Mathematics High School

What is the 12th term of the sequence? 3, −9, 27, −81, 243, ...

531441
−531441
177147
−177147

Answers

Answer 1
The answer would be B. -531,441.

There are 2 ways you can find this.

A. You can find this by starting with 3, and multiply -3 then multiply -3 to each product after that 11 times. Or...

B. Simply find 3 to the 12th power. Then add a negative since each even term (term 2, 4, 6, etc) are negative.

I hope this helps!

Related Questions

A bag contains 12 red marbles and 6 blue marbles. two marbles are drawn with replacement. find the probability.

Answers

248376203488451-5814-0395681-03581-403951-0958904680968590147514095714095714-5714578140587109p54

Find the surface area of the following triangular prism

Answers

The surface area of the triangular prism is 144 ft³

How to find the surface area

The surface area of the prism is solved using the formula

= 2 * area of the base + Lateral surface area

Area of the base

= 2 * 1/2 * 6 * 8

= 48

Lateral surface area

= (10 + 6 + 8) * 4

= 24 *  4

= 96

Total surface area

= 48 + 96

= 144 ft³

What’s the quadratic expression for this one

Answers

We have the following expression:
 (2x + 5) * (7-4x)
 Rewriting we have:
 14x - 8x ^ 2 + 35 - 20x
 Grouping terms with the same exponent:
 -8x ^ 2 + x (14-20) + 35
 Rewriting:
 -8x ^ 2 - 6x + 35
 Answer:
 the quadratic expression for this is:
 -8x ^ 2 - 6x + 35

Evaluate the expression for = −3 and = 5.

r^{-4} s^2

Answers

If r = -3 and s = 5:
(r^-4)(s^2) = (-3^-4)(5^2) = (1/81)(25) = 25/81

If r = 5 and s = -3:
(r^-4)(s^2) = (5^-4)(3^2) = (1/625)(9) = 9/625
If r = -3 and s = 5:
(r^-4)(s^2) = (-3^-4)(5^2) = (1/81)(25) = 25/81

A painter places an 8.5 ft ladder against a wall. the bottom of the ladder is 4 ft from the base of the wall. how high up the wall does the ladder reach?

Answers

Use the Pythagorean Theorem:
a² + b² = c²
4² + b² = 8.5²
16 + b² = 72.25
        b² = 56.25
        b = 7.5

 The ladder reaches a height of 7.5 ft on the wall

Please give an explanation with you answer, thank you :)

Answers

[tex]f(x)=2( \sqrt[3]{27})^{2x} [/tex]

Here 2 on left most side is the coefficient, 2x is the exponent and the of the function is cube root of 27.

So,

[tex]Base= \sqrt[3]{27} \\ \\ Base= \sqrt[3]{3^{3} } \\ \\ Base=3 [/tex]

Thus, the simplified base for the function is 3. So correct answer is option  B

Assuming that one-pint is equal to 473 ml., how many pints can be found in one liter?

Answers

we know that
 1 pint is equal to --------> 473 ml
1 liter is equal to--------> 1000 ml
so
1 pint is equal to --------> 473 ml
x pints------------------> 1000 ml
x=1000/473-----> 2.11 pints

the answer is
2.11 pints can be found in one liter
For this case we can make the following rule of three:
 1 pint -------> 473 ml
 x -------------> 1000 ml
 Clearing x we have:
 x = (1000/473) * (1)
 x = 2.114164905
 Rounding off we have:
 x = 2
 Answer:
 can be found 2 pints in one liter

In the ancient chinese proverb, there are more than how many different ways to breathe

Answers

Answer: 40

What we all know is that there is only one way to breath (inhaling and exhaling) For the ancient Chinese, as cited on ancient proverb there are forty (40) ways.  These different ways promote relaxation thru breathing on the lower stomach. 

A vegetable store sold 3 tons of vegetables less on the first day than on the second, and on the third day it sold 5/9 of the amount sold in the first two days. How many vegetables was the store selling every day if it sold altogether 98 tons of vegetables for the three days?

Answers

let
x---------> quantity (ton) of vegetables sold the first day
y---------> quantity (ton)  of vegetables sold the second day
z---------> quantity (ton) of vegetables sold the third day

we know that
x=y-3---------> equation 1
z=(5/9)*(x+y)------> equation 2
x+y+z=98-----> equation 3
substitute equation 2 in equation 3
x+y+[(5/9)*(x+y)]=98----> multiply by 9----> 9x+9y+5x+5y=882
14x+14y=882-----> equation 4

to resolve the equations system formed by
x=y-3
14x+14y=882

using a graph tool
see the attached figure
the solution is
x=30
y=33
x+y+z=98----> z=98-(x+y)----> z=98-63---> 35

the answer is
vegetables sold the first day----> 30 ton
vegetables sold the second day----> 33 ton
vegetables sold the third day------> 35 ton

Answer:
amount sold on first day = 30 tons
amount sold on second day = 33 tons
amount sold in third day = 35 tons

Explanation:
Assume that the amount of vegetables sold on the second day is x.
We are given that:
Amount of vegetables sold on the first day is 3 tons less that sold on the second day.
This means that:
amount sold on first day = x - 3 
Amount of vegetables sold on the third day is 5/9 the amount sold on the first two days.
This means that:
amount sold on third day = (5/9) (x + x - 3)
amount sold on third day = [tex] \frac{10}{9} x - \frac{5}{3} [/tex]

Now, we know that:
Total amount sold is 98 tons.
This means that:
98 = x - 3 + x + [tex] \frac{10}{9} x - \frac{5}{3} [/tex]

Now, we will solve for x as follows:
98 = [tex] \frac{28}{9} x - \frac{14}{3} [/tex]

882 = 28x - 42
882 + 42 = 28x
924 = 28x
x = 924/28
x = 33 tons

This means that:
amount sold on first day = x - 3 = 33 - 3 = 30 tons
amount sold on second day = x = 33 tons
amount sold on third day = [tex] \frac{10}{9} x - \frac{5}{3} [/tex] = [tex] \frac{10}{9} (33) - \frac{5}{3} [/tex] = 35 tons

Hope this helps :)

Simplify the expression 9xy + 6xy − 2xy. What is the coefficient of the simplified expression?

Answers

Hi there!

To find our answer we need to collect the terms of the expression.

[tex]9xy + 6xy - 2xy = \\ 15xy - 2xy = \\ 13xy[/tex]

The coefficient (which is the number just before the variable) of the simplified expression is 13.
9xy + 6xy - 2xy
13xy is the answer. THey are all like terms so just add then subtract.

Find the dimensions of a rectangle whose width is 6 miles less than its length and whose area is 55 square miles.

Answers

let
x-----------> the length of a rectangle
y-----------> the width of a rectangle

we know that
area of a rectangle =length*width
area=55 mi²
55=x*y--------> equation 1
y=x-6-------> equation 2
substitute equation 2 in equation 1
55=x*[x-6]------> 55=x²-6x----------> x²-6x-55=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
x=11 mi
y=x-6-----> y=11-6-----> y=5 mi

the answer is
 the length of a rectangle is 11 miles
the width of a rectangle is 5 miles



Where does Pythagorean identity come from and how does it relate to right triangles

Answers

The Pythagorean identity is based from the three trigonometric identities that apply to the Pythagorean theorem. The three identities are founded on the concept that the hypotenuse is equal to the sum of the squares of the two sides of the right triangle. The identities can be determined through the substitution of sine and cosine in the right triangles measurements.

Find area of trapezoid using the Pythagorean theorem

Answers

You should either divide or add
This is a multistep problem. So, let's split it up.

Finding the height:
We need to look at the equation for find the diagonal of a triangle.
a²+b²=c²
We don't have leg one, but we have leg two. If we subtract the longer base by the shorter base, we have leg two.
11-7=4
a²+4²=5²
a²+16=25; let's subtract 16 from both sides.
a²=9
a=3

So, the height is 3.

Finding the area of the trapzoid:
Let's look at the formula for finding the area.
(b1+b2)(h÷2)=A; let's fill the variables in.
(7+11)(3÷2)=A
(18)(1.5)=A
27=A

So, the area of the trapezoid is 27 in²

What is the equation, in slope-intercept form, of the line that passes through (0, 3) and has a slope of −6?
y = 3x + 6
y = 3x − 6
y = −6x − 3
y = −6x + 3

Answers

Y = 3x - 6, slope is the last number in the equation.

Answer:

y=-6x+3

Step-by-step explanation:

Using the formula,

[tex](y-y_{1})=m(x-x_{1})\\(y-3)=(-6)(x-0)\\y-3=-6x\\y=-6x+3[/tex]

Solve 4x - 2= 86
thanks

Answers

4x-2=86
   +2  +2            (-2 and +2 cancel each other out)
_______
4x=88               ( divide 4 on both sides)

x=22
x = 22

4x-2=86
    +2  +2
_______
4x=88
4x/4=x
88/4=22

An empty box weighs 200g the box is filled with birthday party goozy bags and now weighs 6.2kg Each goody bag weighs 150Work out how many goody bags are inside the box

Answers

For this case, the first thing we are going to do is define variables.
 We have then:
 x: number of birthday party goozy bags
 y: total weight
 We then have the following equation:
 y = 150x + 200
 For y = 6200 we have:
 6200 = 150x + 200
 Clearing x:
 x = (6200-200) / (150)
 x = 40
 Answer:
 there are 40 goody bags inside the box

Answer:

40

Step-by-step explanation:

Compare the functions shown below:


f(x) = −3x − 5
g(x)

cosine function with y intercept at 0, negative 3 h(x) = 2 cos(2x − π) + 4


Which function has the greatest y-intercept?

a. f(x)
b. g(x)
c. h(x)
d. all three functions have the same y-intercept

Answers

Find all y-intercepts:

1. For f(x): when x=0 you have that f(0)=-3·0-5=-5, then y-intercept is a point (0,-5).

2. For g(x): from the task conditions you have that g(x) is cosine function with y intercept at 0, negative 3, then y-intercept is a point (0,-3).

3. For h(x): when x=0 you have that h(0)=cos(2·0-π)+4=cos(-π)+4=-1+4=3, then y-intercept is a point (0,3).

As you can see the greatest y-intercept has function h(x).

Answer: correct choice is C.

Answer:

C

Step-by-step explanation:

I just took the test. :)

For Jack's birthday, his mom is taking him and 12 friends to the zoo. If she pays $11 for each ticket using her credit card, what impact will it have on the available credit left on her credit card?

Answers

The impact on Jack's mom's available credit after purchasing zoo tickets for Jack and 12 friends at $11 each will be a reduction of $143.

When Jack's mom pays $11 for each zoo ticket for him and his 12 friends, she will be purchasing a total of 13 tickets (one for Jack plus 12 for his friends). To calculate the total cost, multiply the number of tickets by the price per ticket:

Number of tickets: 13 (Jack + 12 friends)Price per ticket: $11Total cost: 13 tickets × $11 per ticket = $143

The total impact on her credit card's available credit will be a reduction of $143. If she had some available credit limit before this purchase, we just subtract this amount from her available credit to determine the new available credit.

At 7 a.m. Gene left Austin and headed south at 10 miles per hour. At 8 a.m. Anne left from the same place and headed south on the same road. If Anne was 60 miles ahead by 3 p.m. on the same day, what was her speed?

Answers

The answer is 20 miles

Anne's speed is 20 miles per hour. If she returned home by the same path 7 hours and 30 minutes after she left, her average speed for the entire trip is 18.67 miles per hour while her average velocity is zero.

To answer this question, we need to calculate Anne's speed based on the information given. Gene started at 7 a.m. traveling at 10 miles per hour. By the time Anne starts at 8 a.m., Gene has already covered 10 miles (since he travels for 1 hour). The time from 8 a.m. to 3 p.m. is 7 hours. Both Anne and Gene travel the same path for these 7 hours, but Anne is 60 miles ahead of Gene by 3 p.m. Therefore, we need to calculate the total distance Gene traveled in 8 hours, add 60 miles to that distance, and then divide by 7 to find Anne's speed.

First, we determine Gene's total travel distance by 3 p.m., which is 10 miles/hour * 8 hours = 80 miles. Anne is 60 miles ahead, meaning she traveled 80 miles + 60 miles = 140 miles in 7 hours. Thus, Anne's speed is 140 miles \/ 7 hours = 20 miles per hour.

For part (c), if Anne returned home by the same path 7 hours and 30 minutes after she left, the total trip time would be 15 hours (7 hours to 3 p.m. and another 7 hours and 30 minutes back). Since the round trip distance is 140 miles out and 140 miles back, the total distance is 280 miles. Her average speed is total distance divided by total time, hence 280 miles / 15 hours = 18.67 miles per hour. The average velocity for the round trip is zero because she ends up at the starting point, so the overall displacement is zero.

Karen makes $5 per hour baby-sitting and $12 per hour giving music lessons. one weekend, she worked a total of 18 hours and made $139. how many hours did she spend baby-sitting?

Answers

Let the number of hours she spent in baby- sitting is x

and the number of hours she spent in music lessons is y.

Now, we have been given that she worked a total of 18 hours. Hence, we have

[tex]x+y=18\\ y=18-x...............................(1)[/tex]

And she made $139. Thus, we have

[tex]5x+12y=139..............................(2)[/tex]

Substituting the value of y from equation 1 in 2, we get

[tex]5x+12(18-x)=139\\ 5x+216-12x=139\\ -7x=-77\\ x=11[/tex]

Therefore, she spent 11 hours in baby-sitting.

Final answer:

Karen spent 11 hours baby-sitting and 7 hours giving music lessons.

Explanation:

Let x be the number of hours spent baby-sitting, and let y be the number of hours spent giving music lessons.

We are given the following information:


 Karen makes $5 per hour baby-sitting, so she earned 5x dollars from baby-sitting.
 Karen makes $12 per hour giving music lessons, so she earned 12y dollars from giving music lessons.
 She worked a total of 18 hours, so x + y = 18.
 She made a total of $139, so 5x + 12y = 139.



We can now set up a system of equations:


 x + y = 18
 5x + 12y = 139


To solve this system, we can use substitution or elimination method. Let's use the elimination method:


 Multiply the first equation by 5 to make the coefficients of x the same: 5x + 5y = 90.
 Subtract this new equation from the second equation: (5x + 12y) - (5x + 5y) = 139 - 90.
 Simplify both sides of the equation: 7y = 49.
 Divide both sides of the equation by 7: y = 7.
 Substitute y = 7 into the first equation: x + 7 = 18.
 Solve for x: x = 11.

Therefore, Karen spent 11 hours baby-sitting and 7 hours giving music lessons.

Learn more about Solving Systems of Equations here:

https://brainly.com/question/29050831

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Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).

Answers

2x + 4y = 6
4y = -2x + 6
y = -1/2x + 3/2
slope = -1/2

y = mx + b 
y = -1/2x + b

At point (6, 4)
4 = -1/2(6) + b
4 = -3 + b
b = 7

Equation : y = -1/2x + 7

each of the circles below has an area of 196 pi square units find the perimeter of the rectangle

Answers

Answer:

Step-by-step explanation:

Alright lets get started.

We have given the area of each circle as 196 pi square units.

since the area of the circle =[tex]\pi*radius^2[/tex]

so,the radius of the circle :

[tex]196\pi =\pi r^2[/tex]

[tex]r^2=196[/tex]

[tex]r=14[/tex]

therefore the diameter of the circle will be [tex]2*radius=2*14=28[/tex]

the perimeter of the rectangle=[tex]2*(length+ width)[/tex]

the length of the rectangle will be addition of diameters of the circle=[tex]28+28=56[/tex]

breadth of the rectangle is equal of the diameter =28

Perimeter of the rectangle =[tex]2*(56+28)=168[/tex]

Answer  168 units.

The perimeter of the given rectangle is 168 units

Given that area of each of the circles are [tex] 196 \pi [/tex] sq units and we know that the area of circle [tex]=\pi r^{2}[/tex] using this radius of the circle will be

[tex]\pi r^{2} =196\pi\\ r^{2} = 196\\ \\ r=14[/tex]

So, the diameter of the circle is twice the radius which is

[tex]2\times r\\ 2\times 14 =28 [/tex]

Here we can see that length of rectangle is equal to twice the diameter of the circle and breadth is equals to twice the radius

[tex]length= 28+28=56[/tex]

[tex]breadth = 2\cdot14=28[/tex]

How to find the perimeter of the given rectangle ?

To find the perimeter we use the formula

Perimeter of rectangle = [tex]2\cdot(length + breadth)[/tex]

On solving we get ,

[tex]2\cdot(56 +28)\\ 168 units[/tex]

Therefore, The perimeter of the given rectangle is 168 units

Learn more about perimeter here : https://brainly.com/question/3492380


Out of the 180 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing.

Use a two-way table to organize the information and answer the following question:

Approximately what percentage of students signed up for neither canoeing nor trekking?

72%
40%
54%
98%

Answers

There are 72 students that signed up for canoeing, and 23 students that signed up for trekking. 13 of these 23 students also signed up for canoeing.

Use the following equation to find the amount of people that signed up for an activity:

[tex]72 + 23 - 13 = 82[/tex]

82 students signed up for canoeing or trekking.

Subtract this total from the total amount of students to find the total that did not sign up for an activity:

[tex]180 - 82 = 98[/tex]

Divide this number by the total amount of students in the camp:

[tex]98 \div 180 = 0.54[/tex]

Multiply this decimal by 100 to convert into a percentage:

[tex]0.54 * 100 = 54[/tex]

54% of students did not sign up for neither canoeing nor trekking.
Even though Kanest's answer is verified and correct, the attached picture is how the 2 way table should be set up:

ANOTHER FILL IN THE BLANKS QUESTION, MARKING BRAINLIEST FOR CORRECT ANSWER

Answers

Hi, again!
First blank: multiplication property of equality
Both sides of the equation were multiplied by (1/2). 

Second blank: m<E
Angle E is an inscribed angle intercepting arc FGD, so by the inscribed angle theorem, its measure is half the measure of the arc.

Third blank: m<G
Same explanation as the prior blank

Fourth blank: substitution property of equality
Since angle E is equal to half the measure of arc FGD, we can replace that term. Likewise with angle G.

x/3+6=9
what does x equal
x=___?

Answers

9514 1404 393

Answer:

  9

Step-by-step explanation:

  x/3 +6 = 9 . . . . . given

  x/3 = 3 . . . . . . . subtract 6 from both sides

  x = 9 . . . . . . . multiply both sides by 3

Now we have to,

find the required value of x.

→ x/3 + 6 = 9

→ x/3 = 9 - 6

→ x/3 = 3

→ x = 3 × 3

→ [x = 9]

Hence, 9 is the value of x.

46 points for yall, i need math help.

Answers

Your answer would be the fourth choice, 6/13.
(4x-8)=(-9x-2)

4x= -9x+6

-5x= 6

x= -(6/5)



The perimeter of a rectangular floor is 50 feet. find the dimensions of the floor if the length is four times the width.

Answers

length is 20 
width is 5 

let me know if you need more details 

The dimensions of the rectangle are width = 5 feet and length = 20 feet.

What is the perimeter of the rectangle?

The perimeter of a rectangle is defined as the addition of the length and width.

The perimeter of a rectangle = 2(L + W)

Where W is the width of the rectangle  and L is the length of the rectangle

We have been given that the perimeter of a rectangular floor is 50 feet.

The length is four times the width.

Let the width of the rectangle is x

So the length of the rectangle = 4x

The perimeter of a rectangle = 2(L + W)

50 = 2(4x + x)

50 = 2(5x)

50 = 10x

10x = 50

x = 50 /10

Apply the division operation,

x = 5

So the length of the rectangle = 4(5) = 20 feet

Therefore, the dimensions of the rectangle are width = 5 feet and length = 20 feet.

Learn more about the perimeter of the rectangle here:

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(05.07 mc) mandy needs to paint all the faces and the base of a model pyramid she made for her history project. the dimensions of the pyramid are shown here. what is the total surface area of the pyramid? a square pyramid is shown. the side of the square is 10 inches. the height of the triangular faces is 9 inches.

Answers

To find the area of the square pyramid you will consider the shapes that make up the net of the pyramid (what it looks like when it is unfolded).

There are 4 congruent (same size and shape) triangles and a square.

The area of the square is
A = bh
     10 in x 10 in
A = 100 square inches.

The area of one triangle is
A = 1/2bh
    1/2 x 10 in x 9 in
A = 45 square inches

45 square inches x  4 (for the 4 triangles)

180 square inches of triangles

180 + 100 = 280

The total surface area of the square pyramid is 280 square inches.

Answer:

280

Step-by-step explanation:

i n e e d p o i n t s

Eric plans to rent a car for a day from Easy Car Rental. He has a coupon for 25% off the daily base rate of $40. He will also have to pay an additional $0.15 for each mile he drives. Which expression represents the situation?

Answers

Let x represent the number of miles he drives

Base rate: 40 - (40 · 0.25)  plus  mileage: 0.15 · x
Total cost = 30 + 0.15x

Use the given information to match the answers.

ABC is a right triangle.

1. 2√13
2. √5
3. 3√3

1. If b = 2 and c = 3, then a =
2. If a = 3 and c = 6, then b =
3. If a = 4 and b = 6, then c =

Answers

using formula
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
1)
[tex] {3}^{2} = {a}^{2} + {2}^{2} \\ a = \sqrt{ {3}^{2} - {2}^{2} } \\ a = \sqrt{5} [/tex]
2)
[tex] {6}^{2} = {3}^{2} + {b}^{2} \\ b = \sqrt{ {6}^{2} - {3}^{2} } \\ b = \sqrt{27} \\ b = \sqrt{9} \sqrt{3} \\ b = 3 \sqrt{3} [/tex]
3)
[tex] {c}^{2} = {4}^{2} + {6}^{2} \\ c = \sqrt{ {4}^{2} + {6}^{2} } \\ c = \sqrt{52} \\ c = \sqrt{4} \sqrt{13} \\ c = 2 \sqrt{13} [/tex]
Hey there!

Solve them by using
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]


1.
[tex] {a}^{2} + {2}^{2} = {3}^{2} \\ {a}^{2} + 4 = 9 \\ {a}^{2} = 9 - 4 \\ {a}^{2} = 5 \\ a = \sqrt{5} [/tex]

2.
[tex] {3}^{2} + {b}^{2} = {6}^{2} \\ 9 + {b}^{2} = 36 \\ {b}^{2} = 36 - 9 \\ {b}^{2} = 27 \\ b = \sqrt{9 \times 3} \\ b = 3 \sqrt{3} [/tex]

3.
[tex] {4}^{2} + {6}^{2} = {c}^{2} \\ 16 + 36 = {c}^{2} \\ {c}^{2} = 52 \\ c = \sqrt{13 \times 4} \\ c = 2 \sqrt{13} [/tex]

Hope this helps. - M
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