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3 years ago

Please give an explanation on why the answer is the answer

Mathematics

1 answer:

NISA [10]3 years ago

4 0

Answer: A

Step-by-step explanation: Because 4 quarts equal a gallon and 4+4 equals 8

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Lin runs 5 laps around a track in 6 minutes. How many minutes per lap is that? ___minutes How many laps per minute is that? ___

snow_lady [41]

Answer:

a. 1.2 minutes

b. 0.83 laps

c. 25.2 minutes

Step-by-step explanation:

Lin runs 5 laps around a track in 6 minutes.

a. How many minutes per lap is that?

5 laps = 6 minutes

1 laps = x minutes

Cross Multiply

x minute × 5 laps = 6 minutes × 1 laps

x minute = 6 minutes × 1 laps/5 laps

x laps = 1.2 minutes

Hence, it is 1.2 minutes per lap

b. How many laps per minute is that?

6 minutes = 5 laps

1 minute = x laps

Cross Multiply

6 minutes × x laps = 1 minute × 5 laps

x laps = 1 minute × 5 laps/6 minutes

x laps = 0.8333333333 laps

Hence, it is 0.83 laps per minute.

c. If Lin runs 21 laps at the same rate,

5 laps = 6 minutes

21 laps = x minutes

Cross Multiply

x minute × 5 laps = 6 minutes × 21 laps

x minute = 6 minutes × 21 laps/5 laps

x laps = 25.2 minutes

Hence, it takes her 25.2 minutes

3 0

3 years ago

Write the equation of the circle below to complete the square. Also determine the area of the circle.

diamong [38]

Answer: $(x-7)^2+(y+2)^2=11^2$ ; $A=121\pi$

Step-by-step explanation:

I have never done a problem like this, so this is my first time attempting it.

The standard form for the equation of a circle is:

$(x-a)^2+(y-b)^2=r^2$

Begin by grouping the 'x' terms and 'y' terms:

$(x^2-14x)+(y^2+4y-68)=0$

Complete the square for the second polynomial:

$(\frac{b}{2} )^2=(\frac{4}{2} )^2=4$

$(x^2-14x)+(y^2+4y+4-4-68)=0$

$(x^2-14x)+(y^2+4y+4)-4-68=0$

$(x^2-14x)+(y^2+4y+4)-72=0$

$(x^2-14x)+(y+2)^2-72=0$

Do the exact same process with the other polynomial:

$(x^2-14x-72)+(y+2)^2=0$

Complete the square:

$(\frac{14}{2} )^2=49$

$(x^2-14x+49-49-72)+(y+2)^2=0$

$(x^2-14x+49)-49-72+(y+2)^2=0$

$(x^2-14x+49)-121+(y+2)^2=0$

$(x-7)^2-121+(y+2)^2=0$

Bring the 121 to the other side to get:

$(x-7)^2+(y+2)^2=121$

$(x-7)^2+(y+2)^2=11^2$

The above expression is the equation of our circle in standard form. It is centered at the coordinates (7, -2) and has a radius of 11 units. The area of a circle if given by:

$A=\pi r^2=121\pi$

8 0

2 years ago

Please help w my geometry! I need to show my work too. 10 points

salantis [7]

Because AB is a midsegment, the length of AB is half he length of XZ so basically you do
2(3x-1)=34.
Divide 2 by both sides to get 3X-1=17
Add 1 to boh sides to get 3X=18
Divide 3 from boh sides to get X=6
Hope this helps :)

3 0

4 years ago

A bowling ball is pushed with a force of 22.0 N and accelerates at 5.5 m/s2. What is the mass of the bowling ball? Ik the answer

KiRa [710]

Step-by-step explanation:

You should always use the least number of significant figures. The exception is exact numbers or constants.

For example, there are 60 minutes in an hour. Even though this number has one significant figure, it is an exact number. So 15 minutes converted to hours would be 0.25 hr.

5 0

3 years ago

Find the Area of the Shaded Region.

Mrac [35]

9514 1404 393

Answer:

610 m²

Step-by-step explanation:

If we extend the horizontal line across the right-hand portion of the figure, then the figure is divided into two rectangles:

bottom: 5 m × 50 m = 250 m²

top: 18 m × 20 m = 360 m²

The sum of these areas is the shaded area:

shaded area = 250 m² +360 m² = 610 m²

4 0

3 years ago