Select all the expressions that are equivalent to 4 ^ - 3

Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.

It is simple to establish whether the inverse of a function is also a function using the horizontal line test.

Because it fails the vertical line test, a function's inverse might not actually be a function.

Graph of the line

f\left( x \right) = - x + 2

f(x)=−x+2.

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The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.

To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:

0 = -b * log(base a)(3 - h) + k

Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:

2 = -b * log(base a)(0 - h) + k

Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.

In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.

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Answer:

10% chance if the probability is 1/10

Answer:

y-1 = -⅗(x-5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 cos(A+45)cos (B-45)

=2[cos A cos 45-sin A sin 45][cos B cos 45+sin B sin 45]

=2[cos A ×1/√2-sin A ×1/√2][cos B×1/√2+sin B×1/√2]

=2[1/√2(cos A-sin A)][1/√2(cos B-sin B]

=2×1/√2×1/√2 (cos A-sin A)(cos B+sin B)

=cosA cos B+cos A sin B-sin A cos B-sin A sin B

=cos A cos B-sin A sin B-(sin A cos B-cos A sin B)

=cos (A+B)-sin (A-B)

i think there should be A in place of B.

then

=cos (A+A)-sin (A-A)

=cos 2A-sin 0

=cos 2A

as sin 0=0

Using cosine rule, angle x In the triangle is

The angles are found first using cosine rule by the formula

cos A = (b² + c² - a²) ÷ 2bc

Solving for the angle x

substituting the values

cos x = (7² + 5² - 3²) ÷ 2 * 7 * 5

cos x = (65) ÷ 70

x = arc cos ( 0.9286 )

x = 21.79 degrees

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

5

Step-by-step explanation:

Answer:

5 centimeters

Step-by-step explanation:

You have to look at where it says 2 inches, and follow the line up to where the red stops and see how many centimeters it crosses

Answer:

The type of ∠3 and ∠11 are corresponding angles

The transversal is line B

lines C and D are parallel

Step-by-step explanation:

From the given figure

∵ Lines C and D are intersected by line B

∴ Line B is the transversal of lines C and D

∵ ∠3 and ∠11 In the same side of line B

∵ ∠3 is above line C and ∠11 is above line D

∴ ∠3 and ∠11 are in the corresponding position

∴ ∠3 and ∠11 are corresponding angles

∴ The type of ∠3 and ∠11 are corresponding angles

∴ The transversal is line B

∵ ∠3 ≅ ∠11

∵ ∠3 and ∠11 in the corresponding position

∵ ∠3 and ∠11 between lines C and D

∴ lines C and D are parallel.

Answer:

4. 12 in.

5. 3 in.

6. 3in per hour

7. slope would=3

Step-by-step explanation:

Answer:

|3x+7|>2 =5/3 x yang memenuhi

Answer:

AB= 12                      AB=18

Step-by-step explanation:

sin(30)=AB/AC

=> AB=Sin(30)*AC

sin(30)=0.5

=>AB=0.5*24=15

sin(30)=AB/AC

=> AB=Sin(30)*AC

sin(30)=0.5

=>AB=0.5*36=18

Answer:

part a: AB = 12cm

part b: AB = 18cm

Step-by-step explanation:

sin(angle)=OPP/HYP

sine of an angle is a ratio of two sides of a right triangle. For sine, the ratio is the opposite side over the hypotenuse. In part a the marked angle is 30° and AB is the opposite side. The hypotenuse is given, 24cm.

So the sin 30°

= opp/hyp

= AB / 24

also given is the fact that sin30°=.5

Substitute that into our equation also.

sin30° = AB/24

.5 = AB/24

multiply both sides by 24.

.5×24 = AB

12 = AB

AB is 12 cm.

Part b is an identical calculation except the hypotenuse is 36cm.

sin30° = AB/36

.5 = AB/36

.5×36 = AB

18 = AB

AB is 18cm.

They may be trying to lead you to discover some shortcut patterns in a 30°-60°-90° triangle. That is that the short leg is HALF the hypotenuse OR the hypotenuse is double the short leg.

Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.

What is percentage ?

Percentage can be defined as product of ratio of given value, total value and hundred.

To find out how much Leo Gandolfi saves by paying off the loan early, we need to first calculate how much interest he would pay if he were to continue making payments for the full 6-month term of the loan.

The total interest on the loan for the full 6 months can be calculated as:

Total interest = Total payments - Loan amount

We know the loan amount is $1,800, and the monthly payment is $310.50, so the total payments for the full 6 months would be:

Total payments = Monthly payment x Number of payments

Total payments = $310.50 x 6 = $1,863

Therefore, the total interest paid over the 6-month term of the loan would be:

Total interest = $1,863 - $1,800 = $63

Now, we need to calculate how much interest Leo Gandolfi would pay if he were to pay off the loan after making 4 payments.

The remaining balance on the loan after 4 payments is $612.34, so if Leo were to make one more payment, the remaining balance would be:

Remaining balance = $612.34 - $310.50 = $301.84

To calculate the interest paid on this remaining balance, we need to calculate the interest for one month:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 12% / 12 = 1%

Monthly interest = Monthly interest rate x Remaining balance

Monthly interest = 1% x $301.84 = $3.02

Therefore, if Leo were to make one more payment, he would pay $310.50, which includes both the principal and the interest. So, the amount of interest he would pay if he were to pay off the loan after 4 payments is:

Interest paid = Total payment - Remaining balance

Interest paid = $310.50 - $301.84 = $8.66

So, by paying off the loan early, Leo Gandolfi would save:

Savings = Total interest - Interest paid

Savings = $63 - $8.66 = $54.34

Therefore, Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.

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Answer:

------------------------------

Let the equation be in the form:

Then its solution is:

Add up the two equations:

Find b:

The equation is:

Answer:

6e+7

Step-by-step explanation:

divide the volume value by 1e+6

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

c can stand for any number

Step-by-step explanation:

C stands for any number because both sides of the equation have the same math problem so c is equal to any natural number.

HOPE THIS HELPED

Answer:

equation has infinite solutions

Step-by-step explanation:

Given

2c + 3 = 2c + 3

Since the terms on both sides are the same, then any real value of x is a solution to the equation, that is

The equation has infinite solutions

Hey there!

Here is a graph of the points:

A scatterplot is a graph, but the points won't be able to connect in a straight line, and they have no relation.

A line of best fit is a line that goes evenly through the points, or as best as it could.

Answer:

Step-by-step explanation:

A: -1/3x+1

B: 1/4x -2

Answer:

Given Below.

question (a)

coordinates:

(0,1), (3,0)

slope:

\(\frac{0-1}{3-0}\)

\(-\frac{1}{3}\)

equation:

\(y - y1 = m(x - x1)\)

\(y - 1 = -\frac{1}{3} (x-0)\)

\(y = -\frac{1}{3}x+1\)

question (b)

coordinates:

(0,-2) , (4, -1 )

slope:

\(\frac{-1--2}{4-0}\)

\(\frac{1}{4}\)

equation:

\(y - y1 = m(x - x1)\)

\(y + 1 = \frac{1}{4} (x - 4)\)

\(y=\frac{1}{4} x -1-1\)

\(y=\frac{1}{4} x -2\)

An applicant needs 84.04 minutes to finish the test in order for 97 percent of them to pass.

An aptitude test is required of job candidates. Let's assume that the test's completion time has a mean of 69 minutes and a standard deviation of 8 minutes.

To get how much time an applicant should be given so that 97 percent of them will be able to complete the test.

Mean (μ) = 69

standard deviation (σ) =8

Hence, due to population standard deviation (σ) is known to use the normal distribution.

x_ Norm (μ,σ)

x_ Norm (69,8)

Therefore, x_ random variable that represents the time of applicant;

P(X<x) = 0.97

Corresponding to the left tail area of 0.97 lies in the z-table of z row of 1.8 and column 0.08.

P(z < 1.88) = 0.97

z < 1.88

(X - μ)/σ < 1.88

X < 1.88 (8) + 69

X < 84.04

The time taken by an applicant so that 97 percent of them will be able to complete the test is 84.04 minutes.

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Answer:

\(n=-\frac{16}{3} (or) -5\frac{1}{3}\) (or) -5.3 repeating

Answer: D

Step-by-step explanation:

It’s really obvious just circle D

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer:

y doesn't have multiple awnser, y = 47.5

Step-by-step explanation:

(y + 7) + (3y - 17) = 180

=> 4y = 190

=> y = 47.5

Answer:

47.5

Step-by-step explanation:

If r is parallel to s, then by the Alternate Exterior Angles Theorem:

x+56 = 3y-17. Additionally, (x+56)° is supplementary to (y+7)° because they make up a line.

So: 180 = x+56 + y+7 or

180-y-7 = x+56

Substitute into x+56 = 3y-17 so that 180-y-7 = 3y-17.

Solve for y to get y = 47.5

Salut/Hello!

Step-by-step explanation:
/ - fraction line
Ben's probability to pass is 0,8
to make it simpler for you to understand I'm going to use percentages.

We can transform 0,8 in a fraction so 8/10 and amplify it by 10 so 80/100
so the percentage showing that Ben will pass is 80% to find out the percentage that Ben will fail we subtract 80% from 100% which results in 20%

so the probability that Ben will fail is 0,2
and Tom's probability to fail is 0,3


To find out the answer to b) we need to understand how we calculate it.

Take as an example a dice. A dice has 6 faces and you need 1 side to get out of jail (let's say you need a 6). Your probability to get that side is 1/6

But what if you have two dice and you need both to be 6? Well in that case it'll be 1/6 x 1/6 which is 1/36

So, to find out the probability of both passing, we have to do 8/10 x 7/10 which is 56/100 and it's equal to 0,56. And you might wonder why the probability both will pass seems bigger than their probability to pass. Well 0,8 actually can mean 0,800000... and so on but it's easier to just let it as 0,8

For c) the probability that only one will pass is: 0.12

We first need to find the probability both fail
100% - 56% = 44%

and we subtract 44% from 56% which is equal to 12% or 0.12


I hope it was helpful! :]