Given:
The equation is:
The graph of the 
and 
are given on a coordinate plane.
To find:
The solution of the given equation from the given graph.
Solution:
From the given graph it is clear that the graphs of and intersect each other at points (1.24,5.24) and (16,20).
It means the values of both functions and are equal at 
and 
.
So, the solutions of given equation are and .
Therefore, the correct option is only F.
<span> a • (6ab2 + 2ab - 2a - 3b2 + 4b)
</span>
Step by step solution :<span>Step 1 :
</span><span>Equation at the end of step 1 :</span> (3ab • (2ab + 2a - b)) - 2a • (2ab + a - 2b)
<span>Step 2 :</span><span>Equation at the end of step 2 :</span> 3ab • (2ab + 2a - b) - 2a • (2ab + a - 2b)
<span>Step 3 :</span><span>Step 4 :</span>Pulling out like terms :
<span> 4.1 </span> Pull out like factors :
<span> 6a2b2 + 2a2b - 2a2 - 3ab2 + 4ab</span> =
<span> a • (6ab2 + 2ab - 2a - 3b2 + 4b)</span>
Final result :<span> a • (6ab2 + 2ab - 2a - 3b2 + 4b)</span>
Answer:
<em>The third choice gives the correct sequence.</em>
Step-by-step explanation:
<u>The Number Line</u>
To represent numbers in the line, we use arrows starting from the mark for zero up to the given number. If the number is positive, the arrow points to the right and if the number is negative, the arrow points to the left.
The number -3 must be represented as an arrow to the left side of length 3. Subtracting something from the number should also point to the left side, but if the number is negative, then the new arrow points to the right side.
To subtract -1, the arrow should point to the right starting from -3
The third choice gives the correct sequence.
Answers:
- Part A) There is one pair of parallel sides
- Part B) (-3, -5/2) and (-1/2, 5/2)
====================================================
Explanation:
Part A
By definition, a trapezoid has exactly one pair of parallel sides. The other opposite sides aren't parallel. In this case, we'd need to prove that PQ is parallel to RS by seeing if the slopes are the same or not. Parallel lines have equal slopes.
------------------------
Part B
The midsegment has both endpoints as the midpoints of the non-parallel sides.
The midpoint of segment PS is found by adding the corresponding coordinates and dividing by 2.
x coord = (x1+x2)/2 = (-4+(-2))/2 = -6/2 = -3
y coord = (y1+y2)/2 = (-1+(-4))/2 = -5/2
The midpoint of segment PS is (-3, -5/2)
Repeat those steps to find the midpoint of QR
x coord = (x1+x2)/2 = (-2+1)/2 = -1/2
y coord = (x1+x2)/2 = (3+2)/2 = 5/2
The midpoint of QR is (-1/2, 5/2)
Join these midpoints up to form the midsegment. The midsegment is parallel to PQ and RS.
Answer:
y = - 3x² - 24x - 60
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 4, - 12 ), thus
y = a(x + 4)² - 12
To calculate a substitute (- 7, - 39) into the equation
- 39 = a(- 7 + 4)² - 12 ( add 12 to both sides )
- 27 = 9a ( divide both sides by 9 )
- 3 = a
y = - 3(x + 4)² - 12 ← in vertex form
Expand (x + 4)²
y = - 3(x² + 8x + 16) - 12
= - 3x² - 24x - 48 - 12
y = - 3x² - 24x - 60 ← in standard form
= - 3(x²
