Answer:
Step-by-step explanation:
a. The vertex is (1, -9). False. The vertex is (-1, -9).
b. The graph opens upward. True. That coefficient '6' is positive.
c. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units. False. It's DOWN 9 units.
d. The graph is steeper than the graph of f(x) = x^2. True. The given function increases 6 times faster than does x^2.
e. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.
Let's put f(x) = 6(x + 1)^2 -9 into standard form. Expanding the first term, we get f(x) = 6(x^2 + 2x + 1) - 9, or f(x) = 6x^2 + 12x + 6 - 9. YES, TRUE
Answer:
As given, measure of angle 4 is 70°
Then what would be the measure of ∠8.
Following cases comes into consideration
1. If ∠4 and ∠8 are supplementary angles i.e lie on same side of Transversal, then
∠4 + ∠8=180°
⇒70°+∠8=180° [∠4=70°]
⇒∠8=180°-70°
⇒∠8=110°
<u>2nd possibility</u>
But if these two angles i.e ∠4 and ∠8 forms a linear pair.Then
⇒ ∠4 + ∠8=180°
⇒70°+∠8=180° [∠4=70°]
⇒∠8=180°-70°
⇒∠8=110°
<u>3rd possibility</u>
If ∠4 and ∠8 are alternate exterior angles.
then, ∠4 = ∠8=70°
<u>4th possibility</u>
If If ∠4 and ∠8 are corresponding angles.
then, ∠4 = ∠8=70°
Out of four options given Option A[ 110° because ∠4 and ∠8 are supplementary angles], Option B[70° because ∠4 and ∠8 are alternate exterior angles.] and Option D[70° because ∠4 and ∠8 are corresponding angles.] are Correct.
Answer:
See Explanation
Step-by-step explanation:
To write an equivalent expression, we can combine like terms. So m +7m is 8 and we get 6(8m+2).
Here are a few others:
48m+12
6(m+m+m+m+m+m+m+m+2)
3(16m+4)
6m+12+42m
6m+6m+6m+6m+6m+6m+6m+6m+2
and the list goes on...
Answer:
the height of the pyramid is 8 ft
Step-by-step explanation:
Considering the base of the pyramid to be square whose area is 144 sq ft
This means the side of the base would be √144 = 12 ft.
Now, if you will imagine a pyramid we can easily observe that
Height(H) , slant height( L=10 ft) and half of the side length( 6ft) make a right angle triangle. We can easily calculate height from Pythagoras theorem as
10^2 = H^2 +6^2
⇒ H^2 = 10^2-6^2 = 100-36 = 64
⇒ H = 8 ft
Therefore, the height of the pyramid is 8 ft
I'll start 18 and 22 for you, and you should then be able to do the rest on your own!
For 18, what we literally do is apply the distance formula for all the points and add them up. For B to C, we get the distance between them to be
sqrt((x1-x2)^2+(y1-y2)^2)=sqrt((0-4)^2+(3-(-1))^2)=sqrt((-4)^2+4^2)=sqrt(16+16)=sqrt(32). Repeat the process for C to E, E and F, and F to B then add the results up to get your answer!
For 22, since the area of a rectangle is length*width (we know given the right angles and that the opposite sides are equal in how long they are), we can multiply 2 perpendicular lines, for example, BC and CE to get sqrt(32)*sqrt(8)=16 as the area