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Nuetrik [128]
3 years ago
14

5 1/6 + (7 1/3)l <60

Mathematics
1 answer:
agasfer [191]3 years ago
7 0

Answer:

l

Step-by-step explanation:

Given the inequality

5\dfrac{1}{6}+7\dfrac{1}{3}l

First, convert mixed numbers to improper fractions:

5\dfrac{1}{6}=\dfrac{5\cdot 6+1}{6}=\dfrac{31}{6}\\ \\7\dfrac{1}{3}=\dfrac{7\cdot 3+1}{3}=\dfrac{22}{3}

Now the inequality looks like

\dfrac{31}{6}+\dfrac{22}{3}l

Multiply it by 6:

\dfrac{31}{6}\cdot 6+\dfrac{22}{3}l\cdot 6

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Show work and Factor 4x^2+xy-18y^2
grigory [225]

Answer:

4x^2+xy-18y^2=(4x+9y)\,(x-2y)

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2

so we want the following to happen:

a\,c = 4\\ad+bc=1\\bd--18

Notice as well that ad+bc =1 means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product bd=-18, then we can consider the case in which one of this  (b or d) is the negative factor. So let's then assume that a\,\,and \,\,c are positive.

We can then try combinations for  a\,\,and \,\,c  such as:

a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4

Just by selecting the first one (a=4;\,\,c=1)

we get that 4d_b=1\\b=-4d-1

and since

bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

d=-18/(-2)\\d=9

Now we have a good combination of parameters to render the factoring form of the original trinomial:

a=4; \,\,b=9;\,\,c=1;\,\,d=-2

which makes our factorization:

(4x+9y)\,(x-2y)=4x^2+xy-18y^2

6 0
3 years ago
Determine whether AB ← → and CD ← → − are parallel, perpendicular, or neither. A(-6, 2), B(−3, -4), C(1, -3), D(3, 4)
guapka [62]
Neither they connect but don’t make a 90 degree angle

6 0
3 years ago
Jason and Martin want to share 3 cookies equally. How much cookie will Jason and Martin each receive? Write an equation and expr
Verdich [7]

Answer: each will get 3/2

Step-by-step explanation:

They will each get a whole cookie with one left over that they can break in half.

6 0
3 years ago
Solve<br> x+y= -1<br> x - y = -7<br> using elimination.
Andreas93 [3]

Answer:

(-4, 3)

x = -4, y = 3

6 0
3 years ago
A house is purchased for $375000 and has gained 12% for the last 5 years. What is it now ?
Ksenya-84 [330]

Answer:

  $420,000

Step-by-step explanation:

The added percentage can be turned into a multiplier to make the problem easier.

  value + 12%×value = value(1 +0.12) = 1.12×value

  1.12×$375,000 = $420,000

It is $420,000 now.

7 0
3 years ago
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