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2 years ago

It took Shane 2 hours to drive 120 miles. If she continues at this rate, how far will she travel in 4 hours and 30 minutes?

Mathematics

1 answer:

vodomira [7]2 years ago

6 0

Answer:

270 miles

Step-by-step explanation:

If she drove 120 miles in 2 hours, that means she drives at 60 miles per hour. 4 hours and 30 minutes can be seen as 4.5, since 30 minutes is half an hour. So then you multiply 60 by 4.5 and get 270.

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A deposit of 4,000 at 6.5% for 270 days

atroni [7]

Some institutions use 360 days a year (because then they charge more interest than 365 days).

Assuming the 360 days a year rule, the the daily rate is
6.5% for a year, or 270/360*6.5% for 270 days.
The future amount is then
4000*(1+0.065*270/360)
=$4195 (simple interest).

5 0

4 years ago

Three of these expressions are equal to the volume of the barn shown. Which expression is not?

timurjin [86]

The statement that does not match the others is the one at lower right.

_____

The barn's volume can be decomposed into a rectangular prism and a triangular one. Thus the upper right expression is a true represenation of the barn's volume:

... Volume of triangular prism + Volume of rectangular prism

The volume of a rectangular prism is the product of its dimensions. The dimensions of the rectangular prism portion of the barn's volume are a, b, c, so the volume of that portion is ...

... Volume of rectangular prism = a·b·c

The volume of a triangular prism is the area of the triangular base multiplied by the length of the prism. Here, the triangular base has base dimension b and height (d-c), so its area is ...

... Area of triangular barn end = (1/2)b(d-c)

Since the length of the barn is "a", the volume of the triangular prism is ...

... Volume of triangular prism = (1/2)b(d-c)a = (1/2)·a·b·(d-c)

The total volume is the sum of the volumes of the parts ...

... a·b·c + (1/2)·a·b·(d-c) . . . . . . matches the upper right selection

This can be factored by removing a·b to outside parentheses:

... a·b·((1/2)·(d-c) + c) . . . . . . . . . matches the lower left selection

___

Since the two left selections match the one at upper right, the odd one is the one at lower left.

7 0

3 years ago

Read 2 more answers

The standard form of a quadratic equation is given as y=ax^2+bx+c and vertex form is given as y=a(x−h)^2+k. Write a formula that

Tju [1.3M]

Answers:

$h = -\frac{b}{2a}\\\\k = \frac{-b^2+4ac}{4a}\\\\$

where 'a' cannot be zero.

=========================================================

Explanation:

The vertex is (h,k)

The x coordinate of the vertex is h which is found through this formula

$x = -\frac{b}{2a}$

For example, if we had the quadratic $y = 3x^2-6x+5$ , then we'll plug in a = 3 and b = -6 to get: $h = -\frac{b}{2a} = -\frac{-6}{2*3} = 1$

------------

To find the value of k, we plug that h value into the original standard form of the quadratic and simplify.

$y = ax^2+bx+c\\\\k = ah^2+bh+c\\\\k = a\left(\frac{-b}{2a}\right)^2+b\left(\frac{-b}{2a}\right)+c\\\\k = a*\frac{b^2}{4a^2}+\frac{-b^2}{2a}+c\\\\k = \frac{b^2}{4a}+\frac{-b^2}{2a}+c\\\\$

$k = \frac{b^2}{4a}+\frac{-b^2}{2a}*\frac{2}{2}+c*\frac{4a}{4a}\\\\k = \frac{b^2}{4a}+\frac{-2b^2}{4a}+\frac{4ac}{4a}\\\\k = \frac{b^2-2b^2+4ac}{4a}\\\\k = \frac{-b^2+4ac}{4a}\\\\$

It's interesting how we end up with the numerator of $-b^2+4ac$ which is similar to $b^2-4ac$ found under the square root in the quadratic formula. There are other ways to express that formula above. We need $a \ne 0$ to avoid dividing by zero. The values of b and c are allowed to be zero.