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erastova [34]
3 years ago
5

It took an ice cream 28 minutes to drive through one neighborhood. The truck stopped driving through the neighborhood at 2:05 pm

When did the truck start driving through the neighborhood? Choose 1 answer:
Mathematics
1 answer:
VMariaS [17]3 years ago
6 0

Answer:

Starting time: 1:37

Step-by-step explanation:

Instead of proof to solve the problem, let us prove that the starting time above is correct;

1. There are 60 minutes in an hour, so 60 - 37 = the minutes 'till 2:00, or 23 minutes

2. Knowing that the time the truck stopped driving through the neighborhood was 5 minutes past 2:00, the minute difference being 23 + 5, or <em>28 minutes</em>

<em>Proved: 28 minutes</em>

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The average cost represents the slope of the line of the graph.
Increasing the slope of the graph increases the steepness of the line.
Therefore, increasing the average cost of gas from $1.50 to $2.20 will increases the steepness of the line. (i.e. the line becomes closer to the vertical line).
8 0
3 years ago
A factory needs to produce 1,800 jars of peanut butter on a certain day.
finlep [7]

Answer:

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Step-by-step explanation:

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7 0
2 years ago
Which equation has a solution of x = -5?
lyudmila [28]
The first equation has a solution of X=-5
3 0
3 years ago
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Ms. Nina has 10 lbs of 25% sugar syrup. How much water does she need to add to make 10% sugar syrup?
ryzh [129]
She has 10lbs of 25% syrup... so, in the 10lbs, 25% of that is syrup, the rest, namely the 75% remaining is water or other substances.

let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.

how much is 25% of 10lbs?  well, (25/100) * 10, or 2.5.

the water has no sugar syrup in it, so is just pure water, so the amoun of syrup in it is 0%, how much is 0% of "x" lbs?  well, (0/100) * x, or 0.00x, which is just 0.

how much is 10% of "y" lbs?  well (10/100) * y, or 0.10y.

whatever "x" and "y" are, we know that 10 + x = y.

we also know that the syrup amount in that is also 2.5 + 0.00x = 0.10y, thus


\bf \begin{array}{lccclll}&#10;&\stackrel{lbs}{syrup}&\stackrel{concentration~\%}{syrup}&\stackrel{concentration}{amount}\\&#10;&------&------&------\\&#10;\textit{25\% syrup}&10&0.25&2.5\\&#10;\textit{pur water}&x&0.00&0.00x\\&#10;------&------&------&------\\&#10;\textit{10\% mixture}&y&0.10&0.10y&#10;\end{array}&#10;\\\\\\&#10;\begin{cases}&#10;10+x=\boxed{y}\\&#10;2.5+0.00x=0.10y\\&#10;----------\\&#10;2.5 = 0.10\left( \boxed{10+x} \right)&#10;\end{cases}&#10;\\\\\\&#10;2.5=1 + 0.10x\implies 1.5=0.10x&#10;\\\\\\&#10;\cfrac{1.5}{0.10}=x\implies 15=x
8 0
2 years ago
Read 2 more answers
A wire b units long is cut into two pieces. One piece is bent into an equilateral triangle and the other is bent into a circle.
mezya [45]
1. Divide wire b in parts x and b-x. 

2. Bend the b-x piece to form a triangle with side (b-x)/3

There are many ways to find the area of the equilateral triangle. One is by the formula A= \frac{1}{2}sin60^{o}side*side=   \frac{1}{2} \frac{ \sqrt{3} }{2}  (\frac{b-x}{3}) ^{2}= \frac{ \sqrt{3} }{36}(b-x)^{2}
A=\frac{ \sqrt{3} }{36}(b-x)^{2}=\frac{ \sqrt{3} }{36}( b^{2}-2bx+ x^{2}  )=\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}

Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6

3. Let x be the circumference of the circle.

 2 \pi r=x

so r= \frac{x}{2 \pi }

Area of circle = \pi  r^{2}= \pi  ( \frac{x}{2 \pi } )^{2} = \frac{ \pi }{ 4 \pi ^{2}  }* x^{2} = \frac{1}{4 \pi } x^{2}

4. Let f(x)=\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}+\frac{1}{4 \pi } x^{2}

be the function of the sum of the areas of the triangle and circle.

5. f(x) is a minimum means f'(x)=0

f'(x)=\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x=0

\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x=0

(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) x=\frac{ \sqrt{3} }{18}b

x= \frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }

6. So one part is \frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) } and the other part is b-\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }

4 0
3 years ago
Read 2 more answers
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