7. What is the equation of a line that is parallel to -x+3 y=6 and passes through the point (3,5) ?
y=___ x +_____

The explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].

What is a geometric sequence?

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given:

         [tex]a_4=8573.75\\\\a_6=7731.81[/tex]

Now by using the formula for the nth term of a GP, we get

           [tex]a_n = ar^{n-1}\\\\a_4=ar{4-1}\\\\8573.75=ar^3[/tex]

Now for n = 6, we get

           [tex]a_n = ar^{n-1}\\\\a_6=ar{6-1}\\\\7737.81=ar^5[/tex]

Now divide we get

[tex]\frac{ar^5}{ar^3} =\frac{7737.81}{8573.35} \\\\r^2=0.9025\\\\r=0.95[/tex]

Now we can get the value of a,

        [tex]8573.75=ar^3\\\\a = \frac{8573.75}{(0.95)^3}\\\\a = \frac{8573}{0.8573}\\\\a = 10000.87[/tex]

So we can prepare the explicit formula as

            [tex]a_n =10000.87\times (0.95)^{n-1}[/tex]

Hence, the explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].

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Answer: x+7=1+2x

Step-by-step explanation:

If x represents the number,The sum of a number and 7 is x + 7One more than twice the number is 1 + 2xThe IS in the middle of the sentence means =So, x + 7 = 1 + 2x  Solve this equation,If you need further assistance message me.

140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.

An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.

Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.

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To express the given numbers in equation form it can be written as =

140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.

What is an equation?

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Answer:

C.

19.5m2+11.7m

Step-by-step explanation:

hope this helps

Answer:

C.

19.5m2+11.7m

Step-by-step explanation:

what i got on the test

The confidence interval, expressed as a trilinear inequality, is 71.6%

What does a confidence interval mean?

The range of values we see in our sample and expect to find the value that most accurately represents the population are referred to as a confidence interval.

The lower bound is 71.6% - 8.2% = 63.4% and the upper bound is 71.6% + 8.2% = 79.8%.

Thus the confidence interval, expressed as a trilinear inequality, is 63.4% < p < 79.8%, where p= 71.6%.

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Answer: The function F(x) = 32 + 1.87x converts Celsius temperatures to Fahrenheit temperatures. To confirm this, you can plug in a few different values for x (the Celsius temperature) and see if the corresponding value of F(x) (the Fahrenheit temperature) is correct.

For example, if x = 0, the function gives us F(0) = 32 + 1.87 * 0 = 32, which is the correct conversion from Celsius to Fahrenheit for 0 degrees Celsius.

If you want to find a formula for the function C that converts Fahrenheit temperatures to Celsius temperatures, you can start by rearranging the formula for F(x). The Fahrenheit temperature is equal to the Celsius temperature plus 32, multiplied by 1.8.

If we solve for the Celsius temperature, we get:

x = (F - 32) / 1.8

This is the formula for the function C that converts Fahrenheit temperatures to Celsius temperatures. To use this function, you would plug the Fahrenheit temperature into the function as the input, and it will give you the corresponding Celsius temperature as the output.

For example, if you want to convert 100 degrees Fahrenheit to Celsius, you would plug 100 into the function as the input:

C(100) = (100 - 32) / 1.8 = 37.78 degrees Celsius.

The missing sides of triangle ABC, If M is the centroid of triangle ABC, AM = 44, CE =54, and DM = 23, are FM = 22, AM = 44.

Three medians of a triangle intersect to produce the centroid of the triangle. It is one of a triangle's four points of concurrency. When the midpoints of the triangle's opposite sides are linked, the triangle's vertices become the triangle's medians.

Given:

The [tex]M[/tex] is centroid of triangle ABC, AM = 44, CE = 54, and DM = 23,

The centroid of a triangle divides the median in the ratio [tex]2 : 1[/tex]

Therefore, [tex]AM : FM = 2 : 1[/tex]

Let AM = 2x and FM = x

Since, AM = 44

Hence, 2x = 44

x = 44 / 2

x = 22

FM = 22

Therefore, the missing sides are FM = 22 and AM = 44.

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The missing figure is attached below.

Answer:

b

step by step explanation

The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

When compounded continuously , the Compound Interest Amount is calculated by the formula ,

A = Pe^rt

Given data ,

Let the investment be P

The value of P = $ 1100

The rate of interest r = 5 %

The number of years t = 7 years

The Compound Interest Amount when compounded continuously is calculated by the formula ,

A = Pe^rt

Substituting the values in the equation , we get

A = 1100 x e ^ 0.05 x 7

A = 1100 x e ^ 0.35

A = 1100 x 2.718 ^ 0.35

A = 1100 x 1.419067

A = $ 1560.97

Therefore , the value of the amount is A = $ 1560.97

Hence ,

The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97

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Answer:

156

Step-by-step explanation:

4x + 3 = 3(2x - 5)

4x + 3 = 6x - 15

3 = 2x - 15

2x = 18

x = 9

4(9) + 3

= 36 + 3

= 39

39 * 4 = 156

Hope it helps!

Answer: 156 inches

Step-by-step explanation:

So we know that all of the sides are equal to each other.

Now we need to know what x equals.

4x + 3 = 3(2x -5)

4x + 3 = 6x - 15

3 = 2x -15

18 = 2x

9 = x

Plug 9 into one of the equations.

4(9) + 3

36 + 3 = 39

39 * 4 = 156

Perimeter = 156 inches

Hope this helps!!! :)

Answer:

Your answer is 7 + a - 5b.

Step-by-step explanation:

All you have to do is subtract the numbers.

Hope this helped! :D

After using the trigonometry method the answer is sin 2 (pi/7)/2

What principle underlies trigonometry?

The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the branch of mathematics known as "trigonometry." Therefore, using trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.

What distinguishes geometry from trigonometry?

The study of triangle properties, particularly those of right triangles, is known as trigonometry. But the study of geometry focuses on the characteristics of all geometrical figures.

Given that:

sinπ/7·cosπ/7

if we can divide and multiply 2 so it can be converted to sin 2 theta

sin 2 (pi/7)/2

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The diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

Given is a graph as shown in the figure.

Since the dimensions of a right rectangular prism are not given, assume the length, width and height to be [L], [W] and [H]. Then the diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

Therefore, the diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

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Answer:

O A. 3, 11, 23, 21

OB. 7, 17, 29

OC. 2, 3, 5

OD. 2, 5

Step-by-step explanation:

ŷ= 6.45x + 31.5 is the equation of the regression line for the given data

Construct the table of the data as follows:

x    >>>>     y  >>>>  x²  >>>>  y²  >>>>   xy

1                39            1            1521         39

2               45            4           2025       90

3               52             9          2704       156

4               49            16          2401        196

5               61             25         4096       305

5               72            25          5184        360

................................................................................................

20             318           80          17931       1146

.................................................................................................

∑x = 20,  ∑y = 318, ∑x²= 80, ∑xy = 1146,  n = 6 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (6×1146 - 20×318) / ( 6×80-20² )

a = 6876-6360 / 480-400

a = 516 / 80

a = 6.45

x' =  ∑x/n

x' = 20/6 = 10/3

y' = ∑y/n

y' = 318/6 = 53

b = y' - ax'

b = 53 - 6.45×(10/3)

b = 53 - 21.5

b = 31.5

ŷ = ax + b

ŷ= 6.45x + 31.5

Thus,  the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)

(a) x=3 hours

ŷ= 6.45(3) + 31.5 = 50.85

(b) x=4.5 hours

ŷ= 6.45(4.5) + 31.5 = 60.525

(c) x=13 hours

ŷ= 6.45(13) + 31.5 = 115.35

(d) x=1.5 hours

ŷ= 6.45(1.5) + 31.5 = 41.175

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Answer:

1 gallon of gas is $2.95

9.5 gallons of gas is $28.025

Step-by-step explanation:

[tex]\frac{12.2}{35.99} =\frac{1}{y}[/tex]

Cross Multiply.

12.2 · y = 1 · 35.99

12.2y = 35.99

12.2y ÷ 12.2 = 35.99 ÷ 12.2

y = 2.95

1 gallon of gas is $2.95.

[tex]\frac{1}{2.95} =\frac{9.5}{y}[/tex]

1 · y = 2.95 · 9.5

y = 28.025

9.5 gallons of gas is $28.025.

Answer:

4

Step-by-step explanation:

n/2 + 7 = 9

n/2 + 7 - 7 = 9 - 7

n/2 = 2

n = 4

Answer:

Step-by-step explanation:

160/3

Answer:

Step-by-step explanation:

The formula you want is: fv=p(1+int/c)^(nc)

future value

principal

int

compound

years

fv=4000(1.04/4)^(16)=$4690.31

The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is  49.5%.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

The no. of people who don't have a college degree is (1000 - 100) = 900.

45% of the people who did not have a college degree voted in the last presidential election hence (100 - 45) = 55% of the people who did not have a college and did not vote in the last presidential election.

∴ (55/100)×900.

= 495 people.

∴ The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is,

= 495/1000.

= 0.495.

= 49.5%.

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The simplification of complex fraction -⅔/⅚ is - 4/5

A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.

In fraction when the numerator is bigger than the denominator , then it is called improper fraction, when a fraction consist of whole number and proper fraction is called mixed fraction

-2/3 ÷ 5/6

= -2/3×6/5

= -4/5

Therefore -⅔/⅚ can be simplified to -⅘

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36 houses are left to be sold.

We need to convert 1/4 and 2/5 into decimals. We do this by dividing the numerator by the denominator:

1 ÷ 4 = 0.25

2 ÷ 5 = 0.4

Now, we can set up this equation to find out how many were sold in the first month:

0.25 x 80 = 20

Now, 20 isn't the answer, it is 60 houses left, because 80 - 20 = 60.

Let's do the next one:

0.4 x 60 = 24

60 - 24 = 36

36 houses are left to be sold.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

Missing term [tex]\dfrac{1}{4}[/tex]

Factored term on RHS:   [tex]$(x+\dfrac{1}{2})^{2}$[/tex]

Step-by-step explanation:

Answer:

B (192 ft^2)

Step-by-step explanation:

The area of the blue shaded region: total area - small rectangle

This is:

(11x20) - (4x7)

= 220 - 28

= 192 ft^2

Hope this helps,

:]

Answer:

A.

Explanation:

20*11=220

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If she starts with £400 in her account, her balance for the next three years IS; $608.35

The general formula for exponential equation is;

y = a(b)ˣ

where;

a represents an initial value or amount

b is the constant multiplier, is a growth factor or factor of decay.

We are given;

Initial value; a = £400

constant multiplier; b = an increase of 15% yearly = 1.15

Thus, her balance for the next three years is;

y(3) = 400(1.15)³

y(3) = $608.35

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Answer:

11(12w+5)

Step-by-step explanation:

common factors of 132 and 55 is 11

So we can take it out by dividing both terms by 11

11(12w+5)

Hopes this helps

Answer:I hope this is helps

good luck

Step-by-step explanation:

132w+55

Factor out from the expression
11(12w+5) this is the distributive Property

By using fraction, it can be calculated that

30 boards are required to cover a floor of width 205 inches wide

What is fraction?

Suppose there is a collection and a part of collection has to be taken.

The part which is taken is called fraction. In other words part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction

Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches.

Total width of floor = 205 inches.

Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30

30 boards are required

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The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as,

ax + by + d = 0

The equation of the line is given below.

y = - x - 2

x + y + 2 = 0

Then the equation of the line that is parallel to x + y + 2 = 0 is given as,

x + y + d = 0

The line is passing through (2, -2), then we have

2 + (-2) + d = 0

d = 0

The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.

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