Parallel, intersecting or skew?
AB and BC.
AE and BF.
EF and AD.
Plane ABC and Plane ABF.
Plane AED and Plane BFC.
HELP!!!

Answer:

You use cotx = cosx/sinx.

Step-by-step explanation:

I guess you mean cotx sinx = cosx.

You substitute the identity cotx = cosx / sinx:

cotx sinx = (cosx / sin x) * sin x

The sin x ' s cancel to give cosx.

Final answer:

To verify that cot(x)sin(x) + cos(x) is a basic trigonometric identity, we can use the Pythagorean Identity which states that sin²(x) + cos²(x) = 1. The expression cot(x)sin(x) + cos(x) simplifies to 2cos(x), which confirms that it is a basic trigonometric identity.

Explanation:

To verify that cot(x)sin(x) + cos(x) is a basic trigonometric identity, we can use the Pythagorean Identity which states that sin²(x) + cos²(x) = 1. Let's start by expressing cot(x) in terms of sin(x) and cos(x). Since cot(x) = cos(x)/sin(x), we can substitute this into the equation:

cot(x)sin(x) + cos(x) = cos(x)/sin(x) * sin(x) + cos(x) = cos(x) + cos(x) = 2cos(x).

So, the given expression reduces to 2cos(x), which is indeed a basic trigonometric identity.

Answer:

a=0, b=-4

Step-by-step explanation:

a+b=-4.....(1)

a-b=4.......(2)

(1)+(2): 2a=0

a=0

0+b=-4

b=-4

(a, b) =(0,-4)

Solution:

Let "x" be the number of tables

Let "y" be the number of booths

The restaurant has 38 seating units

Therefore,

x + y = 38

x = 38 - y ------- eqn 1

Hometown Buffet has tables that can seat 6 people and booths that can seat 4 people

Total of 188 people

Therefore,

6x + 4y = 188 ------ eqn 2

Substitute eqn 1 in eqn 2

6(38 - y) + 4y = 188

228 - 6y + 4y = 188

2y = 40

y = 20

Substitute y = 20 in eqn 1

x = 38 - 20

x = 18

Thus there are 18 tables and 20 booths are at the restaurant

Answer:

based on how many minutes it pass, it the time pass one minute it will be 14.5 degrees.

Answer:

1. Angel - 0.08 mins, Jayden - 0.067 mins

2. Angel - 12.5 km, Jayden - 15 km

3. Jayden runs faster.

Step-by-step explanation:

The length of the track (1 lap) is 25 km.

Angel ran 1 lap in 2 mins. That means he ran 25 km in 2 mins.

Jayden ran 3 laps in 5 mins. That means he ran 75 km (3 * 25 km) in 5 mins.

1. To find the time it takes to run 1 km, we divide the total time taken by the total distance run.

The number of minutes it takes Angel to run 1 km will be:

T = 2 / 25 = 0.08 minutes

The number of minutes it takes Jayden to run 1 km will be:

T = 5 / 75 = 0.067 minutes

2. To calculate the distance they run in 1 min, we divide the total distance run by the total time taken.

The distance Angel runs in 1 min is:

D = 25 / 2 = 12.5 km

The distance Jayden runs in 1 min is:

D = 75 / 5 = 15 km

3. Jayden runs faster because he runs more kilometres per minutes (15 km/min) than Angel (12.5 km/min).

In other words, Jayden clocks a faster speed than Angel.

Answer:

X = 4, -6

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

x = 4 and x = -6

Step-by-step explanation:

We can use the Zero Identity Property, which states that 0 * n = 0, where n is any number.

Here, in order for (x - 4)(x + 6) = 0 to be true, either x - 4 must equal 0 or x + 6 must equal 0. So set each of them equal to 0 and solve for x:

x - 4 = 0

x = 4

x + 6 = 0

x = -6

The answers are x = 4 and x = -6.

Hope this helps!

Answer:

D

Step-by-step explanation:

The statements are shown below:

A) She used the wrong number as a repeated factor and should have evaluated -2x2x2x2x2x2x2x2.

B) She used the wrong number as a repeated factor and should have evaluated -(8x8).

C) She misinterpreted the exponential form and should have multiplied -2 and 8.

D) She made a sign error when multiplying and should have had 256 as a final answer.

Solution:

The problem to simplify is:

[tex](-2)^{8}[/tex]

Haley's steps are shown below:

[tex](-2)^{8}=(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)=-256[/tex]

Generally,

[tex](a)^b[/tex]  is actually "a" multiplied "b" times.

So, Haley wrote "-2" eight times multiplied together. That is okay.

Now,

We are dealing with negative numbers.

Haley wrote "-2" eight times, which is EVEN number of times, so the answer would be POSITIVE. But, Haley's answer is negative. Which is wrong. But "256" is right.

Haley's error is:

Answer choice D

Answer:

the answer is D

Step-by-step explanation:

Answer:

104,196 square meter

Step-by-step explanation:

This question can be solved by using the formula of area of four side in a

rectangular prism

In the given problem we have

Length of building = 218m

width of building = 158m

height of building = 160

Area of four walls is given by formula = 2*(L + B) * H

where L is length of rectangular prism

B is width of rectangular prism

H is height of rectangular prism

Therefore total surface area of building = 2*(218 + 158)* 160 = 376*320= 120,320

___________________________________________________

No of doors in the building = 4

length of door = 139m

width of door = 29 m

area of one door = length * width = 139* 29 = 4,031

area of four door = 4* 4,031 = 16,124

___________________________________________________

we have to find surface area of building when doors are open

To find this we can subtract total area of four door from total surface area of four walls which we have calculated above

total surface area of four walls - total area of four door

=> 120,320 - 16,124 = 104,196

104,196 is the buildings outside surface area when the doors are open

Answer:

Arithmetic sequence

f(n)=30-2(n-1)

Step-by-step explanation:

Chinedu's problem-solving sequence is arithmetic. The explicit formula for the sequence is f(n) = 32 - 2n.

Chinedu's homework problem involves a sequence where he solves 2 problems each minute, starting with 30 problems. To determine the number of problems left at the beginning of the nth minute, we can use an arithmetic sequence since the number of problems decreases by a constant amount (2 problems) each minute.

In an arithmetic sequence, the nth term can be expressed using the formula:

f(n) = a + (n - 1)d

where a is the first term and d is the common difference.

Steps:

f(n) = 30 + (n - 1)(-2) = 30 - 2(n - 1) = 32 - 2n

So, the explicit formula for the sequence is f(n) = 32 - 2n.

Answer:

The correct option is option (B)

Yes, he will have enough poster board because 10 = 2.5 feet. Then, 2.5 x 2 = 5 square feet .

Step-by-step explanation:

1 foot = 12 inches.

Fabian needs 45 square feet of poster board for an art.

Actually, the area of the poster is 4.5  square feet.

[Since the unit of 4.5 is  square feet, so it is unit of area.]

He buys a sheet of poster board with length 30 inches and a width 2 feet.

The units of length and width are not same.

So, first we need to convert the width in inches.

The length of the sheet is = 30 inches

                                         =(30÷12) inches

                                         =2.5 feet.

Total area of the sheet = length×width

                                      =(2.5×2) square feet

                                      = 5 square feet

So, the area of sheet is more than the area of poster.

Yes, he will have enough poster board because 10 = 2.5 feet. Then, 2.5 x 2 = 5 square feet .                                      

Answer:

Better deal : dozen bars for $3.72 (It is a better deal by 12 cents)

Step-by-step explanation:

Since one has half of the amount that the other has, you multiply the price by two, and you end up with (for a dozen) $3.72, (and for 2 boxes of 6) $3.84. So, the singular box of a dozen bars wins.  

:) Hope this helps! <3

Answer: the box of dozen is cheaper by 0.12

Step-by-step explanation:

3.72 /12= 0.31

1.92*2= 3.84

3.84/12= 0.32

3.84-3.72=0.12

Answer:

5.9 x 10^-5

Step-by-step explanation:

Move the point to the right . The power of the exponent becomes negative because we’re moving the point from left to right. The opposite is the case if we move the point to the left .

To two significant figures, move the point until you have just two figures left. So

5.9 x 10^-5 is the answer

Answer: 3.3×10^-3

Step-by-step explanation:

0.003259 in standard form

When you see a standard form questions like this,you have to be patient

You will have to count the zeros backward

How many zeros are in front of the 3,that's two right

That means you take the decimal to the back of 3,that means the decimal is jumping three numbers

Since you are counting backward, that will be negative

So we have,

3.259×10^-3

Now to two significant figures

You will round up the 5 behind the 2 to 1 and add to the 2

Making 3,

So we have

3.3×10^-3

Answer:

(300-28)7

Step-by-step explanation:

You always do parenthesis first and then the 7 means to do multiplication if it is right next to the parenthesis

Answer:

7(300-28)

Step-by-step explanation: All you have to do is put the 300-28 in parentheses (300-28) and then you would put the 7 on the outside of the parentheses and your answer would be 7(300-28)

Answer:

[tex] 420 \: {feet}^{3} [/tex]

Step-by-step explanation:

Space occupied by storage locker in the warehouse will be equal to its volume.

[tex] \therefore \: volume \: of \: storage \: locker \\ = 5 \times 6 \times 14 \\ = 30 \times 14 \\ = 420 \: {feet}^{3} [/tex]

Hence, storage locker will occupy 420 cubic feet of space in the warehouse.

Answer:8

Step-by-step explanation:

Multiple 2 five times and multiple 2 two times than divide

2*2*2*2*2=32

2*2=4

32/4=8

Answer:

15:32

Step-by-step explanation:

15:5+3+4×6

Using BODMAS rule

15:5+3+(4×6)

15:5+3+24

So add up

15:32

Since the two cannot be divided by the same number,we will have to leave the answer as

15:32

Answer:

Step-by-step explanation:

PUT y  or f(x) = 0......then find x

Answer:

2 • (x - 20) • (x + 5) • (x + 40)

Step-by-step explanation:

Final answer:

To solve the equation (x-20) (2x+10) (x+40)=0, we set each factor equal to zero and solve for x, resulting in three solutions: x = 20, x = -5, and x = -40.

Explanation:

To find the value of x in the equation (x-20) (2x+10) (x+40) = 0, we need to use the property that if a product of factors equals zero, at least one of the factors must be zero. This gives us three separate equations to solve: x - 20 = 0, 2x + 10 = 0, and x + 40 = 0.

Step-by-Step Solution:

Solve x - 20 = 0: Add 20 to both sides, which gives x = 20.

Solve 2x + 10 = 0: Subtract 10 from both sides and then divide by 2, giving x = -5.

Solve x + 40 = 0: Subtract 40 from both sides, which gives x = -40.

Therefore, the solutions to the equation are x = 20, x = -5, and x = -40.

Answer:

3/-2

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

The first number is 2, so 2 must be plotted on the X radius (because it goes by X first). B plots X on the Y axis so therefore, by process of elimination, A is the answer.

Answer:

I believe D is the answer

Step-by-step explanation:

For the square root of a number to be a whole number, we would need to have a perfect square. 14 is given to us, so to find the missing number, all we have to do is square 14 (or multiply it by itself).

14 x 14 = 196

The missing number is 196.

Hope this helps! :)

Answer:  x=7x−1

Step-by-step explanation:

Answer:

(4x - 2y³)²

Step-by-step explanation:

a² - 2ab + b² = (a - b)²

16x² = 4²x² = (4x)²  , Therefore, a = 4x

4y⁶=2²(y³)² = (2y³)² = b² , Therefore, b = 2y³

2ab = 2*4x*2y³ = 16xy³

16x² - 16xy³ + 4y⁶ = (4x)² - 2* 4x * 2y³ + (2y³)²

                            = (4x - 2y³)²

Answer:(4x - 2y³)²

Step-by-step explanation:

Solution:

The ladder, wall and base of the ladder from wall forms a right angled triangle

Length of ladder forms the hypotenuse

Length of ladder = 12 foot

base of the ladder from wall = 2 feet

To find: height of wall

By pythagoras theorem.

[tex]c^2 = a^2+b^2[/tex]

Where,

"c" is the Length of ladder

"a" is the base of the ladder from wall

"b" is the height of wall

Substituting the values,

[tex]12^2 = 2^2+b^2\\\\144 = 4 + b^2\\\\b^2 = 140\\\\b = \pm 11.832 \\\\Ignore\ negative\ value\\\\b \approx 11.8[/tex]

Thus, the ladder will reach a height of 11.8 feet on wall

Answer:

Dale buys pencils that come in packs of 12. He gets y total pencils for buying x packs.

Step-by-step explanation:

12x in the equation is the 12 pencils in each pack times the number of packs (x). In the equation, y is the total, and the answer says he gets y total pencils.

Hope this helps! ☺

Answer:

11

Step-by-step explanation:

You are adding 2 every time:

1+2=3

3+2=5

5+2=7

7+2=9

9+2=11

The next term in the sequence is 11.

Therefore the complete the series is : 1, 3, 5, 7, 9, 11 .

Arithmetic sequence : Sequence in which the difference between two consecutive terms is same .

Given, Arithmetic sequence : 1, 3, 5, 7, 9 .

So, after analyzing the sequence the common difference between two consecutive terms is 2.

Thus in the sequence add 2 to the first term , then the next term is obtained. Like,

1 + 2 = 3

3 + 2 = 5

5 + 2 = 7

7 + 2 = 9

Therefore the next term will be,

9 + 2 = 11

Know more about arithmetic sequence,

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To find the time required for an investment to grow to a certain amount with compound interest, we can use the formula Final Balance = Principal(1 + interest rate/number of compounding periods)^(number of compounding periods * time). In this case, the investment of $5000 will take approximately 4.08 years to grow to $6000 at an interest rate of 7.5% per year, compounded quarterly.

To find the time required for an investment to grow to a certain amount with compound interest, we can use the formula:

Final Balance = Principal(1 + interest rate/number of compounding periods)^(number of compounding periods * time)

In this case, the initial principal is $5000, the final balance is $6000, the interest rate is 7.5% (or 0.075), and the interest is compounded quarterly (so there are 4 compounding periods per year).

Using a calculator, we can solve for time to find that the investment will take approximately 4.08 years to grow from $5000 to $6000.

The expressions which have the final answer 8000 will be equal to Andre's answer.

Multiplication is the process of adding a number repeatedly up to the times as that of the another number which is being multiplied with the given number.

For example 2 × 3 means 2 is added to itself 3 times or 3 is added to itself 2 times.

Andre says, “I multiplied 4 by 5, then cubed the result.”

Mathematically the expression is (4 × 5)³.

(4 × 5)³ = (4 + 4 + 4 + 4 + 4)³

            = 20³

Now a number cubed means it is multiplied to itself 3 times.

20³ = 20 × 20 × 20

      = 8000

Hence the resultant of the expression (4 × 5)³ = 8000. So all expressions which will result in an answer of 8000 will be equal to Andre's answer.

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