Answer:
a) 5units
b) (4.5, 4)
Step-by-step explanation:
Let the coordinate of P and Q be P(3, 2) and Q(6, 6)
PQ can be gotten using the distance formula;
PQ =√(6-2)²+(6-3)²
PQ = √4²+3²
PQ =√16+9
PQ =√25
PQ = 5units
Midpoint M is expressed as;
M(X, Y) = {(x1+x2)/2, y1+y2/2}
X = x1+x2/2
X = 3+6/2
X= 9/2
X = 4.5
Similarly;
Y = y1+y2/2
Y = 2+6/2
Y = 8/2
Y = 4
Hence the midpoint of PQ is (4.5, 4)
<span><span> y2(q-4)-c(q-4)</span> </span>Final result :<span> (q - 4) • (y2 - c)
</span>
Step by step solution :<span>Step 1 :</span><span>Equation at the end of step 1 :</span><span><span> ((y2) • (q - 4)) - c • (q - 4)
</span><span> Step 2 :</span></span><span>Equation at the end of step 2 :</span><span> y2 • (q - 4) - c • (q - 4)
</span><span>Step 3 :</span>Pulling out like terms :
<span> 3.1 </span> Pull out q-4
After pulling out, we are left with :
(q-4) • (<span> y2</span> * 1 +( c * (-1) ))
Trying to factor as a Difference of Squares :
<span> 3.2 </span> Factoring: <span> y2-c</span>
Theory : A difference of two perfect squares, <span> A2 - B2 </span>can be factored into <span> (A+B) • (A-B)
</span>Proof :<span> (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 <span>- AB + AB </span>- B2 =
<span> A2 - B2</span>
</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication.
Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.
Check : <span> y2 </span>is the square of <span> y1 </span>
Check :<span> <span> c1 </span> is not a square !!
</span>Ruling : Binomial can not be factored as the difference of two perfect squares
Final result :<span> (q - 4) • (y2 - c)
</span><span>
</span>
Answer:
the value of x=33
the measure of each base angle = 42 ,69,69
Step-by-step explanation:
Bases od isosceles triangles are congruent,so
2(2x+3)=4x+6 (This is the sum ob both anlgles base)
All angles in a triangle add to 180
4x+6 + 42 = 180
4x = 132
x=33
2(33)+3= 69
69+69+42 = 180
We need to expand the square binomial and then multiply:
<span>3x(x + 3)^2
= 3x(x + 3)</span>(x + 3<span>)
= 3x(x^2 + 6x + 9)
= 3x^3 + 18x^2 + 27x</span>
Hey!
Hope this helps...
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The first thing we know is that all the answers equal 99, so we cannot cross any answer off, however, what we want to know is what answer (after distribution) looks like 36 + 63...
A.) 11(3 + 6) > 33 + 66
Does 33+66 look like 36+63?
NO
B.) 9(4 + 7) > 36 + 63
Does 36+63 look like 36+63?
YES
C.) 11(4 + 5) > 44 + 55
Does 44+55 look like 36+63?
NO
D.) 3(15 + 18) > 45 + 54
Does 45+54 look like 36+63?
NO
So...
The answer is: B.) 9(4 + 7)
