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3 years ago

Select the correct answer.

Mathematics

1 answer:

schepotkina [342]3 years ago

3 0

Answer:

He drove the rest of the trip at 30 miles per hour

Step-by-step explanation:

The rule of the distance is D = v × t, where

v is the speed

t is the time

∵ It is 170 miles from Bruce's house to the city where his brother lives

∴ D = 170 miles

∵ He drove for 2 hours at 55 miles per hour

∴ t1 = 2 hours and v1 = 55 miles/hour

→ By using the rule above find the distance of this part of his trip

∴ D1 = 55 × 2 = 110 miles

∵ The rest of the trip took 2 hours

∴ t2 = 2 hours

∵ D = D1 + D2

→ Substitute the values of D and D1 to find D2

∴ 170 = 110 + D2

→ Subtract 110 from both sides to find D2

∴ 60 = D2

∴ D2 = 170 - 110 = 60 miles

∵ The rest of the trip is 60 miles

∵ It took 2 hours

∵ D2 = v2 × t2

∴ 60 = v2 × 2

→ Divide both sides by 2

∴ 30 = v2

∴ v2 = 30 miles/hour

∴ He drove the rest of the trip at 30 miles per hour

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Read the word problem below.

salantis [7]

Answer:

1 3/5 miles/hr

Step-by-step explanation:

Let C be the speed of the current

Let D be the distance between Chan's house and the park

We know that Distance, D, is = Speed x Time

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Chan's speed going upstream is (8 - C)mph.

That gives us:

D = (8-C)(3 hr)

Chan's speed going downstream is (8+C)mph

So we have:

D = (8+C)(2 hr)

We know that the d is the same for these two equations, so:

(8-C)(3 hr) = (8+C)(2 hr)

24 - 3C = 16 + 2C

5C = 8

C = (8/5) or 1 3/5 mph

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2 years ago

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This question is from the similarity chapter. It would be really kind of you if you would answer this question.

katen-ka-za [31]

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

1) Determine what is required for the answers

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

2) Prove similarity

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

Angles AYX and ACB are corresponding and they both measure 90 degrees
Both triangles share angle A

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

3) Solve for part A

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

$\frac{XY}{BC}=\frac{AY}{AC}$

Plug in known values

$\frac{2}{300}=\frac{11}{AC}$

Cross-multiply

$2AC=11*300\\2AC=3300\\AC=1650$

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

4) Solve for part B

To find the length of AB, we can use the Pythagorean theorem:

$a^2+b^2=c^2$ where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

$300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c$

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

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3 years ago

My Hero Acadmeia season 5 is out!!!!

wariber [46]

Step-by-step explanation:

In many parts of the world, the year is made up of four different seasons. These seasons are spring, summer, fall, and winter. Each has its own pattern of weather and varying hours of sunlight during the days. The northern and southern parts of Earth have different seasons at the same time.

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3 years ago

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Find an equation of the line passing through the given points (1,-3) and (3,3)

chubhunter [2.5K]

ANSWER: y= 3x - 6

STEP-BY-STEP EXPLANATION:

(1,-3) and (3,3)

X1=1 X2=3

Y1= - 3 Y2=3

1) Find the slope of the line.

To find the slope of the line passing through these two points we need to use the slope formula:

m = $\frac{Y2-Y1}{X2-X1}$

m= $\frac{3-(-3)}{3-1}$ m= $\frac{6}{2}$ = 3

2)Use the slope to find the y-intercept.

Now that we know the slope of the line is 3 we can plug the slope into the equation and we get:

y= 3x+b

Next choose one of the two point to plug in for the values of x and y. It does not matter which one of the two points you choose because you should get the same answer in either case. I generally just choose the first point listed so I don’t have to worry about which one I should choose.

y= 3x+b point (1,-3)

-3= 3(1) + b

-3-3=b

-6=b

3)Write the answer.

Using the slope of 3 and the y-intercept of -6 the answer is:

y = 3x - 6

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3 years ago

When a book of 100 pages is opened, the sum of the facing page numbers can be divided by 5, the quotient is a product of 3 and 7

statuscvo [17]

Sum means the result of addition.
Quotient means the result of division.
Product means the result of multiplication.

The product of 3 and 7 is 21, because:
3 × 7 = 21

Therefore, the quotient is 21.

Let the sum of the facing page numbers = x:
Therefore, x/5 = 21
Rearranging the equation to find x (the sum of the facing page numbers) gives us:
x = 21 × 5
= 105
So the sum of the facing page numbers is 105.

The only two adjacent numbers which add up to 105 are 52 and 53, so the facing page numbers must be 52 and 53.

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3 years ago