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3 years ago

Maggie's brother is three years younger than twice her age. The sum of their ages is 24 how old is maggie?

1 answer:

6 0

The variable for Maggie will be M and 2x-3 be her younger brothers age (Twice her age). We then would turn this into an algebraic problem. (m+2x -3=24).

3x-3=24, we would add 3 to both sides (-3 and 24). 24 + 3 equals 27, we now have to divide -3x and 27 on both sides, which equals 9. (x=9)

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Identify if the given equation represents exponential growth or decay.

charle [14.2K]

Answer:

The first is decay, seeing as it is in between 1 and 0

The second is growth, as it is greater than 1

Step-by-step explanation:

It's exponential growth when the base of our exponential is bigger than 1, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.

5 0

3 years ago

Drag the tiles to the boxes to form correct pairs. Match the pairs of equivalent expressions.

Rashid [163]

Answer:

The following pairs/results are matched:

$5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$
$3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Step-by-step explanation:

Lets solve all the expressions to match the results.

$5\left(2t+1\right)+\left(-7t+28\right)$

Solving the expression

$5\left(2t+1\right)+\left(-7t+28\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$5\left(2t+1\right)-7t+28$

$10t+5-7t+28$

$3t+33$

Therefore, $5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$

$3\left(3t-4\right)-\left(2t+10\right)$

Solving the expression

$3\left(3t-4\right)-\left(2t+10\right)$

$9t-12-\left(2t+10\right)$

$9t-12-2t-10$

$7t-22$

Therefore, $3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$

Solving the expression

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$4t-\frac{8}{5}-\left(3-\frac{4}{3}t\right)$

$4t-\frac{8}{5}-\left(-\frac{4t}{3}+3\right)$

$4t-\frac{8}{5}-3+\frac{4t}{3}$

$-3-\frac{8}{5}:\quad -\frac{23}{5}$ and $\frac{4t}{3}+4t:\quad \frac{16t}{3}$

So,

$4t-\frac{8}{5}-3+\frac{4t}{3}$ will become $\frac{16t}{3}-\frac{23}{5}$

Therefore, $\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$

Solving the expression

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$-\frac{9}{2}t+3+\frac{7}{4}t+33$

$\mathrm{Group\:like\:terms}$

$\frac{9}{2}t+\frac{7}{4}t+3+33$

$\mathrm{Add\:similar\:elements:}\:-\frac{9}{2}t+\frac{7}{4}t=-\frac{11}{4}t$

$-\frac{11}{4}t+3+33$

$-\frac{11}{4}t+36$

Therefore, $\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Thus, the following pairs/results are matched:

$5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$
$3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Keywords: algebraic expression

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5 0

3 years ago

Read 2 more answers

A country's population in 1995 was 164 million. in 2001 it was 169 million. estimate the population in 2015 using the exponentia

Vaselesa [24]

1995. 164 million
2001. 169 million
t = 2001 - 1995 = 6
169 = $164 * p^{6}$
$p^{6} = \frac{169}{164}= 1.0304878 \\ p = \sqrt[6]{1.0304878}$
p = 1.00502
t 1 = 2015 - 2001 = 14
f ( t1 ) = $169 * 1.00502^{14}$
f (t1) = 169 * 1.0762 = 181.27
Answer: a country´s population in 2015 will be 181 million.

4 0

3 years ago

Use the substitution method to solve the system of equations. Choose the correct ordered pair. x + y = 11 -x = -y - 9

suter [353]

$x+y=11 \\
-x=-y-9 \\ \\
\hbox{substitute the second equation by -1} \\ \\
x+y=11 \\
x=y+9 \\ \\
\hbox{substitute y+9 for x in the first equation} \\ \\
y+9+y=11 \\
2y=11-9 \\
2y=2 \\
y=\frac{2}{2} \\
y=1 \\ \\
x=y+9 \\
x=1+9 \\
x=10 \\ \\
(x,y)=(10,1)$

The answer is B.

5 0

3 years ago

Read 2 more answers

Question 1

Alexxx [7]

Answer:

Water needed for pool = 486 cubic feet

Plastic liner required for the pool = 298.3 feet

Step-by-step explanation:

Top view of the pool is a composite figure, having one rectangle and a trapezoid.

1). Water needed for the pool = volume of the pool

Volume of the pool = Area of the base × Depth

= (Area of the rectangle + Area of the trapezoid)× depth

Area of the trapezoid = $\frac{1}{2}(b_{1}+b_{2})\times h$

= $\frac{1}{2}(11+9)\times (12-1.5)$

= 105 ft²

Area of the rectangle = Length × width

= 11 × 1.5

= 16.5 ft²

Now, volume of the pool = (105 + 16.5) × 4

= 121.5 × 4

= 486 cubic feet

b). Liner required = surface area of the pool excluding top

= Surface area of the walls + Area of the pool base

= (Perimeter of the pool) × depth + area of the base

= (12 + 11 + 1.5 + 10.7 + 9)×4 + 121.5

= 176.8 + 121.5

= 298.3 square feet

Therefore, amount of water required = 486 cubic feet

liner needed = 298.3 square feet

8 0

3 years ago