All categories

3 years ago

In the following system of equations, determine whether the system has a unique

Mathematics

1 answer:

Rina8888 [55]3 years ago

5 0

Answer:

the system has a unique solution

Step-by-step explanation:

Start with an equation of a line in standard form,

$ax + by = c$

Solve it for y to put it into the slope-intercept form:

$by = -ax + c$

$y = -\dfrac{a}{b}x + \dfrac{c}{b}$

The slope is -a/b.

Now look at your system of equations. The slope of the first equation is -a/b = -2/3. The slope of the second equation is -a/b = -6/5.

You have a system of two linear equations with two lines with different slopes, so the lines must intersect at a single point.

Answer: the system has a unique solution

You might be interested in

The initial population of a town is 2600, and it grows with a doubling time of 10 years. Determine how long it will take for the

choli [55]

Answer:

It will take the 20 years for the population to quadruple.

Step-by-step explanation:

Exponential population growth:

An exponential model for population growth has the following model:

$P(t) = P(0)(1+r)^t$

In which P(0) is the initial population and r is the growth rate, as a decimal.

It grows with a doubling time of 10 years.

This means that $P(10) = 2P(0)$ . We use this to find r. So

$P(t) = P(0)(1+r)^t$

$2P(0) = P(0)(1+r)^10$

$(1+r)^10 = 2$

$\sqrt[10]{(1+r)^10} = \sqrt[10]{2}$

$1+r = 2^{\frac{1}{10}}$

$1 + r = 1.0718$

$P(t) = P(0)(1+r)^t$

$P(t) = P(0)(1.0718)^t$

Determine how long it will take for the population to quadruple.

This is t for which P(t) = 4P(0). So

$P(t) = P(0)(1.0718)^t$

$4P(0) = P(0)(1.0718)^t$

$(1.0718)^t = 4$

$\log{(1.0718)^t} = \log{4}$

$t\log{1.0718} = \log{4}$

$t = \frac{\log{4}}{\log{1.0718}}$

$t = 20$

It will take the 20 years for the population to quadruple.

5 0

3 years ago

Help ! Will mark brainliest

Burka [1]

The answer would be that she now has $530.40 in her account. The table has nothing to do with the question

8 0

3 years ago

Read 2 more answers

Sarah took out a $30,000 loan for 11 years at a 4.7% interest rate to put a new pool in her backyard. If

MissTica

The amount of the loan after 11 years is $34,113.53 and the intereest earned is $4,113.53

<h3>How to calculate the compound interest</h3>

The formula for calculating the exponential function is expressed as:

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

Given the following

P = 30,000
r = 0.047
t = 11 years
n = 4

Substitute into the formula to have:

$A=30000(1+\frac{0.047}{4} )^{11}\\A =30000(1.13711)\\A =\$34,113.53$

Hence the amount of the loan after 11 years is $34,113.53

<h3>Find the interest earned</h3>

Interest = A - P

Interest = 34,113.53 - 30000

Interest = 4,113.53

Hence the intereest earned is $4,113.53

Learn more on compound interest here: brainly.com/question/24924853

7 0

2 years ago

Solve for b -2b + 11 - 5b = 5 - 6b

Colt1911 [192]

Answer:

B = 6

Step-by-step explanation:

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

4 0

3 years ago

Read 2 more answers

Show your work on how you got the answer<br><br> please helppp

skelet666 [1.2K]

Answer:

250

Step-by-step explanation:

4/16 = 1/4 = .25

When dividing exponents, subtract the bottom from the top, so $10^{5}$ ÷ $10^{2}$ = $10^{3}$

So, .25 * $10^{3}$ = 250

5 0

2 years ago