Which of the following systems of inequalities has point D as a solution?

Two linear functions f of x equals 3 times x plus 4 and g of x equals negative one half times x minus 5 intersecting at one point, forming an X on the page. A point above the intersection is labeled A. A point to the left of the intersection is labeled B. A point below the intersection is labeled C. A point to the right of the intersections is labeled D.

A. f(x) ≤ 3x + 4
g of x is less than or equal to negative one half times x minus 5
B. f(x) ≥ 3x + 4
g of x is less than or equal to negative one half times x minus 5
C. f(x) ≤ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
D. f(x) ≥ 3x + 4
g of x is greater than or equal to negative one half times x minus 5

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

for such more question on inverses

https://brainly.com/question/15066392

#SPJ8

The probability\(\( P(0 \leq z \leq 0.59) \)\) is approximately 0.2236.

To calculate the probability, we need to find the area under the standard normal curve between 0 and 0.59. This can be done by using the standard normal distribution table or a calculator.

The table provides the cumulative probability up to a given z-value. For 0, the cumulative probability is 0.5000, and for 0.59, the cumulative probability is 0.7224. To find the probability between these two values, we subtract the cumulative probability at 0 from the cumulative probability at 0.59:

0.7224

−

0.5000

=

0.2224

0.7224−0.5000=0.2224. Rounded to four decimal places, the probability is approximately 0.2217.

Learn more about  probability

brainly.com/question/31828911

#SPJ11

Answer:

The proportional equation is \(\frac{5}{3}\) = \(\frac{7}{4.20}\)

Cross product are both equal to 21.

Step-by-step explanation:

5 peanut butter biscuits for $3

7 beef treats for $4.20

So, proportional equation is

\(\frac{5}{3}\) = \(\frac{7}{4.20}\)

Cross multiply

21=21

Answer:

21

Step-by-step explanation:

Source: Trust me bro

The average rate of change between x and y in the given data is -1.

We have,

To find the average rate of change between two variables, we need to calculate the difference in the values of the variables and divide it by the difference in their corresponding inputs.

In this case, we have the following data points:

x: -2, -1, 0, 1

y: 7, 6, 5, 4

To find the average rate of change, we'll consider the first and last data points.

Change in y: 4 - 7 = -3

Change in x: 1 - (-2) = 3

Average rate of change = Change in y / Change in x = -3 / 3 = -1

Therefore,

The average rate of change between x and y in the given data is -1.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

The 90% confidence interval that estimates the average age of cars sold for the first time is (2.56, 10.30).

To calculate the confidence interval, we can use the formula:

CI =\(\bar{X}\)  ± tα/2 * (s/√n)

where \(\bar{X}\) is the sample mean, s is the sample standard deviation, n is the sample size, tα/2 is the critical value from the t-distribution table with (n-1) degrees of freedom and a confidence level of 90%.

Using the given data, we find that the sample mean is 6.43 years and the sample standard deviation is 2.69 years. With a sample size of 7, the critical value from the t-distribution table is 1.895.

Plugging in these values, we get:

CI = 6.43 ± 1.895 * (2.69/√7)

Simplifying this expression gives us the confidence interval (2.56, 10.30). Therefore, we can say with 90% confidence that the average age of cars sold for the first time is between 2.56 and 10.30 years.

To know more about average age, refer here:

https://brainly.com/question/29694423#

#SPJ11

Answer:

63.25 KG

Step-by-step explanation:

Convert 15% to a decimal, then add 1 and multiply 15.

\(55 \times (1 + 0.15) = 63.25\)

Check the picture below.

    Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

The slope of parallel lines is the same. By converting the line 2x -4y = 8 to slope intercept form, first determine its slope.

4y = 8-2x y = 1/2x - 4 2x + 4y = 8

Here, the slope is 1/4

Fill in the point slope form with (-2, -4) and m = 1/4 After that, simplify to obtain the standard form and slope intercept form.

The slope intercept form is y = 1/4x + 6, while the point slope form is y - (-4) = 1/4(x+4).

Now, by rearranging the terms into the formula Ax + By = C, the standard form may be discovered.

6 becomes -1/4x + y = 6 when y= 1/4x + 6. Since fractions for A or B cannot be expressed in standard form, the equation is multiplied by 4 to get x + 4 y = 24.

To Learn more About Parallel lines, Refer:

https://brainly.in/question/1399334

#SPJ9

The value of QR is 3√290.

Given, In triangle PQR

PQ = 39 in PR = 17 in Height PN = 15 in

We need to find QR.

In the right-angled triangle PNR, using Pythagoras theorem,

PN² + PR² = NR²15² + 17²

= NR²NR² = 15² + 17²NR

= √(15² + 17²)NR = √(225 + 289)NR

= √514

Now, in the right-angled triangle PQN,

using Pythagoras theorem,

QR² = PN² + PQ²QR² = 15² + 39²QR²

= 225 + 1521QR² = 1746QR

= √1746QR = 3√290

Thus, the value of QR is 3√290.

learn more about Pythagoras theorem here

https://brainly.com/question/22340031

#SPJ11

Since y is directly proportional to x then the value of y is 8

In a proportional relationship, one variable is always equal to the constant value of the other.

It is clear that y increases in proportion to x by applying the direct proportionality formula, y = kx.

Given y is directly proportional to x.

Therefore y = kx

now at x = 20 , y = 16/5

∴16/5 = 20 k

or, k = 16 /100

Now at x = 50 ,

Y = 16 /100 × 50

or, y = 8

Therefore that value of y is 8.

To learn more about proportional relationship visit:

brainly.com/question/12917806

#SPJ1

Answer:

What is the equation?

Step-by-step explanation:

Answer:

Step-by-step explanation: what is the probelm i can help.

Answer:

7.75

Step-by-step explanation:

(I'm assuming you need to find the missing side of the triangle)

To find missing values in a right angle. we will use the pythagoras theorem which states that:

h^2 = a^2 + b^2

16^2 = 14^2 + b^2

256 = 196 + b^2

256 - 196 = b^2

60 = b^2 (take sqaure root)

b= 7.75

Answer from Gauthmath

Answer:

5.2 cubic ft

Step-by-step explanation:

took the test

The volume of given cone is 5.23 cubic feet.

Volume is the measure of the capacity that an object holds.

\(v = \frac{1}{3} \pi r^{2} h\)

where,

v is the volume of cone

r is the radius of cone

h is the height of cone

According to the question we have

Diameter of cone is 2ft

⇒ radius of the cone = \(\frac{2}{2} = 1 feet\)

Height of the cone is 5ft.

Therefore,

The volume of the cone  = \(\frac{1}{3}(1)\pi( 1)^{2} (5)\)

Volume of cone = \(\frac{1}{3} (3.14)(1)(5) = 5.23 cubic feet\)

Hence, hence the volume of given cone is 5.23 cubic feet.

Learn more about the volume of cone here:

https://brainly.com/question/1984638

#SPJ2

The table represents Autumn's total pay based on the number of computers she sells. The equation P = $90 + ($2.50 * x) represents Autumn's total pay (P) in terms of the number of computers sold (x).

To create a table of values representing Autumn's total pay based on the number of computers she sells, we can use the given information.

Let's assume the number of computers sold is represented by "x." The base pay is $90, and the commission per computer sale is $2.50.

Using this information, we can create the following table:

| Number of Computers (x) |   Total Pay (P)            |

|---------------------------------------|  |--------------------------|

| 0                                          | $90                      |

| 1                                           | $90 + ($2.50 * 1)        |

| 2                                          | $90 + ($2.50 * 2)        |

| 3                                          | $90 + ($2.50 * 3)        |

| ...                                          | ...                      |

| x                                           | $90 + ($2.50 * x)        |

To write the equation for P (total pay) in terms of x (number of computers sold), we can express it as:

P = $90 + ($2.50 * x)

The base pay of $90 is added to the commission of $2.50 multiplied by the number of computers sold to calculate Autumn's total pay.

Learn more about ”commission” here:

brainly.com/question/20987196

#SPJ11

Answer:

All Real Numbers

Step-by-step explanation:

Step 1:

3x - 9 = 3 ( x - 3 )        Equation

Step 2:

3x - 9 = 3x - 9       Multiply

Step 3:

- 9 = - 9       Subtract 3x on both sides

Answer:

All Real Numbers

Hope This Helps :)

Answer:

12

Step-by-step explanation:

w+z(3x-2y)

3+(-2)(3*2-2*-4)

3-2(6+6)

3-2(12)

12

Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

y = -1/2x is the equation of example of the direct variation.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

Given four linear equations in them we need to state which equation is an example of direct variation.

The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Or in other words, the direct variation equation always passes through the origin point of a cartesian plane or (0, 0).

Therefore, in the given options y = -12/x is the only equation that is an example of direct variation.

Learn more about polynomials here:

https://brainly.com/question/11536910

#SPJ1

we must evaluate the domain points in the function

x=0

x=1

x=2

x=3

x=4

x=5

x=6

x=7

the points are

now, locate each point on the graph and join with a line

Answer:

True

Step-by-step explanation:

Answer:

y=-1/4x+2

Step-by-step explanation:

Answer:

Step-by-step explanation:

add all the # and see what you get

Answer:

your answer would be B

Step-by-step explanation:

every item is 9 dollars divide the cost by the number of items it is always 9 meaning 9 is the constant. hope this helps.

Answer:

18  

To verify the constant you only have to verify every option by adding those options by itself and the one that matches your information is the correct answer

Given:

\(\Delta FUN\cong \Delta TEA\)

To find:

Identify the congruent corresponding parts of \(\angle N\cong \angle \_\_\).

Solution:

We have,

\(\Delta FUN\cong \Delta TEA\)

We know that corresponding parts of congruent triangles are congruent.

\(\angle F\cong \angle T\)

\(\angle U\cong \angle E\)

\(\angle N\cong \angle A\)

Therefore, the required corresponding part is  \(\angle N\cong \angle A\).

Answer:

What is the volume, in cubic ft, of a rectangular prism with a height of 17ft, a width of 13ft, and a length of 12ft?

Step-by-step explanation:

What is the volume, in cubic ft, of a rectangular prism with a height of 17ft, a width of 13ft, and a length of 12ft?What is the volume, in cubic ft, of a rectangular prism with a height of 17ft, a width of 13ft, and a length of 12ft?What is the volume, in cubic ft, of a rectangular prism with a height of 17ft, a width of 13ft, and a length of 12ft?

The given bounded region is the set

\(R = \left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^4 \le y \le x^{1/4} \right\}\)

assuming the curves are \(y=x^4\) and \(x=y^4\implies y=x^{1/4}\) (since \(x>0\) in the first quadrant).

The coordinates of the centroid are \((\bar x, \bar y)\) where \(\bar x\) and \(\bar y\) are the average values of \(x\) and \(y\), respectively, over the region \(R\). These are given by the ratios

\(\bar x = \dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \bar y = \dfrac{\displaystyle \iint_R y\,dA}{\displaystyle \iint_R dA}\)

Compute the area of \(R\).

\(\displaystyle \iint_R dA = \int_0^1 \int_{x^4}^{x^{1/4}} dy \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \frac45 - \frac15 = \frac35\)

Integrate \(x\) and \(y\) over \(R\).

\(\displaystyle \iint_R x \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} x \, dy \, dx \\\\ ~~~~~~~~ = \int_0^1 x \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{5/4} - x^5\right) \, dx \\\\ ~~~~~~~~ = \frac49 - \frac16 = \frac5{18}\)

\(\displaystyle \iint_R y \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left((x^{1/4})^2 - (x^4)^2\right) \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left(x^{1/2} - x^8\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(\frac23 - \frac19\right) = \frac5{18}\)

Then the centroid's coordinates are

\(\bar x = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}} \approx 0.463\)

\(\bar y = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}}\)

In quadrant IV, \(\cos(A)\) is positive. So

\(\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258\)

Then by the definition of tangent,

\(\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}\)