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irina1246 [14]
4 years ago
7

Hailey's family is driving to her aunt's house. The family travels 239.4 miles between the hours of 9:10 am and 1:40 pm. What eq

uation can Hailey use to determine their average rate of travle R, rounded to the nearest mile per hour? Use the given numbers and operations to create an equation that represents the problem. Then, solve the problem
Mathematics
1 answer:
lapo4ka [179]4 years ago
4 0

Answer:

53.2mph

Step-by-step explanation:

The average rate of travel is total distance traveled over total time.

Average\:Rate=\frac{Distance}{Time}

Total distance is 239.4 miles

Total time is 1:40pm-9:10am=13hrs:40mins-9hrs:10mins=4hrs:30mins or 4.5hrs

Average\:Rate=\frac{239.4}{4.5}mph=53.2mph

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3 years ago
Alistair has a rectangular picture measuring 8 inches by 7 inches. He makes a frame for the picture, shown by the shaded area in
andre [41]

Answer:

1) Equation to model the area of frame is 34= (8+2x)\times (7+2x)

2) The equation is quadratic.

3) The width of picture fame is \frac{-15\pm \sqrt{137}}{4}

Step-by-step explanation:

Given: Dimension of rectangular picture is 8 inches by 7 inches

           Area of picture frame is 34 inches²

Solving to find the dimension of picture frame.

Assuming that picture frame has uniform width of "x".

using the area of rectangle formula to solve.

Area of frame= length\times width

34= (8+2x)\times (7+2x)

Using distributive property of multiplication

⇒34= 56+16x+14x+4x^{2}

Subtracting both side by 34

⇒4x^{2} +30x+22=0  (quadratic equation)

Taking GCF as 2

⇒ 2(2x^{2} +15x+11)=0

dividing both side by 2

⇒ 2x^{2} +15x+11=0

Solving by using quadratic formula.

Formula: \frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}

∴ In the expression 2x^{2} +15x+11, we have a= 2, b= 15 and c= 11.

Now, subtituting the value in the formula.

= \frac{-15\pm \sqrt{15^{2}-4(2\times 11) } }{2\times 2}

= \frac{-15\pm \sqrt{15^{2}-4(22) } }{4}

Opening parenthesis.

= \frac{-15\pm \sqrt{225-88 } }{4}

= \frac{-15\pm \sqrt{137}}{4}

∴ x=  \frac{-15\pm \sqrt{137}}{4}

Hence; 1) Equation to model the area of frame is 34= (8+2x)\times (7+2x)

2) The equation is quadratic.

3) The width of picture fame is \frac{-15\pm \sqrt{137}}{4}

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=20%2B3x-15%2Bx%3D27" id="TexFormula1" title="20+3x-15+x=27" alt="20+3x-15+x=27" align="absmidd
lianna [129]

Answer:

x=11/2

Step-by-step explanation:

First we can combine similar terms on the left side. 3x + x is 4x and 20-15 is 5

Now that we have combined them, we are left with 4x+5=27

Subtract 5 on both sides to cancel out the 5.

4x=22

Divide both sides by 4

x=22/4

Simplify

x=11/2

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