For the geometric series
1+ 4+ 16 + 64 + 256
what is the value of n?

Answer:

Add the equations to eliminate x

Step-by-step explanation:

Let's go through each of these statements

1) Add the equations to eliminate x

   y = x + 10

+

   y = -x + 3

   _______

  2y = 13

This works!

Answer:

Add the equation to eliminate x.

Step-by-step explanation:

Add the equation to eliminate x.

Let's actually do the work!  

y = x + 10

y = −x + 3

------------------

2y = 13, so y = 6.5.

Subbing 6.5 for y in either of the equations above lets us calculate y.  For example, in the second equation, 6.5 = -x + 3, or 3.5 = -x, or x = -3.5.

The solution is (-3.5, 6.5).

Answer:

C) 110.

Step-by-step explanation:

To find it you must multiply in number by 5.

22*5=110.

To prove it you must divide it into 5, since 20 is the fifth part of 110.

110/5=22.

Answer:

Step-by-step explanation:

[tex]\bold{Method\ 1}\\\\\begin{array}{ccc}22&-&20\%\\x&-&100\%\end{array}\qquad\text{cross multiply}\\\\20x=(22)(100)\\20x=2200\qquad\text{divide both sides by 20}\\x=110[/tex]

[tex]\bold{Method\ 2}\\\\\begin{array}{cccc}22&-&20\%&\text{multiply both sides by 5}\\5\cdot22&-&5\cdot20\%\\110&-&100\%\end{array}[/tex]

[tex]\bold{Method\ 3}\\\\p\%=\dfrac{p}{100}\to 20\%=\dfrac{20}{100}=0.2\\\\n-number\\\\20\%\ of\ n\ is\ 22\to0.2x=22\qquad\text{divide both sides by 0.2}\\\\x=\dfrac{22}{0.2}\\\\x=\dfrac{220}{2}\\\\x=110[/tex]

Equation of line whose slope is 3 and passing point (2, 5) is y = 3x - 1.

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.

Here, Slope of line = 3

          Passing point (2, 5)

Equation of line

          (y - y₁) = m (x - x₁)

          y - 5 = 3 (x - 2)

          y - 5 = 3x - 6

          y = 3x - 6 + 5

          y = 3x - 1

Thus, equation of line whose slope is 3 and passing point (2, 5) is y = 3x - 1.

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Answer:

[tex]553\ acres[/tex]

Step-by-step explanation:

Let

z------> the crop yield

x----> the number of bushels harvested

y----> the number of acres used for the harvest

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=94,010\ bushels[/tex]

[tex]z=170\ bushels/acre[/tex]

substitute and solve for y

[tex]170=\frac{94,010}{y}[/tex]

[tex]y=\frac{94,010}{170}=553\ acres[/tex]

Answer:

553

Step-by-step explanation:

The unit price of the 9-kilogram cement bag, rounded to the nearest cent, is $1.36.

Here's the complete answer:

1. **Unit Price Formula: Unit price is calculated by dividing the total cost by the quantity. It represents the cost per unit of the item.

2. **Given Information**:

  - Weight of cement bag = 9 kilograms

  - Cost of cement bag = $12.22

3. **Calculation**:

  - Unit price = Total cost / Quantity

  - Unit price = $12.22 / 9 kilograms

4. **Calculate Unit Price**:

  - Unit price = $1.358888... (dividing $12.22 by 9)

5. **Rounded to Nearest Cent**:

  - Since we're asked to round to the nearest cent:

    - $1.358888... is closer to $1.36 than $1.35.

6. **Final Answer**:

  - The unit price of the cement bag, rounded to the nearest cent, is **$1.36**.

To find out how many tickets were sold at the gate, we can set up and solve a system of equations. From equation 1, we can express x in terms of y: x = 600 - y. Substituting this expression into equation 2, we get 1.00(600 - y) + 1.50y = 700. Simplifying the equation, we find 600 - y + 1.50y = 700. Combining like terms, we have 0.50y = 100. Dividing both sides by 0.50, we get y = 200.

The question provides information about the cost of tickets for a school football game. Before the day of the game, tickets cost $1.00, while tickets bought at the gate cost $1.50 each. The total number of tickets sold for the homecoming game was 600, with total receipts of $700. To find out how many tickets were sold at the gate, we can set up and solve a system of equations.

Let's assume that x tickets were sold before the day of the game and y tickets were sold at the gate. We can create two equations based on the given information:

To solve this system of equations, we can use the substitution method. From equation 1, we can express x in terms of y: x = 600 - y. Substituting this expression into equation 2, we get 1.00(600 - y) + 1.50y = 700. Simplifying the equation, we find 600 - y + 1.50y = 700. Combining like terms, we have 0.50y = 100. Dividing both sides by 0.50, we get y = 200.

Therefore, 200 tickets were sold at the gate.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=5x+3&(1)\\y=4x+6&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\5x+3=4x+6\qquad\text{subtract 3 from both sides}\\5x=4x+3\qquad\text{subtract 4x from both sides}\\x=3\\\\\text{Put the value of x to (1):}\\\\y=5(3)+3\\y=15+3\\y=18[/tex]

Answer:

Step-by-step explanation:

(-)(-) = (+)

(+)(+) = (+)

(-)(+) = (+)(-) = (-)

--------------------------------------

16 - (-53) = 16 + 53 = 69

Hoi there!

First, we can open parenthesis.

10+6x+x+10

Then combine like terms.

20+4x

We can put it in parenthesis (if you need it that way).

4(5+x)

So, your answer would be:

20+4x in not factored form.

4(5+x) in factored form.

Hope I helped, sorry if I'm wrong ouo.

~Potato.

Copyright Potato 2019.

Trademark Potato 2019.

Answer:

The value of discriminant is 384

There are two different real roots for the equation

Step-by-step explanation:

* Lets explain what is the discriminant

- In the quadratic equation ax² + bx + c = 0, the roots of the

 equation has three cases:

1- Two different real roots

2- One real root or two equal real roots

3- No real roots means imaginary roots

- All of these cases depend on the value of a , b , c

∵ The rule of the finding the roots is  

   x = [-b ± √(b² - 4ac)]/2a

- The effective term is b² - 4ac to tell us what is the types of

 the roots

# If the value of b² - 4ac is positive means greater than 0

∴ There are two different real roots

# If the value of b² - 4ac = 0

∴ There are two equal real roots means one real root

# If the value of b² - 4ac is negative means smaller than 0

∴ There is no real roots but the roots will be imaginary roots

∴ We use the discriminant to describe the number and type of roots

* Now lets solve the problem

∵ -3x² - 18x + 5 = 0

∴ a = -3 , b = -18 , c = 5

∵ Δ = b² - 4ac ⇒ (Δ is the discriminant symbol)

∴ Δ = (-18)² - 4(-3)(5) = 324 - (-60) = 324 + 60 = 384

∴ The value of discriminant is 384

∵ The value of discriminant greater then 0

∴ There are two different real roots for the equation

Answer:

[tex]x^{2}+y^{2} +4x-2y+1=0[/tex]

Step-by-step explanation:

we know that

The general form of the equation of a circle is

[tex]x^{2} +y^{2}+ Dx + Ey + F=0[/tex]

where D, E, F are constants

step 1

Find the radius of the circle

Remember that the distance from the center to any point on the circle is equal to the radius

so

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex](-2,1)\\(-4,1)[/tex]  

substitute the values

[tex]r=\sqrt{(1-1)^{2}+(-4+2)^{2}}[/tex]

[tex]r=\sqrt{(0)^{2}+(-2)^{2}}[/tex]

[tex]r=2\ units[/tex]

step 2

Find the equation of the circle in standard form

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

In this problem we have

center ( -2,1)

radius r=2 units

substitute

[tex](x+2)^{2} +(y-1)^{2}=2^{2}[/tex]

[tex](x+2)^{2} +(y-1)^{2}=4[/tex]

Step 3

Convert to general form

[tex](x+2)^{2} +(y-1)^{2}=4\\ \\x^{2}+4x+4+y^{2}-2y+1=4\\ \\x^{2}+y^{2} +4x-2y+1=0[/tex]

The answer is:

The correct option is:

A) Jeff, 4.5 hours; Julia 9 hours.

To solve the problem, we need to write two equations using the given information.

So, writing the first equation we have:

We know that Jeff can weed the garden twice as fas as his sister Julia, so:

[tex]JeffRate=2JuliaRate[/tex]

Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:

[tex]JeffRate+JuliaRate=\frac{1garden}{3hours}[/tex]

Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:

[tex]JeffRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]2JuliaRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]2JuliaRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]3JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]JuliaRate=\frac{1garden}{3hours*3}=\frac{1garden}{9hours}[/tex]

We have that Julia could weed the garden by herself in 9 hours.

So, calculating how long will it take to Jeff, we have:

[tex]JeffRate=2*JuliaRate\\\\JeffRate=2*\frac{1garden}{9hours}=\frac{2garden}{9hours}=\frac{1garden}{4.5hours}[/tex]

We have that Jeff could weed the same garden by himself in 4.5 hours.

Hence, the correct option is:

A) Jeff, 4.5 hours; Julia 9 hours.

Have a nice day!

Answer:

A

Step-by-step explanation:

It is an acute angle and it is more likelt to be B. 42 degrees

Pls mark brainliest answer

Answer:

130.5

Step-by-step explanation:

145% of 90 = 145% * 90

145% = 1.45

Substitute: 1.45 * 90

Multiply: 130.5

If the cone are similar, the volume ratio of Cone A to Cone B will be 1:25.

The right circular cone is one in which the line from the cone's peak to the center of the circle's base is perpendicular to the base's surface.

Assume that the radius of the right circular cone under consideration is 'r' units, and the height 'h' units. Then the volume is then expressed as;

[tex]\rm V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

If the cone are similar, the volume ratio of Cone A to Cone B;

[tex]\rm \frac{V_A}{V_B}=(\frac{R_A}{R_B})^3 } \\\\\ \frac{V_A}{V_B}=( \frac{5}{25} )^3 \\\\\ \frac{V_A}{V_B}=\frac{1}{125}[/tex]

If the cone are similar, the volume ratio of Cone A to Cone B will be 1:25.

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Answer:

similar triangles

Step-by-step explanation:

did it on usatestprep

Similar triangles are triangles with congruent angles and proportional sides.

In mathematics, triangles with congruent angles and proportional sides are called similar triangles.

Similar triangles have the same shape, but their sides may have different lengths. Two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

For example, if angle A in triangle ABC is congruent to angle X in triangle XYZ, and the ratio of the length of AB to XY is equal to the ratio of the length of BC to YZ, then triangle ABC is similar to triangle XYZ.

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Answer:

300cm

Step-by-step explanation:

First you get the length, width, and height. The length is 15, the width is 12, and the height is 10.

15*12=180

Since their is 2 you multiply by 2

180*2=360

12*10=120

Since their is 2 you multiply by 2

120*2=240

Then you divide by 2 since it is a triangle but before that you add the products up

360+240=600

600/2=300

Answer:

x = 0

Step-by-step explanation:

Given

x² = - 4y ( divide both sides by - 4 )

y = - [tex]\frac{1}{4}[/tex] x²

Which is a parabola opening vertically down with it's vertex at (0, 0) and symmetrical about the y- axis

Hence equation of axis of symmetry is x = 0

using the composition of the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] as defined by the table, we get that [tex]\((f \circ g)(1) = 17\).[/tex]

To find [tex]\((f \circ g)(1)\)[/tex], we need to first find  and then find the value of [tex]\(f\)[/tex] at that result.

1. Identify [tex]\(g(1)\)[/tex]: We need to evaluate the function [tex]\(g\)[/tex] at [tex]\(x = 1\)[/tex]. Looking at the table under the row for [tex]\(g(x)\)[/tex] and the column where \(x = 1\), we find that [tex]\(g(1) = 6\).[/tex]

2. Evaluate [tex]\(f\)[/tex] at [tex]\(g(1)\)[/tex]: Now that we have that [tex]\(g(1) = 6\)[/tex], we need to evaluate the function [tex]\(f\)[/tex] at [tex]\(x = 6\)[/tex]. Looking at the table under the row for [tex]f(x)\)[/tex] and the column where [tex]\(x = 6\)[/tex], we find that [tex]\(f(6) = 17\).[/tex]

3. **Combine the results**: We have [tex]\(f(g(1)) = f(6)\)[/tex]. Since we found out that [tex]\(f(6) = 17\)[/tex], we can conclude that [tex]\((f \circ g)(1) = 17\).[/tex]

So, using the composition of the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] as defined by the table, we get that [tex]\((f \circ g)(1) = 17\).[/tex]

Answer:251.2m^2

Step-by-step explanation:

8^2+2*8*11.7

Answer: The answer to 3.25÷0.5 is 6.5 :)

Step-by-step explanation:

C. Expression

An inequality must contain a sign relating magnitude.

An equation must contain an equal sign.

An expression cannot have an equal sign or any symbols of inequality.

A fraction must contain a bar representing division.

Hope this helps!!

The values of 12C4 and 11P4 are 495 and 7920, respectively

The expressions are illustrations of permutation and combination, and they are calculated using:

[tex]^nC_r = \frac{n!}{(n -r)!r!}[/tex]

and

[tex]^nP_r = \frac{n!}{(n -r)!}[/tex]

So, we have:

[tex]^{12}C_4 = \frac{12!}{(12 -4)!4!}[/tex]

Evaluate the difference

[tex]^{12}C_4 = \frac{12!}{8!4!}[/tex]

Evaluate the factorials

[tex]^{12}C_4 = \frac{479001600}{967680}[/tex]

Divide

[tex]^{12}C_4 = 495[/tex]

Also, we have:

[tex]^{11}P_4 = \frac{11!}{(11 -4)!}[/tex]

Evaluate the difference

[tex]^{11}P_4 = \frac{11!}{7!}[/tex]

Evaluate the quotient

[tex]^{11}P_4 = 7920[/tex]

Hence, the values of 12C4 and 11P4 are 495 and 7920, respectively

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Final answer:

The value 0.9 represents the 90% of the original price a customer pays after applying a 10% discount. It is used to calculate the discounted price by multiplying the original price by 0.9.

Explanation:

In the context of this question, 0.9 (or 0.90) represents the remainder of the original price G after a 10% discount is applied. When Ray uses his coupon for 10% off the price of ginger roots, this discount factors out 10% of the cost, leaving him to pay just 90% of the original price. This is why the price he pays can be represented as 0.9G, which is the same as saying 90% of G.

The 0.9 is a decimal representation of the percentage that remains after the discount. So, if the original price G is, for example, $10.00, with a 10% discount Ray would be saving $1.00, and thereby paying 90% of the original price, or $9.00. So, 0.9 in this calculation effectively means 90% of the original price.

Representing changes in price using decimals and percentages is a common method in mathematics to describe percentage change or discounts succinctly.

Answer:

Step-by-step explanation:

-3 is the number u will get. Hope this helps!!

To represent the expression -8 + 5 on a number line, start at -8 and move 5 units to the right, ending at -3.

To represent the expression -8 + 5 on a number line, we start at -8 and move 5 units to the right. Since we are adding a positive number, the arrow on the number line will point to the right.

So the number line that represents the expression -8 + 5 would start at -8 and have an arrow pointing to the right, ending at -3.

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Answer:

Sur. area = 360 area unit , vol = 54√3 volume unit

Step-by-step explanation:

Sur. area = 6×(6×10)

Volume= (n/4)X² (cot(180/n)) , n is number of sides and X is side length

Answer:

Step-by-step explanation:

8.8 laps because of the concepts of molecular osmosis used to provide a detailed explanation to kermit. Thereby omitting the theory of dark matter into the universe and thus replacing it with the new compulsive theory of 50 % growth of human anatomical secretory sections.

Answer:

D) 8.8 laps.

Step-by-step explanation:

We have been given that each player on the football team is required to run 1.5 miles in less than 15 minutes. One lap around the field is 300 yards.

We know that 1 mile equals 1760 yards.

First of all, we will convert 1.5 miles into yards by multiplying 1.5 by 1760.

[tex]\text{1.5 miles}=\text{1.5 miles}\times \frac{\text{1760 yards}}{\text{Mile}}[/tex]

[tex]\text{1.5 miles}=1.5\times \text{1760 yards}[/tex]

[tex]\text{1.5 miles}=2640\text{ yards}[/tex]

We have been given that one lap around the field is 300 yards. To find the number of laps a player must run, we will divide 2640 by 300.

[tex]\text{Number of laps a player must run}=\frac{2640\text{ yards}}{300\text{ yards}}[/tex]

[tex]\text{Number of laps a player must run}=8.8[/tex]

Therefore, a player must run 8.8 laps to meet the requirement.

Answer:

C

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 )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3)

m = [tex]\frac{-3-0}{0+1}[/tex] = - 3

note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = - 3x - 3 ← in slope- intercept form

Add 3x to both sides

3x + y = - 3 ← in standard form → C

Answer:

Part 1)  [tex]f^{-1}(x)=3(x+17)/2[/tex] ----> [tex]f(x)=\frac{2x}{3}-17[/tex]

Part 2) [tex]f^{-1}(x)=x+10[/tex] -----> [tex]f(x)=x-10[/tex]

Part 3) [tex]f^{-1}(x)=\frac{x^{3}}{2}[/tex] ----> [tex]f(x)=\sqrt[3]{2x}[/tex]

Part 4) [tex]f^{-1}(x)=5x[/tex] ----> [tex]f(x)=x/5[/tex]

Step-by-step explanation:

Part 1) we have

[tex]f(x)=\frac{2x}{3}-17[/tex]

Find the inverse

Let

y=f(x)

[tex]y=\frac{2x}{3}-17[/tex]

Exchange the variables, x for y and y for x

[tex]x=\frac{2y}{3}-17[/tex]

Isolate the variable y

Adds 17 both sides

[tex]x+17=\frac{2y}{3}[/tex]

Multiply by 3 both sides

[tex]3(x+17)=2y[/tex]

Divide by 2 both sides

[tex]y=3(x+17)/2[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=3(x+17)/2[/tex]

Part 2) we have

[tex]f(x)=x-10[/tex]

Find the inverse

Let

y=f(x)

[tex]y=x-10[/tex]

Exchange the variables, x for y and y for x

[tex]x=y-10[/tex]

Isolate the variable y

Adds 10 both sides

[tex]y=x+10[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=x+10[/tex]

Part 3) we have

[tex]f(x)=\sqrt[3]{2x}[/tex]

Find the inverse

Let

y=f(x)

[tex]y=\sqrt[3]{2x}[/tex]

Exchange the variables, x for y and y for x

[tex]x=\sqrt[3]{2y}[/tex]

Isolate the variable y

elevated to the cube both sides

[tex]x^{3}=2y[/tex]

Divide by 2 both sides

[tex]y=\frac{x^{3}}{2}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=\frac{x^{3}}{2}[/tex]

Part 4) we have

[tex]f(x)=x/5[/tex]

Find the inverse

Let

y=f(x)

[tex]y=x/5[/tex]

Exchange the variables, x for y and y for x

[tex]x=y/5[/tex]

Isolate the variable y

Multiply by 5 both sides

[tex]y=5x[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=5x[/tex]

The inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

Functions are shown in the picture.

We have to find the inverse of a function.

[tex]\rm f(x) = \dfrac{2x}{3}-17[/tex]

To find the inverse of a function plug in the place of f(x)→x and x→f(x) ⁻¹

[tex]\rm x = \dfrac{2f^-^1(x)}{3}-17[/tex]

f(x) ⁻¹ = 3(x + 17)/2

Similarly, we can find the rest of the inverse of the function as follows:

f(x) = x - 10

f(x) ⁻¹ = x + 10

f(x) = ∛2x

f(x) ⁻¹ = x³/2

f(x) = x/5

f(x) ⁻¹ = 5x

Thus, the inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.

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