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3 years ago

Write the equation: Amy made $75 for 5 hours. At the same rate, how much would she make for 7 hours of work?

Mathematics

2 answers:

stich3 [128]3 years ago

7 0

Answer:

y =75x

Step-by-step explanation:

Lets say we are trying to figure out what she made in 5 hours we would multiply like this : 75(5) =375. So we know that 75 stays the same no matter what and the only thing that changes are her hours. so our equation will be 75x = y

x being hours worked

y being how much she made

jeyben [28]3 years ago

6 0

Answer:

She would make $105 for 7 hours of work.

Step-by-step explanation:

5 hours __ $75

7 hours ___ x = $105

(7 hours * $75) / 5 hours = $105

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Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

KonstantinChe [14]

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

$2x^2-3x-6=0$

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

$2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}$

We have to find the value of (a+2)(b+2).

Putting the values:

$(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4$

3 0

3 years ago

B. Suppose Q is the midpoint of PR. What is the<br> justification for the statement that PQ = QR?

Natasha2012 [34]

The midpoint bisects PR, making it 2 equal halves.

5 0

3 years ago

If c is the curve given by \mathbf{r} \left( t \right = \left( 1 5 \sin t \right \mathbf{i} \left( 1 3 \sin^{2} t \right \mathbf

jonny [76]

With the curve $C$ parameterized by

$C:\mathbf r(t)=\underbrace{15\sin t}_{x(t)}\,\mathbf i+\underbrace{13\sin^2t}_{y(t)}\,\mathbf j+\underbrace{12\sin^3t}_{z(t)}\,\mathbf k$

with $0\le t\le\dfrac\pi2$ , and given the vector field

$\mathbf f(x,y,z)=x\,\mathbf i+y\,\mathbf j+z\,\mathbf k$

the work done by $\mathbf f$ on a particle moving on along $C$ is given by the line integral

$\displaystyle\int_C\mathbf f\cdot\mathrm d\mathbf r=\int\limits_{t=0}^{t=\pi/2}\mathbf f(x(t),y(t),z(t))\cdot\frac{\mathrm d\mathbf r(t)}{\mathrm dt}\,\mathrm dt$

where

$\mathrm d\mathbf r=(15\cos t\,\mathbf i+26\sin t\cos t\,\mathbf j+36\sin^2t\cos t\,\mathbf k)\,\mathrm dt$

The integral is then

$\displaystyle\int_0^{\pi/2}(15\sin t\,\mathbf i+13\sin^2t\,\mathbf j+12\sin^3t\,\mathbf k)\cdot(15\cos t\,\mathbf i+13\sin2t\,\mathbf j+18\sin t\sin2t\,\mathbf k)\,\mathrm dt$
$=\displaystyle\int_0^{\pi/2}(432\sin^5t\cos t+338\sin^3t\cos t+225\sin t\cos t$
$=269$

6 0

3 years ago

Please answer this correctly

Lynna [10]

Answer:

557

Step-by-step explanation:

l x w

13x24

13x7

22x7

557

4 0

3 years ago

68. If Fran can only pay $250 per month, what is the most expensive boat she can buy without a down payment?

damaskus [11]

Answer:

If she buys a boat without a down payment, then the affordable price is 5,700.

Step-by-step explanation:

Her bank charges 5% interest per year.

Let, payment = p,

p = 250(\frac{1-(1+\frac{0.05}{12})^-24}{\frac{0.05}{12}})

p = 5698.47

After round off p = 5700

3 0

3 years ago