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Leto [7]
3 years ago
15

Factor each expression 36abc +54ad

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
7 0

Answer:

18a(2bc + 3d)

Step-by-step explanation:

36abc + 54ad

Step 1: Find the Highest Common Factor of each

36abc = 2×2×3×3×a×b×c = 18a × 2bc

54ad = 2×3×3×3×a×d = 18a × 3d

HCF = 2×3×3×a = 18a

Step 2: Factor out with HCF

18a(2bc + 3d)

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What are the solutions of the quadratic equation (x + 3)(x +3) = 49? Ax = -2 and x = -16 Bx = 2 and x = -10 Cx = 4 and x = -10 D
Ivahew [28]

Answer:

4 and -10

Step-by-step explanation:

\displaystyle (x + 3)(x +3) = 49 \\ x^2+3x+3x+9=49 \\ x^2 +6x+9=49 \\ x^2 + 6x + 9 - 49 = 0 \\x^2+6x-40=0 \\\\ \Delta=b^2-4ac \\ \Delta=6^2-4 \cdot 1 \cdot (-40) \\ \Delta=36+160 \\ \Delta=196 \\ \\ X_{1,2}=\frac{-b \pm \sqrt{\Delta} }{2a}  \\ \\ X_1=\frac{-b+\sqrt{\Delta} }{2a} = \frac{-6+14}{2} = \frac{8}{2}=4 \\ \\ X_2=\frac{-b-\sqrt{\Delta} }{2a}  = \frac{-6-14}{2}=\frac{-20}{2} = -10

4 0
3 years ago
Anna is draining water out of a 50 gallon rain barrel. The graph shows the relationship between time in minutes and the gallons
tatiyna

Answer:

6 < x ≤ 20

Step-by-step explanation:

First, let's use the points (0, 50) and (20, 0) to find the equation of the line.

m = Δy / Δx

m = (0 − 50) / (20 − 0)

m = -2.5

y = -2.5x + 50

Now find the time when y = 35.

35 = -2.5x + 50

-15 = -2.5x

x = 6

So there is less than 35 gallons in the barrel when 6 < x ≤ 20.

7 0
3 years ago
Find the measure of c. A. 40 B. 70 C. 90 D. 50
Juliette [100K]

Answer:

D. 50

Step-by-step explanation:

a = 90° (angle subtended in semicircle)

a + c + 40° = 180° (by angle sum postulate of a triangle)

90° + c + 40° = 180°

c + 130° = 180°

c = 180° - 130°

c = 50°

4 0
3 years ago
If two-thirds of Sam's weekly income is $480, what is one-fourth of his weekly income?
telo118 [61]

Answer:

180

Step-by-step explanation:

If two-thirds of Sam's weekly income is $480

so total is $720

720$/4= 180$

8 0
3 years ago
Read 2 more answers
The graph shows the value of a certain model of car compared with its age. Which statement is false?
uranmaximum [27]
Answer: Choice B

===================================

A more in depth look

Choice A is true because the points are going downward as you read from left to right. The points aren't all on the same line but they are close to one. We can cross choice A off the list.

Choice B is false. So this is the answer. The fact that the points are close to the same line indicates that the r value is close to -1 rather than 0. If the points were randomly scattered about, or if they fell on a curve such as a parabola, then the linear correlation coefficient r would be (closer to) zero.

Choice C is true. The explanatory variable is the independent variable x. We can cross choice C off the list. 

Choice D is true. The points are fairly close to the same straight line. It's not perfect but it's good enough. We can cross choice D off the list.
4 0
3 years ago
Read 2 more answers
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