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zavuch27 [327]
3 years ago
15

If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?

Mathematics
1 answer:
Dmitrij [34]3 years ago
8 0
A is the point (-4, 1)

i) reflection over the y-axis projects a point (a, b) to (-a, b):

(-4, 1) is projected to (4, 1), 

ii) reflection over the x axis projects a point (a, b) to (a, -b):

(4, 1) is projected to (4, -1),

iii) rotation 180 degrees: projects (a, b) to (-a, -b):

so (4, -1) is projected to (-4, 1)


Answer: A'(-4, 1)
 
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Drew needs to air up his teams 8 soccer balls. Each ball has a diameter of 70cm. In terms of pi, what is the total volume of air
Liula [17]

Answer:

1.44m^3

Step-by-step explanation:

Given data

Number of balls= 8

Diameter of ball = 70cm = 0.7m

Radius= 35cm= 0.35m

We know that a ball has a spherical shape

The volume of a sphere is

V= 4/3πr^3

substitute

V= 4/3*3.142*0.35^3

V= 0.18m^3

Hence if 1 ball has a volume of 0.18m^3

Then 8 balls will have a volume of

=0.18*8

=1.44m^3

7 0
3 years ago
Find the x- and y- intercepts of the graph of each equation. 2x+3y=6
Eva8 [605]
X = 3 that is you x intercept 
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8 0
3 years ago
Explain​ how, in​ general, riemann sum approximations to the area of a region under a curve change as the number of subintervals
Lyrx [107]

As you increase the subintervals the area will be closer and closer to the real value. In other words your approximation gets better.

As you increase the intervals, there will be more rectanagles and the added area of these rectangles are converging towards the actual area under the curve.

5 0
3 years ago
The approximate height, h, in meters, traveled by golf balls hit with two different clubs over a horizontal distance of d meters
inna [77]

Answer:

a) 100 metres

b) 10 metres

Step-by-step explanation:

Given: the approximate height, h, in meters, travelled by golf balls hit with two different clubs over a horizontal distance of d meters is given by the functions: h=-0.002d^2+0.3d\,,\,h=-0.004d^2+0.5d

To find: distances when the ball is at the same height when either of the clubs  are used. Also, to find this height

Solution:

(a)

-0.002d^2+0.3d=-0.004d^2+0.5d\\d(-0.002d+0.3)=d(-0.004d+0.5)\\-0.002d+0.004d=0.5-0.3\\0.002d=0.2\\d=\frac{0.2}{0.002}=100\,\,metres

(b)

Put d = 100 in h=-0.002d^2+0.3d

h=-0.002(100)^2+0.3(100)\\=-20+30\\=10\,\,metres

4 0
3 years ago
What if the value of x? show all work
alina1380 [7]
For this case we can make use of the Pythagorean theorem.
 We have then:
 (root (117)) ^ 2 = x ^ 2 + 6 ^ 2
 Clearing x we have:
 x ^ 2 = (root (117)) ^ 2 - 6 ^ 2
 Rewriting:
 x = root (117-36)
 x = root (81)
 x = 9
 Answer:
 
The value of x is given by:
 
x = 9 cm
4 0
3 years ago
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