3^2•3^n simplifies to 3^20 what is the value of the exponent n?

6√2 ≈ 8.485 inches

The radii and the chord together make an isosceles right triangle with legs 6 inches long. The hypotenuse of such a triangle is √2 times the leg length. So, the chord will be 6√2 in long.

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Comment on isosceles right triangle

It is worth remembering that the hypotenuse of an isosceles right triangle is √2 times the leg length. This is easily found using the Pythagorean theorem:

... c² = a² + b²

... c² = 1² + 1² = 2 . . . . for legs of length 1

... c = √2 . . . . . . . . . . take the square root.

Scale this result as needed for any particular problem. Here, the scale factor is 6 inches.

"The correct fraction representing Japan's petroleum consumption as a percentage of the world's total is [tex]\(\frac{5.4}{100}\).[/tex]

To express the given percentage as a fraction, one must divide the percentage by 100, since percentages are parts per hundred. T

hus, 5.4% can be written as a fraction by placing 5.4 over 100, which gives us [tex]\(\frac{5.4}{100}\)[/tex].

Finally, this fraction can be reduced by dividing both the numerator and the denominator by their greatest common divisor, which is 2 in this case, yielding the simplified fraction [tex]\(\frac{27}{500}\).[/tex]

When reduced to a fraction without a decimal,  [tex]\(\frac{27}{500}\)."[/tex]

Answer:

1.2 acres of grass

Step-by-step explanation:

It takes 6.7 lb of seed to plant one acre of grass. The ratio of interest is 6.7 lb seed:1 acre of grass. We can find the acres of grass that can be planted with 8.04 pounds of seed using a conversion fraction.

8.04 lb × (1 acre/6.7 lb) = 1.2 acre

We can plant 1.2 acres of grass with 8.04 pounds of seed.

Answer:

Kevin has 5 quarters and 8 dimes.

Step-by-step explanation:

First of all, a quarter is worth 0.25 dollars, while a dime is worth 0.10 dollars. As Kevin has 13 coins in his pocket which in sum make $2.05, and all of them are either dimes or quarters, in order to determine how many dimes and quarters does he have, we have to take into account that he's got an odd number of quarters, since the final amount of money sums $2.05, that is, it ends in 5.

Therefore, if he had 1 quarter and 12 dimes (0.25 + 12x0.10 = 1.45), he would have $1.45.

If he had 3 quarters and 10 dimes (0.25x3 + 10x0.10 = 1.75), he would have $1.75.

If he had 5 quarters ahd 8 dimes (0.25x5 + 8x0.10 = 2.05), he would have $2.05, so this is the correct option.

Answer:

The fifth term of [tex]a_n = 2(-1)^n[/tex] is, -2

Step-by-step explanation:

Given the sequence:

[tex]a_n = 2(-1)^n[/tex]             .....[1]

where,

n is the number of terms.

To find the fifth term of the given sequence:

Substitute n = 5 in [1]  we have;

[tex]a_5 = 2 \cdot (-1)^5[/tex]

⇒[tex]a_5 = 2 \cdot -1 = -2[/tex]

Therefore, the value of fifth term of [tex]a_n[/tex] is, -2

Answer is B. -2√3+2√15

By using distributive property, 12 × (-1 + [tex]\sqrt{5}[/tex]) = 14.832.

According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Given

12 × (-1 + [tex]\sqrt{5}[/tex])

Apply distributive property

= 12 × (-1) + 12 × [tex]\sqrt{5}[/tex]

= -12 + 12[tex]\sqrt{5}[/tex]

≅ 14.832

Hence by using distributive property, 12 × (-1 + [tex]\sqrt{5}[/tex]) = 14.832.

Find out more information about distributive property here

https://brainly.com/question/5637942

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Answer:The measurement of angle O is greater than angle Q is the correct statement.

Explanation: Since, According to the question,  MQ = QP = PO = ON and MP is greater than NP.

Then, In first option, segment OP is longer than segment MQ is false because OP=MQ.

In second option, MN=MP can not be possible because NP is greater than MP.

In third option, The measure of angle Q equals the measure of angle O also can not be possible because MN is not parallel to QO.

But, In fourth option, Since MP is greater than NP thus NO makes larger angle than MQ.

Thus, fourth option is correct.

The minimum number of identical square tiles required to completely cover an 84 cm x 112 cm tabletop is 12 tiles, each with side lengths of 28 cm.

To determine the minimum number of identical square tiles required to completely cover a rectangular tabletop with dimensions 84 cm x 112 cm, we need to find the greatest common divisor (GCD) of the two side lengths. This is because using tiles that match the GCD will ensure that they fit perfectly across both lengths and widths without needing to cut any tiles.

The GCD of 84 and 112 is 28. Therefore, the side length of the square tile that Chen should use is 28 cm x 28 cm. To find the number of tiles needed, we then divide the area of the tabletop (which is 84 cm x 112 cm or 9408 square cm) by the area of one tile (which is 28 cm x 28 cm or 784 square cm).

The calculation is as follows: 9408 square cm / 784 square cm = 12. Therefore, Chen needs a total of 12 tiles of 28 cm x 28 cm to cover the entire tabletop.

Answer:

Question 1: 1, 7, 29, 203

Question 2: 203, 29, 7, 1

Step-by-step explanation:

Given the equation is 7x² + 6 = 13.

Solving the quadratic equation using square roots :-

7x² + 6 = 13

Step 1 :- subtracting 6 from both sides

7x² + 6 - 6 = 13 - 6

7x² = 7

Step 2 :- Dividing by 7 on both sides

[tex] \frac{7x^{2}}{7} = \frac{7}{7} \\\\
x^{2} = 1 [/tex]

Step 3 :- Taking square root on both sides

[tex] \sqrt{x^{2}} = \sqrt{1} \\\\
x = -1 \;\;OR\;\; x=1 [/tex]

So, x = -1 or x = 1 is the final answer.

The probability that a spinner with 14 equal areas lands on a multiple of 5 or a multiple of 2 is 4/7, after identifying the unique numbers from 1 to 14 that fit the criteria and dividing by the total number of possible outcomes.

The student is asking about the probability of an event occurring after spinning a spinner with 14 equal areas numbered 1 through 14. Specifically, the question seeks the probability that the result is either a multiple of 5 or a multiple of 2 when the spinner is spun once.

To solve this, first identify the multiples of 5 and 2 between 1 and 14: for 5, the multiples are 5 and 10; for 2, the multiples are 2, 4, 6, 8, 10, 12, and 14. Here, the number 10 is a multiple of both 5 and 2, so it should only be counted once. In total, there are 8 unique numbers that are multiples of 2 or 5 on the spinner. Since there are 14 possible outcomes, the probability is:

Probability = Number of favorable outcomes / Total number of outcomes = 8 / 14 = 4/7.

Thus, the probability that the spinner lands on a multiple of 5 or a multiple of 2 is 4/7.