The formula for simple interest is I=Prt
a. Solve the formula for t, when r is the simple interest per year.
t=_
b. Use the new formula to find the value of t in the table.
The value of t in the table is _ years

Answer:

  remainder: 3/4

Step-by-step explanation:

You want to divide the polynomial (2x^4-9x^3-x^2+2) by (2x-1).

The attachment shows the division worked out.

Your work has a sign error in the second product: (-4x²)(2x-1) should be (-8x³+4x²).

The factor theorem tells you that if division by (2x-1) gives a remainder of 0, then (2x-1) is a factor of the dividend polynomial. Alas, here, the remainder is not zero, so 2x-1 is not a factor.

The remainder theorem tells you that the remainder of p(x) divided by (x-a) is p(a). We can evaluate the polynomial for x=1/2, the value that makes the divisor zero:

  f(1/2) = ((2(1/2) -9)(1/2) -1)(1/2)^2+2 = ((-8)(1/2) -1)(1/4) +2 =(-5)(1/4) +2 = 3/4

The remainder from division by (2x -1) is 3/4.

__

Additional comment

We did the polynomial evaluation by writing it in Horner form. This minimizes the number of arithmetic operations required, and generally makes them simpler.

Answer:

-4

Step-by-step explanation:

In this case, rate of change will be equivalent to the gradient of the line.

Standard form of Equation of Line:

y = mx + c

where

m = Gradient

c = y - intercept

From the given information, we can substitute x = -1 and y = 0, and c = b = -4 (y-intercept) to find m (Gradient)

0 = -1m - 4

m = -4

Therefore, the rate of change is -4.

The correct form of the partial fraction decomposition for the expression 7x+18/x^2+9x is  2/x + 5/(x + 9).

What is the Fraction?

Here,

x ² + 9x = x (x + 9), so the partial fraction decomposition would be

(7x + 18) / (x ² + 9x) = a/x + b/(x + 9)

where a, b are some constants. To find them, multiply both sides by x ² + 9x :

7x + 18 = a (x + 9) + bx

Solve for a and b :

7x + 18 = (a + b) x + 9a

[ a + b = 7

[ 9a = 18

→   a = 2, b = 5

So

(7x + 18) / (x ² + 9x) = 2/x + 5/(x + 9)

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The equation in slope intercept form of the line having the slope m= 1/2 and y intercept 4 is [tex]y=\frac{1}{2}x+4[/tex]

Given,

The slope of the line = [tex]\frac{1}{2}[/tex]

The y-intercept = 4

We know,

The slope intercept form of the line y = mx + b

Substitute the values in the equation

y= [tex]\frac{1}{2}x+4[/tex]

Hence, the equation in slope intercept form of the line having the slope m= 1/2 and y intercept 4 is [tex]y=\frac{1}{2}x+4[/tex]

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Answer:

m<LHK = 101

Step-by-step explanation:

Ok, so the straight line is equal to 180 degrees. And we already know the side of one angle, that is 79 degrees. So, simply subtract 79 from 180, and you get 101 degrees. I took geometry last year, and this might not be the "correct" way to do it, but it is easier and you get the same correct answer

Answer:

<LHK = 101

Step-by-step explanation:

angle on a straight line add up to 180

180 - 79 = 101

The answers are given below:-

The length of one side of the garage​ originally was 17.9 ft.

The length of one side of the garage​ now is 21.9 ft.

The percent increase in the length of one​ side was 22.35%.

The area of a square of side s is given by s squared, that is:

A = s².

The original area was 320 ft², hence the original length was:

s² = 320

s = √(320)

s = 17.9 ft.

The area increased by 50%, hence the new area is:

A = 1.5 x 320 = 480 ft².

The current length of one side is:

s² = 480

s = √(480)

s = 21.9 ft.

The percent increase is the change divided by the initial length and multiplied by 100%, hence:

(21.9 - 17.9)/17.9 x 100% = 22.35%.

The percent increase in the length of one​ side was 22.35%.

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The standard form of a given number is scientific notation which is given by the form of exponents of ten and written as 5.67 ×10⁵.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

Standard form is a way of writing down in the easy form very large or very small numbers.

Let E is the standard form of a given number

E = 567000

E = 500000 + 67000 + 7000

E = 0.567 × 10⁶ = 5.67 ×10⁵

E = 5.67 × 10⁵

Hence, the standard form of a given number is 5.67 ×10⁵.

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The unknown variable's result of the equation 30² + 35² = x² is 46.10

To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:

30² + 35² = x²

900 + 1225 = x²

x² = 2125

x = [tex]\sqrt{}[/tex]2125

x = 46.10

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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The acceleration of the object is 2 m/s²

From the question, we are to determine the acceleration of the object

From Newton's second law of motion, we have that

F = ma

∴ a = F/m

Where F is the net force

m is the mass

and a is the acceleration

From the given information,

m = 5kg

From the diagram,

Net force = 30 N - 20N

Net force = 10 N

Then,

a = F/m

a = 10/5

a = 2 m/s²

Hence, the acceleration of the object is 2 m/s²

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Answer:

112 mm^2.

Step-by-step explanation:

Total surface area

2(4*8 + 4*2 + 2*8)

= 2 * 56

= 112 mm^2.

The complete table for the electrician charges is shown below:

               x                  y

               1                 125

               2                175

               3                225

               4                275

According to the statement, there are two variables. First, the number of hours of work (x) and, second, the total fee. The total fee changes linearly with the number of hours and the expression is defined below:

y = x' + (Δy / Δx) · x      (1)

Where:

If we know that x' = 75, Δx = 1 h and Δy = 50, then the values of the table are shown below:

x = 1

y = 75 + 50 · 1

y = 125

x = 2

y = 75 + 50 · 2

y = 175

x = 3

y = 75 + 50 · 3

y = 225

x = 4

y = 75 + 50 · 4

y = 275

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Answer:

corresponding angles are equal

Step-by-step explanation:

89*=(6x+5)*

89-5=6x

84=6x

x=14

I hope I could help.

The coordinates of Parallelogram CDEF after a reflection across y = x are C'(-1,2), D'(1,7), E(-2,6) and (-4,1)

What does coordinate mean in this case?

We want to find the coordinates of Parallelogram CDEF with vertices C(2, -1), D(7,1), E(6,-2), and F(1,-4) after a reflection across y = x.

We can find these coordinates by following the following rule:

Reflection over y = x rule : ( x , y ) ---> ( y , x )

the x and y values simply swap places .

Applying rule to coordinates:

C(2,-1) --- swap 2 and - 1 ---> C'(-1,2)

D(7,1) --- swap 7 and 1 ---> D'(1,7)

E(6,-2) --- swap 6 and -2 ---> E'(-2,6)

F(1,-4) --- swap 1 and -4 ---> F'(-4,1)

The coordinates of Parallelogram CDEF after a reflection across y = x are C'(-1,2), D'(1,7), E(-2,6) and (-4,1)

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Answer:

-6.2

=

7°c ÷ 5hrs (difference between 3pm to 8pm)= 1.4

3×1.4= 4.2

7+4.2=11.2

5-11.2=-6.2

(sorry if it's wrong)

Answer: The number 8,000 represents the change in height necessary to dodge the storm.

The integer representing the altitude after passing the storm is 30,000

Use appropriate tools, draw a number line to represent the airplanes changed altitude = 34000

Step-by-step explanation:

In the picture that is attached, the diagram for this query is displayed.

We are informed that the aircraft's starting height was 30,000 feet.

A. What integer represents the airplane's change in altitude to avoid the storm.?

During the storm:

The plane flew at at altitude of 38,000 feet

We will deduct the end altitude from the starting altitude to obtain the change in altitude.

change of altitude = final altitude - initial altitude

change of altitude = 38,000 - 30,000

                               = 8,000 ft

Therefore, the integer representing the change of altitude to avoid the storm is 8,000

B. What integer represents the airplanes change in altitude immediately after passing the storm?

After the storm:

We are aware that the aircraft returned to its original height following the storm.

The number reflecting the altitude after passing the storm would be 30,000 ft given that the starting altitude is 30,000 ft.

C. Use appropriate tools, draw a number line to represent the airplanes changed altitude.​

See a picture.

Use appropriate tools, draw a number line to represent the airplanes changed altitude = 34000

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Answer: D, reciprocal parent function

Step-by-step explanation:

Answer:

x = 9.

Step-by-step explanation:

12x + 7 = 115

12x + 7 - 7 = 115 - 7

12x = 108

x = 9.

From the figures and the properties of the parallelogram was possible to find that: UT=27, ST=18, RV=7 and US=14.

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  the opposite sides are equal and parallel, for a parallelogram. In a parallelogram is noted too that the opposite angles and the diagonals are equal.

From the properties: the opposite sides are equal and parallel for a parallelogram. It is possible to find:

UT=RS=27

ST=RU=18

Considering that UV=7, then VS= 7 since V is the midpoint of the diagonal US. Therefore, US=14.

From the property: the diagonals are equal for a parallelogram. It is possible to find:

US=RT=14

RV=RT/2=14/2=7

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The population of China is 28 times greater than that of South Korea, calculated using solving of basic linear equation.

As per the question statement, the population of China is about (1.4 × 10⁹) people, while that of South Korea is approximately 50,000,000 people.

We are required to calculate that, by how many times is the is the population of China greater than that of South Korea.

To solve this question, let us assume that, the population of China is "x" times greater than that of South Korea. Hence, we will form a linear equation of single variable (x) and solving for "x", we will obtain our desired answer.

Since the population of China is assumed to be "x" times greater than that of South Korea,

[tex](50000000*x)=1.4*10^{9}\\ or,5*10^{7}*x=1.4*10^{9}\\or,5x=\frac{1.4*10^{9}}{10^{7}} \\or, 5x=1.4*10^{2}\\ or,5x=1.4*100\\or,5x=140\\or,x=\frac{140}{5}\\ or,x=28[/tex]

That is, The population of China is 28 times greater than that of South Korea.

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The sum is 40,000.

The difference between compound interest and simple interest is 324 on a certain sum at 9% for 2 years.

So,

Compound interest - Simple interest = 324

C.I - SI = 324

The formula for compound interest is given as:

C.I = P( 1 + r/100 )ⁿ - P

Where P is the principal amount, r is the rate and n is the time in years.

Therefore,

C.I = P( 1 + 9/100)² - P

C.I = P( 1 + 0.09)² - P

C.I = P(1.09)² - P

C.I = 1.1881P - P

C.I = 0.1881P

Now, the formula for simple interest is given as:

S.I = ( P × R × T / 100 )

Where P is the principal amount, R is the rate and T is time in years.

Therefore,

S.I = ( P × 9 × 2 / 100 )

S.I = 18P / 100

S.I = 0.18P

Now,

C.I - S.I = 324

0.1881P - 0.18P 324

0.0081P = 324

P = 324 / 0.0081

P = 324 × 10000 / 81

P = 4 × 10000

P = 40000

Hence, the principal amount is 40,000.

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The equation of the line in slope-intercept form passing through the point (-7 , 10) and parallel to 2x - 3y = -3 is y = (2/3)x + 44/3.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

If the line is parallel to 2x - 3y = -3, then their slopes are equal. First, express the equation in slope-intercept form y = mx + b to get the slope, m.

2x - 3y = -3

-3y = -2x - 3

y = -2/-3 x - 3/-3

y = 2/3 x + 1

m = 2/3

Substitute the values of the slope and the point to solve for the y-intercept, b.

y = mx + b

10 = 2/3(-7) + b

b = 44/3

Write the equation of the line by plugging in the value of the slope and y-intercept.

y = mx + b

y = (2/3)x + 44/3

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The value of the x in the vertical angles are the 7/2.

According to the statement

We have to find that the value of the x in the given angles.

So, For this purpose, we know that the

An angle is formed when two straight lines or rays meet at a common endpoint.

From the given information:

If angle A is 4x+2 and angle B is 11x.

Then from the given figure, The given angles are the verticals.

We know that the Verticals angles are equal.

Then

4x+2 = 11x

7x = 2

x = 2/7.

Here the values of the x in the given vertical angles are 7/2.

So, The value of the x in the vertical angles are the 7/2.

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the answer to this question is

O h(x) = 1/4x

The linear function for the height of the taller candle after t hours is given by:

h(t) = 18 - 3.1t.

The missing information is that a 18 inch candle is burning at a rate of 3.1 inches an hour.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

Hence the linear function for the height of the taller candle after t hours is given by:

h(t) = 18 - 3.1t.

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[tex]V = 1.17 * 10^{-29} m^{3}[/tex]  is  volume of a sphere is a function .

What is surface area of volume?

The quantity of surface area per unit volume of an object or collection of objects is known as the surface-area-to-volume ratio, sometimes known as the surface-to-volume ratio and variously abbreviated as sa/vol or SA:V.

Convert the radius from picometers to meters

r = 141     pm = 1.41 * [tex]10^{-10} m[/tex]

V  = 4/3 π r³

 = 4/3 π  ( 1.41 * [tex]10^{-10}[/tex])³

[tex]V = 1.17 * 10^{-29} m^{3}[/tex]

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The direct variation is y = 3/2 x, the value of y for x = 3 is 9/2.

A direct variation is defined as having variables that are directly proportional. When one variable's value rises, the other variable's value rises as well, and vice versa. Assuming k is constant, the following is how a direct variation is expressed:

y=kx

As y varies directly with x,

using direct variation,

y = kx

given, y = 3/4 when x = 1/2,

⇒ 3/4 = k 1/2

⇒ k = 3/2

when x = 3,

the value of y will be -

y = kx

⇒ y = 3/2. 3

⇒ y = 9/2

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Answer:

so the cell phone plan is $70 per month

Step-by-step explanation:

solution in question

yes

when equations are parallel

&

when you solve the equations you have

DIFFERENT NUMBERS on either side of the equal sign

for example when you do the math you would end up with something like :

7 = 0

mrviolamath

khan academy

The maximum amount of revenue the carnival can expect in the town in the 5th night is; $4746.093.

A geometric progression is defined as a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.

For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.

We are told that Revenue in the first night = $15000

Now revenue of new night is 75% of the previous night. Thus;

2nd night = 15000 × 75/100 = $11250

3rd night = $11250 × 75/100  = 8437.5

Therefore, the given geometric sequence is ;

15000, 11250, 8437.5 ...

First term; a = $15000

Common ratio (r) = 11250/15000 = 0.75

The formula for the nth term of a GP is given by ;

aₙ = arⁿ ⁻ ¹

Thus, revenue for the 5th night is;

a₅ = ar⁵⁻¹

a₅ = 15000(0.75)⁴

a₅ = 4746.093

We conclude that the revenue in the 5th night in two will be $4746.093.

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