Find the inverse of the function. y = 2^x2 –4

The solution of the system of equations is (5, 2).

Here we want to solve the system of equations:

-3x + y = -13

4x - 2y = 16

By the elimination method.

If we take the first equation and we multiply it by 2, we will get:

2*(-3x + y) = 2*-13

-6x + 2y = -26

Now we can add the two equations to get:

(-6x + 2y) + (4x - 2y) = -26 + 16

-2x = -10

x = -10/-2

x = 5

And the value of y is given by evaluating one of the equations in x = 5, using the first one.

-3*5 + y = -13

-15 + y = -13

y = 15 - 13 = 2

The solution is (5, 2)

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Answer:

Step-by-step explanation:

4 x 6= 24

24+2=26

The value of x in the triangle is 6√5

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

The triangle

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

x/20 = 9/x

Cross multiply the equation

so, we have the following representation

x^2 = 180

TAke the square root of hoth sides

This gives

x = 6√5

Hence, the solution of x is  6√5

Read more about triangles at

https://brainly.com/question/14285697

#SPJ1

The inequality represented by the graph is given as follows:

y < 4x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -2, hence the intercept b is given as follows:

b = -2.

When x increases by 1, y increases by 4, hence the slope m is given as follows:

m = 4.

The values to the left of the line are shaded, hence the inequality represented by the graph is given as follows:

y < 4x - 2.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Vertices :

Edges:

Step-by-step explanation: A vertex is a corner on shape. And edge is a line segment between faces. A face is singular flat surface.

Answer:

Based on these observations, the inequality represented by the graph is y > mx + b, where m is a positive number and b is a negative number.

Step-by-step explanation:

The graph represents a linear function. To find the inequality, we can find the equation of the line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

From the graph, it can be seen that the slope of the line is positive, which means that as x increases, y also increases. Also, the y-intercept is negative, which means that the line crosses the y-axis at a negative value.

Based on these observations, the inequality represented by the graph is y > mx + b, where m is a positive number and b is a negative number.

Note that the exact values of m and b can be found by using two points on the line and solving for the slope and y-intercept using the formula for a line.

The probability that the player takes exactly 5 shots before missing one is approximately 0.0539, or 5.39%.

The probability of missing a free throw shot is 0.12, and the probability of making a free throw shot is 0.88 (which is 1 - 0.12).

To find the probability that the player takes exactly 5 shots before missing one, we can use the geometric distribution, which models the number of independent and identical Bernoulli trials needed to get a success.

In this case, a "success" is missing a free throw shot, and the "trials" are the number of shots the player takes before missing one. The probability of success (missing a shot) is p = 0.12, and the probability of failure (making a shot) is q = 0.88. The probability of taking exactly 5 shots before missing one is:

P(X = 5) = q^4 * p

where X is the random variable representing the number of shots the player takes before missing one.

Plugging in the values, we get:

P(X = 5) = (0.88)^4 * 0.12

= 0.0539

To learn more about probability click on,

https://brainly.com/question/20979342

#SPJ4

Answer: are have a raztation speed of 20 rotation a min

Step-by-step explanation:W anwer

Ashton has 4.5 bags of pecans. since you can't have half a bag, he might need to round up to 5 bags

A fraction represents a part of a whole.

If Ashton used 1/4 of the pecans in a soup recipe, he has 3/4 of the pecans left.

To find out how many pounds of pecans he has left.

we can multiply the original amount of pecans by 3/4:

3/4 x 6 pounds = 4.5 pounds

So Ashton has 4.5 pounds of pecans left to split into bags.

If he splits the remaining pecans into 1-pound bags, then he has:

4.5 pounds ÷ 1 pound/bag = 4.5 bags

Therefore, Ashton has 4.5 bags of pecans. However, since you can't have half a bag, he might need to round up to 5 bags

To learn more on Fractions click:

brainly.com/question/10354322

#SPJ9

The complete question

Ashton picked 6 pounds of pecans. He used 1/3 of the pecans in a soup recipe. Ashton puts the pecans that are left in 1/4 pound bags. How many bags of pecans does he have

Answer:

Step-by-step explanation:

He is now 14 years old because if you minus 21 and 7, it will be 14

Answer:

If your friend says that he will be 21 years old in seven years, then he is currently 21 - 7 = 14 years old.

Step-by-step explanation:

By using a statistical method called regression to model the relationship between the number of earthquakes and various factors that may influence them, such as geological features or human activities.

To answer this question, we need to use a statistical concept called variance. In simple terms, variance measures how spread out a set of data is from its mean or average value.

In the case of earthquakes, we can use historical data to calculate the average number of large earthquakes that occur in the US per year, and then calculate the variance to see how much variation there is in the actual number of earthquakes from year to year.

By doing so, we can make predictions about the expected number of earthquakes in the future and estimate their variance.

In mathematical terms, the variance of a random variable X can be calculated as follows:

Var(X) = E[(X - μ)²]

Where E is the expected value operator, μ is the mean or average value of X, and ² means "squared." This formula tells us to subtract the mean from each value of X, square the result, take the average of these squared differences, and that gives us the variance of X.

To know more about variance here

https://brainly.com/question/14116780

#SPJ4

Answer:

**DUE TOMORROW, NEED ANSWER ASAP**

NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).

a.) An ultraviolet telescope in space

b.) An optical telescope in a remote location in Michigan's upper peninsula

c.) A radio telescope in the Mojave desert in Arizona

d.) An x-ray telescope in the Andes mountains in Chile

e.) An optical telescope in space

Step-by-step explanation:

For the given matrix A, a 3x2 matrix B such that AB=I, where I is the 2x2 matrix B =  [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex] when AB=I

Given matrix A = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₂ₓ₃

B = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₃ₓ₂

In such a way we know that, that AB = I ₂ₓ₂

therefore = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

we can say that [tex]\left[\begin{array}{ccc}a+2c+e&b+2d+f\\a+c+e&b+d+f\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

then, a+2c+e=1

then, when elaborated we get, a+2(-a-e)+e=1

a-2a-2e+e=1

-a-e=1

a+e = -1

2c-c = 1, c = 1 hence we get the value for c

similarly we can do the same steps for the other values

b+2d+f=0

1-d+2d=0

1+d = 0

d = -1

we get the value of d as well now for the value of a and e we can proceed as shown below:

a+c+e=0

c= -a-e

a+e= -c

a+e= -1

a= -2, e=1

similarly we can proceed as shownfor the values of b and f

b+d+f=1

b+f=1-d

b+f=2

b=1, f=1

when we put these values in the correct order and place we get the value for matrix b such as shown below,

therefore, matrix B =  [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex]

To learn more about matrix, click here:

brainly.com/question/28180105

#SPJ4

The missing side is [tex]5\sqrt{3}[/tex].

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

In a Right-angled triangle, the tangent of an angle is equal to the opposite side/adjacent side.

from the given figure,

tan 60° = x/5

[tex]\sqrt{3}=\frac{x}{5}\\ x=5\sqrt{3}[/tex]

Therefore, The missing side is [tex]5\sqrt{3}[/tex].

To learn more about trigonometric functions, refer below:

https://brainly.com/question/25618616

#SPJ1

Answer: The tip is $2.90

Step-by-step explanation: 20% of 14.50 is 2.9

The value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.

What do you mean by Expression?

In mathematics, an expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions can be combined and simplified to solve problems, find relationships, and evaluate the truth of statements. For example, the expression "3 + 4" is a simple expression that represents the value 7 when evaluated.

Expressions can also be more complex, involving multiple operations, variables, and functions. For example, the expression "2x + 3y - z" is a more complex expression that involves three variables and three different operations.

Given the expression (3x + 5)(8x + 10), to find the value of x and y, we have to multiply the two expressions inside the parentheses and simplify the result.

Multiplication of the expressions:

(3x + 5)(8x + 10) = 24x^2 + 76x + 50

So, the value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.

Learn more about mathematical expression

https://brainly.com/question/30350742

#SPJ1

Answer:

Step-by-step explanation:

Dont cheat on your homework

Answer:

256

Step-by-step explanation:

65% is 208

15% is 48

15% + 65% is 80%

So, just add 48 and 208 together:

48 + 208 = 256

Therefore, 80% of that number is 256.

Answer:

256

Step-by-step explanation:

We know that 65% of a number is 208 and 15% is 48, so we can simply add 208 + 48 to get 256.

The value of the inverse relation is y'(0) = 1/6

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

The point (1/6,0) is on the curve

The notation (y^-1)' (0) is an inverse notation

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

(1/6,0) means y(1/6) = 0

This also means that

y'(0) = 1/6

Hence, the solution is 1/6

Read more about inverse function at

https://brainly.com/question/3831584

#SPJ1

The probability that the sample average amount of time taken on each day is at most 11 min:

P([tex]\bar{X_1}[/tex] < 11) =  0.8682

P([tex]\bar{X_2}[/tex] < 11) =  0.8897

We know that the formula for the z-score is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Let X be the time taken by a randomly selected applicant for a mortgage to fill out a certain form

[tex]\mu_x[/tex] = 10

[tex]\sigma_x[/tex] = 2

Here, five individuals fill out a form on one day and six on another.

This means that the population is the same on both days, but the samples of different sizes.

On Day 1 the average[tex]\bar{X_1}[/tex] ∼Norm(10, 2/[tex]\sqrt{5}[/tex])

We find the probability using z-score.

The probability that the sample average amount of time taken on day 1 is at most 11 min:

P([tex]\bar{X_1}[/tex] < 11)

=[tex]P(\frac{\bar{X_1}-10}{(\frac{2}{\sqrt{5} } )} < \frac{11-10}{(\frac{2}{\sqrt{5} } )})[/tex]

= P(z < 1.118)

= 0.8682

Similarly, on Day 2 the average[tex]\bar{X_1}[/tex] ∼Norm(10, 2/[tex]\sqrt{6}[/tex])

So the probability that the sample average amount of time taken on day 1 is at most 11 min:

P([tex]\bar{X_2}[/tex] < 11)

=[tex]P(\frac{\bar{X_2}-10}{(\frac{2}{\sqrt{6} } )} < \frac{11-10}{(\frac{2}{\sqrt{6} } )})[/tex]

= 0.8897

Learn more about the probability here:

https://brainly.com/question/15124899

#SPJ4

The complete question is:

The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min?

Answer:

$1522.5

Step-by-step explanation:

(7.25 x 15)14

(108.75)14

= 1522.5

Answer:

-19 > k

Step-by-step explanation:

-4 > k + 15

Subtract 15 from each side.

-4-15 > k + 15-15

-19 > k

Any value less than -19 would make this statement true

Answer:

- 19 > k

Step-by-step explanation:

- 4 > k + 15

Subtract 15 from both sides.

- 4 - 15 > k

- 19 > k

Increase the accuracy of your measurements by using a more precise instrument or tool, such as a protractor or ruler.

The accuracy of the intersection of your three circles may not have been exact due to imprecise measurements taken. To improve the results, you could use a more precise instrument or tool, such as a protractor or ruler. With a protractor , you can measure the angle of the intersection of the circles more accurately. If a ruler is used, make sure that it is a straight edge, and measure the distance between the circles to ensure they intersect at the same point . Once the measurement is taken, draw the circles and their intersection accordingly. Doing this will help improve the accuracy of the intersection of the three circles and yield better results.

Learn more about protractor here

https://brainly.com/question/3229631

#SPJ4

Answer:

D

Step-by-step explanation:

f(x)=20 cos (pi/5x + pi/2)+25

Answer:

  about 2.43 seconds

Step-by-step explanation:

You want the time when the height described by h = -16t² +36t +7 is equal to zero.

The quadratic equation ...

  -16t² +36t +7 = 0

can be solved using the quadratic formula. It tells you the solution to ...

  ax² +bx +c = 0 is ...

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

Then the solutions to the given quadratic are ...

  [tex]x = \dfrac{-36\pm\sqrt{36^2-4(-16)(7)}}{2(-16)}=\dfrac{9\pm\sqrt{109}}{8}\approx\{-0.180,2.430\}[/tex]

The ball will hit the ground after about 2.43 seconds.

the angle between the vectors is: θ = cos⁻¹ (- 12 / √145)

A quantity or phenomena with independent directions and magnitudes is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Science uses vectors to express everything with a direction and a magnitude. They are typically shown as pointed arrows, with the length of the arrow representing the magnitude of the vector.

Let, a(vector) = < -1, -2 >

a(vector) = -i -2j

||a(vector)|| = √(-1)² + (-2)² = √5

b(vector) = < -2, 5 >

b(vector) = -2i + 5j

||b(vector)|| = √(-2)² + (5)² = √29

Next, a(vector) . b(vector) = (-i -2j) . ( -2i + 5j)

a(vector) . b(vector) = (1 × (-2)) + (-2 × 5) = - 12

Thus, angle between these two vectors:

cosθ = a(vector) . b(vector) / ||a(vector)|| . ||b(vector)||

cosθ = - 12 / (√5 . √29)

cosθ = - 12 / √145

θ = cos⁻¹ (- 12 / √145)

To know more about vectors refer to:

https://brainly.com/question/15519257

#SPJ1

Number of cubes with edge length 1/2cm that fit in the prism is 11160 and the volume of the prism is 1395 cubic centimeter

Dimensions of the rectangular prism = [tex]7\frac{1}{2}[/tex] cm × 12 cm × [tex]15\frac{1}{2}[/tex] cm

Convert the mixed fraction to the simple fraction

The dimensions of the rectangular prism = 15/2 cm × 12 cm × 31/2 cm

The volume of the rectangular prism = w × l × h

Where

w is the width

l is the length

h is the height

The volume of the rectangular prim = 15/2 × 12 × 31/2

= 1395 cubic centimeter

The side off the cube = 1/2 cm

Volume of the cube = a^3

= (1/2)^3

= 0.125 cubic centimeter

Number of cubes will fit in rectangular prism = Volume of rectangular prism /  Volume of the cube

= 1395 / 0.125

Divide the terms

= 11160 cubes

Therefore, 11160 cubes will fit in the rectangular prism and the volume of the prism is 1395 cubic centimeter

Learn more about rectangular prism here

brainly.com/question/21308574

#SPJ4