what does "cross the line, change the sign" means.

Answer:

[tex]g^{-1} (7)=5[/tex]

Step-by-step explanation:

We are asked to find [tex]g^{-1} (7)[/tex].

One thing to remember about the inverse of a function is what exactly an inverse means.

If we have the ordered pair [tex](a,b)[/tex] of function [tex]g[/tex], then the corresponding ordered pair of [tex]g^{-1}[/tex] would be [tex](b,a)[/tex].

As we are asked to find [tex](7,b)[/tex] of  [tex]g^{-1}[/tex], we can instead find [tex](b,7)[/tex] of [tex]g[/tex].

This means that we are looking for where [tex]g(b)=7[/tex].

From the graph, we can see that for this to be true, [tex]b=5[/tex]

This means that [tex]g^{-1} (7)=5[/tex]

The value of g^-1(7) is 5.

What is the value of g^-1(7)?

A function f from a set X to a set Y is said to be invertible if for every y in Y and x in X, there exists a function g from Y to X such that f(g(y)) = y and g(f(x)) = x. function is invertible only if each input has a unique output. That is, each output is paired with exactly one input. That way, when the mapping is reversed, it will still be a function.

Given that:

One thing to remember about the inverse of a function is what exactly an inverse means.

If we have the ordered pair (a, b) of function g , then the corresponding ordered pair of g^-1 would be (b, a).

As we are asked to find (7,b)  of  g^-1, we can instead find (b, 7) of g .

This means that we are looking for where  g(b)=7.

From the graph, we can see that for this to be true, b=5.

So, the value of g^-1(7) is 5.

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Answer:

Consider the ratio of corresponding sides, you would find out:

Option A is correct

Step-by-step explanation:

Check figure 1 and figure 2: 8/12 = 16/24 = 10/15 = 1/3

=> they are similar.

Check figure 2 and figure 3 (or fig. 1 and fig. 3): Not satisfied.

Hope this helps!

:)

Answer:

A

Step-by-step explanation:

1 and 2

8/12 = 16/24 = 10/15

2/3 = 2/3 = 2/3

Same ratio, so similar

2 and 3

12/28 = 24/36 = 15/30

3/7 = 2/3 = 1/2

Ratio not constant, so not similar

Answer:

C=62 maybe

Step-by-step explanation:

3x=x+20

-x    -x

2x=20

divide by 2

x=10

2*10=20+38=58

10+20=30

3*10=30

30+30=60+58=118

180-118=62

Answer:

d: 1/2

Step-by-step explanation:

Answer:D. 1/2 c

Step-by-step explanation:A recipe is 100% and 3/4 is 75%. 75% of 2/3 is 1/2.

Answer:

13. 20°

14. 15°

15. 50°

Step-by-step explanation:

Please see the attached pictures for full solution.

For negative angles, the arrow turns clockwise.

Answer:

  13. 20°

  14. 15°

  15. 50°

Step-by-step explanation:

From a mathematical point of view, the reference angle is the smaller of α and (180°-α), where α = θ mod 180°.

That is, add or subtract multiples of 180° until the result is in the range 0–180°. Then choose the smaller of the angle and its supplement.

It is convenient to let a spreadsheet calculate these when you have a bunch of them.

__

From a geometrical point of view, the reference angle is the positive angle between the terminal ray and the nearest x-axis.

__

For the angles here, the reference angles (in degrees) are shown in the attachment.

Answer:

x stands for the number of cars washed with the supplies.

Step-by-step explanation:

Given;

Profit equation; y = 4x - 45

Price of supplies = $45

Amount received per car wahed = $4

From the equation given, we can notice that the higher the value of x the higher the profit generated.

Since, for washing a car brings $4, 2 car is $8 and so on... So the value of x is the number of cars washed with the supplies.

x stands for the number of cars washed with the supplies.

For example, if we wash 15 cars. x = 15

y = 4(15) - 45 = 60 - 45

y = $15

Answer:

Y = $2x + 8

Step-by-step explanation:

Variable cost per line = $2.00

For 3 lines, the Variable cost = $2 x 3 = $6

Total cost for 3 lines = $14.00

Fixed Charges = $14 - $6 = $8

Using the formula, total cost, Y = $2x + $8 = $14

Where x = number of lines needed.

Therefore, total cost, Y = ($2 x 3) + $8 = $14

Answer:

[tex] \frac{1}{2} {cm}^{3} [/tex]

Step-by-step explanation:

[tex]v = whl \\ = \frac{1}{4} \times 2 \times 1 \\ = \frac{2}{4} \\ = \frac{1}{2} {cm}^{3} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

The mathematical operation which took place between the first step and the second step from the derivation of the quadratic formula is: B. completing the square.

A quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula can be derived as follows:

x² + b/ax +c/a = 0

x² + b/ax  = -c/a

x² + b/ax + (b/2a)² = - c/a + (b/2a)² [completing the square]

(x + b/2a)² = b²/4a² - c/a

x + b/2a = √(b²/4a² - c/a)

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

In conclusion, the step which is shown in the image above for the derivation of the quadratic formula was derived by using completing the square method.

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Answer:   THE CORRECT ANSWER IS    Factoring a perfect square trinomial

Step-by-step explanation:

Answer:

Step-by-step explanation

The two other forms are written form and expanded from. That first blank is for written from and the answer is four and eight-hundred twenty-sixth thousandths. For the other ones i think for the first blank it is 4 then 8 then 20 and then 6.

Answer:

a

Step-by-step explanation:

its a because i looked it up and it said a

Answer:

None of the options represent the right answer. (Real answer: [tex]y = 24\cdot x^{2}[/tex])

Step-by-step explanation:

The parabola shown above is vertical and least distance between focus and directrix is equal to [tex]2\cdot p[/tex]. Then, the value of p is determined with the help of the Pythagorean Theorem:

[tex]2\cdot p = \sqrt{(0-0)^{2}+[6-(-6)]^{2}}[/tex]

[tex]2\cdot p = 12[/tex]

[tex]p = 6[/tex]

The general equation of a parabola centered at (h,k) is:

[tex]y-k = 4\cdot p \cdot (x-h)^{2}[/tex]

It is evident that parabola is centered at origin. Hence, the equation of the parabola in standard form is:

[tex]y = 24\cdot x^{2}[/tex]

None of the options represent the right answer.

Answer:

  y equals 1 divided by 24 x squared  

Step-by-step explanation:

Just took the test

Distance formula: d = √(x2-x1)^2 + (y2-y1)^2

d = √(5-2)^2 + (10-6)^2

d = √3^2 + 4^2

d = √9 + 16

d = √25

d = 5

The distance is 5 units.

Best of Luck!

Answer:

344.2m/s

Step-by-step explanation:

The parameters given are:

Distance=895meter

Time=2.6seconds

Therefore the speed of sound is:

Speed of sound= distance/time taken

= 895/2.6

=344.23

=344.2m/s ( to the nearest tenth)

Answer:

d 344.2 meters per second

Step-by-step explanation:

edge 2021

Answer:

x>-1.25

Step-by-step explanation:

3(5x-10)<30x

15x-20<30x

-20<15x

-20/15<x

-1.25<x

x>-1.25

Step-by-step explanation:

Step 1:  Distribute

[tex]3(5x - 10) < 30x[/tex]

[tex](3 * 5x) + (3 * -10) < 30x[/tex]

[tex]15x - 30 < 30x[/tex]

Step 2:  Subtract 15x from both sides

[tex]15x - 15x - 30 < 30x - 15x[/tex]

[tex]-30 < 15x[/tex]

Step 3:  Divide both sides by 15

[tex]-30 / 15 < 15x / 15[/tex]

[tex]-2 < x[/tex]

Answer:  [tex]x > -2[/tex]

Answer:l think it's 6

Step-by-step explanation:

You 1/2×4×3

=6

Answer:

[tex]76.0m^2[/tex] (you have to have the .0 since it says to round to the nearest tenth)

Step-by-step explanation:

The formula for the surface area of a rectangular prism is:

[tex]A=2(wl+hl+hw)[/tex]

So just plug in the values.

Height= 4

Width=2

Length=5

[tex]A=2((2)(5)+(4)(5)+(4)(2))\\A=2(10+20+8)\\A=2(38)\\A=76m^2[/tex]

Answer:

12 pi

Step-by-step explanation:

First find the area of  full circle

A = pi r^2  where r is the radius

A = pi (4)^2

A = 16 pi

This is 3/4 of a circle so multiply the area by the fraction of a circle

3/4*16pi = 12 pi

Answer:

[tex]12\pi[/tex] or 37.70 (rounded)

Step-by-step explanation:

To work this out you would first need to work out the area of this circle. You can do this by multiplying pi by the radius of 4 squared, this gives you 50.27 or [tex]16\pi[/tex].

Then in order to work out the area of this part of the circle you would have to divide the area 50.27 or 16pi by 4, this gives you 4 pi or 12.57. This is because the angle of the missing part is 90 degrees or a right angle, and because 360 divided by 4 is 90 this meant that the question is asking to work out [tex]\frac{3}{4}[/tex]of a circle and so by dividing it by 4 we are working out the area of one quadrant.

Then the final step is to multiply 4 pi or 12.57 by 3, this gives you 12 [tex]\pi[/tex] and 37.70.

1) Multiply pi by 4 squared.

[tex]\pi*4^{2} =16\pi or 50.27[/tex]

2) Divide 50.27 by 4.

[tex]16\pi or 50.27 /4=4\pi or 12.57[/tex]

3) Multiply 12.57 by 3.

[tex]12.57*3=12\pi or 37.70[/tex]

Answer:

[tex]9\pi[/tex], which is approximately [tex]28.26[/tex].

Step-by-step explanation:

Consider two sectors in the same circle. The area of the two sectors is proportional to their central angles. In other words, if the central angle is [tex]\theta_1[/tex] for the first sector in this circle, and [tex]\theta_2[/tex] for the second, then:

[tex]\displaystyle \frac{\text{Area of Sector 1}}{\text{Area of Sector 2}} = \frac{\theta_1}{\theta_2}[/tex].

In this question, think about the whole circle as a sector. The central angle of this "sector" would be [tex]360^\circ[/tex] (a full circle.) Compare the area of this circle to that of the [tex]60^\circ[/tex]-sector in this circle:

[tex]\displaystyle \frac{\text{Area of Circle}}{\text{Area of $60^\circ$-Sector}} = \frac{360^\circ}{60^\circ} = 6[/tex].

In other words, the area of this circle is six times that of the [tex]60^\circ[/tex]-sector in it.

The area of that [tex]60^\circ[/tex]-sector is [tex]\displaystyle \frac{3}{2}\pi[/tex]. Therefore, the area of this full circle will be [tex]\displaystyle 6 \times \frac{3}{2}\pi = 9\pi \approx 28.26[/tex].

Answer:

The answer is C.

(6 times 6 times 6 times 6 times) times (6 times 6 times 6)

(6 * 6 * 6 * 6) * (6 * 6 * 6)

(6 × 6 × 6 × 6) × (6 × 6 ×6)

(6^4) × (6^3)

Answer:

All of the above

Step-by-step explanation:

dy/dt = y/3 (18 − y)

0 = y/3 (18 − y)

y = 0 or 18

d²y/dt² = y/3 (-dy/dt) + (1/3 dy/dt) (18 − y)

d²y/dt² = dy/dt (-y/3 + 6 − y/3)

d²y/dt² = dy/dt (6 − 2y/3)

d²y/dt² = y/3 (18 − y) (6 − 2y/3)

0 = y/3 (18 − y) (6 − 2y/3)

y = 0, 9, 18

y" = 0 at y = 9 and changes signs from + to -, so y' is a maximum at y = 9.

y' and y" = 0 at y = 0 and y = 18, so those are both asymptotes / limiting values.

Answer:

169.6

Step-by-step explanation:

We can use trig to find the missing side (sin specifically).  sin(x)=opposite/hypotenuse.  where x is the angle.  VWX is 20 degrees.  The side opposite to that angle is VX or 58.  We dont know the hypotenuse.  If we were to substitute values into sin(x)=opposite/hypotenuse, we would get sin(20)=58/hypotenuse.  sin(20) in the calculator is 0.342020143...  so we can rewrite the equation as 0.342020143=58/hypotenuse.  Lets call the hypotenuse h.  If we multiply h on both sides, we can try to find what h is equal to.  0.342020143h=58.  Now we can divide 0.342020143 on both sides to isolate h.  h=169.58... or if we round it, we get 169.6

Answer:

it will gemetry and get 15

Answer:

Step-by-step explanation:

The correct answer by using divisibility rules is:

a) Exactly one of these statements is false.

Statement 1: If two numbers are co-primes, at least one of them must be prime.

This statement is true. Two numbers are considered co-prime if their greatest common divisor (GCD) is 1. If both numbers are not prime, it means they have factors other than 1 and themselves. In that case, their GCD would be greater than 1, contradicting the definition of co-prime numbers. Therefore, at least one of the two co-prime numbers must be prime.

Statement 2: If a number exactly divides two numbers, then it must also divide their sum.

This statement is false. Just because a  number divides two other numbers, it does not necessarily mean that it will divide their sum. For example, consider the numbers 6, 8, and 14. 6 and 8 are both divisible by 2, but their sum, 14, is not divisible by 2.

Based on the analysis above, exactly one of these statements is false.

Therefore, the correct answer by using divisibility rules is:

a) Exactly one of these statements is false.

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Answer:

Irrational numbers

Step-by-step explanation:

To find out which subsets of real numbers [tex]\sqrt{42}[/tex] is in, we can look at what it does not fall into.

Natural numbers- These include 1, 2, 3..., which means that [tex]\sqrt{42}[/tex] cannot be a part of it

Whole numbers - These include 0, 1, 2 ..., which means that [tex]\sqrt{42}[/tex] cannot be a part of it

Integers- These include -2, -1, 0, 1, 2..., which means that [tex]\sqrt{42}[/tex] cannot be a part of it.

Rational - These include all the previous as well as anything that can be written as a fraction, which means that [tex]\sqrt{42}[/tex] cannot be a part of it

Irrational numbers - This includes anything that continues on endlessly, which this does when converted to a decimal, which means that this is the subset of real numbers that [tex]\sqrt{42}[/tex] belongs.

Answer:

21.24

Step-by-step explanation:

Edge 2020

The required arc length of the circle is 9.42 inches

The arc is a portion of the circumference of a circle.

Area of a sector of a circle = θ/360 × πr², where r is the radius of the circle and θ is the central angle.

To calculate the length of the arc, we use the formula:

S = 2πr (θ/360°)

where,

S = arc length

r = radius of the circle

θ = central angle

As per the given question, we have

r =  9 inches, and θ = 60°

Substitute the values in the above equation, we get:

S = 2π(9) (60°/360°)

S = 2π(9)/60°

S ≈9.42

Hence, the arc length of the circle is 9.42 inches.

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The question seems to be incomplete, here is the complete question:

Given a radius of 9 inches intercepted by the central angle of 60°. Estimate the length of arc 'S' to the nearest hundredth.

The probability is 1/36.

The outcome of the first roll does not affect the outcome of the second roll, and so the probability of rolling any number on a fair six-sided die remains 1/6 for both rolls. This means that the probability of rolling a 5 the first time and a 6 the second time are both 1/6, and to find the probability of 2 things happening we have to multiply, so we end up with 1/6 × 1/6 = 1/36

I hope this helps! Let me know if you have any questions :)

Answer:

1). [tex]f^{-1}(x)[/tex] = (200 - [tex]\frac{x}{0.85}[/tex])

2). Inverse function represents the age of the client and 'x' represents the maximum heart rate of the client.

Step-by-step explanation:

Function representing the maximum heart rate is,

f(x) = 0.85(220 - x)

Here x = age of the client

Equation form of the function will be,

y = 0.85(220 - x)

To get the inverse of the given function, replace 'x' by 'y' and 'y' by 'x' and solve for y.

x = 0.85(220 - y)

220 - y = [tex]\frac{x}{0.85}[/tex]

y = 220 - [tex]\frac{x}{0.85}[/tex]

Now convert this equation into a function.

[tex]f^{-1}(x)[/tex] = (200 - [tex]\frac{x}{0.85}[/tex])

Here inverse function represents the age of the client and 'x' represents the maximum heart rate of the client.

ANSWER: D.180

EXPLANATION:  A straight angle is 180 degrees

A straight angle changes the direction to point the opposite way. Sometimes people say "You did a complete 180 on that!" ... meaning you completely changed your mind, idea or direction.

Answer:

hope this help

Step-by-step explanation:

10x + 4 = 10x + 16 -12 = 10x + 4

infinite solution of x ( for x is real number)