multiply or divde as indicated. simplify your answer, if possible.
x⁻⁸/x⁵

The input and output table that works for both rules is input = 20 and output = 10.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the output and x represent the input.

From the first rule:

y = x/2

From the second rule:

y = x - 10

To work for both rules:

x/2 = x - 10

x = 2x - 20

x = 20

y = 20 - 10 = 10

The input and output table that works for both rules is input = 20 and output = 10.

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Answer:

My best guess would be 19.5

Step-by-step explanation:

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Answer:

3. f(3) = 16

4. h(3) = 4

Step-by-step explanation:

3.

f(x) = x² + 7

f(3) = 3² + 7

f(3) = 16

4.

h(x) = 12/x

h(3) = 12/3

h(3) = 4

Answer:

(100/500) *200 =40%

Step-by-step explanation:

Answer: lol she was lowkey trying to call out the lady in front of you without directly addressing her. Or she was just trying to mess with you cuz that's how moms are

Step-by-step explanation:

Answer:

3/16

Step-by-step explanation:

16 pupils, 11 play both, 1 plays piano only and 1 flute only

⇒ 11 + 1 + 1 = 13 pupils who play at least one instrument

⇒ 16 - 13 = 3 pupils who don't play either instrument

⇒ Out of the 16 total pupils, 3 play neither, putting this into numbers:

\(\frac{3}{16}\) which is then also the answer.

Dividing f(x) by 2x + 5 leaves the same remainder as division by x + 5/2. By the remainder theorem, it is equal to f (-5/2), so the remainder here is

f (-5/2) = 8 (-5/2)³ + 4 (-5/2)² - 13 (-5/2) + 3 = -129/2

Answer:Can somebody also help me with this. i'm confused please hurry!

Step-by-step explanation:

Answer:

Step-by-step explanation:

4). By applying cosine rule for angle R,

    cos(∠R) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

    cos(33°) = \(\frac{x}{19}\) [Equation]

    x = 19cos(33°)

       = 8.39

5). By applying sine rule,

    cos(20°) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

    cos(20°) = \(\frac{15}{x}\) [Equation]

    x = \(\frac{15}{\text{cos}20}\)

    x = 15.96

6). By applying tangent rule,

    tan(40°) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

    tan(40°) = \(\frac{15}{x}\) [Equation]

     x = \(\frac{15}{\text{tan}40}\)

     x = 17.88

The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.

The Central limit theorem is used to find the probability

Data given:

sample size = 5.

mean, μ = 9.70 ounces

standard deviation, σ = 0.03 ounce.

To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.

x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

For the sample mean of 9.65 ounces in 5 boxes:

z = (9.65 - 9.70) / (0.03 / √5)

z ≈ -0.05 / (0.03 / √5)

Using a calculator, we find that the probability is approximately 0.4801.

Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.

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Answer:

36 units²

Step-by-step explanation:

rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

we use the inverse formula

12 * 3 =

36 units²

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

check

36 : 12 = 3

the answer is good

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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To graph the inequality k > 5 on a number line, mark an open circle at 5 and shade the region to the right.

To graph the solutions to the inequality k > 5 on a number line, follow these steps:

Draw a horizontal line and mark a point for the number 5 on the line.

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

0 1 2 3 4 5 6 7 8 9 10

Since the inequality is k > 5, the solution includes all values greater than 5. Therefore, draw an open circle (○) at the number 5 to represent that 5 itself is not included in the solution.

-------------------|---|---|---|---○---|---|---|---|---|---|

0 1 2 3 4 5 6 7 8 9 10

Shade the region to the right of the open circle. This shading represents all values that are greater than 5 and satisfy the inequality k > 5.

-------------------|---|---|---|---○===================>

0 1 2 3 4 5 6 7 8 9 10

The resulting number line graph illustrates that any value to the right of the open circle (excluding 5 itself) satisfies the inequality k > 5.

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Please find attached the graph of the piecewise function; f(x) = -e⁻ˣ for x ≤ 0, f(x) = \(\frac{x^2+x - 6}{x^2+2\cdot x-3}\) for x > 0

A piecewise function is a function for which the rules of the function depends on the interval to which it is applied.

The graph of the piecewise function in the question can be obtained by plotting the graph using the data in the following table, generated with MS Excel

x   \({}\)     f(x) = -e⁻ˣ

-1.5 \({}\)   -4.5

-1.4 \({}\)   -4.1

-1.1 \({}\)    -3.0

-1 \({}\)      -2.7

-0.9 \({}\)  -2.5

-0.8 \({}\)   -2.2

-0.5 \({}\)   -1.6

-0.4 \({}\)   -1.5

-0.3 \({}\)   -1.3

-0.2 \({}\)   -1.2

-0.1 \({}\)    -1.1

x \({}\)         \(f(x) = \frac{x^2+x-6}{x^2+2\cdot x -3}\)

0 \({}\)        -1

0.1 \({}\)     -2.3

0.2 \({}\)    -2.8

0.3 \({}\)     -3.3

0.4 \({}\)     -4

0.5 \({}\)     -5

0.6 \({}\)     -6.5

0.8 \({}\)     -14

0.9 \({}\)     -29

1.1 \({}\)        31

1.4 \({}\)        8.5

1.5 \({}\)        7

1.6 \({}\)        6

The graph of the piecewise function can be plotted using the data in the above table and the Insert Chart function in MS Excel.

Please find attached the graph of the piecewise function with the characteristics of an asymptote at x = 1/1 = 1

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Answer:

Externalities refer to situations when the effect of production or consumption of goods and services imposes costs or benefits on others that are not reflected in the prices charged for the goods and services being provided.

the picture below is an example of what it looks like

WHAT EXTERNALITY IS : externality is a economic cost or sometimes a benefit that is the´´by product´´ of the economic activity. the activity that is allacated outside of the system. the resources are likely to be misallocated when there is a externality.

the fact of existing outside the perceiving subject.

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63. Option D

To find the relative frequency of students with red hair among the sample population of students with gray eyes, we need to divide the number of students with gray eyes and red hair by the total number of students with gray eyes.

From the given table, we can see that there are 22 students with gray eyes and red hair.

The total number of students with gray eyes is the marginal total for gray eyes, which is 35.

To find the relative frequency, we divide the number of students with gray eyes and red hair by the total number of students with gray eyes:

Relative frequency = Number of students with gray eyes and red hair / Total number of students with gray eyes

Relative frequency = 22 / 35

Simplifying the fraction, we have:

Relative frequency = 0.6286

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63.

Therefore, the correct answer is option OD) 0.63.

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Answer:

a parallel line: is coplanar lines that never interact

a skew: is lines that are not on the same plane and never intersect

an interior angle: is interior lines that lie on the same side of transversal

an exterior angle: is a line that lies between parallel lines that are cut by transversal

a consecutive interior angle: is a line that lies on the same side both parallel lines and the transversal

a corresponding angle: lies in the region not between parallel lines that are cut by transversal

a tranversal: is a line that interacts 2 or more coplanar lines at 2 different points

Have a great day love!

Step-by-step explanation:

Answer:

1 ½ scoops more then white sugar

Answer:

B

Step-by-step explanation:

slope intercept form - y = mx + b

where m = slope and b = y intercept

first let's find the y intercept

The y intercept is the y value of the coordinate where the line passes the y axis

The line passes the y axis at (0,2)

The y value of this coordinate is 2 so b = 2

* plug in 2 *

now we have y =  mx + 2

Now we want to find the slope.

slope is equal to the change in y over the change in x

As y goes up 3 x goes down 1

so slope = 3/-1 or -3

hence m = -3

* plug in -3 *

now we have y = -3x + 2

The answer is B

Answer:

Step-by-step explanation:

if you mean graph each of the slope-intercept lines , it's pretty helpful to use Desmos for this, just input the line formula .  as below

Answer:

substitute x=-3 :

-(-3^2)+1= -(9)+1= -8

Answer:

99

= 11 × 9

= 11 × 3 × 3 ----- 99 as the product of its prime factors.

Answer: 99

= 11 × 9

= 11 × 3 × 3 ----- 99 as the product of its prime factors.

Answer:

Radical Approximation

of A=5√2

of B=2√13

of C is 3√7

Hello!

Answer:

72 cm^2

Hope this helps!

Answer: 875 square feet

Step-by-step explanation: none atm

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Option D is the correct answer.

We have,

Edouard Manet's painting "Luncheon on the Grass" was first rejected by the Paris Salon in 1863, as it was considered scandalous due to the nudity of the female figure in the painting.

In response to this rejection,

Emperor Napoleon III ordered an exhibition to be held for all the rejected paintings, which was known as the Salon des Refusés (Salon of the Refused).

Thus,

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

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By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.

In trigonometry, an unit circle is a circle with a radius of 1 and used to determine the values of trigonometric functions. There are two fundamental trigonometric functions: (i) sine, (ii) cosine, and the tangent is a derivate trigonometric function, which is defined below:

tan θ = y/x     (1)

If we know that x = 1 and y = 0, then the tangent of the terminal point of angle is:

tan θ = 0/1

tan θ = 0

By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.

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Answer:

tan= 0

Step-by-step explanation:

^^^correct :)