Consider functions f and g.
\(g(x)=\sqrt(4x-12)+15\)
\(f(x)=\sqrt(x-3)\)
What is the sum of these functions?

The ordered pair that show a combination of 12 coins from the graph is (10, 2)

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

The graph

The purple line represents the combination of 12 coine

Using the above as a guide, we have the following:

The equation is

x + y = 12

From the list of options, we have

(10, 2): 10 + 2 = 12

Hence, the ordered pair is (10, 2)

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1. The vertex from of the parabola y = x² - 6x + 5 is y = (x - 3)² - 4, the vertex is (3, -4). The four points are (0, 5), (0, 6), (1, 0), and (5, 0).

2. The vertex from of the parabola y = x² + 12x + 30 is y = (x + 6)² - 6, the vertex is (-6, -6). The four points are (0, 30), (-10, 10), (-2, 10), and (-9, 3).

3. The vertex from of the parabola y = x² - 4x + 7 is y = (x - 2)² + 3, the vertex is (2, 3). The four points are (0, 7), (-1, 12), (5, 12), and (4, 7).

4. The vertex from of the parabola y = x² + 10x + 32 is y = (x + 5)² + 7, the vertex is (-5, 7). The four points are (0, 32), (-10, 32), (2, 16), and (-8, 16).

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Question 1:

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic function as follows:

y = x² - 6x + 5

y = x² - 6x + (-6/2)² + 5 - (-6/2)²

y = x² - 6x + 9 + 5 - 9

y = (x - 3)² - 4

Vertex (h, k) = (3, -4).

Question 2:

y = x² + 12x + 30

y = x² + 12x + (12/2)² + 30 - (12/2)²

y = x² + 12x + 36 + 30 - 36

y = (x + 6)² - 6

Vertex (h, k) = (-6, -6).

Question 3:

y = x² - 4x + 7

y = x² - 4x + (-4/2)² + 7 - (-4/2)²

y = x² - 4x + 4 + 7 - 4

y = (x - 2)² + 3

Vertex (h, k) = (2, 3).

Question 4:

y = x² + 10x + 32

y = x² + 10x + (10/2)² + 32 - (10/2)²

y = x² + 10x + 25 + 32 - 25

y = (x + 5)² + 7

Vertex (h, k) = (-5, 7).

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In the balance sheet, mortgage notes payable are reported as a long-term liability only.

Mortgage notes payable represent the amount owed by a company for a mortgage loan. These loans are typically long-term obligations that are expected to be repaid over an extended period, often several years. Therefore, mortgage notes payable are classified as long-term liabilities in the balance sheet.

Current liabilities are obligations that are expected to be settled within a short period, usually one year or less. Since mortgage notes payable typically have a longer repayment term, they do not meet the criteria to be classified as current liabilities.

By reporting mortgage notes payable as a long-term liability, the balance sheet provides a clear distinction between the company's short-term and long-term obligations, helping stakeholders understand the company's financial position and obligations over different time horizons.

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Answer:1250

Step-by-step explanation:

The probability that student chosen at random is 16 years is 0.28.

The table shows the distribution of student by age in a high school with 1500 students. Therefore, the probability that randomly chosen student is  16 years can be found as follows:

Therefore,

probability = number of favourable outcome to age / total number of possible outcome

Hence,

probability that student chosen at random is 16 years =  420 / 150

probability that student chosen at random is 16 years = 0.28

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Answer:

Supplementary angle= two angle that sum upto 180 degrees.

Step-by-step explanation:

\(180 - 22 = 158\)

Supplementary angle of 22° is 158°

The option that gives chart elements a realistic, three-dimensional look is D. Plot Area.

The option that gives chart elements a realistic, three-dimensional look is the plot area. The plot area is the portion of the chart that displays the data points and is typically the main focus of the chart. Adding shading and depth to the plot area, can give the chart a more lifelike appearance and make the data more visually engaging. Additionally, three-dimensional charts can also be created by using specialized charting software that allows for the creation of 3D visualizations. These types of charts can be useful for highlighting patterns and trends in the data, especially when dealing with large datasets.
In a chart, the plot area is the space where the actual data points, bars, lines, or pie slices are displayed. By applying three-dimensional effects to the plot area, you can make the chart elements appear more realistic and visually appealing. This can enhance the viewer's understanding of the data being represented and make the chart more engaging.
In summary, to give chart elements a realistic, three-dimensional look, you should focus on the plot area (Option D). The axis (Option A), chart area (Option B), and legend (Option C) do not directly contribute to creating a three-dimensional appearance for the chart elements.

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(a) With 10 rectangles using left endpoints, 5 rectangles are contributing negative area values to the estimated net area. This means that the function is below the x-axis in those intervals.

The remaining 5 rectangles are contributing positive area values, as the function is above the x-axis in those intervals.

When using midpoints, the number of positive and negative rectangles may not be the same. It depends on the behavior of the function within each subinterval. The use of midpoints can result in a different distribution of positive and negative rectangles compared to using left endpoints.

(b) The error when using midpoints with 10 subintervals can be determined by calculating the difference between the estimated net area using midpoints and the actual net area.

To calculate the error, we need to evaluate the definite integral of the function over the given interval and subtract the estimated net area using midpoints.

Error = Actual Net Area - Estimated Net Area using Midpoints

Since the exact values are not provided, the specific error value cannot be determined without further information or calculations.

Using left endpoints with 10 rectangles, 5 rectangles contribute negative area values and 5 contribute positive area values. When using midpoints, the distribution of positive and negative rectangles may differ. The error when using midpoints can be calculated by subtracting the estimated net area using midpoints from the actual net area, but the exact error value cannot be determined without further information or calculations.

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Answer:

V = hpi(r)^2

 =  20(3.14)(17)^2 = 18,149.20 cubic mm

More accurately,

V = 20(3.14159)(17)^2 = 18158.39 mm^3

Step-by-step explanation:

The percentage of adults who have an IQ score higher than 128 points using the z score is 0.26%.

Given that,

The distribution of IQ scores for adults can be modeled with a normal distribution.

Mean, μ = 100

Standard deviation, σ = 10

We have to find the percentage of adults who have an IQ score higher than 128 points.

z score = (x - μ) / σ

            = (128 - 100) / 10

            = 2.8

Percent of adults who are below 2.8 = 0.9974

Percent of adults who are above 2.8 = 1 - 0.0026 = 0.26%

Hence the required percentage is 0.26%.

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As from the graph, it is clear that when one page is printed the price charged for one page is $0.50

Simalrly, when the second page is printed the price charge for second page is also $0.50

Therefore, the unit price is $0.50 per page. The correct answer is (C)

Answer:

for exapmle:  (2, 5)          {5=2•2.5}

                       (8, 20)        {20=8•2.5}  

                       (-5,  -12.5}    {-12.5=-5•2.5}

Step-by-step explanation:

    -3y+3x    -3y+3x

            ÷2     ÷2

Answer:

neither

Step-by-step explanation:

Answer:

s' 44

Step-by-step explanation:

step is s

Given data:

The first number is 4/9.

The second number is 5/10.

The first number can be written as,

The second number can be written as,

Now compare both numbers as they have same denominator.

Thus, the < symbol must be used between both n

Answer:

No error

Step-by-step explanation:

Everything is true

all drive to work ( includes Gavin because he go to work)

(can I please have brainiest, I am one crown away )

Answer:

The answer is -1

Step-by-step explanation:

-[(5-8)+12] ÷ 9

-[-3+12] ÷ 9

[3-12] ÷ 9 {becoz (- × + = -) (- × - = +)}

-9 ÷ 9

-1

Hope this may help you to solve these problems ☺

A roster of twenty-four players divided into four teams can be represented by the expression 24/4.

Given

24 players total

(4) teams total.

This can be expression as = 24 / 4.

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Answer:

Step-by-step explanation:

\(0.6y + 0.8 = 0.28y + 1.12\)

Move the variable to L.H.S and change its sign:

\(0.6y - 0.28y + 0.8 =1.12\)

Move the constant to R.H.S and change its sign:

\(0.6y - 0.28y = 1.12 - 0.8\)

Calculate

\(0.32y = 0.32\)

Divide both sides of the equation by 0.32

\( \frac{0.32y}{0.32} = \frac{0.32}{0.32} \)

Calculate

\(y = 1\)

Hope this helps...

Good luck on your assignment..

Answer:

Hello!

`~~~~~~~~~~~~~~~~~~~~

0.6y + 0.8 = 0.28y + 1.12 =

\(y = 1\)

~~~~~~~~~~~~~~~~~`~~~

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you. Brainliest would be nice!

☆_________________❤︎_________________☆

According to the information given, it is found that in total, the group hiked 10.96 miles.

The distances of each step, in miles, are:

Hence, the total distance is:

\(d = 4.875 + 1.67 + 3.833 + 0.583 = 10.96\)

The group hiked 10.96 miles.

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Answer:

\(12\) cm

Step-by-step explanation:

If Kelsey knit a total of \(6\) cm of scarf over \(2\) nights, then we know that she can knit \(\frac{6}{2}=3\) cm each night. Therefore, after \(4\) nights of knitting, Kelsey would have knit a total of \(3*4=12\) cm of scarf in total. Hope this helps!

Answer:

Step-by-step explanation:

8y-2=6

8y=8

y=1

Answer:

y=1

Step-by-step explanation:

i got a 100 on the test

Answer:

no its not a function

Step-by-step explanation:

Answer:

It is not a 1 to one function

Answer:

1

Step-by-step explanation:

To find the median number of musical instruments played, we first need to arrange the data in ascending order:

0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3

Next, we count the total number of responses, which is 15. Since 15 is an odd number, the median will be the average of the middle value.

The middle value is 1

Hence, the median number of musical instruments played is 1.

The number of people who know about the celebrity's proposal will continue to grow exponentially each day, starting from 888 and increasing by 50% each day. Let's analyze the growth in the number of people who know about the celebrity's proposal day by day.

Initially, 888 people know about the proposal. On the first day, the number of people who know increases by 50% of 888, which is (50/100) * 888 = 444 people. Therefore, after the first day, the total number of people who know is 888 + 444 = 1332.

On the second day, the number of people who know increases by 50% of 1332, which is (50/100) * 1332 = 666 people. Thus, the total number of people who know after the second day is 1332 + 666 = 1998.

Following this pattern, we can determine the number of people who know on subsequent days:

- On the third day: 1998 + (50/100) * 1998 = 2997 people.

- On the fourth day: 2997 + (50/100) * 2997 = 4495.5 (rounded to 4496) people.

- On the fifth day: 4496 + (50/100) * 4496 = 6744 people.

- And so on...

The growth in the number of people who know follows an exponential pattern since it increases by a certain percentage each day. The formula to calculate the number of people who know after a certain number of days can be written as:

N = 888 * (1 + 0.5)^d

where N is the total number of people who know after d days

In conclusion, the number of people who know about the celebrity's proposal will continue to grow exponentially each day, starting from 888 and increasing by 50% each day.

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The height of the structure is 15 feet.

We have,

Hypotenuse = √261 feet

Base= 6 feet

Using Pythagoras theorem

H² = P² + B²

(√261)² = P² + 6²

261 = P² + 36

261 - 36 = P²

P² = 225

P = 15 unit

Thus, the height of the structure is 15 feet.

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Answer: 4 i think

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

50%=10

100%=20

Answer:

20

Step-by-step explanation:

50% basically means half, so if 10 is 50% then the other 50% is also 10.

so 10x2=20

The length of the rectangular prism is 15 feet.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given that:  the volume of the rectangular prism is 7800 cubic feet, the width is 40 feet, and the height is 13 feet.

We can substitute these values into the formula and solve for the length:

V = w × h × l

7800 = 40 × 13 × l

7800 = 520 × l

l = 7800 / 520

l = 15 ft

Therefore, the measure of the length is 15 feet.

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The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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