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navik [9.2K]
3 years ago
10

Sandra normally takes 2 hours to drive from her house to her grandparents' house driving her usual speed. However, on one partic

ular trip, after 40% of the drive, she had to reduce her speed by 30 miles per hour, driving at this slower speed for the rest of the trip. This particular trip took her 228 minutes. What is her usual driving speed, in miles per hour?
Mathematics
1 answer:
Rudiy273 years ago
3 0

Answer:

Her usual driving speed is 38 miles per hour.

Step-by-step explanation:

We know that:

s = \frac{d}{t}

In which s is the speed, in miles per hour, d is the distance, in miles, and t is the time, in hours.

We have that:

At speed s, she takes two hours to drive. So

s = \frac{d}{2}

d = 2s

However, on one particular trip, after 40% of the drive, she had to reduce her speed by 30 miles per hour, driving at this slower speed for the rest of the trip. This particular trip took her 228 minutes.

228 minutes is 3.8 hours. So

0.4s + 0.6(s - 30) = \frac{d}{3.8}

So

3.8(0.4s + 0.6s - 18) = d

3.8s - 68.4 = 2s

1.8s = 68.4

s = 38

Her usual driving speed is 38 miles per hour.

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Which expression gives the distance between the points (2,5) and (-4, 8)?
german

Answer:

A. (2+4)² +(5-8)²

Step-by-step explanation:

To find then distance between two points, we will follow the steps below;

write down the formula

D = √(x₂-x₁)²+(y₂-y₁)²

(-4, 8)

x₁=-4

y₁ = 8

(2,5)

x₂=2

y₂=5

we can now proceed to insert the values into the formula

D = √(x₂-x₁)²+(y₂-y₁)²

   

   = √(2+4)²+(5-8)²

    =√(6)² + (-3)²

   =√36+9

   =√45

Therefore the expression which gives the distance between two the two points is  (2+4)² +(5-8)²

7 0
3 years ago
Which graph represents the function f (x) = StartFraction 2 Over x minus 1 EndFraction + 4?
Pepsi [2]

Answer:

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4

Step-by-step explanation:

The given function is presented as follows;

f(x) = \dfrac{2}{x - 1} + 4

From the given function, we have;

When x = 1, the denominator of the fraction, \dfrac{2}{x - 1}, which is (x - 1) = 0, and the function becomes, \dfrac{2}{1 - 1} + 4 = \dfrac{2}{0} + 4 = \infty + 4 = \infty therefore, the function in undefined at x = 1, and the line x = 1 is a vertical asymptote

Also we have that in the given function, as <em>x</em> increases, the fraction \dfrac{2}{x - 1} tends to 0, therefore as x increases, we have;

\lim_  {x \to \infty}  \dfrac{2}{(x - 1)} \to 0, and \  \dfrac{2}{(x - 1)}  + 4 \to 4

Therefore, as x increases, f(x) → 4, and 4 is a horizontal asymptote of the function, forming a curve that opens up and to the right in quadrant 1

When -∞ < x < 1, we also have that as <em>x</em> becomes more negative, f(x) → 4. When x = 0, \dfrac{2}{0 - 1} + 4 = 2. When <em>x</em> approaches 1 from the left, f(x) tends to -∞, forming a curve that opens down and to the left

Therefore, the correct option is on a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.

5 0
2 years ago
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Answer:

Thank you have fun in quarantine

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Answer:

y=x+7

Step-by-step explanation:

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3 years ago
What is the area of the following trapezoid in square feet?
tangare [24]

Answer:

82.5 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = \frac{1}{2} h (b₁ + b₂)

where h is the perpendicular height and b₁, b₂ the parallel bases

Here h = 7.5, b₁ = 7 and b₂ = 15 , then

A = \frac{1}{2} × 7.5 × (7 + 15) = 0.5 × 7.5 × 22 = 82.5 ft²

4 0
3 years ago
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