All numbers that are evenly divisible by both 6 and 14 are also divisible by which of the following numbers? A. 8
B. 12
C. 21
D. 28

Answers

Answer 1

Answer: divisble by 6 means it is divible by 2 and 3
divisblle by 14 means divisble ty 2 and 7

therefor the number is divisble by 2,3 and 7

test
A. 8 is not divible by 3
B. 12 is not divisble by 7
C. 21 is not divisble by 2
C. 28 is divisble

answer is D

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Alex and Ben were given a total of £360 they shared the money in the ratio 5:7 Ben received more money then Alex.how much more?

You borrow $2000 from the bank at 1% annual interest compounded monthly. The monthly payment is $100. What is the balance after the third payment?

Answers

The balance after the third payment is $1715.05.

How to find the compound interest?

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

$a = p(1 + (r)/(n))^(nt)$

We are given that;

Amount= $2000

Rate= 1%

Monthly payment = $100

Now,

Plugging these values into the formula, we get:

A = 2000 (1 + 0.01/12)^(12 * 3/12) A

≈ 2015.05

=2015.05 - 100 * 3

= $1715.05

Therefore, by the given interest the answer will be $1715.05

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Answer:

$2.52

Step-by-step explanation:

If you start with the balance being $2000, the monthly payment is $100 with the percentage rate being 1%. You would way 0.84 per month and if you multiply that by three months, you get $2.52.

Find the perimeter of the rectangle shown below

Answers

Since the triangle is a right triangle, we can use the pythagorean theorem to solve for the one remaining side.

Plug in your values

a = 9

b = ?

c = 15

9^2 + b^ = 15^2. Square root 9 and 15

81 + b^2 = 225. Subtract 81 from each side.

b^2 = 144. Take the square root of each side.

b = 12.

Now we know the length and width of the rectangle.

Perimeter = 2(12 + 9)

Perimeter = 42 in

Select the x-coordinate of the vertex of the parabola defined by the function f(x)=-9x^2+7x+8

Answers

$f(x)=-9x^2+7x+8\n\na=-9;\ b=7;\ c=8\n\nx_(vertex)=(-b)/(2a)\n\nx_(vertex)=(-7)/(2\cdot(-9))=(-7)/(-18)=(7)/(18)$

$x_v=-(b)/(2a)\n x_v=-(7)/(2\cdot(-9))\n x_v=(7)/(18)\n$

Paulo has 39 patches from states he and his relatives have visited he wants to pin the onto a board and arrange them equally in 3 rows how many patches will be in each row

Answers

Given:

Total number of patches = 39

Total number of rows = 3

To find:

The number of patches in each row.

Solution:

We have,

Total number of patches = 39

Total number of rows = 3

We need to divide the total number of patches by total number of rows to find the number of patches in each row.

$\text{Number of patches in each row}=(39)/(3)$

$\text{Number of patches in each row}=13$

Therefore, the number of patches in each row is 13.

Antoine is on vacation with his family. They have a vacation budget of $1,400. Antoine predicts they will spend $110 each night on the hotel, $80 a day on food, and $100 a day on activities. They will also spend $120 on gasoline for the entire trip. Write an inequality to find how many nights, n, they afford to stay on vacation. What is the longest vacation they can take?

Answers

Answer:

290n + 120 ≤ 1400

4 days

Step-by-step explanation:

Given that:

Vacation budget = $1400

Cost on hotel = $110 per night

Cost on food = $80 per day

Cost on activities = $100 per day

Cost on gas = $120 for entire trip

Number of nights they can afford to stay

Let the Number of nights they can afford = n

((110 + 80 + 100) * number of nights) + 120 ≤ vacation budget

290n + 120 ≤ 1400

290n ≤ 1400 - 120

290n ≤ 1280

n ≤ 1280 / 290

n ≤ 4.4137

Hence, longest vacation they can take is 4 days

Final answer:

The family can afford up to 4 nights for their vacation, as per the inequality 290n + 120 ≤ 1400, where 'n' stands for the number of nights.

Explanation:

Let's first define the total expenses per day as the sum of the hotel costs ($110), food costs ($80), and the daily amount for activities ($100). This adds up to $290 per day. So for 'n' nights, the family will be spending $290n. In addition, there's a $120 onetime expense for gasoline. Hence, the inequality representing their spending will be: 290n + 120 ≤ 1400.

To find the longest vacation this family can afford, we simply need to solve this inequality. Pay attention as we do this: 290n ≤ 1280 (subtracting 120 from both sides), and then n ≤ 4.41 (dividing both sides by 290).

Since the number of nights 'n' should be a whole number, the family can afford up to 4 nights on their vacation.

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Which terms give is the perfect square of 3x4? A. 6x8 B. 6x16 C. 9x8 D. 9x16

Answers

A perfect square is the product when a number is multiplied to itself. Hence,the square of (3x4) is (3 x 4 x 3 x 4). We can rearrange this and have (3 x 3) x (4 x 4) which gives you 9 x 16. Thus, we have the perfect square of (3x4) re-written as (9 x 16). Thus, the answer is D: 9 x 16.

Answer:

The correct option is C.

Step-by-step explanation:

The given term is 3x⁴.

We have to find the perfect square of 3x⁴.

$(3x^4)^2=3^2* (x^4)^2$ $[\because (ab)^x=a^xb^x]$