30 POINTS!!! Calculate the percent increase or decrease between the starting and ending quantities below. Round your answer to one decimal place.


1) Start: 3 End: 10


2) Start: 9 End: 20


3) Start: 100 End: 85

(a) The explicit rule to model the sequence formed by the number of seats in each row is [tex]a_{n}=15+3n[/tex]

(b) The 35th row has 120 seats

Step-by-step explanation:

The rule of the nth term of an arithmetic sequence is

[tex]a_{n}=a+(n-1)d[/tex] , where

∵ There are 18 seats in the 1st row

∵ There are 21 seats in the 2nd row

∵ 21 - 18 = 3

∵ The number of seats is increased by 3 with each additional row

- The number of seats in each row represents an arithmetic

   sequence because there is a common difference between

   each two consecutive rows

∴ The number of seats in each row formed an arithmetic sequence

∵ The number of seats in the first row = 18 seats

∴ a = 18

∵ The number of seats in a row continues to increase by 3 with each

   additional row

∴ d = 3

- Substitute the values of a and d in the rule of nth term

∴ [tex]a_{n}=18+(n-1)3[/tex]

- Simplify the right hand side

∴ [tex]a_{n}=18+3n-3[/tex]

- Add like terms

∴ [tex]a_{n}=15+3n[/tex]

(a) The explicit rule to model the sequence formed by the number of seats in each row is [tex]a_{n}=15+3n[/tex]

∵ There are 120 seat in a row

- Substitute [tex]a_{n}[/tex] by 120 in the rule above

∴ 120 = 15 + 3n

- Subtract 15 from both sides

∴ 105 = 3n

- Divide both sides by 3

∴ n = 35

∴ The number of the row is 35

(b) The 35th row has 120 seats

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Answer:

4 times more

Step-by-step explanation:

80/20=4

Number of adults = 40

Number of children = 156

Step-by-step explanation:

Let x be the number of adults and

y be the number of children

Then according to given statements

[tex]x+y=196\ \ \ Eqn\ 1\\2.0x+1.50y = 314\ \ \ Eqn\ 2\\[/tex]

From equation 1:

[tex]x+y = 196\\x = 196-y[/tex]

Putting in equation 2

[tex]2(196-y) + 1.50y = 314\\392-2y+1.50y = 314\\392-0.5y = 314\\-0.5y=314-392\\-0.5y=-78[/tex]

Dividing both sides by -0.5

[tex]\frac{-0.5y}{-0.5} = \frac{-78}{-0.5}\\y = 156[/tex]

Putting y = 156 in equation 1

[tex]x+156 = 196\\x = 196 - 156\\x = 40[/tex]

Hence,

Number of adults = 40

Number of children = 156

Keywords: Linear equations, Variables

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Answer:

-12

Step-by-step explanation:

x - 8 = -20  (add 8 to both sides)

x = -20 + 8

x = -12

Answer:

-12

Step-by-step explanation:

-12 + -8 is -20.

x= -12 because if you added 28 or 12, the answer would be positive. If you subtracted -28 from -8 your answer would be -36.

So the only answer is -12.

Answer:

Step-by-step explanation:

Yes, you like AirPods due to zero wires, comfortable fit and long lasting 24 hours battery life.

Step-by-step explanation:

The current technology employed in Apple devices has attracted most users.For example in the AirPods technology, users can enjoy features such as instant connection to  other Apple devices, easy switching from Mac to Os devices, comfortable fit and long battery hours. Even with the current price of AirPods at $159 the advantages outweigh the cost.

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Answer: Yeah you like airpods

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

5x+4=19

5x=19-4

5x=15

x=15/5

x=3

Answer:

x = 3

Step-by-step explanation:

Given

5x + 4 = 19 ( subtract 4 from both sides )

5x = 15 ( divide both sides by 5 )

x = 3

25t means "25 times t" where t is some unknown number. It is a placeholder for a number.

To find what the number is, we undo what is happening to t. So we divide both sides by 25 to undo the operation "multiply by 25"

----------

25*t = 1125

25*t/25 = 1125/25 divide both sides by 25

t = 45

---------

As a check, we can plug t = 45 into the equation and we should get the same value on both sides

25*t = 1125

25*45 = 1125 replace every t with 45

1125 = 1125 the answer is confirmed

Answer:

45

The drawings will help

The true statements are:

The ordered pair (−4 , 0) is a solution to the first equation because it makes the first equation true ⇒ 1st answer

The ordered pair (−4 , 0) is a solution to the second equation because it makes the second equation true ⇒ 2nd answer

The ordered pair (−4, 0) is a solution to the system because it makes both equations true ⇒ 4th answer

Step-by-step explanation:

To prove that point (a , b) is a solution of an equation

∵ The system of equations is:

2x + y = -8 ⇒ (1)

x - y = -4 ⇒ (2)

The ordered pair is (-4 , 0)

Substitute x by -4 and y by 0 in each equation

∵ x = -4 and y = 0

∵ The left hand side in equation (1) is 2x + y

∵ 2(-4) + 0 = -8 + 0 = -8

∴ The left hand side = -8

∵ The right hand side = -8

∴ The left hand side = the right hand side

∴ (-4 , 0) is a solution of equation (1)

The ordered pair (−4 , 0) is a solution to the first equation because it makes the first equation true

∵ The left hand side in equation (2) is x - y

∵ (-4) - 0 = -4 - 0 = -4

∴ The left hand side = -4

∵ The right hand side = -4

∴ The left hand side = the right hand side

∴ (-4 , 0) is a solution of equation (2)

The ordered pair (−4 , 0) is a solution to the second equation because it makes the second equation true

∵ The ordered pair (-4 , 0) makes the two equations true

∴ The ordered pair (-4 , 0) is the solution of the system of equations

The ordered pair (−4, 0) is a solution to the system because it makes both equations true

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In a quadrilateral inscribed in a circle, opposite angles are supplementary. Hence, opposite angles J and M in quadrilateral JUMP are supplementary, totaling 180 degrees.

In the given diagram, quadrilateral JUMP is inscribed in a circle. According to the property of inscribed angles, when a quadrilateral is inscribed in a circle, opposite angles are supplementary, meaning they add up to 180 degrees.

Given that angles J and M are opposite angles in quadrilateral JUMP and must be right angles, it implies that they are supplementary. This is because right angles measure 90 degrees each, and the sum of two right angles equals 180 degrees, making them supplementary.

Therefore, we conclude that angles J and M are supplementary, with a combined measure of 180 degrees.

To summarize, in the inscribed quadrilateral JUMP, opposite angles J and M are supplementary, totaling 180 degrees, due to the property of angles in a quadrilateral inscribed in a circle.

The question probable may be:

In the diagram below, quadrilateral JUMP is inscribed in a circle. Opposite angles J and M must be right 2. complementary 3. congruent 4 supplementary

Answer:

87

(3 times 9)+(10 times 6)

Step-by-step explanation:

PEMDAS

36/6=6

Answer:

The volume of paint that covers the whole car is [tex]1\frac{1}{4}[/tex] gallons or one and a quarter gallons.

Step-by-step explanation:

Let the volume of paint required to cover whole car be 'x'.

Given:

Volume of paint to cover one-fifth of a car = one-fourth of a gallon.

We use unitary method to determine the volume of paint required.

∵ One-fifth of a car requires paint = [tex]\frac{1}{4}\ gal[/tex]

∴ Whole volume of car requires paint = [tex]\frac{\frac{1}{4}}{\frac{1}{5}}[/tex]

[tex]=\frac{1}{4}\times \frac{5}{1}\\=\frac{5}{4}\\=1\frac{1}{4}\ gal[/tex]

Therefore, the volume of paint that covers the whole car is [tex]1\frac{1}{4}[/tex] gallons or one and a quarter gallons.

Answer:

y-3=-1/2(x-4)

Step-by-step explanation:

y-y1=m(x-x1)

perpendicular means negative reciprocal of the current slope,

and the negative reciprocal of 2 is -1/2.

y-3=-1/2(x-4)

Answer:

D, My original answer was A (-6,2) B (-6,5) but that's particular order is not an option but if you flip it you get answer D

Answer:

Well isosceles triangle has two angle that are the same and one different

if one angle is 90 degrees that means the other two angles have to be 45 cause all three angles of a triangle equal 180.

Answer:

The rule which allows us to change the sign of an exponent is called the negative exponent rule.

Step-by-step explanation:

Consider the provided information.

The negative exponent rule is the rule which allows to change the sign of an exponent.

[tex]x^{-1}=\frac{1}{x}[/tex]

According to negative exponent rule: A negative exponents in the numerator moved to the denominator and become positive exponents.

If A negative exponents in the denominator moved to the numerator and become positive exponents.

Hence, the required statement is: The rule which allows us to change the sign of an exponent is called the negative exponent rule.

Answer:

y = 2x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange y - 2x = 3 into this form by adding 2x to both sides

y = 2x + 3 ← in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To find c substitute (3, 1) into the partial equation

1 = 6 + c ⇒ c = 1 - 6 = - 5

y = 2x - 5 ← equation of line

Answer:

it would be 0.2

Step-by-step explanation:

When you multiply 0.4*0.5 it would equal 0.2 since 4*5=20 then 4.0*0.5= 0.2 since 0.2 in fraction form is 2/10 or 20/100.

Answer:

Paul Hastings checkbook balance be  $1753

Explanation:

We are given Paul Hastings

current checkbook balance is equal to $1345.00

and a deposit of $423.00  is said to be made in the bank

so the new balance will be addition of this deposit in the current balance also there's a deduction of $15 as service fee.

So the total checkbook balance will be after subtracting $15 from sum of current balance and deposit.

So his checkbook balance = $1345 + $423 - $15

                                             = $1753

which is the required value of checkbook.

Answer:

well if it is a square then 10ft by 10ft. Otherwise, since you haven't given me the scale drawing, just find the area through 5cm. Then multiply your answer by 2 and instead of cm have ft.

Step-by-step explanation:

you need to put the decimal somewhere but if it comes at the beginning then 203463is your answer.

Answer:

here is an actual answer

203463

Step-by-step explanation:

Answer:

x = -4 or 2

Step-by-step explanation:

-4x² + 10x − 40 = -9x²

First, move the x terms to one side and the constant to the other.

5x² + 10x = 40

Divide by the leading coefficient:

x² + 2x = 8

Take half of the b coefficient, square it, then add to both sides.

(2/2)² = 1

x² + 2x + 1 = 8 + 1

x² + 2x + 1 = 9

Factor the perfect square:

(x + 1)² = 9

Solve for x:

x + 1 = ±3

x = -1 ± 3

x = -4 or 2

Answer:x=2,-4

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

(1/2)/4=(1/2)(4/1)=4/2=2

Answer:

1/8

Step-by-step explanation:

1/2 ÷ 4

= 1/2 x 1/4

= 1x1/2x4

= 1/8

Answer:

larger no=19, smaller no=-15

Step-by-step explanation:

let X be the larger no &Y be the smaller no

so [tex]X+Y[/tex]=4.....(1)

[tex]4X+3Y[/tex]=31............(2)

from [tex](2)- (1)*3[/tex]

[tex]4X+3Y-3X-3Y[/tex]=[tex]31-12[/tex]

X=19

Y=-15

To find the two numbers, we can set up a system of equations and use the method of substitution to solve it.

Let's represent the two numbers as x and y. We are given that x + y = 4 and 4x + 3y = 31.

To solve this system of equations, we can use the method of substitution. From the first equation, we can express x = 4 - y. Substituting this into the second equation, we have 4(4 - y) + 3y = 31.

Simplifying this equation gives us 16 - 4y + 3y = 31. Combining like terms, we get -y + 16 = 31. Subtracting 16 from both sides, we have -y = 15. Finally, multiplying both sides by -1, we find that y = -15.

Substituting this value back into x + y = 4, we get x + (-15) = 4, which gives us x = 19.

Therefore, the larger number is 19 and the smaller number is -15.

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Answer:

920,000

Step-by-step explanation:

943,361-24,200=919,161=920,000

there are 784 different committees possible that consist of 2 women and 2 men.

To form a committee of 4 people consisting of 2 women and 2 men, we need to choose 2 women from the 8 available women and 2 men from the 8 available men.

We can calculate the number of ways to choose 2 women from 8 using combinations, denoted as ( C(n, k) \), which is calculated as:

[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]

Where:

- ( n ) is the total number of items (in this case, the number of women)

- ( k ) is the number of items to choose (in this case, 2)

- ( n! ) denotes the factorial of ( n ), which is the product of all positive integers up to ( n )

Similarly, we can calculate the number of ways to choose 2 men from 8.

Once we have chosen 2 women and 2 men, we multiply these numbers together to find the total number of possible committees.

Let's calculate it step by step:

1. Choose 2 women from 8:

[tex]\[ C(8, 2) = \frac{8!}{2!(8-2)!} = \frac{8!}{2!6!} = \frac{8 \times 7}{2 \times 1} = 28 \][/tex]

2. Choose 2 men from 8:

[tex]\[ C(8, 2) = \frac{8!}{2!(8-2)!} = \frac{8!}{2!6!} = \frac{8 \times 7}{2 \times 1} = 28 \][/tex]

3. Multiply the number of ways to choose women and men:

[tex]\[ \text{Total number of committees} = 28 \times 28 = 784 \][/tex]

So, there are 784 different committees possible that consist of 2 women and 2 men.

To determine the number of days you have read, an equation is set up as 150 - 3x = 60, where x represents the number of days. After solving, it reveals that you have read for 30 days.

To find the number of days, x, that you have read, given that there are 60 pages left and you read 3 pages per day in a 150-page book, we can set up the following equation:

150 - 3x = 60

This equation represents the total number of pages in the book (150) minus 3 pages for each day that you read (3x) equal to the number of pages left (60).

Now, solve for x to determine the number of days you have been reading:

150 - 60 = 3x

90 = 3x

x = 30 days

Therefore, you have been reading for 30 days.

Answer:

In this problem and with any rational number, the zero product property will be applied. If ab = 0, then either a = 0 or b = 0, or both. A product of factors is zero if and only if one or more of the factors is zero.

And excuse me, but where's the other 75 points?

Answer:

y=2x-1

Step-by-step explanation: