Which of the following functions has a factor of x−7?
f(x)=x3−16x2+53x+63
f(x)=x3−2x2−73x−70
f(x)=x3−16x2+53x+70
f(x)=x3−2x2−73x−77

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

The surface is C

Step-by-step explanation:

Answer:

None of the options

Step-by-step explanation:

Given

Trapezoids: ABCD and A'B'C'D'

Required

Select type of transformation

Notice that width and length of ABCD are larger than that of A'B'C'D'

This means that the transformation applied on ABCD shrinks it size to A'B'C'D'

From the list of given option'

None of the 3 options describes this type of transformation.

The applied transformation is Dilation because it affects the size of ABCD

Hence;

None of the options is correct

Answer:

The answer is Reflection

Step-by-step explanation:

Answer:

The basic unit for measuring weight is a Newton but for an elephant a kilo Newton would be more appropriate.

Step-by-step explanation:

Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer:

45 or positive 45

Step-by-step explanation:

Answer: 45

Step-by-step explanation:

Answer:

$18.28

Step-by-step explanation:

To complete this problem is a straightforward answer:

First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!

you need to subtract 7 in each section of the inequality is

-7< x<2

-7< x and x<2

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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The angle that the ramp makes with the ground is approximately 28.07 degrees.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
The sin of the angle θ is the ratio of the opposite side (height of the ramp) to the adjacent side (length of the inclined portion of the ramp):

Sin(θ) = 8/17

We can use a calculator to find the inverse sin of this ratio to get the angle θ:

θ = sin⁻¹(8/17)

θ ≈ 28.07 degrees

Therefore, the angle that the ramp makes with the ground is approximately 28.07 degrees.

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37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.

Equations can be categorized as identities or conditional equations.

w = (455.95-155.95)/(37.50)

=300/37.50

=8

So, number of weeks = 8

As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.

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Step-by-step explanation:

Heron's formula when all 3 sides (a, b, c) are given :

s = (a + b + c)/2

A = sqrt(s(s-a)(s-b)(s-c))

in our case

s = (34+73+89)/2 = 98

A = sqrt(98(98-34)(98-73)(98-89)) =

= sqrt(98×64×25×9) = sqrt(98)×8×5×3 =

= sqrt(2×49)×120 = sqrt(2)×7×120 =

= sqrt(2)×840 = 1,187.939392... ≈ 1,188 in²

3900000×18% = 702000

702000÷2500 = 280.8 per share dividend

450×280.8 = 126360

Answer:

Step-by-step explanation:

We know that:

Work:

Hence, the sum of the first 30 terms of this arithmetic sequence is 209. Hoped this helped.

\(BrainiacUser1357\)

Answer:

The sum of first 30 terms of arithmetic sequence is 3225.

Step-by-step explanation:

Here's the required formula to find the sum of the arithmetic sequence :

\( \star{\underline{\boxed{\sf{S_n = \dfrac{n}{2}\Big[2a + (n - 1)d\Big]}}}}\)

Substituting all the given values in the formula to find the sum of arithmetic sequence :

\({\implies{\sf{S_n = \dfrac{n}{2}\Big[2a + (n - 1)d\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[2 \times 6 + (30 - 1)7\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+ (29)7\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+ 29 \times 7\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+203\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[ \: 215 \: \Big]}}}\)

\({\implies{\sf{S_{30} = 15\Big[ \: 215 \: \Big]}}}\)

\({\implies{\sf{S_{30} = 15 \times 215}}}\)

\({\implies{\sf{S_{30} = 3225}}}\)

\( \star{\underline{\boxed{\sf{S_{30} =3225}}}}\)

Hence, the sum of first 30 terms of arithmetic sequence is 3225.

\(\rule{300}{2.5}\)

The cross-price elasticity of demand between good X and good Y will be 0.5. Thus, the correct option is A.

Given that5:

Old Quantity = 1,100

New Quantity = 900

The percentage change of good Y is calculated as,

P = ((900 - 1,100) / 1,100) * 100

P = (-200 / 1,100) * 100

P = -18.18%

Next, let's calculate the percentage change in the price of good X:

Old Price = GH¢6

New Price = GH¢4

The percentage change in the price of good X is calculated as,

P = ((4 - 6) / 6) * 100

P = (-2 / 6) * 100

P = -33.33%

The cross-price elasticity of demand is calculated as,

⇒ (-18.18% / -33.33%)

⇒ 0.546 or 0.5

Thus, the correct option is A.

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The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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Answer:

the number of t-shirts sold to breakeven is 56 t-shirts

Step-by-step explanation:

The computation of the number of t-shirts sold to breakeven is shown below:

= Fixed cost ÷ (Selling price - cost price)

= $350 ÷ ($10 -  $3.75)

= $350 ÷ 6.25

=  56 t-shirts

Hence, the number of t-shirts sold to breakeven is 56 t-shirts

Answer:

just do 68986

- 64997

______

3,989

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

Answer: 2(3x+1)

Step-by-step explanation:

2(3x+1) ==> 2(3x)+2(1)

6x+2

Answer:

2(3x + 1)

Hope that helps! :)

Step-by-step explanation:

Given statement solution is :- Interpreting the steady matrix:

The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.

The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.

The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.

To analyze the steady matrix for this situation, let's consider the two groups of customers: those who turn in tickets and those who do not turn in tickets.

Let's denote the proportion of customers who turn in tickets as X and the proportion of customers who do not turn in tickets as Y.

According to the given information:

40% of the customers who turn in tickets do not turn in tickets the following week. This means that 60% of the customers who turn in tickets will turn in tickets again the following week.

30% of the customers who do not turn in tickets will turn in tickets the following week. This means that 70% of the customers who do not turn in tickets will continue not turning in tickets the following week.

Based on these percentages, we can construct the steady matrix:

java

Copy code

     |  Customers turning in tickets (X) | Customers not turning in tickets (Y) |

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

Next week 0.6 0.3

This week 0.4 0.7

Interpreting the steady matrix:

The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.

The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.

The value 0.4 in the bottom left cell represents the proportion of customers who do not turn in tickets this week but will turn in tickets next week.

The value 0.7 in the bottom right cell represents the proportion of customers who do not turn in tickets this week and will continue not turning in tickets next week.

These values describe the transition probabilities between the two customer groups. For example, if there are 100 customers in total, 60 of them will turn in tickets next week, and 40 of them will not. Similarly, 30 customers who turn in tickets this week will not do so next week, while 70 customers who do not turn in tickets this week will continue to not turn them in next week.

The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.

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Answer:

Hi there!

The simplified version is:

18x-20

Step-by-step explanation:

2(4x-6) -8 +10x

First, multiply the 2 by the parentheses.

8x -12 -8 +10x

Next, combine like terms

18x -20

This is the simplified version!

Hope this helps

The greatest number of children that can distribute the mangoes equally is 481. Each child will receive 481/481 = 1 mango.

In order to distribute the mangoes equally among children, we first need to determine the total number of mangoes in the bag.

If there are 215% (or 2.15) of 224 mangoes in the bag, we can calculate the total number of mangoes by multiplying these values: 2.15 * 224 = 481.6 mangoes.

Since we cannot have fractional mangoes, we round down to the nearest whole number, which gives us a total of 481 mangoes in the bag.

To distribute these mangoes equally among the children, we divide the total number of mangoes by the number of children. Let's assume there are 'x' children.

Each child will receive 481/x mangoes.

To determine the greatest number of children, we need to find a value for 'x' that evenly divides 481. We can do this by finding the factors of 481. The factors of 481 are 1, 13, 37, and 481.

Therefore, the greatest number of children that can distribute the mangoes equally is 481. Each child will receive 481/481 = 1 mango.

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Answer:

78.54

Step-by-step explanation:

The formula is \(A = \pi r^2\\\). So, substitute the values into the equasion and get the answer.

According to the order of operations, we square the radius first, then multiply by pi. 5^2 = 25. 25 * pi = 78.5398163397. I just rounded it to the nearest hundereth.

Answer:

We can start by finding how many pages Jordayn reads per hour:

Pages per hour = 72 ÷ (1 1/2) = 72 ÷ 3/2 = 48

So, Jordayn reads 48 pages per hour.

To find out how long it would take her to read a 168-page book, we can use the following formula:

Time = Pages ÷ Pages per hour

Time = 168 ÷ 48

Time = 3.5

Therefore, it would take Jordayn 3.5 hours to read a 168-page book, assuming her reading speed remains constant