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ruslelena [56]
3 years ago
12

Write the equation of the following graph in vertex form.

Mathematics
1 answer:
Marat540 [252]3 years ago
6 0

Answer:

Correct choice is 2. f(x)=0.4(x+2)(x-5)

Step-by-step explanation:

We have been given a graph of the quadratic function. Now we need to use that graph to find the equation of the graph in vertex form. By the way given choices written in intercept form so to be accurate we are going to find the equation in intercept form.

from graph we see that x-intercepts are at 5 and -2.

we know that if x=a is x-intercept then (x-a) must be factor.

So (x+2)(x-5) is the factor.

when leading coefficient is positive then graph opens upward.

so that means leading coefficient is 0.4

Hence correct choice is 2. f(x)=0.4(x+2)(x-5)

You might be interested in
What’s the angle of cda
Anastaziya [24]

Answer:

∠ CDA = 32.3°

Step-by-step explanation:

See the given figure attached to this answer.

Draw perpendiculars from B and C on AD which is BE and CF.

Now, Δ ABE is a right triangle and AE² = AB² - BE² = 7.5² - 6² = 20.25

⇒ AE = 4.5 cm

Now, DF = AD - EF - AE = 24 - 10 - 4.5 = 9.5 cm {Since BC = EF}

And CF = BE = 6 cm.

Now, Δ CFD is a right triangle and  

\tan \beta  =\frac{CF}{FD} = \frac{6}{9.5}  = 0.6315 {Where β = ∠ CDA}

⇒ \beta  = \tan^{-1} (0.6315)=32.27 Degree.

So, ∠ CDA = 32.3° {Correct to one decimal place} (Answer)

8 0
3 years ago
In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1
Serga [27]

Answer:

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

1999:

20 out of 100 in the bottom third, so:

p_1 = \frac{20}{100} = 0.2

s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04

2001:

10 out of 100 in the bottom third, so:

p_2 = \frac{10}{100} = 0.1

s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03

Test if proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

At the null hypothesis, we test if the proportion is still the same, that is, the subtraction of the proportions in 1999 and 2001 is 0, so:

H_0: p_1 - p_2 = 0

At the alternative hypothesis, we test if the proportion has been reduced, that is, the subtraction of the proportion in 1999 by the proportion in 2001 is positive. So:

H_1: p_1 - p_2 > 0

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

From the two samples:

X = p_1 - p_2 = 0.2 - 0.1 = 0.1

s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05

Value of the test statistic:

z = \frac{X - \mu}{s}

z = \frac{0.1 - 0}{0.05}

z = 2

P-value of the test and decision:

The p-value of the test is the probability of finding a difference of at least 0.1, which is the p-value of z = 2.

Looking at the z-table, the p-value of z = 2 is 0.9772.

1 - 0.9772 = 0.0228.

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

5 0
3 years ago
-14 farenheit in the morning, dropped by 7 farenheit.
umka21 [38]
The answer is negative 21
7 0
3 years ago
Read 2 more answers
A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What
ivann1987 [24]

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the measures of other two angles of triangle.

\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

We know that,

  • The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.

Angle sum property,

  • The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.

\rule{200}{3}

\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

  • 3x
  • 3 × 10
  • 30°

∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

Third AnglE :

  • 14x
  • 14 × 10
  • 140°

∴ Hence, the measure of the third angle of the triangle is 140°.

5 0
2 years ago
The sixth grade art students are making a mosaic using tiles in shapes of right triangles. Each tiles has the leg measures of 5.
Drupady [299]

Given:

Each right triangular tiles has the leg measures of 5.2 cm and 6 cm.

There are 150 tiles in the mosaic.

To find:

The area of the mosaic.

Solution:

We know that, the area of a triangle is:

A=\dfrac{1}{2}\times Base\times height

So, the area of Each right triangular tile is:

A=\dfrac{1}{2}\times 5.2\times 6

A=\dfrac{1}{2}\times 31.2

A=15.6

There are 150 tiles in the mosaic. So, the area of the mosaic is:

Area=15.6\times 150

Area=2340

Therefore, the total area of the mosaic is 2340 cm ².

5 0
3 years ago
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