find the common difference in the outputs to help find the missing outputs in the table

Answer:

[tex]\large\boxed{Domain:\ x\in\left(0;\ \dfrac{1}{4}\right>\to0<x\leq\dfrac{1}{4}}[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{x-1},\ g(x)=\dfrac{1}{4x}\\\\f\bigg(g(x)\bigg)-\text{instead of x in the function equation f(x) put}\ \dfrac{1}{4x}:\\\\f\bigg(g(x)\bigg)=\sqrt{\dfrac{1}{4x}-1}=\sqrt{\dfrac{1}{4x}-\dfrac{4x}{4x}}=\sqrt{\dfrac{1-4x}{4x}}\\\\\text{The domain}\ D:\\\\\dfrac{1-4x}{4x}\geq0\ \wedge\ 4x\neq0\\\\\dfrac{1-4x}{4x}\geq0\iff(1-4x)(4x)\geq0\\\\1-4x=0\to4x=1\to x=\dfrac{1}{4}\\\\4x=0\to x=0\\(look\ at\ the\ picture)\\\\(1)\qquadx\in\left<0,\ \dfrac{1}{4}\right>\\\\\\4x\neq0\qquad\text{divide both sides by 4}\\\\(2)\qquad x\neq0[/tex]

[tex]\text{From}\ (1)\ \text{and}\ (2)\ \text{We have}\ x\in\left(0,\ \dfrac{1}{4}\right>[/tex]

Answer:

[tex]\frac{x}{y}[/tex] = [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4x-y}{3y}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2(4x - y) = 3y ← distribute left side

8x - 2y = 3y ( add 2y to both sides )

8x = 5y ( divide both sides by 8 )

x = [tex]\frac{5}{8}[/tex] y ( divide both sides by y )

[tex]\frac{x}{y}[/tex] = [tex]\frac{5}{8}[/tex]

Answer: The constant of proportinality is 150.

Step-by-step explanation:

The equation of inverse proportion has the following form:

[tex]y=\frac{k}{x}[/tex]

Where "k" is the constant of proportionality.

In this case, you can observe that R is inversely proportional to d², because it has the form of inverse proportion:

[tex]R=\frac{150}{d^2}[/tex]

Therefore, you can identify that the constant of proportionality "k" is:

[tex]k=150[/tex]

Answer: A. 150

Step-by-step explanation:

Answer:

m∠1 = 123°

Step-by-step explanation:

Since a straight line is always a supplementary angle, it equals 180°. To solve for the unknown angle, we can subtract the known angle from 180°.

180° - 57° = 123°

So m∠1 = 123°

180-57= 123 is the measurement for angle 2

All straight line is equal to 180

Answer:

No, she used the diameter instead of the radius measure.

Step-by-step explanation:

we know that

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=10/2=5\ units[/tex] ----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}\pi (5)^{3}[/tex]

[tex]V=\frac{500}{3}\pi\ units^{3}[/tex]

Answer:

No, she used the diameter instead of the radius measure.

Step-by-step explanation:

The formula for the sphere is:

[tex]\pi \frac{4}{3} r^{3}[/tex]

So she should have calculated the radius before inserting the values into the formula, the radius is half the diameter, so the radius of that sphere is 5.

In order to calculate it right you have to put 5 instead of the 10 so teh formula would look like this:

[tex]\pi \frac{4}{3} r^{3}[/tex]

[tex]\pi \frac{4}{3} 5^{3}[/tex]

[tex]\pi \frac{4}{3}(125)[/tex]

[tex]250\pi }[/tex]

The answer would be:

[tex]250\pi }[/tex]

Answer:

The corresponding point of (-3 , 6) is (-3 , 2)

Step-by-step explanation:

* Lets talk about some transformation to solve the problem

- A vertical stretching is the stretching of the graph away from

 the x-axis

- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

 by multiplying each of its y-coordinates by k.

- A vertical compression is the squeezing of the graph toward

 the x-axis.

- If 0 < k < 1 (a fraction), the graph is f(x) vertically compressed

 by multiplying each of its y-coordinates by k.

* Now lets solve the problem

∵ f(x) transformed to be 1/3 f(x)

∴ The graph of f(x) is stretched or compressed vertically

∵ k = 1/3

∴ 0 < k < 1

∴ The graph is compressed vertically

- The y-coordinate must be multiplying by k

∵ The y-coordinate of the point is 6

∵ 6 × 1/3 = 2

∴ The image of the point (-3 , 6) is (-3 , 2)

* The corresponding point of (-3 , 6) is (-3 , 2)

Answer:

A. 12 in^2

Step-by-step explanation:

Polygon ABCD is a kite. The area of a kite is equal to the product of the diagonals divided by 2.

One diagonal is segment AC.

AC = AE + CE = 2 + 2 = 4

The other diagonal is segment BD.

BD = BE + ED

BD = BE + 2BE

BD = 3BE

BD = 3(2) = 6

The diagonals measure 4 inches and 6 inches.

area = diagonal1 * diagonal2/2

area = 4 * 6 /2

area = 24/2

area = 12

Answer: A. 12 in^2

Answer:

6.40

Step-by-step explanation:

Answer:

168 cents or = $1.68

Step-by-step explanation:

  11 inches of wire cost 66 cents

28 inches of wire cost  x? cents

x = 28 * 66 / 11 = 168 cents or = $1.68

Answer

168 cents or = $1.68

Answer:

7500

Step-by-step explanation: 750 * 10

Answer:75 kilograms

You would have to divide 750 by 10 and you would get 75

Answer:

5(x + 1)(x - 1)

Step-by-step explanation:

Given

5x² - 5 ← factor out 5 from each term

= 5(x² - 1) ← x² - 1 is a difference of squares

= 5(x + 1)(x - 1)

The factors are 5, (x + 1) and (x - 1)

Final answer:

When the expression 5x² − 5 is completely factored, one of its factors is 5, and after applying the difference of squares, the fully factored form is 5(x + 1)(x − 1).

Explanation:

When the expression 5x2 − 5 is completely factored, what we're looking for is a common factor that can be taken out of both terms. In this case, both terms have a factor of 5, so we can factor out 5 from the expression, yielding:

5(x² − 1).

This expression can be further factored as the difference of squares, which is a special factoring rule that applies to expressions in the form of a² − b²:

5(x + 1)(x − 1).

So, one of the factors is 5, another factor is (x + 1), and the last factor is (x − 1).

0.13 times 15 is 1.95. Which means the coral reef grows 1.95 m in 15 weeks.

For this case we have reef coral grows 0.13 meters per week, if we want to indicate how much will have grown in 15 weeks we have the following rule three:

0.13 metrs ---------------> 1 week

x -------------------------------> 15 weeks

Where "x" is the number of meters reef coral grows in 15 weeks.

[tex]x = \frac {15 * 0.13} {1}\\x = 1.95 \ m[/tex]

Thus, in 15 weeks it grows 1.95 meters.

Answer:

[tex]1.95 \ m[/tex]

Answer:

AB = 21 and DE = 23

Step-by-step explanation:

Given 2 intersecting chords inside the circle then

The products of the measures of the parts of one chord is equal to the products of the measures of the parts of the other chord, that is

x(x + 13) = (x + 10)(x + 1) ← distribute parenthesis on both sides

x² + 13x = x² + 11x + 10 ← subtract x² + 11x from both sides

2x = 10 ( divide both sides by 2 )

x = 5

Hence

AB = x + 10 + x + 1 = 2x + 11 = (2 × 5) + 11 = 10 + 11 = 21

DE = x + x + 13 = 2x + 13 = (2 × 5) + 13 = 10 + 13 = 23

Answer:

16 and 82 degrees

Step-by-step explanation:

You can sum all of the angles together and solve for x.

(x - 1) + (5x - 3) + (5x - 3) = 180

11x - 7 = 180

11x = 187

x = 17

The first angle is 16 degrees. (17 - 1)

The other two angles are 82 degrees(5(17) - 3)

Answer:

16 and 82 degrees

Step-by-step explanation:

You can sum all of the angles together and solve for x.

(x - 1) + (5x - 3) + (5x - 3) = 180

11x - 7 = 180

11x = 187

x = 17

The first angle is 16 degrees. (17 - 1)

The other two angles are 82 degrees(5(17) - 3)

Answer:

4 (as in 25/4)

Step-by-step explanation:

Write and solve an equation of ratios:

 x        15

------ = ------

 10       24

Then 24x = 150, and x = 150/24 = 6.25.  This is equivalent to 25/4.

Answer:

x = 25/4

Step-by-step explanation:

If the rectangles are similar, the ratio of the side lengths have to be similar

10         24

------ = --------

x            15

Using cross products

10*15 = 24*x

150=24x

Divide each side by 24

150/24=24x/24

150/24=x

Divide the top and bottom by 6

25/4 = x

Answer:

if you are looking for a possible solution

x + 3y = 3

3 + 3(0) = 3

2x + y = 11

2(4) + 3 = 11

Step-by-step explanation:

In this the solution is y = -1 and x = 6.

Answer:

the answer will be the letter Y

Step-by-step explanation:

because the darker shaded side are at the bottom and one is at the top and don't forget about the two triangles

Answer:

2. B

3. C

4. B

5. D

Step-by-step explanation:

2) The sequence is multiplying by -2 each time. This means that it is geometric.

The next two terms would be:

[tex]32*-2=-64\\-64*-2=128\\128*-2=-256[/tex]

This means that the answer is B

3) The sequence is being multiplied by [tex]\frac{1}{3}[/tex] each time. This means that it is geometric.

The next 3 terms would be:

[tex]3*\frac{1}{3} =1 \\\\1*\frac{1}{3} =\frac{1}{3} \\\\\frac{1}{3} *\frac{1}{3} =\frac{1}{9}[/tex]

I am assuming that the answer is C and that you were unable to type the fractions.

4) We know that the common difference is 1.5, so that is the coefficient of our variable and the starting value is 15. This means that we can write an equation as follows

[tex]f(x)=1.5(x-1)+15[/tex]

Now we can find the first 4 terms

[tex]f(1)=15.0\\f(2)=16.5\\f(3)=18.0\\f(4)=19.5[/tex]

This would mean that the answer is B

5) We know that this is a geometric series, we know the common ratio, and we know the first term. This means we can write the equation as follows

[tex]f(x)=4.5(10)^{x-1}[/tex]

Now we can find the first 4 terms

[tex]f(1)=4.5\\f(2)=45\\f(3)=450\\f(4)=4500[/tex]

Unless you meant that the ratio was [tex]\frac{1}{10}[/tex], the answer is D, none of the above

Answer:

the answer is 3 i believe

Step-by-step explanation:

[tex]20 / 4[/tex]

ANSWER

(2,2)

EXPLANATION

Since f(x) and its inverse function are symmetric about the line y=x, if (a,b) lies on the graph of f, then (b,a) must lie on f inverse.

The point (2,2) lies on f and the same time on f inverse.

The solution is a point that satisfies both equations.

Hence the correct choice is:

(2,2)

Answer:

Did the test. Answer is (2,2).

Answer:

Linear   Quadratic   Exponential

Step-by-step explanation:

Answer:

First table models Linear, second quadratic and third one exponential functions.

Step-by-step explanation:

To find whether the given table models a linear function there should be a constant change in y values with the constant change in x values of the table.

We take the example of first table written as linear.

Here change in x values is

6 - 5 = 1

7 - 6 = 1

8 - 7 = 1

Similarly change in y values is

1 - 4 = -3

-2 - 1 = -3

-5 -(-2) = -3

There is a common difference in y values = -3

So the given table models linear function.

We take the second table.

For quadratic function with the constant change in x values, difference of difference in y values is constant.

Change in x - values

6 - 5 = 1

7 - 6 = 1

8 - 7 = 1

Difference in y values

1 - 0 = 1

4 - 1 = 3

9 - 4 = 5

Now difference in difference of y values

3 - 1  = 2

5 - 3 = 2

Here, difference in difference of y values is 2

So the given table models a quadratic equation.

Now we take the third table.

For exponential function in the form of [tex]f(x) = a(r)^{n}[/tex] there should be a common ratio in the terms of y values.

[tex]\frac{\text{Second term of y}}{\text{First term of y }}= \frac{2}{1}=2[/tex]

[tex]\frac{\text{Third term of y}}{\text{Second term of y }}= \frac{4}{2}=2[/tex]

So there is a common ratio of 2 in each term.

Therefore, the given table models exponential equation.

First table models Linear, second quadratic and third one exponential functions.

Answer: C. [tex]25.6\ cm^2 [/tex]

Step-by-step explanation:

Given: Circle M has a radius = 7.0 cm.

The shortest distance between P and Q on the  circle (arc length)= 7.3 cm.

Now, the central angle 'x' is given by :-

[tex]x=\dfrac{l}{r}\\\\\Rightarrow\ x=\dfrac{7.3}{7}=1.04285714286\ radian[/tex]

Now, the area of sector is given by :-

[tex]A=\dfrac{1}{2}r^2x\\\\\rightarrow\ A=\dfrac{1}{2}(7)^2(1.04285714286)\\\\\Rightarrow\ =25.55\approx25.6\ cm^2 [/tex]

Answer:

C.

Step-by-step explanation:

I did the test.

Answer:

Step-by-step explanation:

The question here is "how many pages does this book have?"

In 4 hrs, at 55 pages/hr, he reads 220 pages.

Adding the number of pages read (220) to the number of pages left to read (350) yields a total of 570 pages in this book.

Next time, please try to be more specific about what you want to find.  "functions formula" is very ambiguous and unhelpful.

The equation is [tex]\( y = 570 - 55x \)[/tex], where [tex]\( y \)[/tex] is pages left and [tex]\( x \)[/tex] is hours passed.

To complete the equation for the relationship between the number of pages left and the number of hours, we first need to determine the rate at which Naoya is reading the book.

Since he read 55 pages per hour, after 4 hours he would have read [tex]\( 55 \times 4 = 220 \)[/tex] pages.

Given that after 4 hours he still had 350 pages left to read, we can find out how many pages he had initially:

Initial number of pages = Total pages - Pages read

Initial number of pages = 350 pages + 220 pages

Initial number of pages = 570 pages

Now, let's use the formula for the relationship between the number of pages left and the number of hours:

[tex]\[ y = 570 - 55x \][/tex]

Where:

- [tex]\( y \)[/tex] represents the number of pages left to read after [tex]\( x \)[/tex] hours.

- [tex]\( x \)[/tex] represents the number of hours.

So, the complete equation for the relationship is:

[tex]\[ y = 570 - 55x \][/tex]

The complete question is here:

Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read.

Let y represent the number of pages left to read after x hours.

Complete the equation for the relationship between the number of pages left and number of hours.

y=

Answer:

M equals -4/3 or -1 and 1/3

Answer:

M = -4/3

Step-by-step explanation:

Begin by cross multiplying

-2*-7 = 6(-3 - 4M)            Combine the left

14 = - 18 - 24M                 Add 18 to both sides.

14 + 18 = - 18+18 - 24M    Combine

32 = -24M                        Divide by - 24

32/-24 = -24/-24 * M

- 4/3 = M

To calculate the finance charge and new balance, first find the finance charge with the formula: Previous balance x Annual rate / 12 months. Add this to the previous balance and any new purchases, then subtract any payments or credits. The resulting figure will be the new balance. In this example, the finance charge is $2.32 and the new balance is $223.26.

In this financial calculation, the annual rate of 14% is used to calculate the finance charge on the previous balance of $199.19. The formula to calculate the finance charge is: Previous balance x Annual rate / 12 months. Moving forward, the finance charge will be added to the previous balance and any new purchases, then any payments or credits will be subtracted from this total to find the new balance.

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The finance charge is $75.75.

To calculate the finance charge and new balance using the previous balance method, you can follow these steps:

In this case, the finance charge would be $27.89, calculated as $199.19 * 0.14.

The new balance would be $321.84, calculated as ($199.19 + $97.50) - $75.75.

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ANSWER

The area of the triangle is 48.6 square feet to the nearest tenth.

EXPLANATION

The area of the triangle is calculated using the formula

[tex]Area= \frac{1}{2} bc \sin(A) [/tex]

where A=94° is the included angle, b=7.5 inches and c=13 inches.

We substitute the values into the formula to obtain:

[tex]Area= \frac{1}{2} \times 7.5 \times 13 \sin(94 \degree) [/tex]

Area=48.6 ft² to the nearest tenth.

Answer:

x, log7(x)

1, 0 (B)

7, 1 (D)

49, 2 (E)

1/7, -1 (G)

1/49, -2 (H)

Step-by-step explanation:

Powers of 7 are ...

7^-2 = 1/7^2 = 1/49

7^-1 = 1/7^1 = 1/7

7^0 = 1

7^1 = 7

7^2 = 49

The log (base 7) of the number on the right is the exponent on the left. That is ...

log7(7) = log7(7^1) = 1

log7(1/49) = log7(7^-2) = -2

Answer:

-2[tex]y^{4}[/tex] - 5y² + 42

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

y²(- 2y² + 7) + 6(- 2y² + 7) ← distribute both parenthesis

= - 2[tex]y^{4}[/tex] + 7y² - 12y² + 42 ← collect like terms

= - 2[tex]y^{4}[/tex] - 5y² + 42 ← in standard form

[ standard form means the first term has the largest exponent of the variable, followed by other terms in descending powers of the variable. ]

Answer:

2625080

Step-by-step explanation:

just multiply by 365

Answer: 2,625,080

Explanation: 1 day = 7192, 365 days x 7192 = 2,625,080

Answer:

[tex]\sin (\frac{\pi}{12})=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]

Step-by-step explanation:

We want to find the exact value of

[tex]\sin \frac{\pi}{12}[/tex]

We rewrite the given expression to obtain:

[tex]\sin \frac{\pi}{12}=\sin (\frac{\pi}{3}-\frac{\pi}{4})[/tex]

We use the identity:

[tex]\sin (A-B)=\sin A \cos B-\sin B \cos A[/tex]

[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\sin \frac{\pi}{3} \cos \frac{\pi}{4}-\sin \frac{\pi}{4} \cos \frac{\pi}{3}[/tex]

[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} \times \frac{1}{2}[/tex]

[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]

The exact value of sin(π/12) is ±√(2 - √3)/2 by using half-angle formula

To find the exact value of sin(π/12), we can use the half-angle formula for sine:

sin(x/2) = ±√[(1 - cos(x))/2]

In this case, x = π/6.

Therefore, we can use the half-angle formula with x = pi/6 to find the exact value of sin(π/12).

sin(pi/12) = ±√[(1 - cos(π/6))/2]

Let's calculate the value step by step:

cos(π/6) = √3/2

sin(π/12) = ±√[(1 - √3/2)/2]

To simplify further, let's rationalize the denominator:

sin(π/12) = ±√[(2 - √3)/4]

sin(π/12) = ±√(2 - √3)/2

Therefore, the exact value of sin(π/12) is ±√(2 - √3)/2.

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