Find the vertex of each of the following parabolas by averaging the x-intercepts. Then write each equation in graphing form. y=(x-3)(x-11)

Answer:

25/9

Step-by-step explanation:

3 1/3 ÷ 1 1/5

3 1/3 = 10/3

1 1/5 = 6/5

10/3 ÷ 6/5 = 10/3 x 5/6 = 50/18 = 25/9

So, the answer is 25/9

Answer:

11,520

Step-by-step explanation:

192×60

60 is the minute so

192×60=11520

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

Standard form: -35x^3 - 39x^2 + 25x

Answer:

2144.7cm³

Step-by-step explanation:

volume =  \(\frac{4}{3}\) pi 8³

Answer:

c. Place one end of the reflective device on the vertex B and swing the other end until you can see the reflected line segment BC coincide with line segment AB

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution, the central limit theorem and difference between normal variables.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

Subtraction of normal sample means:

When we subtract two distribution of the sample means, which are normal, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of standard errors squared.

Sample size of 55 men with mean 785 and standard deviation 489

This means that:

\(\mu_A = 785\)

\(s_A = \frac{489}{\sqrt{55}} = 65.9367\)

Sample size of 40 women with mean 670 and standard deviation of 419

This means that:

\(\mu_B = 670\)

\(s_B = \frac{419}{\sqrt{40}} = 66.2497\)

Difference between sample means:

The mean and the standard deviation are, respectively:

\(\mu = \mu_A - \mu_B = 785 - 670 = 115\)

\(\sigma = \sqrt{s_A^2+s_B^2} = \sqrt{65.9367^2+66.2497^2} = 93.47\)

What is the probability of obtaining a difference between sample means of 110 mg or more?

This is 1 subtracted by the pvalue of Z when X = 110. So

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

\(Z = \frac{110 - 115}{93.47}\)

\(Z = -0.053\)

\(Z = -0.053\) has a pvalue of 0.4812.

1 - 0.4812 = 0.5188

0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more

Answer: 9/4

Step-by-step explanation:

Reciprocal means flip the fraction

The reciprocal of 4/9  is  9/4

Answer: the rciprocal is 9/4

Step-by-step explanation:

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

The distance between the points (-6, 4) and (5, 4) is 11 units.

To find the distance between two points in a Cartesian coordinate system, we can use the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Given the two points (-6, 4) and (5, 4), we can plug in the coordinates into the distance formula:

Distance = √[(5 - (-6))² + (4 - 4)²]

        = √[(5 + 6)² + 0²]

        = √[11² + 0]

        = √[121]

        = 11

Therefore, the distance between the points (-6, 4) and (5, 4) is 11 units.

In this case, since the y-coordinates of both points are the same (4), the distance between them only considers the difference in their x-coordinates. As the x-coordinate of the second point is 11 units greater than the x-coordinate of the first point, the distance between them is simply the absolute value of the difference, which is 11.

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The side length of the the rectangular garden are 20 feet by 5 feet.

Let

s = side length of the square garden

l = length of the rectangular garden

w = width of the rectangular garden

From the problem statement,

area of the square garden = area of the rectangular garden

Since the area of a square is just the side length squared, we can write:

s² = l * w

We also know that the length of the rectangular garden is 10 feet longer than the side of the square garden, and that the width of the rectangular garden is 5 feet shorter than the side of the square garden. We can express them as:

l = s + 10

w = s - 5

Now we can substitute these expressions for l and w into our first equation:

s² = (s + 10) * (s - 5)

Expanding the right-hand side, we get:

s² = s² + 5s - 50

0 = 5s - 50

5s = 50

Dividing both sides by 5, we get:

s = 10

Since the side length of the square garden is 10 feet.

We can use this to find the dimensions of the rectangular garden:

l = s + 10 = 10 + 10 = 20

w = s - 5 = 10 - 5 = 5

So the dimensions of the rectangular garden are 20 feet by 5 feet.

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Answer:

A=E

B=F

C=G

D=H

Step-by-step explanation:

Answer:

Step-by-step explanation:

Angle in Upper Intersection Corresponding Angle in Lower Intersection

A E

B F

C G

D H

Answer:

367.5

Step-by-step explanation:

5% of 350 is 17.5

$350+$17.5=367.5

Answer:

3080983

Step-by-step explanation:

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The $100 start-up fee and $25 monthly rental gives;

The cost of using the phone for 1 month = $125

The cost of using the phone for 6 months = $250

The cons of using the phone for n months = $(100 + 25·n)

Please find attached the graph of the cellphone plan over a period of two years (24 months)

A graph is a visual representation of the variation of one variable of a function with respect to other variables of the function.

The start-up fee of the cell phone plan = $100

The amount charged each month = $25

First part;

The total cost for the start-up fee and monthly rental for 1 month = $100 + $25

The total cost for 1 month = $125

The total cost for 6 months = $100 + 6 × $25 = $250

The total cost for n months = 100 + n × 25 = $(100 + 25·n)

Please find the graph of the total cost to the number of months created with MS Excel

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a) The net for the sale is: $4,500

b) The capital gain is $2,200

We know that you had 100 shares, now the value of each of these is $45.00, then the amount that you make if you sell the 100 shares is:

S = 100*$45.00 = $4,500

The capital gain is the difference between the amount we found above and the amount you paid for the shares.

The price of the shares was $23.00, then the amount you paid is:

C = $23.00*100 = $2,300

Then the capital gain is:

g = $4,500 - $2,300 = $2,200

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Answer:

(a) After 9 months, the unpaid balance is $125,874.09.

(b) Over the 9 months, she paid a total of $4,918.56 in interest.

To create the amortization table, we can use the formula for calculating the monthly payment of a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where:

P = monthly payment

r = monthly interest rate

A = loan amount

n = total number of payments

In this case, we have:

A = $128,000.00

n = 25 years * 12 months/year = 300 months

r = 5.3% / 12 = 0.00441666667

Using the formula, we can calculate the monthly payment:

P = (0.00441666667 * $128,000.00) / (1 - (1 + 0.00441666667)^(-300))

P = $770.82

Now, we can create the amortization table:

Answer:

Its C

Step-by-step explanation:

The equation in slope-intercept form to find the height is y = 0.75x + 5 and the number of years it will take the tree to reach 20 feet is 24

The given parameters in the question are

Growth = 9 inches per year

Length of the tree after 4 years = 5 feet

Convert inches to feet

So, we have

Growth = 0.75 feet per year

A linear equation of this scenario is represented as

Length = Growth * Number of years + Initial length

So, we have

y = Growth * x + Initial length

This gives

5 = 0.75 * 4 + Initial length

Evaluate

Initial length = 2

So, the equation is

y = 0.75x + 2

This means that

y = 20

Recall that

y = 0.75x + 2

So, we have

0.75x + 2 = 20

Evaluate

0.75x = 18

Divide by 0.75

x = 24

Hence, the number of years is 24

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Answer:

Below

Step-by-step explanation:

SO Loto walked  ( 6+5) = 11 N   and   (8+12) = 20 E (yards)

You can now use Pythagorean Theorem ( or 'distance' formula)

d =distance

d^2 = 11^2 + 20^2

d^2 = 121 + 400

d^2 = 521

d = sqrt (521) =22.8 yards

The circle equations for each center and radius are:

1) x² + y² = 81

2)  (x + 8)² + (y - 3)² = 16

The general equation for a circle of radius R and center (a, b) can be written as:

(x - a)² + (y - b)² = R²

1) We want to find the equation for a circle whose center is (0, 0) and the radius is R = 9, then the equation is:

(x - 0)² + (y - 0)² = 9²

x² + y² = 81

b) Now the center is (-8, 3) and the radius is 4, so the equation is:

(x - (-8))² + (y - 3)² = 4²

(x + 8)² + (y - 3)² = 16

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The two different trinomials that have a greatest common factor of  \(5x^{2} y^{3}\) are:

a) \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\)

b) \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z\\\)

Let us verify,

a)  Consider the trinomial   \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\),

The Greatest Common Factor  of 35, 5, 15 is 5

The Greatest Common Factor  of  \(x^{2} ,x^{4} ,x^{3} =x^{2}\)

The Greatest Common Factor  of  \(y^{5} ,y^{9} ,y^{3} = y^{3}\)

There is no G.C.F for z because it is missing in the 3rd term.

So, the G.C.F  of the trinomial   \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\) =  \(5x^{2} y^{3}\)

b) Consider the trinomial   \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z\\\),

The Greatest Common Factor  of 25, 5, 10 is 5

The Greatest Common Factor  of \(x^{4} ,x^{7} ,x^{2} =x^{2}\)

The Greatest Common Factor  of \(y^{3} ,y^{8} ,y^{4} = y^{3}\)

There is no G.C.F for z because it is missing in the 2nd term.

So, the G.C.F of the trinomial  \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z = 5x^{2} y^{3}\)

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Answer:

The logs do not form a right-angle triangle

Step-by-step explanation:

Given

\(Logs: 9ft, 11ft, 21ft\)

Required

Do the logs form a right-angled triangle

Applying Pythagoras theorem

\(a^2 = b^2 + c^2\)

Where a is the length of the longest log.

So, we have:

\(21^2 = 9^2 + 11^2\)

\(441 = 81 + 121\)

\(441 \ne 202\)

The above shows an inequality.

Hence, the logs do not form a right-angle triangle

The length of the two segments, written as radicals, are:

AB = √117

PQ = √244

Remember that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the length of the segment is:

L = √( (x₂ - x₁)² + (y₂ - y₁)²)

First, for the segment AB the endpoints are:

A = (-4,  -4)

B = (2, 5)

Then the length is:

L =  √( (-4 - 2)² + (-4 - 5)²)

L = √117

For the segment PQ the endpoints are:

P = (-6, 8)

Q = (6, -2)

The length is:

L =  √( (-6 - 6)² + (8 + 2)²)

L = √244

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Answer: 1,3,5

I got them right on my assignment

Option (A) The solution set is unbounded, (C) There is one point of intersection of the boundary curves, (E) The boundary curves intersect at approximately (-3, 0) are correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have two inequality:

x² - 9y² < 9

y > 2×

After plotting on the graph:

From the graph:

The correct options are:

The solution set is unbounded

There is one point of intersection of the boundary curves.

The boundary curves intersect at approximately (-3, 0).

Thus, option (A) The solution set is unbounded, (C) There is one point of intersection of the boundary curves, (E) The boundary curves intersect at approximately (-3, 0) are correct.

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Answer: x = (b-c)/d

Step-by-step explanation:

xd + c = b

xd = b-c

x = b-c/d

The capacitive reactance of the circuit with capacitance of 4 x 10⁻⁸ farad and the AC power source of 2 Khz is X[C] = 1.99 x 10⁻⁷ ohms.

The capacitance of a body is defined as the charge holding ability of a body. Mathematically, capacitance is the ratio of charge and potential as follows -

C = dQ/dV

Given is the total capacitance measures .04 microfarad. If the circuit is supplied by an AC power source operating at 2 kHz.

From this we can write -

Capacitance [C] = 0.04 microfarad = 4 x 10⁻⁸ farad.

Frequency of AC supply [f] = 2 KHz = 2 x 10³ Hz

The capacitive reactance is given by -

X[C] = 1/2πfC

X[C] = (1/2 x 3.14 x 2 x 10³ x 4 x 10⁻⁸)

X[C] = 1/(50.24 x 10⁻⁵)

X[C] =  0.0199 x 10⁻⁵

X[C] = 1.99 x 10⁻⁷ ohms

Therefore, the capacitive reactance of the circuit with capacitance of 4 x 10⁻⁸ farad and the AC power source of 2 Khz is X[C] = 1.99 x 10⁻⁷ ohms.

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Answer:

(0,-4)

Step-by-step explanation: