What is the explicit formula for this geometric sequence? 8, 4, 2, 1

32,000 divided by 500 = 64

Answer: 32000/500= 64 approximately

Step-by-step explanation:

64 is the answer because 31969/488= 65.51

the lesser number is 5.

Let the first number = x

Let the second number = y

set up two equations

x + y = 17

2/3 x -3 = y

sub the second equation into the first one

x + 2/3 x - 3 = 17

collect like terms (1x = 3/3 x)

5/3 x - 3 = 17

add 3 to both sides

5/3 x = 20

multiply by 3 on both sides

5x = 60

divide by 5 on both sides

x = 12

sub back in one of the equations and solve to find the other number:

x + y = 17

12 + y = 17

y= 5

•have a good day• :) ~ ♡lipika♡

The lesser number is 5.

Let us consider that first number is x .

Since, second number is 3 less than 2/3 of the other number.

So that, second number [tex]=\frac{2}{3}x-3[/tex]

The sum of both number is 17.

             [tex]x+\frac{2}{3}x-3=17\\\\\frac{5}{3}x=17+3\\\\\frac{5}{3}x=20\\\\x=20*\frac{3}{5}=12[/tex]

Lesser number is. [tex]=\frac{2}{3}x-3=\frac{2}{3}*12-3=5[/tex]

Hence, the lesser number is 5.

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Answer:false

Step-by-step explanation: divide each side by 7 you get b ≤ -7. The red line needs to go the other way since it is less than

Answer:

False, it is incorrect

Step-by-step explanation:

7b≤ -49

Divide by 7

7b/7 ≤-49/7

b ≤-7

We have a closed circle at -7  (closed because of the equals)

b is less than so the lines goes to the left

I think it's d but not sure

To find the slope of a line passing through the origin and a point, use the formula slope = (y2 - y1)/(x2 - x1). For a line passing through origin and the point (-8,-5), the slope is 5/8.

The topic at hand revolves around the concept of slope and the algebra of straight lines. The slope is calculated by finding the change in y (vertical axis) over the change in x (horizontal axis). To find the slope of a line passing through the origin and the point (-8,-5), use the formula slope = (y2 - y1)/(x2 - x1).

In this case, the origin is point (0,0) and the given point is (-8,-5). So to find the slope, we substitute these values into the slope formula: slope = (-5 - 0)/(-8 - 0) = 5/8. Therefore, the slope of the line passing through the origin and the point (-8,-5) is 5/8.

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The slope of the line is 5/8.

The slope of a line, denoted by m, represents the rate of change between the vertical and horizontal components of two points on the line.

To find the slope of a line passing through the origin and intersecting the point (-8, -5), we can use the slope formula. The slope formula is given by: m = (y2 - y1) / (x2 - x1).

Plugging in the values from the given point gives: m = (-5 - 0) / (-8 - 0)

= -5 / -8

= 5/8.

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Answer:

5.94x10^1

Step-by-step explanation:

In scientific notation all numbers are written in the form of m×10n (m times ten raised to the power of n), where the exponent n is an integer, and the coefficient m is any real number, called the significand or mantissa. If the number is negative then a minus sign precedes m (as in ordinary decimal notation).

Answer:

Equation: $21.50•n=c

Answer:

Step-by-step explanation:

-12x+x+26+15-2-3=0

-11x+36=0

-11x=-36

x=36/11

or x=3.2̅7̅

Answer:

7

Step-by-step explanation:

This is an equation of an ellipse of the form:

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Where a and b are the minor and major intercepts, given a<b

In this question, a<b and a = 3 and b = 7

The distance from the center to the major intercept is b, thus the distance we are seeking for is 7

Answer:

b = 7 units.

Step-by-step explanation:

The given equation of the ellipse is

[tex]\frac{x^{2} }{9} +\frac{y^{2} }{49}=1[/tex]

As we know in an ellipse  [tex]\frac{x^{2} }{a^{2} }+ \frac{y^{2} }{b^{2}}=1[/tex]

a will be major axis and b is the minor axis when ( a > b )

In the given equation 49 > 9 ⇒ b² > a²

so major axis will be = √49

                                  = 7

Therefore, distance from center to the major intercept is b = 7 units.

the answer to the problem is c

The answer is actually B) 1.25

Answer:

C

Step-by-step explanation:

In translating graphs of functions, we can follow 2 rules:

1. The graph of  [tex]f(x)+a[/tex] is the graph of  [tex]f(x)[/tex] shifted a units UP VERTICALLY and the graph of   [tex]f(x)-a[/tex] is the graph of  [tex]f(x)[/tex] shifted a units DOWN VERTICALLY.

2. The graph of  [tex]f(x+a)[/tex]  is the graph of   [tex]f(x)[/tex]  shifted a units to the LEFT HORIZONTALLY and the graph of  [tex]f(x-a)[/tex]  is the graph of  [tex]f(x)[/tex]  shifted a units RIGHT HORIZONTALLY.

If we understand the 2 rules above, we clearly know that f(x+2) will be a horizontal shift to the LEFT, of course, with respect to the function  [tex]f(x)=x^3[/tex]. Looking at the answer choices, C is right.

Answer:

[tex](2,200\pi +8,000)\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the figure is equal to the volume of cube plus the volume of the cylinder

step 1

Find the volume of the cube

The volume of the cube is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=2(10)=20\ ft[/tex] ----> the length side of the cube is equal to the diameter of the cylinder

so

[tex]V=20^{3}=8,000\ ft^{3}[/tex]

step 2

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=10\ ft[/tex]

[tex]h=42-20=22\ ft[/tex]

substitute

[tex]V=\pi (10)^{2} (22)[/tex]

[tex]V=2,200\pi\ ft^{3}[/tex]

step 3

The volume of the figure is equal to

[tex](2,200\pi +8,000)\ ft^{3}[/tex]

The volume of the figure = volume of oblique cylinder + volume of cube = 2,200π + 8,000 cubic feet.

Volume of oblique cylinder = πr²h [radius of cylinder = r].

The volume of the figure = volume of oblique cylinder + volume of cube = πr²h + s³

Given the following:

Plug in the values into πr²h + s³:

The volume of the figure = π(10²)(22) + 20³

The volume of the figure = 2,200π + 8,000 cubic feet.

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Answer:

11.99 ft

Step-by-step explanation:

The formula for the volume of a cyl. of radius r and height h is V = πr²h.

Solving this immediately for h yields:

         V

h = ----------

         πr²

Inserting the known quantities results in:

         V           1356.48 ft³

h = ---------- = ----------------------      Note that r = (1/2)d, so r = (1/2)(12 ft) = 6 ft

         πr²         3.14159 (6 ft)²

   =   11.994 ft

The height of the cyl. is 11.99 ft (to the nearest hundredth foot)

Final answer:

To find the height of the cylinder with a volume of 1,356.48 cubic feet and a diameter of 12 feet, divide the volume by the area of the base (calculated with a radius of 6 feet) to get approximately 11.99 feet.

Explanation:

To calculate the height of a cylinder when the volume and diameter are given, we use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, we have a volume of 1,356.48 cubic feet and a diameter of 12 feet, meaning the radius is 6 feet (half of the diameter). So we can plug these values into our formula to solve for h.

First, calculate the area of the base (πr²): 3.14159 × (6 feet)² = 3.14159 × 36 = 113.0976 square feet. Then we divide the given volume by this area to find the height: 1,356.48 cubic feet / 113.0976 square feet = 11.99 feet. Therefore, the final answer for the height of the cylinder is approximately 11.99 feet.

Answer:

yes

Step-by-step explanation:

Substitute x = - 10 into the equation and if the value obtained equals - 34 then the point satisfies the equation and lies on the line

x = - 10 : y = (3 × - 10) - 4 = - 30 - 4 = - 34 ← agrees

Hence (- 10, - 34) lies on the line y = 3x - 4

Answer:

~

Step-by-step explanation:

There isn't enough context information to solve the following problem.

Answer:

it is bigger by 1/5

Step-by-step explanation:

Answer:15

Step-by-step explanation:h=2 A/b meaning h=2 67.5/9

Answer:

h = 15 meters

Step-by-step explanation:

The area of a triangle is determined by its height multiplied by its base.

The equation is A = 1/2*bh.

Plugging in the numbers gives us 67.5 = 1/2*9h.

Dividing by 4.5 in both sides gives us that h = 67.5/4.5 = 15 meters.

The mortgage loan amount is $82,500. The closing costs are 3 percent of the loan amount. Therefore, the total closing costs are $2,475.

Sarah Wood and her husband are purchasing a house for $87,500.00, but they are making a down payment of $5,000.00. Therefore, the mortgage loan amount is $87,500 - $5,000 = $82,500. The closing cost for this mortgage loan is 3 percent of the loan amount. Thus, to calculate the total closing costs, we multiply the loan amount by 3%. Therefore, total closing costs are $82,500 * 0.03 = $2,475.00.

So, total closing costs are $2,475.00.

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The total closing costs are $2,475.00.

To calculate the total closing costs, we need to find 3 percent of the mortgage loan amount.

First, calculate the mortgage loan amount by subtracting the down payment from the house price: $87,500.00 - $5,000.00 = $82,500.00.

Then, find 3 percent of $82,500.00 by multiplying it by -

0.03: $82,500.00 * 0.03

= $2,475.00.

So, the total closing costs are $2,475.00.

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2/3 is 0.6 repeating

66% is just 66%

same with 0.67

order is 0..67, 2/3, then 66%. i am the stupid.

% = decimal number

Answer:

0.67, 2/3, 66%

Step-by-step explanation:

2/3 decimal is 0.66666666667

66% decimal is 0.66

and 0.67 is 0.67

Hope this helped! Please mark as brainliest! Thanks!

Answer:

y =0

Step-by-step explanation:

From the equation;

8³ × 8⁻⁵×8^y = 8⁻²= 1/8²

From the laws of indices;

aⁿ×aⁿ = a^2n

Therefore;

8³ × 8⁻⁵×8^y = 8^(3+-5+y)

8^(-2+y) = 8^-2 ; but the bases are the same and thus the exponents are the same;

-2 + y = -2

      y = 0

Answer:

The value of y is 0

Step-by-step explanation:

8³ * 8^-5*8^y = 8^-2 or 1/8²

Taking indices of both sides

From first law of indices;

Multiplication sign change to addition; i.e. x^a * x^b = x^(a + b).

So,

8³ * 8^-5*8^y = 8^-2

Becomes

8^(3 + (-5) + y) = 8^-2

Same base of 8 can cancel one another. So, we're left with

3 + (-5) + y = -2

Open the bracket

3 - 5 + y = -2

-2 + y = -2

Make y the subject of formula

y = 2 - 2

y = 0

Hence, the value of y in the equation is 0

Well, this is just a big guess, but probably the most sense-able, B) 400 ft²

Answer:

9

Step-by-step explanation:

Answer:

2/25 is the Answer, as a decimal it is 0.08

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x + 1/50 = 1/10

Step 2: Subtract 1/50 from both sides.

x + 1/50 - 1/50 = 1/10 - 1/50

X = 2/25

Proof that it is the answer

0.02 + 0.08 = 0.1

0.02 is 1/50

0.08 is 2/25

0.1 is 1/10

Hope this helps!

[tex]\bold{Hey\ there!} \\ \bold{\frac{1}{50}+x=\frac{1}{10}}\\ \\ \bold{You\ have\ to\ simplify\ both\ sides\ of\ your\ equation\downarrow}\\ \bold{Like:x+\frac{1}{50}=\frac{1}{10}} \\ \\ \bold{Next,\ you\ have\ to\ \underline{SUBTRACT}\ by\ \frac{1}{50}\ on\ your\ sides} \\ \bold{x+\frac{1}{50}-\frac{1}{50}=\frac{1}{10}-\frac{1}{50}}\\ \\ \bold{Cancel:\frac{1}{50}-\frac{1}{50}because\ it\ equals\ to\0!} \\ \bold{Keep:\frac{1}{10}-\frac{1}{50}\ because\ it\ helps\ us\ solve\ for\ our\ answer!}[/tex]

[tex]\bold{\frac{1}{10}-\frac{1}{50}=\frac{2}{25}} \\ \\ \\ \\ \boxed{\boxed{\bold{Answer:x=\frac{2}{25}}}}\checkmark \\ \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]

Answer:

He must sell $14000 of merchandise

Step-by-step explanation:

The salesperson earns a base salary of $800

This means that he must make

$3600 - $800 = $2800 worth of commisions

Let x, be the value of the mechandise that he needs to sell.

This means that

x*0.20 = $2800

x  = $2800/0.20

x = $14000

He must sell $14000 of merchandise

Answer:

option C is the correct answer

Step-by-step explanation:

The trigonometric equation you are using has a general form

y = A* tan w*(x - r)

Where

A is the amplitude of the function

w is the frequency rad/s

r  is the phase shift

In your case

A = -2

The frequency is

w = (2*pi)/period

period = pi/4

w = 8

r = -pi/2

y = -2* cos 8*(x + pi/2)

The answer is:

[tex]A(13)=107.37Km^{2}[/tex]

We can calculate the area of the lake after 13 years using the following equation:

[tex]A(t)=A(initial)(1-ShrinkingRate)^{t}[/tex]

Where,

A(t), is the area after t time (years)

A(Initial), is the initial area

Shrinking Rate, is the rafe of shrinking and it's 6% or 0.06.

t, is the time

So, substituting we have:

[tex]A(13)=240(1-0.06)^{13}=240*0.447=107.37Km^{2}[/tex]

So, the are after 13 years will be:

[tex]A(13)=107.37Km^{2}[/tex]

Have a nice day!

Answer:

$2280

Step-by-step explanation:

I see you've already found part a, which is to find the amount of interest earned. The next part is easy, to find the balance of the account after four years, just add the interest you've found back to the principal (the original size of the account or loan). $2000 + $280 equals $2280.

The interest earned on the account is $280. The balance of the account after 4 years is $2280.

To find the interest earned on the account, we use the formula for simple interest:

I = PRT

where:

Substituting the given values:

I = $2000 * 3.5/100 * 4 = $280

To find the balance of the account, we add the interest earned to the principal:

Balance = P + I = $2000 + $280 = $2280

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Answer: [tex]f(x)=4^x[/tex]

Step-by-step explanation:

The general exponential function is given by :-

[tex]f(x)=Ab^x[/tex], where A is initial amount , b is multiplicative growth rate and x is time period.

Also, the multiplicative growth rate is the common ratio of the consecutive terms.

From the given table , [tex]b=\dfrac{256}{64}=4[/tex]

Substitute, x = 3 , f(x)=64 and b=4 , we get

[tex]64=A(4)^3\\\\\Rightarrow\ 64=A(64)\\\\\Rightarrow\ A=1[/tex]

Hence, the exponential function represents the data in the table is

[tex]f(x)=(1)(4)^x\\\\\Rightarrow\ f(x)=4^x[/tex]

Answer:

x equals six start fraction one over two end fraction

Step-by-step explanation:

Segments which are parallel have the same slope. Find the slope of of YZ. Then using that value, find the slope WX and solve for the value of x.

Slope of YZ is:

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{6-2}{5-2} =\frac{4}{3}[/tex]

Since they are parallel, then WX has a slope of 4/3 too.

Slope of WX is:

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\\frac{4}{3} = \frac{-4--2}{5-x}\\\\\frac{4}{3} =\frac{-2}{5-x}\\\\ (5-x)\frac{4}{3} = -2\\\\ 20 - 4x = -6\\\\-4x = -26 \\\\ x = 6 \frac{1}{2}[/tex]

The awnser is 20 x 3

Hope this helps!

The area of a rectangle with length 4x^3 and width 5 is expressed as the monomial 20x^3 by multiplying the length and width.

To express the area of a rectangle as a monomial when given the length and width, we simply need to multiply these two dimensions together. In this case, the rectangle has a length of 4x^3 and a width of 5. The area (A) of a rectangle is given by the formula A = length * width.

So, the area of this rectangle can be calculated as:

A = 4x^3  * 5

Now, we multiply the numerical coefficients (4 and 5) and then combine them with the variable part:

A = (4 * 5) x^3

A = 20x^3

This expression, 20x^3, represents the area of the rectangle as a monomial