Plz show ur work! Ty if u do. Will give brainilest!

The output value of (f∘g)(x) is:  \((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)

The domain of (f∘g)(x) is (-∞, -3) U (-3, ∞).

In this scenario, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations (multiplication) in simplified form as follows;

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

g(x) = 4x - 15

Next, we would write the numerators and denominators in factored form as follows;

(x - 6)(4x - 15)

4x² - 15x - 24x + 60

4x² - 29x + 60

Now, we can derive the corresponding composite function of f(x) and g(x);

\((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x + 3 ≠ 0

x ≠ -3

Domain = (-∞, -3) U (-3, ∞).

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Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the \(\sqrt{12}\).

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

The linear function modeling the demand is given as follows:

y = -2500x + 12500.

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

y = mx + b.

In which:

When the price increases by $0.24, the demand decays by 600, hence the slope m is given as follows:

m = -600/0.24

m = -2500.

Hence:

y = -2500x + b.

When x = 4, y = 2500, hence the intercept b is given as follows:

2500 = -4(2500) + b

b = 12500.

Hence:

y = -2500x + 12500.

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The simplest choice is a linear transformation, for example, the one given by the

matrix \(\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right]\)

When you represent a three-dimensional object graphically in the plane con paper, the blackboard, or a computer screen), you have to transform spatial coordinates,

\($\mathrm{x} 1$ & \\\)

\($\mathrm{x} 2$\) & into plane coordinates

\($\mathrm{x} 3$\)& \($\mathrm{y} 1$\)& \($\mid$ \\\)

\($\mathrm{x}$\) &\($\mathrm{y} 2$\) &

The simplest choice is a linear transformation, for example, the one given by the

matrix \(\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right]\)

The complete question is,

When you represent a three-dimensional object graphically in the plane (on paper, the blackboard, or a computer screen), you have to transform spatial coordinates | x 1 | | x 2 | into plane coordinates | y 1 |. | x 3 | | y 2 | The simplest choice is a linear transformation, for example, the one given by the matrix | -1/2 1 0 0 | 1 |.

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Answer: 5/2

Step-by-step explanation:

slope equation: (y2-y1)/(x2-x1)

13-3/5-1 = 10/4 or 5/2

Answer:

2.5

Step-by-step explanation:

Gradient (slope) =

\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)

The answer to the sum is: ∑ k⁴ (k  ranges from 1 to 6)

Express the sum in sigma notation :

According to the question,

1 = lower limit of summation

k = the index of summation

1 + 16 + 81 + 256 + 625 + 1296 = 1² + 4² + 9² + 16² + 25² + 36²

                                                 = 1⁴ + 2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ ( i.e 16 = 4²=(2²)²)

                                                 = ∑ k⁴ (k ranges from 1 to 6)

 So, The answer to the sum is - ∑ k⁴ (k ranges from 1 to 6).    

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Answer:

The answer is 20

Step-by-step explanation:

6 (20 - 8 ) = 72

Answer:

20

Step-by-step explanation:

edge 2021

The power expression "w^5" can be entered as "w^5".

To represent a power using the caret symbol, follow these steps:

Start with the base variable or term, in this case, "w".

Type the caret symbol (^), which can be accessed by pressing SHIFT-6 on your keyboard.

Immediately after the caret symbol, enter the exponent or power value, in this case, "5".

The resulting power expression "w^5" represents the variable "w" raised to the power of 5.

Regarding the use of the fraction tool, it is not required to represent the power "w^5" as it does not involve any fraction. The fraction tool is typically used to enter fractions or rational expressions in the form of numerator/denominator.

Therefore, to represent the power "w^5", simply write it as "w^5" without using the fraction tool.

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Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.

Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.

You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.

Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.

Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.

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So, for values lesser than -1 and greater than -7 this inequality is true.

In this inequality let's work applying the Absolute Value properties

1) -5ln+4l<15 Dividing both sides by 5

-|n+4|<3

|n+4|>-3

2) Applying Absolute value properties

|n+4|>-3

|n+4|>-3

n+4-4>-4-3

n>-4-3

n>-7

|n+4|>3

n+4>3

n+4-4>3-4

n>-1

3) So n < -1 and >-7

So for values lesser than -1 and greater than -7 this inequality is true.

Answer:

4

Hope that this helps!

Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

Answer:

y= 15 and y= -59

Step-by-step explanation:

Given

37 = |y+22|

We have 2 possibilities

-what is inside the absolute value is positive

37 = y+22

-what is inside the absolute value is negative

37 = -(y+22), distribute the negative sign in parenthesis

37 = -y -22

Solve the 2 possibilities to find y:

-when what is inside the absolute value is positive

37 = y+22, subtract 22 from both sides of the equation

37-22 = y +22-22, combine like terms

15 =y

-when what is inside the absolute value is negative

37 = -y -22, add 22 to both sides

37+22 = -y -22+22, combine like terms

59 = -y, multiply both sides by -1

-59 =y

Solution:

y=15 and y=-59

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

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

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

X    |   y

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

-2   |   3

-1   |   0

0   |  -3

1   |  -6

Answer:Below ^-^

Step-by-step explanation:

The amount shaded is 62 out of 100.

Fraction:62/100

Decimal:0.62

Percent:62%

Answer:

Step-by-step explanation:

i dont understand

Answer:

3 months

Step-by-step explanation:

there are 12 months in a year.

.25 is equal to a quarter of a year

12/4=3

Answer: I define the "best" unit to convert a number as the unit that is the lowest without going lower than 1. For 0.25 years, the best unit to convert to is 3 months.

Step-by-step explanation:

The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer::

Tens: 7 Hundredths: 0 Ten Thousandths: 3

Step-by-step explanation:

The numbers before the decimal points don't have "-th" at the end, numbers after the decimal do.

Closest to the left of the decimal: ones, tens, hundreds, thousands....

Closest to the right of the decimal: tenths, hundredths, thousandths, ten thousandths....

Answer:

there are 30 girls in the stem class

Answer:

48

Step-by-step explanation:

girls:boys

6. :. 5

? :. 40

cross multiplication:

40×6÷5=48

Answer:

D

Step-by-step explanation:

this answer is correct , i think if you think of it in logically

Answer:

0.75/.75

Step-by-step explanation:

Answer:

The answers are correct.

Step-by-step explanation:

Please rate the answer and like it if it helped.

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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