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andrew-mc [135]
4 years ago
8

(Score for Question 4 of 6 points)

Mathematics
1 answer:
LuckyWell [14K]4 years ago
3 0

Answer:

a) On Desmos.

b)The solution set {-2,-2}

Step-by-step explanation:

For drawing a line on graph we require minimum two points.

we have,

y=2x+2

Put x = 0,we get

y = 2

∴ Let A (0,2)

Similarly

Put y = 0 we get

x = -1

∴ Let B (-1,0)

Now Draw  line AB

For y = -2

It is the line parallel to X axis where Y value is always -2

Now , by drawing these two lines we will get the intersecting point, and this intersecting point is the solution to the system. Let the point be C (-2,-2)

Here we substitute y= -2 in y = 2x + 2 we get

-2 = 2x +2\\2x=-4\\x=-2\\\therefore (-2,-2)

The solution is {-2,-2}

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Determine all real numbers a$ such that the inequality $ |x^2 2ax 3a|\le2$ has exactly one solution in x$.
vovikov84 [41]

Answer:

x=-1, S=\{x\:\in\mathbb{R}:x=-1\}

Step-by-step explanation:

For the sake of clarity, assuming you meant:

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1) Absolute Value or Modulus functions has one property that assures us that:

If |a|

2) Solving for x

I) x^{2}+2x+3\geqslant -2\Rightarrow x^{2}+2x+5\geqslant 0 \Rightarrow x\geqslant \frac{-2\pm \sqrt{2^{2}-4*1*5}}{2} x'\geqslant \frac{-2+4i }{2} \:and\:x''\geqslant \frac{-2-4i }{2}

Not defined in Real Set of Numbers

Evaluating x^{2}+2x+3\leqslant 2:

x^{2}+2x+3\leqslant 2\\x^{2}+2x+1\leqslant 0\\(x+1)(x+1)\leqslant 0 \Rightarrow S=\{-1\}

3) So, since for the first case the Discriminant Δ <0, then the solutions presented for x^{2}+2x+3\geqslant -2\: \in \mathbb{C}. The only solution in the Real Set for the inequality |x^{2}+2x+3|\le2 is S=\{-1\}, i.e. x=-1.

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3 years ago
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3 years ago
David wants to install a fence around his garden. The garden is rectangular and has an area of 240 square feet. One side of the
oee [108]

Answer:

$996

Step-by-step explanation:

The rectangular plot has an area that is the product of its length and width. We are given the width as 12 feet, and the area as 240 ft², so we can find the length from ...

... A = L×W

... 240 ft² = L×(12 ft)

... 240 ft²/(12 ft) = L = 20 ft

Opposite sides of the rectangle are the same length, so the cost of fence for a side of a given length will be the sum of the costs of the opposites sides.

The 12 ft side has one segment that is $18 per foot, and one that is $15 per foot. For the 20 ft sides, both are $15 per foot. Then the total cost can be figured from ...

... (12 ft)·($18/ft + $15/ft) + (20 ft)·($15/ft +$15/ft) = 12·$33 +20·$30 = $996

5 0
3 years ago
A trucks engine needs 3 1/4 gallons of oil for an oil change how many quarts of oil are needed?
Deffense [45]
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8 0
3 years ago
Read 2 more answers
Given right triangle A w/a hypotenuse length of 3y + x and a leg of y-x, and right triangle B, w/ a hypotense length of y+5 and
Darya [45]
We use the law of correspondence that is 
Hypotenuse = Hypotenuse Leg = Leg 

3y + x = y + 5 
and 
y - x = x + 5 --------------------------------- work on your first problem to find x 
x = -2y + 5 
now you can plug this in to your second equation to sub in for the x 
y - ( -2y + 5 ) = ( -2y + 5 ) + 5 y + 2y - 5 = -2y + 10 3y - 5 = -2y + 10 5y = 15 y = 3 
Now you can plug back in to solve for x 

3y + x = y + 5 3(3) + x = (3) + 5 9 + x = 8 x = -1 
so y = 3 and x = -1
4 0
4 years ago
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