Could someone help me with number 19

Since the exercise is regarding the g function, we will only be using this function.

g(2) means that we will be replacing the x variable in the equation by 2.

We get,

Therefore, g(2) = 7.

Answer:

it is inscribed in the circle.

Step-by-step explanation:

Answer:

(fg)(x) = x^4 - x^3 + 15x^2 - 6x + 54

Step-by-step explanation:

We want to multiply and simplify as much as possible:

f(x) * g(x)

(x^2 + 6)(x^2 - x + 9)

(x^2 * x^2) + (x^2 * - x) + (x^2 * 9) + (6 * x^2) + (6 * - x) + (6 * 9)

Note that when you're multiplying exponents, we add them:

x^4 + - x^3 + 9x^2 + 6x^2 - 6x + 54

Now we add 9x^2 and 6x^2 as they are like terms:

x^4 - x^3 + 15x^2 - 6x + 54

Thus, (fg)(x) simplified is x^4 - x^3 + 15x^2 - 6x + 54.

Optional:  Check the validity of the answer:

We can check that our answer is correct by plugging in a number for x in both the unsimplified and simplified expression and seeing if we get the same answer.  Let's try 5:

Plugging in 5 for x in (x^2 + 6)(x^2 - x + 9):

(5^2 + 6)(5^2 - 5 + 9)

(25 + 6)(25 - 5 + 9)

(31)(20 + 9)

(31)(29)

899

Plugging in 5 for x in x^4 - x^3 + 15x^2 - 6x + 54:

5^4 - (5)^3 + 15(5)^2 - 6(5) + 54

625 - 125 + 15(25) - 30 + 54

625 - 125 + 375 - 30 + 54

500 + 375 - 30 + 54

875 - 30 + 54

845 + 54

899

Thus, our answer is correct.

Answer:

???

Step-by-step explanation:

Answer:

Step-by-step explanation:

To answer this question we just need to calculate areas of the equilateral triangle and the area of the square:

Solution is:

At = (√3/4)×x²  +  ( 20 - 3×x )²/ 16  square units

for    0 ≤ x  ≤ 6.66   and        18.87 ≤  A ≤ 25

In the equilateral triangle, all the interior angles are 60°.

The bisectrix of one of these angles divided one 60°angle into two 30° angles, and the opposite side in half, and two isosceles triangles are formed.

The area of the original equilateral triangle of side x will become the sum of the areas of the two isosceles triangles with common side ( and height)  h = ( √3 /2)×x

cos 30° = √3  / 2     ⇒  h =  (√3  / 2) ×x

Then as Aet = 2 × (1/2)×(x/2)× (√3  / 2) ×x

Aet = (√3/4)×x²  square units

To obtain the area of the square we know that a square of side L will have an area of L², so we only need to find out what is the side of the square.

The length of the wire is 20 f.

we cut off to get the equilateral triangle 3×x then we got left

20 - 3×x so the perimeter of the square is

p = 20 - 3×x  

In the case of square p = 4×L     then  L = p/4

L = ( 20 -3×x)/4

As= [ ( 20- 3×x)/4]²   ⇒   As = ( 20 - 3×x )²/ 16  square units

Finally total area

At = (√3/4)×x²  +  ( 20 - 3×x )²/ 16  square units

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The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

Answer:

m<BAC = 85°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of its intercepted arc.

m<BAC = 170°/2

m<BAC = 85°

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Answer: 440 dollars and -60

Step-by-step explanation:

Add ten to 430 and you’ll get 440. With a withdrawal of 500 and a balance of 440, the answer will be a negative 60 dollars.

Answer:

The original cost of the digital camera is Rs. 18,500.

Step-by-step explanation:

Let c be the original cost of the digital camera

Since VAT of 13% was added then we can say that the amount that was paid was 13% more than the original price. So the payment made was 113% of the original amount or 1.13 in decimal

Payment = original cost + 13% VAT

20, 905 = c + 0.13c

20, 905 = 1.13c

Divide both sides of the equation by 1.13

20905/1.13 = 1.13c/1.13

18,500 = c

c = Rs. 18,500

The percent of the front page taken up by the prom story is 20%

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

The front page

From the front page, we have

Area front page = 5 * 4

Area front page = 20

Also, we have

Prom = 2 * 2

Prom = 4

So, we have

Percentage = 4/20 * 100%

Evaluate

Percentage = 20%

Hence, the percent of the front page taken up by the prom story is 20%

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Answer:

true

Step-by-step explanation:

plz mark brainlyest

Answer: (D) (3x2) x (5x6)

Step-by-step explanation: You can switch them around and it will still have the same answer.

Answer:

(5 x 6)x(3 x 2) is equal to 180

To find the answer, you have to solve them to see if they are equal to 180.

A) (5 + 6) + (3 + 2)    NO

simply cannot work because it's an addition of small numbers. This expression equals 16. Not equivalent.

B) (5 + 6) (3 + 2) (5 x 6) + (3 x 2)  NO

B doesn't make sense as it includes both the expressions together, including the initial expression which we are trying to find an equivalent answer, hence, it is going to equal more than the answer:  x > 180.  Solving for x is unnecessary as we know it is more.  

No C?

D) (3 x 2)x(5 x 6)  YES

This one works as the same numbers as the initial expression are equivalent and the expression uses the same math signs. This displays the commutative property of multiplication

Conclusion:

the Answer is D)

Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.

It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.

The Pythagorean formula can be applied to the illustration to determine the length of the third side:

c²= a²+ b²

c²= 8² + √(17)²

c²= 64 + 17

c² = 81

c = 9

We can now calculate the trigonometry ratios of angles K and L:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

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Step-by-step explanation:

24-12x,and 2(12-6x)

hope it helps

From the linear equation, the option that describes the graph of the two corresponding lines is C. The lines are parallel.

Based on the complete information, it should be noted that the lines are not coinciding and they don't intersect at only one point.

Rather, it can be deduced that the graph of the two corresponding lines in the xy-plane are parallel.

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The length of the segment is 2.4 centimeters.

The scale is 2.4 cm :24 mm.

How to change mm to cm?

One millimeter, or one-thousandth of a meter, is equal to one mm. One centimeter, also known as one hundredth of a meter, is equal to one centimeter.

Accordingly, 1 cm 10 mm. Divide the number of mm by 10 to get the number of cm when converting mm to cm.

Given that length of the segment is 24mm. now we know that,1 mm is equal to 0.1 cm,

So,

\(10 \: mm=1 \: cm \\ or, \: 1 \: mm = \frac{1}{10} \: cm \\ or, 24 \: mm × ( \frac{1}{10} ) = 2.4 \: cm.\)

The scale is 2.4 cm :24 mm.

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Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

You have some data points labeled by \(x\). They form the set {3, 5, 7}.

The mean, \(\bar x\), is the average of these values:

\(\bar x = \dfrac{3+5+7}3 = \dfrac{15}3 = 5\)

Then in the column labeled \(x-\bar x\), what you're doing is computing the difference between each data point \(x\) and the mean \(\bar x\):

\(x=3 \implies x-\bar x = 3 - 5 = -2\)

\(x=5 \implies x-\bar x = 5-5 = 0\)

\(x=7 \implies x-\bar x = 7 - 5 = 2\)

These are sometimes called "residuals".

In the next column, you square these values:

\(x=3 \implies (x-\bar x)^2 = (-2)^2 = 4\)

\(x=5 \implies (x-\bar x)^2 = 0^2 = 0\)

\(x=7 \implies (x-\bar x)^2 = 2^2 = 4\)

and the variance of the data is the sum of these so-called "squared residuals".

The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

How to find  x-intercepts?

To find the x-intercepts, we set y = 0 and solve for x:

(x⁴/4) - x² + 1 = 0

This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.

To find the y-intercept, we set x = 0:

y = (0/4) - 0² + 1 = 1

So the y-intercept is (0, 1).

To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.

To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.

To find the critical points, we take the derivative of the function and set it equal to zero:

y' = x³- 2x

x(x² - 2) = 0

x = 0 or x = sqrt(2) or x = -sqrt(2)

These are the critical points.

To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.

Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).

We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:

Interval (-infinity, -sqrt(2)):

Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.

Interval (-sqrt(2), 0):

Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.

Interval (0, sqrt(2)):

Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.

Interval (sqrt(2), infinity):

Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.

Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).

To find the inflection points, we take the second derivative of the function and set it equal to zero:

y'' = 3x² - 2

3x² - 2 = 0

x² = 2/3

x = sqrt(2/3) or x = -sqrt(2/3)

These are the inflection points.

To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.

Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).

We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:

Interval (-infinity, -sqrt(2/3)):

Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Interval (-sqrt(2/3), sqrt(2/3)):

Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.

Interval (sqrt(2/3), infinity):

Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).

To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:

y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509

Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

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Answer:

It is going to be the first one

Answer:

18

Step-by-step explanation:

6 is twice less than 12

X=9*2=18

The Answer:

Width = 6

Step-by-step explanation:

Let width be w

(3w + 8) x w = 156

3 \(w^{2}\) x 8n - 156 = 0

(w + 8 x 6) (w-6) = 0

w = 6

Required two transformations are translated according to the rule (x, y) → (x + 8, y + 2) reflected across the x-axis.

How to find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″?

To find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″, we can compare the coordinates of corresponding vertices of both pentagons.

Starting with point A, we see that it has been translated 8 units to the right and 2 units up to become A″. Therefore, the first transformation is a translation according to the rule (x, y) → (x + 8, y + 2).

Next, we can compare the y-coordinates of point A and A″ to see if a reflection has been applied. We see that the y-coordinate of A has changed from 5 to -7 in A″, indicating that a reflection has been applied across the x-axis.

Therefore, the two transformations applied to pentagon ABCDE to create A″B″C″D″E″ are:

Translated according to the rule (x, y) → (x + 8, y + 2)

Reflected across the x-axis.

The other options can be ruled out as they do not correctly reflect the transformation that was applied.

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