Solve the following equation for f.

Answer:

A down payment is a portion of the purchase price that reduces the loan amount.

Step-by-step explanation:

The steps of completing the square assuming a parabolic equation of the form ax² + bx  + c is done to get

y = a(x + b/2a)² - (b² - 4ac)/4a = a(x - h)² + k

vertex is given by v(h, k) for h = b/2a and k = -(b² - 4ac)/4a

The standard equation of a parabola is ax² + bx  + c

completing the square is done as follows

write the equation ax² + bx  + c such that c is the other side of the equation

ax² + bx  = -c

divide through by a to get

x² + (b/a)x  = -c/a

add (b/2a)² to the both sides of the equation

x² + (b/a)x + (b/2a)² = (b/2a)² - c/a

solving each side differently,

(x + b/2a)² = x² + (b/a)x + (b/2a)² and

(b/2a)² - c/a = b²/4a² - c/a = (b² - 4ac)/4a²

hence

(x + b/2a)² = (b² - 4ac)/4a²

multiplying by a

a(x + b/2a)² = (b² - 4ac)/4a

rewriting the equation

y = a(x + b/2a)² - (b² - 4ac)/4a = a(x - h)² + k

therefore

h = b/2a

k = -(b² - 4ac)/4a

and vertex is v(h, k)

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TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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Answer:

D

Step-by-step explanation:

i did the assignment.

The correct solution of the system of the equation is -3y = 3.

The correct option is D.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A system of equations,

x – 5y = 6    {equation 1}

–x + 2y = –3    {equation 2}

In order to solve the equations, using linear combination method.

Combining the two equations 1 and 2 to eliminate one of the variables x.

Adding both the equations,

-3y = 3

y = -1.

Therefore, –3y = 3 is the solution.

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Answer:

I think it might be 16 or 24.

Step-by-step explanation:

Pardon if I'm wrong.

Answer:

2.83333333333

Step-by-step explanation:

(3 2/5) / (1 1/5) = 2.83333333333

Answer:

85/30 or 2.833333333

Step-by-step explanation:

When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.

It is also much easier to solve after you convert these numbers to improper fractions.

In this case,

3 2/5 = 17/5

1 1/5 = 6/5

17/5 ÷ 6/5

17/5 x 5/6

85/30 (17/6 reduced)

or

2.83333333333333333333

Answer:

2/5 or 0.4.

Step-by-step explanation:

6/15 = 2/5

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)

Answer:

236 ft^3

Step-by-step explanation:

Base radius = 5 ft

Height = 3 ft

Volume =   πr^2h

              =  π × 5^2 × 3

              =  75π

               =  235.61944901923 feet^3

Nearest Cubic Foot = 236 ft^3

Nearest Cubic Foot:

Hence Answer is:

236 ft^3

Hope this helps!

Answer:

Due to the higher z-score, David has the higher standardized score

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Which student has the higher standardized score

Whoever had the higher z-score.

David:

Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. So \(X = 52, \mu = 70, \sigma = 11\)

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

\(Z = \frac{52 - 70}{11}\)

\(Z = -1.64\)

Steven:

Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. So \(X = 52, \mu = 64, \sigma = 6\)

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

\(Z = \frac{52 - 64}{6}\)

\(Z = -2\)

Due to the higher z-score, David has the higher standardized score

The state spelled out with letter tiles depends on the probability of picking the letter O, and the possible states are Ohio,  Colorado and  Oregon respectively.

To solve this problem, we need to consider the frequency of the letter O in each state's name.

If the probability of picking the letter O is 1/2, then the state must have two O's in its name. The only state that meets this criteria is OHIO.

If the probability of picking the letter O is 3/8, then the state must have three O's in its name. The only state that meets this criteria is COLORADO.

If the probability of picking the letter O is 1/3, then the state must have at least three O's in its name. The only state that meets this criteria is OREGON.

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Answer:

4/7=12/21

18/20=9/10

6/5=30/25

81/90=9/10

Step-by-step explanation:

12 / 21  will be equal to 4/7 and is denoted in the simplest form.

A fraction that possesses the same value as another fraction regardless of how it's denominators and numeric components could be different is said to be equivalent.

12 / 21 can be simplified with the help of 3. This will result in 4/7.

18/20 can be simplified with the help of 2. This will result in a 9/10.

30/25 can be simplified with the help of 5. This will result in 6/5.

81/90 can be simplified with the help of 9. This will result in a 9/10.

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By the frequency table we can say Students at Bayward high are more interested in civics.

Part A : Total Number of students in both 11th grade and 12th grade = 555

Number of 11th grade students = 235

Number of 12th grade students = total - students in 11th grade

= 555 - 235 = 320

In 11th grade ,

Number of students signing up for civics = 105

Number of students signing up for Economics = 75

so , Number of students signing up for World history = 235 - (105 + 75)

= 55

In 12th grade ,

Number of students signing up for world history = 25

Total students signing for economics = 125

so , Number of students of 12th grade signing for economics = 125 - 75

= 50

Number of students signing up for civics = 320 - (25+50)

= 245

Adding 11th grader students and 12th grader signing for civics = 105+245

Total number of students signing for civics = 350

similarly , Total number of students signing for world history = 55 + 25

= 80

Part B : Greatest marginal frequency is of 12th grade students signing up for civics .

It represent that more than half of 12th grade students are interested in civics.

Part C :  Greatest joint frequency is of Students signing up for civics.

It represents that students are more interested in civics .

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Answer: 0.664

Step-by-step explanation: 1.666/0.664=2.5

x¹ = -2 x² = -8

y¹ = -1 y² = 12

Using midpoint formula,

M = ( x¹ + x²/2 ,y¹ + ý²/2)

or,M ={ -2+(-8)/2 , (-1) +12/2}

or, =( -10/2 , 11/2)

:M = ( -5 , 11/2)

The point (2,-4) satisfies y < 3x - 6

The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

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The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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Answer:

It is algebra

Step-by-step explanation:

do you want the answer?

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

Answer:

I did the math there is no answer

ANSWER

EXPLANATION

First, we have to find the volume of both containers.

The volume of a cylinder is given as:

where r = radius; h = height

The diameters of both containers are given instead of their radii.

Radius is half of the diameter, this means that:

Therefore, the volume of container A is:

And the volume of container B is:

As we can see, the volume of container A is less than the volume of container B.

This means that after the water is pumped completely out of container A into container B, the volume of water in container B is equal to the volume of container A (since container A was filled with water).

Therefore, the volume of water in container B after pumping is:

Answer:

10.5 percents

Step-by-step explanation:

1)100+30=130 percents;

2) 130/100*15=19.5percents of discount from the first price

3) 130-19.5=110.5 percents- new price from the initial price

4)110.5-100=10.5 percents - the percentage of profit

Step-by-step explanation:

60 divided by 7 = approx. 8-9 min for each task.

7 tasks per hour

Answer:

a. 8.58 (8.57142857143)

Step-by-step explanation:

The explicit rule for the sequence 4, 3 2/3, 3 1/3, 3.... is f(n) = 4 - 1/3(n - 1)

From the question, we have the following parameters that can be used in our computation:

4, 3 2/3, 3 1/3, 3....

In the above sequence, we can see that 1/2 is subtracted from the previous term to get the new term

Take for instance

2nd = 4 - 1/3 = 3 2/3

3rd = 3 2/3 - 1/3 = 3 1/3

4th = 3 1/3 - 1/3 = 3

And so on

This means that

So, the explicit rule is

f(n) = a + (n - 1)d

This gives

f(n) = 4 - 1/3(n - 1)

Hence, the explicit formula is f(n) = 4 - 1/3(n - 1)

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Complete question

Consider the sequence 4,3 2/3,3 1/3, 3....

What is the explicit rule for this sequence

Answer:

This has no answer. Whats the question? Please tell me so I can help you

Is it probability ???