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3 years ago

6

ben is n years old chloe is twice as old as ben dan is five years younger than ben . the total of bens age chloes age and dans a

ge is t years what is the formula for t in terms of n

1 answer:

zimovet [89]3 years ago

7 0

Answer:

Age of ben = n years

Age of Chloe = 2n years

Age of Dan = (n - 5) years

Now,

Sum of ben, Chloe and Dan's age = t years

or, n +2n + n - 5 = t

or, 4n - 5 =t

This is the required formula

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The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below. V=1/3πR^H Write the formula to

iren [92.7K]

Answer:

$h=\frac{1}{3} \pi r^{2} v$

Step-by-step explanation:

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3 years ago

Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

shtirl [24]

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

$y=\dfrac{1}{4p}(x-h)^2+k$ ...(i)

Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.

The focus of the parabola is at (6,-4).

$(h,k+p)=(6,-4)$

On comparing both sides, we get

$h=6$

$k+p=-4$ ...(ii)

Directrix at y=-7. So,

$k-p=-7$ ...(iii)

Adding (ii) and (iii), we get

$2k=-11$

$k=\dfrac{-11}{2}$

$k=-5.5$

Putting $k=-5.5$ in (ii), we get

$-5.5+p=-4$

$p=-4+5.5$

$p=1.5$

Putting $h=6, k=-5.5,p=1.5$ in (i), we get

$y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)$

$y=\dfrac{1}{6}(x-6)^2-5.5$

Therefore, the equation of the parabola is $y=\dfrac{1}{6}(x-6)^2-5.5$ .

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2 years ago

Let an integer be chosen at random from the integers 1 to 30 inclusive. Find the probability that the integer chosen is not even

mylen [45]

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Thank you for letting me answer your question here on brainly. I like to help people as much as I can, so please let me now if my answers provide any help to you. It means a lot to me to know that my questions help provide support to people in the community to need help. If you want extra help, you can PM me! I get lot of PMs tough, so it might take a while to respond, my apologies. Thanks for reading this, and have a great day! ~ brainily user, Lillyxrose
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3 years ago

Read 2 more answers

Please answer I’ll rate brainlyest

12345 [234]

Answer:

$5P3*6C4=60*15=900$

Step-by-step explanation:

$5P3$ refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;

$5P3=\frac{5!}{(5-3)!}$

The factorial of an integer n is evaluated as;

$n!=n*(n-1)*(n-2)*(n-3).......3*2*1$

Using this concept, the above expression can now be simplified as follows;

$5P3=\frac{5!}{2!}=\frac{5*4*3*2!}{2!}=5*4*3=60$

Therefore, the permutations of 5 items taken 3 at a time is 60.

The next expression, $6C4$ refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;

$6C4=\frac{6!}{4!(6-4)!}=\frac{6!}{4!*2!}=\frac{6*5*4!}{4!*2*1}=\frac{6*5}{2*1}=15$

Therefore, the combinations of 6 items taken 4 at a time is 15.

The final step is to evaluate the product;

$5P3*6C4=60*15=900$

3 0

3 years ago

the length of a rectangle is 5 less than twice the width.if the perimeter of the rectangle is 146,find the area of the rectangle

raketka [301]

Answer:

The area of the rectangle is 1222 units²

Step-by-step explanation:

The formula of the perimeter of a rectangle is P = 2(L + W), where L is its length and W is its width

The formula of the area of a rectangle is A = L × W

∵ The length of a rectangle is 5 less than twice the width

- Assume that the width of the rectangle is x units and multiply

x by 2 and subtract 5 from the product to find its length

∴ W = x

∴ L = 2x - 5

- Use the formula of the perimeter above to find its perimeter

∵ P = 2(2x - 5 + x)

∴ P = 2(3x - 5)

- Multiply the bracket by 2

∴ P = 6x - 10

∵ The perimeter of the rectangle is 146 units

∴ P = 146

- Equate the two expression of P

∴ 6x - 10 = 146

- Add 10 to both sides

∴ 6x = 156

- Divide both sides by 6

∴ x = 26

Substitute the value of x in W and L expressions

∴ W = 26 units

∴ L = 2(26) - 5 = 52 - 5

∴ L = 47 units

Now use the formula of the area to find the area of the rectangle

∵ A = 47 × 26

∴ A = 1222 units²

∴ The area of the rectangle is 1222 units²

7 0

3 years ago