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Daniel [21]
3 years ago
13

What is the x-coordinate of the vertex of the parabola whose equation is y = 3x2 + 9x?

Mathematics
2 answers:
Westkost [7]3 years ago
4 0
The vertex is (-1.5, -6.75). So the x-coordinate is -1.5. Hope this helps and if so please leave a good rating and thanks. I really appreciate it. Have a nice day!
lisabon 2012 [21]3 years ago
3 0

Answer:

-1.5

Step-by-step explanation:

We have been given an equation y=3x^2+9x. We are asked to find the x-coordinate of the vertex of the parabola for our given equation.

We will use formula \frac{-b}{2a} to finc the x-coordinate of vertex of given parabola.

Upon substituting our given values in above formula we will get,

\frac{-9}{2*3}

\frac{-3*3}{2*3}

\frac{-3}{2}

-1.5

Therefore, the x-coordinate of vertex of given parabola is -1.5.

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A circle has the equation x2 + (y−7)2 = 121. What is the length of the diameter of the circle?
Reika [66]

Answer:

22

Step-by-step explanation:

The standard form for an equation of a circle is (x-h)^2+(y-k)^2=r^2, where h is the x coordinate of the center of the circle, k is the y coordinate, and r is the radius of the circle. Therefore, the radius of this circle squared is 121, meaning that the radius of the circle is 11. Since the diameter of a circle is twice the radius, the radius of this circle is 22. Hope this helps!

8 0
3 years ago
X/5 -8=4 find the value of x
elena-s [515]

Answer:

x=60

Step-by-step explanation:

I'm assuming you meant this: (x/5)-8=4

In which case you would add 8 to both sides to get rid of the 8 on the left (your goal is to get x by itself so you want to move the numbers on the x side to the other side of the equal sign)

(x/5)=12

Then you would multiply 5 on both sides to get rid of the fraction with the 5 on the bottom on the left side.

x=60

There's your answer.

6 0
3 years ago
Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the pro
lisov135 [29]

Answer:

0.0326 = 3.26% probability that a randomly selected thermometer reads between −2.23 and −1.69.

The sketch is drawn at the end.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 0°C and a standard deviation of 1.00°C.

This means that \mu = 0, \sigma = 1

Find the probability that a randomly selected thermometer reads between −2.23 and −1.69

This is the p-value of Z when X = -1.69 subtracted by the p-value of Z when X = -2.23.

X = -1.69

Z = \frac{X - \mu}{\sigma}

Z = \frac{-1.69 - 0}{1}

Z = -1.69

Z = -1.69 has a p-value of 0.0455

X = -2.23

Z = \frac{X - \mu}{\sigma}

Z = \frac{-2.23 - 0}{1}

Z = -2.23

Z = -2.23 has a p-value of 0.0129

0.0455 - 0.0129 = 0.0326

0.0326 = 3.26% probability that a randomly selected thermometer reads between −2.23 and −1.69.

Sketch:

3 0
3 years ago
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