Answer:
<em>Part A </em>C = (10,5)<em> Part B </em>C. D'(0,10)
Step-by-step explanation:
<em>Part A</em>
Since c is at the point (2,1) in relation to the origin, we can multiply those distances by our scale factor of 5
(2,1) * 5 = (10,5)
The new point C is going to be (10,5)
<em>Part B</em>
If you dilate with a factor of 5 -- relative to the origin -- you have to multiply the distance from <em>the origin</em> by 5.
In this case, point D is already on the y axis, so it's x value wouldn't be affected. Point D is currently 2 units away from (0,0), so we can multiply 2*5 to get 10 -- our ending point is (0,10)
Answer: x=1.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
10
Answer:
∛27 = 3
Step-by-step explanation:
A radical is simply a fractional exponent: ![a^{(\frac{m}{n})} = \sqrt[n]{a^{m} }](https://tex.z-dn.net/?f=a%5E%7B%28%5Cfrac%7Bm%7D%7Bn%7D%29%7D%20%3D%20%5Csqrt%5Bn%5D%7Ba%5E%7Bm%7D%20%7D)
Hence, ∛27 = 
Since 27 = 3³, then:
You could rewrite ∛27 as ∛(3)³.
![\sqrt[3]{3^{(3)} } = 3^{[(3)*(\frac{1}{3})]}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3%5E%7B%283%29%7D%20%7D%20%3D%203%5E%7B%5B%283%29%2A%28%5Cfrac%7B1%7D%7B3%7D%29%5D%7D)
Multiplying the fractional exponents (3 × 1/3) will result in 1 (because 3 is the <u><em>multiplicative inverse</em></u> of 1/3). The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1.
Therefore, ∛27 = 3.
Answer:
Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.
Step-by-step explanation:
We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.
Triangle ABC:
Measure of angle A= 60°
Measure of angle C= 40°
Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°
Triangle DEF
Measure of angle E= 80°
Measure of angle F= 40°
Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°
The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.
The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.
Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.
