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3 years ago

Which choice is the equation of a line that is parallel to the line 2x + 3y = 9?

Mathematics

1 answer:

lawyer [7]3 years ago

7 0

Hopefully this helps you !

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Which category do all of these shapes belong to

Nataly [62]

Answer:

squares

Step-by-step explanation:

4 0

3 years ago

Otieno is k years old.He is 5 years older than kidole what will be their age fours to come

EleoNora [17]

Answer:

Otieno's age in 4 years: $k+4$

Kidole's age in 4 years: $k-1$

Step-by-step explanation:

$k$ = Otieno's age

$k-5$ = Kidole's age

Their ages will increase by 4 years when 4 years pass.

$k+4$ = Otieno's age in 4 years

$k-5+4$ = Kidole's age in 4 years

$k-1$ = Kidole's age in 4 years (after simplifying the expression)

I hope this helps!

6 0

3 years ago

Angus has $3,000 he want to invest. What interest rate compounded continuously does an account need to offer so that Angus has $

kaheart [24]

Answer:

The interest rate is 7.58%

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

A = P $e^{rt}$ , where

A is the future value of the investment, including interest

P is the principal investment amount (the initial amount)

r is the interest rate in decimal

t is the time the money is invested for

∵ Angus has $3,000 he want to invest

∴ P = 3000

∵ The interest rate is compounded continuously

∵ Angus has $5,500 in 8 years

∴ A = 5500

∴ t = 8

→ Substitute them in the rule above to find r

∵ 5500 = 3000 $e^{8r}$

→ Divide both sides by 3000

∴ $\frac{11}{6}$ = $e^{8r}$

→ Insert ㏑ in both sides

∵ ㏑( $\frac{11}{6}$ ) = ㏑( $e^{8r}$ )

→ Remember ㏑( $e^{n}$ ) = n

∴ ㏑( $\frac{11}{6}$ ) = 8r

→ Divide both sides by 8

∴ 0.07576697545 = r

→ Multiply it by 100% to change it to a percentage

∴ r = 0.07576697545 × 100%

∴ r = 7.576697545 %

→ Round it to the nearest hundredth

∴ r ≅ 7.58

∴ The interest rate is 7.58%

3 0

3 years ago

What number must you add to complete the square?<br> x^2 + 2x = -1

Andru [333]

$\large\begin{array}{l} \textsf{You must add 1 to complete the square.}\\\\ \textsf{There is a very common special product: (square of a sum)}\\\\ \mathsf{(a+b)^2=a^2+2ab+b^2}\\\\\\ \textsf{Take the given equation:}\\\\ \mathsf{x^2+2x=-1\qquad(i)}\\\\\\ \textsf{The first term is a square (x squared)}\\\\ \textsf{The second term is a product of 2, x and 1.} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{We need to find a proper value for b, so that if we add it to}\\\textsf{the left side of the equation, we get a perfect square.}\\\\ \textsf{So,}\\\\ \begin{array}{cccccccccc} \mathsf{a^2}&\!\!\!+\!\!\!&\mathsf{2}&\!\!\!\cdot\!\!\!&\mathsf{a}&\!\!\!\cdot\!\!\!&\mathsf{b}&\!\!\!+\!\!\!&\mathsf{b^2}&=\mathsf{(a+b)^2}\\\\ \mathsf{\downarrow}&&&\!\!\!\!\!&\downarrow&\!\!\!\!\!&\downarrow&&\downarrow\\\\ \mathsf{x^2}&\!\!\!+\!\!\!&\mathsf{2}&\!\!\!\cdot\!\!\!&\mathsf{x}&\!\!\!\cdot\!\!\!&\mathsf{1}&\!\!\!+\!\!\!&\mathsf{1^2}&=\mathsf{(x+1)^2} \end{array}\\\\\\ \textsf{Just by comparing the expressions above, we can conclude that}\\\textsf{b must be equal to 1, so we get a perfect square:}\\\\ \mathsf{(x+1)^2=x^2+2x+1} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{Back to (i), adding 1 to both sides:}\\\\ \mathsf{x^2+2x+1=-1+1}\\\\ \boxed{\begin{array}{c} \mathsf{(x+1)^2=0} \end{array}} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{If you want to solve this equation for x, you will find}\\\\ \mathsf{x+1=0}\\\\ \mathsf{x=-1}\quad\longleftarrow\quad\textsf{(solution)} \end{array}$

If you're having problems understanding the answer, try seeing it through your browser: brainly.com/question/2112248

$\large\begin{array}{l} \textsf{Any doubt? Please, comment below.}\\\\\\ \textsf{Best regards! :-)} \end{array}$

6 0

3 years ago

Read 2 more answers

Jennifer invests $10,000 at 7% simple interest. How much is in her account after 2years ?

kakasveta [241]

Answer:

70,000 i think

Step-by-step explanation:

8 0

3 years ago