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2 years ago

Write the expression as a power and evaluate it. 8*2^7

Mathematics

2 answers:

stiv31 [10]2 years ago

6 0

Answer:

1024 fufufhdjdjyfdhfyehshyfydhsje

cluponka [151]2 years ago

4 0

Answer:

1024

Step-by-step explanation:

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A car purchased for $17,500. After each year the resale value decreases by 20%. What will the resale value be after 4 years? Rou

Tema [17]

The value at the end of the year is 100% - 20% = 0.80 of the value at the beginning of the year. After 4 years of multiplying by this factor, the value is
$17,500·0.80⁴ = $7,168

3 0

3 years ago

Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

3 years ago

Read 2 more answers

Suppose 100 people all toss a hat into a box and then proceed to randomly pick out a hat. what is the expected number of people

tatuchka [14]

1 person because there is 1 in 100 chance that you get your hat back

4 0

3 years ago

Find the distance between (2,7) and (-6,-2)

stepladder [879]

Answer: $\sqrt{145}$

Step-by-step explanation:

1. use the distance formula!

$distance = \sqrt{(x_{2} - x_{1})^{2} +{(y_{2} - y_{1})}^2$

2. then using the distance formula with (2, 7) and (-6, -2) you get...

$distance= \sqrt{2 -(-6)^2 +(7 - (-2)^2}$

$distance= \sqrt{8^2 +9^2}$

$distance= \sqrt{64 +81}$

$distance= \sqrt{145}$

$\sqrt{145}$ is the simplest radical form

6 0

3 years ago

Solve for x: 2x - 2 > 4x + 6

laiz [17]

Isolate the x. Subtract 4x from both sides, and add 2 to both sides

2x (-4x) - 2 (+2) > 4x (-4x) + 6 (+2)

2x - 4x > 6 + 2

Simplify. Combine like terms

-2x > 8

Isolate the x. Divide -2 from both sides. Note that you are <em>dividing a negative number</em>. When doing so, flip the sign.

-2x/-2 > 8/-2

x > 8/-2

x < -4

x < -4, or (1) is your answer

hope this helps

7 0

3 years ago