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IRINA_888 [86]
2 years ago
7

Is (3,-2) a solution to the system below? How do you know?

Mathematics
1 answer:
cricket20 [7]2 years ago
3 0

Step-by-step explanation:

you know by using the x and y coordinates of the point in the equations and see, if both equations are still true.

if yes, it was a solution, and if just only one is false, then it was not a solution.

(3, -2) in

y + 4x = 10

5x - y = 13

so,

-2 + 4×3 = 10

-2 + 12 = 10

10 = 10 true

5×3 - (-2) = 13

15 + 2 = 13

17 = 13 false

so, it was NOT a solution.

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Through how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m. (on the same day)? ​
timofeeve [1]

Answer:

π/8 radians

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION

In 1 h the minute hand on a clock moves through a complete circle, and the hour hand moves through 1 12 of a circle. Through how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m. (on the same day)?

SOLUTION

✓If the minute hand on a clock moves through complete circle in 1 hour, then it means that it goes through a circle and angle of circle in radians is 2π.

Between 1:00 p.m. and 1:45pm in the same day we have 45 minutes i.e (1.45 pm -1pm)

Within the 1hour minutes, the hand can move with complete cycle of 2π radians

Then At time t= 45minutes

Angle through the circle at 45 minutes= 45/60 ×2π radians

= 3π/2 radians

And if the hour hand goes through a complete cycle 1/12 as told in the question we have 1/2 × 2π radians

For t=45 minutes

Then 1/12 × 2π ×45/60

= π/8 radians

Hence, the minute hand and the hour hand move π/8 radians between 1:00 p.m. and 1:45 p.m.

5 0
2 years ago
Which are the center and radius of the circle with equation (x + 5)2 + (y - 4)2 = 9?
alina1380 [7]

Answer:

Center (-5,4) radius 3

Step-by-step explanation:

The standard equation of a circle is

(x-h)^2+(y-k)^2=r^2

where the center is (h,k) and r is the radius

so h=-5 in this case and k is 4

r^2=9 so r=3

4 0
3 years ago
A LARGE RECTANGULAR POSTER IS 3 TIMES AS LONG AND 3 TIMES AS WIDE AS A SMALL RECTANGULA POSTER. THE SMALL POSTER IS 3 FEET LONG
umka2103 [35]

Answer:

the Larger poster is 9ft long by 6ft wide

Step-by-step explanation:

In order to find the length and width values of the large poster we first need to find the width of the smaller poster since we are already given the length. Since we are also provided with the perimeter we can add the length twice and subtract it from the perimeter which would give us the value of both width sides of the rectangle, then we simply divide by 2 to get the value of the individual width.

10ft = 3ft + 3ft + w + w

10ft = 6ft + 2w

4ft = 2w

2ft = w

Since the larger poster is 3 times as big for the length and the width we simply multiply the smaller poster's length and width by 3...

L = 3 * 3 = 9ft

W = 2 * 3 = 6ft

Finally, we can see that the Larger poster is 9ft long by 6ft wide

8 0
3 years ago
In the right triangle the measure of C is 90
liq [111]
The measure of a right angle is 90 degrees
6 0
3 years ago
The line plot shows the results of a survey of 10 boys and 10 girls about how many hours they spent reading for pleasure the pre
elena-14-01-66 [18.8K]
10 students per gender:

Boys:  <span>four Xs over five and one X over zero, two, three, four, ten, and twelve. 
5, 5, 5, 5, 0, 2, 3, 4, 10, 12 </span>→ 0, 2, 3, 4, 5, 5, 5, 5, 10, 12<span>
mean: 5.1
range: 12

</span><span>Girls: three Xs above eight, two Xs above three and four, and one X above two, six and seven.
8, 8, 8, 3, 3, 4, 4, 2, 6, 7 </span>→ 2, 3, 3, 4, 4, 6, 7, 8, 8, 8 
<span>mean: 5.3
range: 6

The boys have the higher range while the girls have the higher mean value.


</span><span>
</span>
8 0
2 years ago
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