A) (x,y)->(4x,4y) because the x and y values are multiplied by 4 when dilated. Ex. U(-1,1) was dilated to U’(-4,4). -1 was multiplied by 4 to get -4 for the x value and 1 was multiplied by 4 to get 4 for the y value.
Answer:
b = 18 m
c = 19.5 m
h = 9 m
Step-by-step explanation:
Call the smaller solid the original one, and call the larger solid the scaled one.
1. Find the scale factor
scale factor = length in scaled one / corresponding length in original one
scale factor = 7.5/5 = 1.5
The scale factor is 1.5
That means if you multiply any linear dimension of the original one by 1.5, you get the corresponding dimension of the scaled one.
Let's check our scale factor to make sure it's correct.
We see that the 5 m side corresponds to the 7.5 m side.
5 m * 1.5 = 7.5 m
Multiplying an original length by the scale factor of 1.5 gives us the scaled up length, so our scale factor of 1.5 is correct. Now we apply the scale factor of 1.5 to find b, c, and h.
b corresponds to 12 m
b = 12 m * 1.5 = 18 m
c corresponds to 13 m
c = 13 m * 1.5 = 19.5 m
h corresponds to 6 m
h = 6 m * 1.5 = 9 m
Answer:
b = 18 m
c = 19.5 m
h = 9 m
1. If y<span>ou have jogged 5 miles from the park at a rate of r miles per hour, then the time you need to do this is
hours (
, where S is distance, v-speed and t-time).
</span>
2. W<span>hen you run back to the park, your average speed increases by 1 mph and become r+1 mph.
</span>
3. I<span>t takes
hours to jog 5 miles back to the park</span>
4. T<span>he total jogging time T is
hours.</span>
<span />
5. If you jogged away from the park at an average speed of 4 miles per hour, then r+1=4 and r=3. The expression
will take look
<span>
hours.</span>
Answer:
$56
Step-by-step explanation:
12% of 50 is 6.
50+6=56
$56
Hope this helped! :)
As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.
The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the
trusty calculator:
B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !
