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2 years ago

What is the axis of symmetry for f(x) = −3x2 + 18x − 7?

Mathematics

1 answer:

katrin2010 [14]2 years ago

4 0

The axis of symmetry of a parabola like

$y=ax^2+bx+c$

is a vertical line of the form

$x = k$

where k is the x coordinate of the vertex of the parabola.

In particular, the x coordinate of the vertex of the parabola is given by

$x = -\dfrac{b}{2a}$

which in your case becomes

$x = -\dfrac{18}{-6} = 3$

So, the axis of symmetry is the line

$x=3$

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2 years ago

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HELP ASAP 40 POINTS REAL ANSWER

Jet001 [13]

Answer:

b) number of flowers.

c) 2830

Step-by-step explanation:

We are given the following in the question:

The number of flowers bloomed is given by the function:

where s is the s is the number of seeds she planted.

The number of seeds planted per week is given by

where w represents the number of weeks.

a) composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks.

The composite function can be written as:

where f(w) gives the number of flowers that bloomed in w weeks.

b) units of measurement for the composite function

The composite functions gives the number of flower that will bloom in w weeks. Thus, the unit of measurement is number of flowers.

c) Number of flowers in 35 weeks.

We put w = 35 in the composite function.

2830 flowers will bloom in 35 weeks.

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Step-by-step explanation:

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2 years ago

8.1.3 A random sample has been taken from a normal distribution and the following confidence intervals constructed using the sam

crimeas [40]

Answer:

a) The value of the sample mean is 50

b) (38.02, 61.98) is the 95% as it covers more values than the other.

Step-by-step explanation:

a) Upper and lower values for the confidence intervals are at the same distance from the mean, as they represent an upper and lower limit for the value, and the most probable value is the one in the middle, which, in a normal distribution is the mean.

As they derive from the same data, both pairs of values should give us the same mean:

$\mbox {mean}=\frac{\mbox{upper value+lower value}}{\mbox{2} }\\\mbox {mean from the first set}=\frac{38.02+61.98}{2}=50 \\\mbox {mean from the first set}=\frac{39.95+60.05}{2}=50$

b) The percentage of the confidence interval tells us which is the area below the bell curve (of the normal distribution) between the limits given.

One could give a value with a 100% CI, but limits should be minus and plus infinity, and as the interval gets smaller, less values are covered (less area), and less certain we are about our value being inside the interval.

Then, we can say that the widest interval must be the 95% CI, i.e. (38.02, 61.98).

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2 years ago

Michaela’s class used a spinner that has 6 spaces of equal area in which the arrow can land. The areas are numbered 1, 2, 3, 4,

diamong [38]

The number of times the spinner landed on a space numbered greater than 4 = 167

Step-by-step explanation:

Step 1 :

Given,

Number of equal area spaces in the spinner = 6

Number of times the spinner was spun = 500

We need to find the number of times the spinner landed on a space numbered greater than 4

Step 2 :

Total number of outcome = 6

Favorable outcomes are = Numbers greater than 4 = 5,6

Total number of favorable outcome = 2

Therefore Probability that the spinner will land on a number that is greater than 4 is $\frac{2}{6}$ = $\frac{1}{3}$

The number of times that the spinner landed on a space numbered greater than 4 = 500 × $\frac{1}{3}$ = 166.67 = 167 (rounded off to the nearest integer)

Step 3 :

Answer :

The number of times the spinner landed on a space numbered greater than 4 = 167

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2 years ago

Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60 centimeter

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So first we are gonna plug in 60 and 63 in their appropriate spots: $60^2+h^2=63^2$

Solve the exponents to get $3600+h^2=3969$

Subtract 3600 on each side to get $h^2=369$

To cancel out the squared power, you have to square root each side of the equation, and your final answer should be $h=19.2$ cm

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2 years ago

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