The period p of a pendulum, or the time it takes for the pendulum to make one complete swing, varies directly as the √L, where Length of the pendulum. If the period of a pendulum is 1.1 s when the length is 2 ft, find the period when the length is 7 ft.

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:

you have to convert them to equivalent units (the same denominators)

Step-by-step explanation:

first, multiply  2 and 7 by 4.

now you have 8/21.

then, make the other fraction the same value.

multiply 1 and 4 by 7.

7/21.

now your equation is 7/21 + 8/21= 15/21.

Answer:

4π

Step-by-step explanation:

Circumference = π X D (D = diameter = 2 X radius).

Diameter = 32.

Circumference = π (32) = 32π.

Divided into 8 slices = 1/8 of the circumference = 32π/8 = 4π.

Sum of the interior angles of any triangle equal 180° .

Thus ;

\(x + 2x + x + 8 = 180\)

\(4x + 8 = 180\)

Subtract sides -8

\(4x + 8 - 8 = 180 - 8\)

\(4x = 172\)

Divided sides by 4

\( \frac{4}{4}x = \frac{172}{4} \\ \)

\(x = 43\)

So the angles are :

x = 43°

2x = 2 ( 43 ) = 86°

x + 8 = 43 + 8 = 51°

Thus the order from least to greatest ,

is : 43° , 51° , and 86°

_________________________________

And we're done.....♥️♥️♥️♥️♥️

Answer:

Step-by-step explanation:

you just give 2 a common factor

2(-5x+1)

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer: 0.2

happy learning

Answer:

\(y = 25x +1950\)

Step-by-step explanation:

Given

\((x_1,y_1) = (30,2700)\)

\((x_2,y_2) = (50,3200)\)

Required

Determine the linear function

We start by calculating the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

So, we have:

\(m = \frac{3200 - 2700}{50 - 30}\)

\(m = \frac{500}{20}\)

\(m = 25\)

The equation is then calculated as:

\(y - y_1 = m(x - x_1)\)

This gives:

\(y - 2700 = 25(x - 30)\)

\(y - 2700 = 25x - 750\)

Make y the subject

\(y = 25x - 750 + 2700\)

\(y = 25x +1950\)

Answer:

13/40

Step-by-step explanation:

The period they have played can be divided into 3 parts:

● The time Amy wins

● The time Lily wins

● The time they tie

So the sum of them is the total time of playing.

Let A be the time Amy wins, L the tile Lily wins and T the time they tie .

●●●●●●●●●●●●●●●●●●●●●●●

Since we have expressed the times using fractions then the total period of playing is 1 wich is 100%.

So:

A + P + T = 1

3/8 + 3/10 + T = 1

Multiply 8 by 10 and 10 by 8 so that you get a common denominator.

Cross multiply the numerators and the denominators.

(3*10+3*8)/80 + T = 1

(30 + 24)/80 + T =1

54/80 + T = 1

(27*2)/(40*2) + T = 1

Simplify by 2

27/40 + T = 1

T = 1 - 27/40

Multiply one by 40 to get a common denominator

T = (40-27)/40

T = 13/40

So they have tied 13/40 of the time

Answer: The maximum height of the wall that can be reached by the ladder on the second truck = 58.19 meters

Step-by-step explanation:

A diagram for the given situation is attached.

To find: AC

In right triangle ABF,

\(\dfrac{AB}{AE}=\sin 70^{\circ}\\\\\Rightarrow\ \dfrac{AB}{30}=0.9397\\\\\Rightarrow\ AB=30\times0.9397\approx 28.19\)

Now AC = AB + BC = 28.19 + 30 meters = 58.19 meters

Therefore, the maximum height of the wall that can be reached by the ladder on the second truck = 58.19 meters

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Answer:

grab

Step-by-step explanation:

hahahahaha

Answer:

$108

Step-by-step explanation:

Let n be the cost of a keychain, then the cost of a T-Shirt would be 4n. We can use this to set up an equation...

4n+n=135

Combine like terms

5n=135

Divide both sides by 5

n=27

Now we need to find how much she made from selling T-Shirts...

4n=4(27)=$108

Answer:18

Step-by-step explanation:15 + 6 u add the 15 and the 6 for it to be 18

Answer:

-40+44i

Step-by-step explanation:

4(-10+11i) = -40+44i

hope its clear

The principle of "Caring about the development of students' mathematical proficiency" is a vital component of the teaching process.

As a teacher, you must be concerned about your student's growth in mathematics to support their success in the subject. The main points of this principle are as follows:

1. Supporting Students: The teacher must strive to provide effective support for each student's learning, based on their needs.

2. Encouraging Students: The teacher should encourage students to improve their proficiency in mathematics and support their learning by providing suitable opportunities for them.

3. Problem-Solving Skills: Teachers must help students develop problem-solving skills to tackle challenging mathematical problems.

4. Feedback and Assessment: The teacher must provide timely feedback and assessment to support the student's growth in mathematics. This feedback should be constructive and should aid in the student's development of mathematical proficiency.

5. Encouraging Student Reflection: The teacher should encourage students to reflect on their learning experiences to recognize areas where they need more support. The development of a student's mathematical proficiency should be the focus of a teacher's teaching, learning, and assessment practices.

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whatever how much the money is for one day on the object just multiply the money by the days it's rented out and add together the snowboard total and the boots total

Answer:

358

Step-by-step explanation:

Answer:

8,855

Step-by-step explanation:

The number of possible orders is 2,30,230.

Combinations are ways to choose things from a collection where the order of the choices is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining the words indicates "Selection of things," where the order of the items is irrelevant.

Given total numbers of flavours = 26

number of dip = 6

Combinations allows us to create various sets of x components from a total of n elements, where their order is irrelevant and no member is repeated.

Combinations can be mathematically stated as:

ⁿCₓ = \(\frac{n!}{(n - x)!x!}\)

we have n = 26

and x = 6

ⁿCₓ =  \(\frac{n!}{(n - x)!x!}\)

²⁶C₆ = \(\frac{26!}{(26 - 6)!6!}\)

26! = 26 x 25 x 24 x 23 x 22 x........ x 1

6! = 6 x 5 x 4 x 3 x 2 x 1

²⁶C₆ = 26!/(20!6!)

²⁶C₆ = 26 x 25 x 24 x 23 x 22 x 21 x 20!/(20!6!)

²⁶C₆ = 26 x 25 x 24 x 23 x 22 x 21/(720)

²⁶C₆ = 2,30,230

Hence the numbers of orders are 2,30,230.

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ANSWER

The width of the rectangle is 4.5ft

The length of the rectangle is 10ft

EXPLANATION:

Given information

To find the dimension of the rectangle, follow the steps below

Step 1: Write the formula for calculating the area of a rectangle

Step 2: Express the length of the rectangle in algebraic form

The length of the rectangle is 1 more than twice the width

Algebraically,

l = 2w + 1

l = 2w + 1

Step 3: Substitute the given data into the formula in step 1

Step 4: Solve the quadratic function in step 3 using the general method

Hence, the width of the rectangle is 4.5ft

Step 5: Find the length of the width by putting w = 4.5

Hence, the length of the rectangle is 10ft

By answering the presented question, we may conclude that Therefore, 1  expressions cm on the map corresponds to a real distance of 3.2 km. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Scale 1:

320000 means that 1 unit on the map represents his 320000 units in the real world.

To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.

1 kilometer = 100000 cm

So,

1 unit on the map = 320000 units in the real world

1 cm on the map = (1/100000) km in the real world

Multiplying both sides by 1 cm gives:

1 cm on the map = (1/100000) km * 320000

A simplification of this expression:

1 cm on the map = 3.2 km

Therefore, 1 cm on the map corresponds to a real distance of 3.2 km. 

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The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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Answer:

x ≈ 30,37

y ≈ 29,00

Step-by-step explanation:

Use trigonometry:

\( \sin(38°) = \frac{9}{x} \)

Now, use the property of the proportion to find x:

\(x = \frac{9}{ \sin(38°) } ≈30.37\)

Do the same thing to find y:

\( \tan(38°) = \frac{9}{y} \)

\(y = \frac{9}{ \tan(38°) } ≈29.00\)

Answer:

arc = 3.75π cm

Step-by-step explanation:

the central angle subtended by the arc is congruent to the arc , that is 45°

the arc length is calculated as

arc = circumference of circle × fraction of circle

    = 2πr × \(\frac{45}{360}\) ( r is the radius )

    = 2π × 15 × \(\frac{1}{8}\)

    = 30π × \(\frac{1}{8}\)

    = \(\frac{30}{8}\) π

   = \(\frac{15}{4}\) π = 3.75π cm

Answer:

yes

Step-by-step explanation:

numbers are 20 and 30 or 30 and 20.

A statement that represents the equality between two mathematical expressions. An equation can have one variable or two variables.

sum of two numbers = 50

sum of their reciprocal = 1/12

what is the 2 numbers.

let, one number is X and the other number is Y

as per the given condition, sum of X and Y is 50

X + Y =50 ...... equation 1

again, sum of the reciprocal of X and Y = 1/12

1/ X + 1/ Y = 1/12 ..... equation 2

 (X + Y)/ XY = 1 /12

(X + Y)12 = XY...  equation 3

from equation 1, we can write, Y = 50 - X

putting this value of Y in the equation 3

12X + 12(50 - X) = X(50 -X)

12X + 600 - 12X = 50X - X²

X² - 50X+600= 0

from the formula for quadratic equation, X = [50 ±√ (50² - 4×600)] / 2×1

                                                         X = (50±10) / 2

                                    X = 30, 20

          Y = 50 -30 = 20

      Y = 50- 20 = 30

hence, the 2 numbers are 20 and 30.

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The translation form of each shape is given as follows:

a) X to Z: (x, y) -> (x + 5, y + 2).

b) Z to X: (x, y) -> (x - 5, y - 2).

The four translation rules are defined as follows:

For the composition of translations, we add the coordinates, hence:

Hence the rule from X to Z is given as follows:

(x, y) -> (x + 5, y + 2).

From Z to X, we have the inverse rule, hence:

(x, y) -> (x - 5, y - 2).

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The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

Option A is the correct answer.

We have,

The problem states that a student must work on i-Ready for at least 4 hours per month to receive a grade of 100.

Since Sophia received a math grade of 100, it means that she has met the requirement of working on i-Ready for at least 4 hours in the last month.

And,

The symbol "≥" means "greater than or equal to," indicating that Sophia worked for at least 4 hours.

Therefore,

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

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Answer:

  13.2 gallons

Step-by-step explanation:

The wall area is the product of the room's perimeter length and the wall height:

  A = Ph = (2(L+W))h = 2(20 +13)(8) = 528 . . . . square feet

The number of gallons required to cover this area is then ...

  (528 ft^2)/(40 ft^2/gal) = 13.2 gal

13.2 gallons of paint are required to paint the walls of the room.