A vertical plane passes through a pyramid that has a horizontal base.

A bottle and a cap together cost $1.10. The bottle costs $1 more than the cap. How much does each cost?

Darya [45]

Answer:

The cap costs 10 cents and the botttle costs $1

Step-by-step explanation:

1.10-1=.10

3 0

3 years ago

Prove that 17^16+17^14 is divisible by 5

fredd [130]

We'll use the exponent rule that a^(b+c) = a^b*a^c

to break up 17^16 into 17^(14+2) = 17^14*17^2

That allows us to factor like so

17^16+17^14

17^14*17^2+17^14*1

17^14(17^2 + 1)

Computing 17^14 is a lot more difficult compared to computing 17^2 + 1, assuming you only could use paper and pencil.

Note that 17^2 = 17*17 = 289, so 17^2 + 1 = 289+1 = 290

Because 290 ends in a 0, this means that 5 is a factor

290 = 5*58

This makes 5 to be a factor of the original expression.

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

So overall,

17^16+17^14 = 17^14(17^2 + 1) = 17^14*290 = 17^14*5*58 = 5*17^14*58

The stuff "17^14*58" doesn't matter. All we care about is that factor of 5.

Since 5 is a factor, this means that 17^16+17^14 is a multiple of 5, or 17^16+17^14 is divisible by 5.

Phrased another way, 17^16+17^14 all divided over 5 leads to some integer. In this case, the integer would be the result of 17^14*58.

6 0

3 years ago

Pentagon ABCDE is shown on the coordinate plane below

77julia77 [94]

Answer: c) B' = (6, -3)

Step-by-step explanation:

The simplest way is to rotate the graph.

Rotating the graph 1 time to the left (counterclockwise) = 90°

Rotating the graph 2 times to the left (counterclockwise) = 180°

Rotating the graph 3 times to the left (counterclockwise) = 270°

The longer way is to reflect over the x-axis and over the y-axis, which is the same as a rotation of 180°

Z = (x, y) → Z' = (-x, -y)

the image below shows the graph rotated 2 times = 180°

5 0

4 years ago

Read 2 more answers

How do u solve A/B + C/D = E

Flauer [41]

You cannot solve this, I don’t see how....

5 0

4 years ago

Score Frequency

RUDIKE [14]

Scores on an AP Exam at a local high school are recorded in the table. What was the average score?

Answer: D) 4.266 is correct

Explanation:

We are given the below frequency table:

Score Frequency

1 | 0

2 | 3

3 | 4

4 | 16

5 | 22

Let's denote the score by $x$ and frequency by $f$ .

The average formula is:

$Average=\frac{\sum fx}{\sum f}$

$=\frac{(1\times0) + (2\times3)+(3\times4) +(4\times16) + (5\times22)}{0+3+4+16+22}$

$=\frac{0+6+12+64+110}{45}$

$=\frac{192}{45}=4.267$

Therefore, the average score was 4.267

Hence the option D) 4.266

7 0

4 years ago