.676 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.676) = 0.90

P( $-1.676 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.676 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.676 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.676 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.676 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.676 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $11.5-1.676 \times {\frac{9.2}{\sqrt{51} } }$ , $11.5+1.676 \times {\frac{9.2}{\sqrt{51} } }$ ]

= [9.34 hours , 13.66 hours]

Therefore, 90% confidence interval for the mean time per week spent listening to the radio is [9.34 hours , 13.66 hours].

4 0

3 years ago

What is the perimeter of the isosceles triangle shown below?

melisa1 [442]

Answer:

Step-by-step explanation:

The horizontal side is 8 units long. By Pythagorean, the equal side lengths are 5, so 5 + 5 + 8 = 18.

3 0

3 years ago