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Readme [11.4K]
3 years ago
10

Fill in the blanks to show the steps in solving the inequality -2x + 12<-4

Mathematics
1 answer:
professor190 [17]3 years ago
8 0
-2x + 12 < - 4......subtract 12 from both sides
-2x + 12 - 12 < -4 - 12....simplify
-2x < -16...divide both sides by -2, changing the inequality sign
(-2/-2)x > -16/-2....simplify
x > 8
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Which equation represents a parabola opening to the right with a vertex at the origin and focus at (9,0) A. X = - 1/36y^2 B. X =
Virty [35]

Answer:

Option C: x = (1/36)*y^2

Step-by-step explanation:

A horizontal parabola is written as

x = f(y) =  a*y^2 + b*y + c

If a is positive, the parabola opens to the right.

if a is negative, the parabola opens to the left.

And the vertex of the parabola has the y-value:

y = -b/2a

and the x value

x = f(-b/2a)

For our parabola, we know that:

Opens to the right:

Then the only options left are:

C) x = (1/36)*y^2

D) x = (1/6)*y^2

Because in both cases b = 0, both of the equations have the vertex in the point (0, 0).

Now let's see wich one has a focus at (9, 0)

If the vertex of our equation is:

(h, k)

Then the focus will be:

(h + a, k)

Where a is the directrix of the equation.

Here we know that the vertex is (0, 0) and the focus is (9, 0)

Then:

(0 + a, 0) = (9, 0)

The directrix is 9.

And the directrix is such that:

(x - h)^2 = 4*a*(y - k)

Replacing the values of h and k (both are zero) we get:

x^2 = 4*a*y

And we know that: a = 9

x^2 = 4*9*y

x^2 = 36*y

if we isolate y, we get:

(1/36)*x^2 = y

This is option C.

Then the correct option is C.  

8 0
2 years ago
How do you know that there exists a real number x&gt;0 such that x^2 = 3?
Oduvanchick [21]

Answer:0x0

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3 years ago
Which expression is equivalent to 10f−5−5f+2? <br> 15f−3<br> 5f−7<br> 15f−7<br> −3+5f
kati45 [8]

Answer:

10f - 5-5f +2 =5f -3= -3+5f

last option

8 0
2 years ago
Read 2 more answers
Allison drove a total of 380 miles on a tank of gas. Of those miles, 120 were driven yesterday and the rest of the miles were dr
Dominik [7]

Answer: 0_0

Step-by-step explanation: 0_0, 0_0, 0_0, my eyes!

4 0
2 years ago
Read 2 more answers
The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1800 hours and a standard deviatio
Vanyuwa [196]

Answer:

99.7%

Step-by-step explanation:

The empirical rule formula states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

Step 1

We have to find the number of standard deviations from the mean

μ = Mean = 1800 hours

σ = Standard deviation = 25 hours

For 1725 hours

μ - xσ =

1800 - 25x = 1725

25x = 1800 - 1725

25x = 75

x = 75/25

x = 3

For 1875 hours

1800 + 25x = 1875

25x = 1875 - 180

25x = 75

x = 75/25

x = 3

Step 2

From the above calculation, the bum of standard deviations from the mean is 3

Hence, the percentage of light bulbs last between 1725 hours and 1875 hours is 99.7%

8 0
3 years ago
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