Simplify. Remove all perfect squares from inside the square root.

1 ) During his morning commute to work in rush hour traffic, Justin's average speed was 30 mi/h. During his afternoon commute ba

Hitman42 [59]

Answer:45 mi/h

Step-by-step explanation:

Recall: Speed = distance / time

Let the time taken for the morning journey be $t_{1}$ and the time taken for the afternoon journey be $t_{1}$ ,and the distance covered be d

that means for the first journey,

30 = $\frac{d}{t_{1}}$

d = 30 $t_{1}$

Also for the afternoon journey,

d = 60 $t_{2}$

Equating the two , since the same distance is being covered , we have

30 $t_{1}$ = 60 $t_{2}$

that is

$t_{1}$ = $\frac{60t_{2}}{30}$

$t_{1}$ = 2 $t_{2}$

Also ,

total distance covered = 30 $t_{1}$ + 60 $t_{2}$

Average speed = total distance / total time

= 30 $t_{1}$ + 60 $t_{2}$ / $t_{1}$ + $t_{2}$

Recall that $t_{1}$ = 2 $t_{2}$ , substitute this into the formula for average speed , then we have

Average speed = 30(2 $t_{2}$ ) +60 $t_{2}$ / 3 $t_{2}$

Average speed = 120 $t_{2}$ / 3 $t_{2}$

Therefore :

Average speed = 40 mi/hr

4 0

3 years ago

A store is having a sale on walnuts and chocolate chips. For 8 pounds of walnuts and 4 pounds of chocolate chips, the total cost

astra-53 [7]

Answer:

x = $3.50; y = $2.25

Step-by-step explanation:

First, come up with your two equations where x= price of walnuts and y= price of chocolate chips: 8x + 4y = 37 and 3x + 2y = 15. Solve the first equation.

3x + 2y = 15

3x = 15 - 2y

x = (15 - 2y)/3

Plug in the answer to your second equation.

8(15 - 2y)/3 + 4y = 37

(120 - 16y)/3 + 4y = 37

120 - 16y + 12y = 111

120 - 4y = 111

-4y = -9

y = 2.25

Plug in your answer to find <em>x.</em>

3x + 2(2.25) = 15

3x + 4.5 = 15

3x = 10.5

x = 3.5

Check your equation.

1) 3(3.5) + 2(2.25) = 15

10.5 + 4.5 = 15

15 = 15

2) 8(3.5) + 4(2.25) = 37

28 + 9 = 37

37 = 37

4 0

3 years ago

A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 38 miles north of the t

andreyandreev [35.5K]

9514 1404 393

Answer:

63.7% or 33.35 miles

Step-by-step explanation:

The hint suggests that we find the points where the drive begins and ends picking up the transmitter. We suspect both of those points will have irrational coordinates, so finding the distance between them will involve dealing with squares and roots of irrational numbers. We want to see if there's an easier way.

The distance from the transmitter to the path being driven can be found using the "distance to a line" formula. First, we need the equation of the line in general form. In intercept form, it is ...

y/38 +x/36 = 1

19x +18y -684 = 0 . . . . . . multiply by LCM(36, 38) and subtract that amount

Then the distance from the origin to the line is ...

d = |19·0 +18·0 -684|/√(19² +18²) = 685/√685 ≈ 26.1243

The distance (x) along the line from the point where the transmitter is first picked up until the point of closest approach can be found from the Pythagorean theorem:

x² + (26.1243)² = 31²

x² = 31² -(684/√685)² = 190429/685

x ≈ 16.6733

The driving distance for which the transmitter is picked up is twice this, so is ...

2x = 2(16.6733) ≈ 33.3466 . . . miles

The total drive length is also given by the Pythagorean theorem:

drive length = √(36² +38²) = √2740 ≈ 52.3450 . . . miles

Then the fraction of the drive during which the signal is picked up is ...

fraction = (33.3466 mi)/(52.3450 mi) ≈ 0.6371 ≈ 63.7%

__

The signal is picked up for 33.35 miles, about 63.7% of the drive.

______

The intercept-form equation for a line is ...

x/(x-intercept) +y/(y-intercept) = 1

The distance from (x, y) to line ax+by+c=0 is given by ...

d = |ax+by+c|/√(a²+b²)

The Pythagorean theorem relates legs a, b and hypotenuse c of a right triangle this way:

c² = a² +b²

4 0

3 years ago

Find the equation of a line, in slope intercept form of a line that passes through the point (-5,-1) and is parallel to the line

Ludmilka [50]

Answer:

y = 1/2x + 3/2

Step-by-step explanation:

Using the equation of the line

y - y_1 = m ( x - x_1)

First find the slope of the line

-2x + 4y = 8

It must be in this form

y = mx + C

4y = 8 + 2x

divide through by 4

4y/4 = 8 + 2x / 4

y = 8 + 2x/4

Let's separate

y = 8/4 + 2x/4

y = 2 + 1/2x

y = 1/2x + 2

Therefore, our slope or m is 1/2

Using the equation of the line

y - y_1 = m ( x - x_1)

With point (-5, -1)

x_1 = -5

y_1 = -1

y - (-1) = 1/2(x - (-5)

y + 1 = 1/2( x + 5)

Opening the brackets

y + 1 = x + 5 / 2

y = x + 5/2 - 1

Lcm is 2

y = x + 5 / 2 - 1/1

y = x + 5 -2/2

y = x +3/2

We can still separate it

y = x /2 + 3/2

y = 1/2x + 3/2

The equation of the line is

y = 1/2x + 3/2

The correct answer is A

3 0

3 years ago

Show all work. Write the equation in point slope form (5, -9); m = 6

eduard

Point slope form:
y+9=6(x-5)

7 0

3 years ago

Simplify. Remove all perfect squares from inside the square root. ​

Simplify. Remove all perfect squares from inside the square root.