Answer:
(D) -k2 + k - 13
Step-by-step explanation:
Pulling out like terms :
2.1 Pull out like factors :
-k2 + k - 13 = -1 • (k2 - k + 13)
Trying to factor by splitting the middle term
2.2 Factoring k2 - k + 13
The first term is, k2 its coefficient is 1 .
The middle term is, -k its coefficient is -1 .
The last term, "the constant", is +13
Step-1 : Multiply the coefficient of the first term by the constant 1 • 13 = 13
Step-2 : Find two factors of 13 whose sum equals the coefficient of the middle term, which is -1 .
-13 + -1 = -14
-1 + -13 = -14
1 + 13 = 14
13 + 1 = 14
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-k2 + k - 13
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Answer:
The answer is 1 13/24 hours or 1 hour, 32.5 minutes
Step-by-step explanation:
Find a common multiple of the denominators 3 and 8, which would be 24. Convert the fractions:
7/8 x 3/3 = 21/24.
2/3 x 8/8 = 16/24
Add the two numerators = 37/24 or 1 13/24.
1/24 of an hour is 2.5 minutes, so 13/24 is 32.5 minutes.
The answer is 1 13/24 hours or 1 hour, 32.5 minutes
Triangle ABC is an isosceles triangle.
Solution:
Given data:
∠ABC = 70° and ∠ACD = 55°
<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>
m∠BAC = m∠ACD
m∠BAC = 55°
<em>Sum of the angles in a straight line add up to 180°.</em>
m∠ACD + m∠ACB + m∠ABC = 180°
55° + m∠ACB + 70° = 180°
m∠ACB + 125° = 180°
Subtract 125° from both sides, we get
m∠ACB = 55°
In triangle ABC,
∠BAC = 55° and ∠ACB = 55°
∠BAC = ∠ACB
Two angles in the triangle are equal.
Therefor triangle ABC is an isosceles triangle.
In quadratic equations,
a + b = -B
ab = C
where a and b are the roots, B is the second term, and C is the constant.
Substituting,
a + b = -12
ab = 35
The values of a and b from the equation is -7 and -5. Thus, the lesser root is -7.
Answer is the picture below:
