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3 years ago

5. BOATING Boat rentals are $50 plus $4 per hour. Write an

Mathematics

1 answer:

KonstantinChe [14]3 years ago

8 0

Answer:

c = 50 + 4h

Step-by-step explanation:

The cost for the boat is 50, and the additional cost for an hour is 4. Then the sdditional cost for h hours is 4h.

So the total cost is 50 + 4h

∴ c = 50 + 4h

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An elevator travels 342 feet as it goes from the lobby of a building to the top floor. It takes 7 seconds to travel the first 13

Mandarinka [93]

Answer:

I THINK 1

Step-by-step explanation:

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3 years ago

-2x/3 + 11 = 14 please help me its not letting me put stuff I want

Bess [88]

Answer:

x = -4 1/2

Step-by-step explanation:

-2x/3 + 11 = 14

subtract 11 from each side of the equation:

-2x/3 = 3

multiply both sides by 3:

-2x = 9

divide both sides by -2:

x = -4 1/2

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3 years ago

A rectangular field has dimension of 91 feet by 60 and 1/3 feet what is the area of the field

Oliga [24]

Answer:

Area = $91*\frac{181}{3}=5490\frac{1}{3}$ square feet

Step-by-step explanation:

The area of a rectangle is given by the formula:

A = length * width

Where length is 91 feet and width is $60\frac{1}{3}$ feet

Before we do the multiplication, we have to change the mixed number [width] into an improper fraction by using the rule shown below:

$a\frac{b}{c}=\frac{(a*c)+b}{c}$

Hence,

$60\frac{1}{3}=\frac{181}{3}$

So, the area is:

Area = $91*\frac{181}{3}=5490\frac{1}{3}$ square feet

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4 years ago

Describe the steps required to determine the equation of a quadratic function given its zeros and a point.

faltersainse [42]

Answer:

Procedure:

1) Form a system of 3 linear equations based on the two zeroes and a point.

2) Solve the resulting system by analytical methods.

3) Substitute all coefficients.

Step-by-step explanation:

A quadratic function is a polynomial of the form:

$y = a\cdot x^{2}+b\cdot x + c$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$a$ , $b$ , $c$ - Coefficients.

A value of $x$ is a zero of the quadratic function if and only if $y = 0$ . By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: $A(x,y) = (r_{1}, 0)$ , $B(x,y) = (r_{2},0)$ and $C(x,y) = (x,y)$

Based on such information, we form the following system of linear equations:

$a\cdot r_{1}^{2}+b\cdot r_{1} + c = 0$ (2)

$a\cdot r_{2}^{2}+b\cdot r_{2} + c = 0$ (3)

$a\cdot x^{2} + b\cdot x + c = y$ (4)

There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:

$a = \frac{\left|\begin{array}{ccc}0&r_{1}&1\\0&r_{2}&1\\y&x&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }$

$a = \frac{y\cdot r_{1}-y\cdot r_{2}}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x+x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}$

$a = \frac{y\cdot (r_{1}-r_{2})}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}$

$b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }$

$b = \frac{(r_{2}^{2}-r_{1}^{2})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}$

$c = \frac{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&0\\r_{2}^{2}&r_{2}&0\\x^{2}&x&y\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }$

$c = \frac{(r_{1}^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x + x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}$

And finally we obtain the equation of the quadratic function given two zeroes and a point.

6 0

3 years ago

Sebastian purchased 1.4 pounds of coffee for $7.65 per pound.

Blizzard [7]

Answer:

$10.71

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers