Please help with this certain math problem

Please Help With This Certain Math Problem

Answers

Answer 1

Answer: For this real-valued function;

[tex]fog = 2\sqrt{x-1} + 1\\ Domain = [1, )[/tex]

Step-by-step explanation:

COMPOSITE FUNCTION

If f and g are functions, then the composite function or composition, of g and f is defined by

[tex]( f o g ) (x) = f(g(x))[/tex]

Given the functions [tex]f(x)=2x+1[/tex] , [tex]g(x)=\sqrt{x-1}[/tex],

Now composition for this;

[tex]fog = f(g(x))f(g(x)) = f(\sqrt{x-1} )[/tex]

[tex]f(\sqrt{x-1})[/tex]means we are to interchange variable x in [tex]f(x)[/tex] with the function [tex]\sqrt{x-1}[/tex]

[tex]f(\sqrt{x-1}) = 2(\sqrt{x-1})+1f(\sqrt{x+1}) = 2(\sqrt{x-1})+1fog = 2(\sqrt{x-1})+1[/tex]

The function inside the square root, x-1, must be more significant than or equal to zero (x-10), for the function to exist on any real-valued function.

[tex]if, x-1 \geq 0\\x\geq 0+1\\x \geq 1[/tex]

As a result, the range of the variable x must only include values that are larger than or equal to 1.

Hence, Domain = [1, )

DOMAIN = The domain of [tex]fog[/tex] is the set of all numbers [tex]x[/tex] in the domain of [tex]g[/tex] such that [tex]g(x)[/tex]  is in the domain of [tex]f[/tex].

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Related Questions

What is the slope of a line that is perpendicular to the line shown on the graph?

Answers

Answer:

4

Step-by-step explanation:

The slope of the line in the image is -1/4. I found that by starting at the point (0,2) and moving down 1, and right 4. This is because slope is rise over run, meaning that you move up/down and then right/left. You can see that the line is sloping downwards, so it is negative.

Perpendicular lines have a slope that is the opposite reciprocal, meaning the sign is opposite and the numerator and denominator are flipped (reciprocal). The current slope is -1/4, so the reciprocal is -4/1 (or just -4). Then just make the negative positive and you get 4.

What is the product of (x² + x + 2) and (x² − 2x + 3)

Answers

Answer:

[tex]x^4-x^3+3x^2-x+6[/tex]

Step-by-step explanation:

Multiply each term in the first equation by all the terms in the second and add them together.

Someone do this please, ty.

Answers

5 is the missing value.

Step-by-step explanation:

12x = 60

x = 60/12

x = 5

Answer:

[tex]\boxed{\rm x = 5}[/tex]

Step-by-step explanation:

[tex] \rm \cfrac{12}{20} = \cfrac{3}{x} [/tex]

Find the missing value.

Solution with work shown:

Use criss-cross multiplication:

[tex]12 \times x = 3 \times 20[/tex][tex]12x = 60[/tex]

Divide both sides by 12:

[tex] \cfrac{12x}{12} = \cfrac{60}{12} [/tex]

[tex]x = 5[/tex]

Hence,the missing value is 5.

How does understanding of 5 x 12 = 60 help to solve for the product of 5
x 120? Explain in words

Answers

Answer:

c6

Step-by-step explanation:

justjustcancacanjustadda0totheproduct of5cxwewtogetthesameresultasx1totoandtimes

3) Number: 640,700

   the value of 4 in this number is 40,000

Number: 64,070

the value of 4 in this number is 4,000

So, times greater: 40,000 ÷ 4,000 = 10 times greater.

4)

The multiplication, 5 × 12 = 60. So, 5 × 120 = 600.

There is an extra zero at the very last of the result as '120' was multiplied with 5 instead of '12' which does not have zero at last which changes the result.

Similar cases with: 5 × 10 = 50. So, 5 × 100 = 500.

Factor: 120u² + 125u + 30.

Answers

Answer:

5(3u+2)(8u+3)

Step-by-step explanation:

lmk if you want an explanation

Answer:

5(3u+2)(8u+3)

Step-by-step explanation:

Well you first want to factor out any GCF which in this case is 5

5(24u² + 25u + 6)

so now a, b, c = 24, 25, 6.

ac = 144

factors of 144 that add up to 25 are 9 and 16

rewrite equation

(24u² + 9u) + (16u + 6)

factor out GCF

3u(8u+3) + 2(8u + 3)

(3u+2)(8u+3)

plug that back into entire equation

5(3u+2)(8u+3)

please help ive been stuck on this question.

Answers

The value of the expression 8 / m - 11 / 3m is  13 / 3m

How to simplify an expression?

8 / m - 11 / 3m

Therefore,

8 / m - 11 / 3m

The factor of the denominator is 3m

Therefore,

8 / m - 11 / 3m = 3(8) - 11/ 3m

3(8) - 11/ 3m = 24 - 11 / 3m

24 - 11 / 3m = 13 / 3m

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Large eggs weigh 1/1/2 pounds per dozen. Dawn bought eight large eggs. How much did the eggs weigh

Answers

Answer:  1 pound

Step-by-step explanation:

Because 12 eggs= 1.5 pounds. So, you divide 1.5/12 = 0.125. And the 0.125 times 8 = 1 pound

Answer:

1 lb

Step-by-step explanation:

Since 1 dozen(12) eggs weigh 1 1/2 or 3/2 lbs, each egg weights 3/2 ÷ 12 = 3/24 lb
So 8 eggs would weight 8 x 3/24 = 1 lb

Homework:Section 5.3 Homework
Question 5, 5.3.21
Part 1 of 2
HW Score: 50%, 4 of 8 points
Points: 0 of 1

Question content area top
Part 1
In airline​ applications, failure of a component can result in catastrophe. As a​ result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.0056 and the system that utilizes the component is part of a triple modular redundancy.
​(a) Assuming each​ component's failure/success is independent of the​ others, what is the probability all three components​ fail, resulting in disaster for the​ flight?
​(b) What is the probability at least one of the components does not​ fail?

Answers

The probability that all three components fail is 1.756 × 10⁻⁷. The probability of at least one of the components does not​ fail 0.9999998244.

What is a Probability?

Probability is the likelihood for an event to occur. In a given statistical distribution, the probability explains the range of values and probabilities that a randomized variable could have.

From the given information;

Assuming each​ component's failure/success is independent of the​ others: the probability that all three components fail is:

P(three components fail) = (0.0056)^3

P(three components fail) = 1.756 × 10⁻⁷

The probability that at least one does not fail is:

P(at least one does not fail) = 1 - P(all three components fail)

P(at least one does not fail) = 1 - 1.756 × 10⁻⁷

P(at least one does not fail) = 0.9999998244

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the density of some steel is7.98gm/cc.how much does 60cc weigh?​

Answers

Substituting into the formula d=m/v,

[tex]7.98=\frac{m}{60}\\\\m=\boxed{478.8 \text{ gm}}[/tex]

Determine if an exponential would be an appropriate model for the data shown in each scatter plot. Select
one that applies.

Answers

Answer:

Yes, No, No

Step-by-step explanation:

The function of an exponential graph is attached below. The first graph fits the look of an exponential graph. The rest do not.

Answer:

Yes, No, No

Step-by-step explanation:

1st graph represents exponential2nd graph represents quadratic3rd graph represents linear

An asset has a cost of $50,000, with a residual value of $10,000. It has a life of 5 years and was purchased on January 1. Under double-declining-balance, what’s the asset’s fourth full year of depreciation expense?

Answers

The asset’s fourth full year of depreciation expense will be $6,666.67.

What is double-declining-balance?

An enhanced technique for recording loss over the lifetime of a product by adjusting the item's starting sales price by a discount factor.

An asset has a cost of $50,000, with a residual value of $10,000.

It has a life of 5 years and was purchased on January 1.

Then the asset’s fourth full year of depreciation expense will be

Annual depreciation = (cost – salvage value)/ useful life

Annual depreciation = (50000 – 10000) / 5 = $8,000

Year 1 Depreciation (for 10 months, from March to December) = $8,000 × 10/12 = $6,666.67.

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The interior angle of a regular polvgon is 9 times the size of its exterior angle
Work out how many sides the polygon has

Answers

Answer:   20 sides

==================================================

Work Shown:

x = exterior angle

9x = interior angle

interior + exterior = 180

9x+x = 180

10x = 180

x = 180/10

x = 18

n = number of sides

n = 360/x

n = 360/18

n = 20

There are 20 sides to the regular polygon.

Side notes:

The formula to determine n only works for regular polygons.A polygon with 20 sides is known as an icosagon.Any pair of adjacent interior and exterior angles are supplementary. They add to 180 degrees.

PLEASE HELP

Question 3 Alexa wants to use an indirect proof to prove that all rectangles are not squares. She first assumes that all rectangles are squares. Alexa then provides the following counterexample to disprove her assumption. She concludes that all rectangles must not be squares. Which statement best describes Alexa's indirect proof? Alexa's proof is incorrect. She followed the steps of an indirect proof in the wrong order. O Alexa's proof is incorrect. She made an error in her assumption. O Alexa's proof is correct and contains no errors. Alexa's proof is incorrect. She made an error in her counterexample. #​

Answers

Hello! Im Tutor Sezina

Answer:
Alexa proof is incorrect. She made an error in her assumption

Solution:
Her Assumptions was wrong. Not all rectangles are square

Alexa's proof is incorrect. She made an error in her counterexample.

What is rectangle?

"It is a quadrilateral whose all angles measure 90°, opposite sides are parallel and equal in length."

What is square?

"It is a parallelogram whose all sides are equal in length and all angles measure 90° "

What is parallelogram?

"It is quadrilateral whose opposite sides are parallel and equal in length."

What is counterexample?

"It is a special kind of example that disproves a statement. "

For given question,

Alexa wants to use an indirect proof to prove that all rectangles are not squares.

We know that, to prove a theorem indirectly, we assume the hypothesis is false, and then arrive at a contradiction. It follows the that the hypothesis must be true.

Alexa first assumes that all rectangles are squares.

Then she provides counterexample as shown in the given diagram.

The diagram represents the parallelogram not a rectangle.

This means  she made an error in her counterexample.

Therefore, Alexa's proof is incorrect. She made an error in her counterexample.

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James has available a 10% alcohol solution and a 60% alcohol solution find how many liters of each solution he shouldn’t mix to make 50 L of a 40% alcohol solution

Answers

He did take over 50l of alabocol and drank the rest so it got to 20

Answer:

20 L

Step-by-step explanation:

I am guessing that you meant should instead of shouldn't.

To solve this we can set the amount of 10% solution needed equal to x. This means that the 60% solution will be the remaining amount needed, so 50 L - x.

We can do 10%*x+60%*(50-x)=50*40%. Solving for x we get:

0.1*x+0.6*50-0.6*x=50*0.4

0.1*x+30-0.6*x=20

-0.5*x=-10

x=20

A triangle with side lengths a, b, and c is shown below.



Which statement about the side lengths must be true?

A a+b>c
B b+c C a+b D a+c

Answers

The statement about the sides must respect to represent a triangle is given as follows:

A. a + b > c.

What is the condition for 3 lengths to represent a triangle?

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

The smaller sides for the triangle are given as follows:

a and b.

Hence the statement is:

a + b > c.

(as the sum of the lengths of the smaller sides a and b must be greater than the length of the larger side, which is of c).

Hence the correct statement is given by option A.

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If a=(-1 -3 2 2 5 -1 -4 -5 -4) and b=(3 3 5 2 -5 2 -4 -1 1) find AB?

Answers

Answer:

what is the control ofprice floir or price celling then scplain one advantage an one dissvantage

The correct answer is -54

HELP!Which linear function represents the line given by the point-slope equation y - 2 = 4(x − 3)? Of(x) = 6x-1 Of(x) = 8x-6 Of(x) = 4x - 14 Ofix) = 4x - 10 Which linear function represents the line given by the point - slope equation y - 2 = 4 ( x − 3 ) ? Of ( x ) = 6x - 1 Of ( x ) = 8x - 6 Of ( x ) = 4x - 14 Ofix ) = 4x - 10​

Answers

[tex]y-2=4(x-3)\\\\y-2=4x-12\\\\y=4x-10\\\\\boxed{f(x)=4x-10}[/tex]

1/4​ ÷9=????????????????????????????????????????????????????????????????????????????????????????????????????????????

Answers

Answer:

1/36

Step-by-step explanation:

¼ / 9

9 as a fraction is 9/1

use KFC (keep flip change)

¼ x ⅑ = 1/36

[tex] \frac{1}{4} \div 9 \\ \\ first \: way \\ 0.25 \div 9 \\ 0.027 \\ \\ second \: way \: \\ \frac{1}{4} \times \frac{1}{9} \\ \frac{1}{36} \\ 0.027[/tex]

PLEASE GIVE BRAINLIEST

Pleas help me please i dont know what this question is ​

Answers

Answer:

A = 6

B = 1

C = 14

Step-by-step explanation:

A = 25 - 19 = 6

B = 6 - 5 = 1

C = 19 - 5 = 14

give brainliest please! <3

Make d the subject of the formula h=d/3+2

Answers

Answer: D=3(h-2)

Explanation —>

evaluate this exponential expression 5 • (3 + 6)^2 - 6^2

Answers

The answer of this expression is 369

We know that to solve a numerical expression, we will calculate with property base form.

When there are symbols in an expression, we first solve the numbers in order that are between:

Parentheses ( ) Brackets [ ] Braces { }

The math signs calculated first in order are;

Power - square root Multiplication - divisionAddition - subtraction

Given the expression, the resolution will be:

5 * ( 3 + 6 )² - 6²

5 * 9² - 6²

5 * 81 - 36

406 - 36

369

So, the value of this numeric expression is 369


Which represents a quadratic function?
f(x) = 2x³ + 2x² - 4
f(x) = -7x²-x+2
f(x)=-3x + 2
f(x) = 0x² + 3x-3

Answers

The second one is the answer

Option B is correct, the function f(x) = -7x² - x + 2  represents a quadratic function

What is quadratic equation?

A quadratic function is a polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to zero.

f(x) = -7x² - x + 2 is a quadratic function because it is of the required form.

Specifically, it has a quadratic term (-7x²), a linear term (-x), and a constant term (2).

The other three functions do not have a quadratic term and thus are not quadratic functions.

f(x) = 2x³ + 2x² - 4 is a cubic function because it has a cubic term (2x³).

f(x) = -3x + 2 is a linear function because it has only a linear term (-3x) and a constant term (2).

f(x) = 0x² + 3x - 3 is also a linear function because it has no quadratic term and only a linear term (3x) and a constant term (-3).

Hence, the function f(x) = -7x² - x + 2  represents a quadratic function

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find SP when profit loss is given​

Answers

Answer:

the formulas for profit and loss percentage are given below profit percentage p profit cost price into 100 loss percentage l is equal to loss cost price is into 100 SP

A city has a population of 1300. If the city’s population grows 30%, what is its new population?

Answers

Answer:

1699

Step-by-step explanation:

30/100*13000

Then add answer with 1300

eg 1300+399

I hope this explanation helps you.Also You can follow me.

Use the given sample data to find Q3.

49 52 52 52 74 67 55 55

Answers

The given sample data the Q3=61

We begin by ordering the data from smallest to largest.

Next, find the median of the data.

The data set has 8 values, so the two middle values are 52 and 55.

49 52 52 52 55 55 67 74

What is the formula for the median?

Median = (52 + 55) / 2

Median= 53.5

The third quartile (Q3) is the 25th percentile or the median of the upper half of the data.

To find the median of all the values that lie above 53.5.

Q3 = (55 + 67)/ 2

Therefore the Q3=61

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What are the coordinates of point P on the directed line
segment from A to B such that P is the length of the
line segment from A to B?

A. (-29/4 , -3/2)
B. (-13/4 , 1/2)
C. (-11/4 , -1/2)
D. (25/4 , -1/2)

Answers

The coordinate of the point P is (-11/4, -1/2) option (C) is correct because point (-29/4, -3/2) lies on the line.

What is a straight line?

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a line segment shown in the picture:

From the graph:

Point A( -5, -1) and B(4, 1)

The equation of the line passing through the points:

[tex]\rm (y -1 ) = \dfrac{1+1}{4+5}(x-4)[/tex]

9(y - 1) = 2(x - 4)

The above equation shows the straight-line passing through points A and B.

From the graph point (-11/4, -1/2) lies on the line the coordinate of the point P is (-29/4, -3/2)

Thus, the coordinate of the point P is (-11/4, -1/2) option (C) is correct because point (-29/4, -3/2) lies on the line.

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3x² - 2x + 1 = [?]
x=4

Answers

Answer:

3x²-2x+1=?

3(4²)-2(4)+1=?

3(16)-8+1=?

48-8+1=?

40+1=41

Sid makes a graph for estimating the y-value.He wants to compare it to the table before he turns it in. Do the table and the graph represent the same function?

Answers

Answer:

No

Step-by-step explanation:

The graph and the table do not show the same function as none of the y values on the graph correspond to the y values on the table.

A house’s was valued at 269,00. After several years, the value increased by 18%. By how much did it increase in dollars? What is the current house value

Answers

Answer:

31742

Step-by-step explanation:

[tex]26900 \times \frac{100 + 18}{100 } = 31742 [/tex]

A vehicle purchased for $20,700 depreciates at a constant rate of 4%. Determine the approximate value of the vehicle 15 years after purchase.

Answers

The approximate value of the vehicle 15 years after purchase is $11,221.19.

What is the approximate value of the vehicle 15 years after purchase?

Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.

Value of the car = purchase price x (1 - rate of decline)^number of years

20,700 x (1 - 0.04)^15 = $11,221.19

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