All categories

3 years ago

Which equation could represent a linear combination of the systems?

Mathematics

1 answer:

n200080 [17]3 years ago

4 0

9514 1404 393

Answer:

(b) 0 = -78

Step-by-step explanation:

Subtracting 6 times the first equation from the second will give ...

(4x +15y) -6(2/3x +5/2y) = (12) -6(15)

0 = -78

You might be interested in

Which of the following does not represent a function?

gregori [183]

I think the answer is C :)

7 0

4 years ago

How do you work out the rate, time and principal from the compound interest formula?

wlad13 [49]

Answer:

Part 1) $P=A/(1+\frac{r}{n})^{nt}$ (see the explanation)

Part 2) $r=n[\frac{A}{P}^{1/(nt)}-1]$ (see the explanation)

Part 3) $t=log(\frac{A}{P})/[(n)log(1+\frac{r}{n})]$ (see the explanation)

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

Part 1) Find the Principal P

The values of A,r,n and t are given

Isolate the variable P

$A=P(1+\frac{r}{n})^{nt}$

Divide both side by $(1+\frac{r}{n})^{nt}$

$P=A/(1+\frac{r}{n})^{nt}$

Part 2) Find the rate r

The values of A,P,n and t are given

Isolate the variable r

$A=P(1+\frac{r}{n})^{nt}$

Divide both sides by P

$\frac{A}{P} =(1+\frac{r}{n})^{nt}$

Elevated both sides to 1/(nt)

$\frac{A}{P}^{1/(nt)} =(1+\frac{r}{n})$

subtract 1 both sides

$\frac{A}{P}^{1/(nt)}-1 =\frac{r}{n}$

Multiply by n both sides

$r=n[\frac{A}{P}^{1/(nt)}-1]$

Part 3) Find the time t

The values of A,P,r and n are given

Isolate the variable t

$A=P(1+\frac{r}{n})^{nt}$

Divide both sides by P

$\frac{A}{P} =(1+\frac{r}{n})^{nt}$

Apply log both sides

$log(\frac{A}{P})=log(1+\frac{r}{n})^{nt}$

Apply property of exponents

$log(\frac{A}{P})=(nt)log(1+\frac{r}{n})$

Divide both side by $(n)log(1+\frac{r}{n})$

$t=log(\frac{A}{P})/[(n)log(1+\frac{r}{n})]$

3 0

3 years ago

I need help me need to match i am getting confuse.

gregori [183]

Answer:

1 A= pi 21^2

2 C=pi 21

3 A= pi 10.5^2

4 C= 2pi 10.5

Step-by-step explanation:

7 0

3 years ago

Simplify the expression (4-5i)(2+6i)-(3-2i) show your work.

Anastaziya [24]

The simplification of the given expression $(4-5i)(2+6i)-(3-2i)$ , we get $-30i^2+16i+5$ .

Given expression is:

$(4-5i)(2+6i)-(3-2i)$

By applying the multiplication, we get

→ $(8-10i+24i-30i^2)-(3-2i)$

By multiplying the (-) sign into the bracket, we get

→ $8-10i+24i-30i^2-3+2i$

→ $5+16i-30i^2$

By arranging the terms, we get

→ $-30i^2+16i+5$

Thus the answer above is right.

Learn more:

brainly.com/question/19593573

4 0

3 years ago

Read 2 more answers

Find the critical value needed to construct a 95% CI of a population mean with an unknown standard deviation and a sample size o

kaheart [24]

Answer:

$t_{\alpha/2}=-2.02, t_{1-\alpha/2}=2.02$

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

In order to find the critical value we need to take in count that we are finding the critical value for the population mean and without the standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . We need to calculate the degrees of freedom are given by:

$df=n-1=39-1=38$

We can find the critical value using the following excel codes:

"=T.INV(0.025;38)" or "T.INV(1-0.025;38)"

And the critical values would be given by:

$t_{\alpha/2}=-2.02, t_{1-\alpha/2}=2.02$

7 0

3 years ago