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VashaNatasha [74]

4 years ago

8

Logan genetically engineered a new type of fir tree and a new type of pine tree. The combined height of one fir tree and one pin

e tree is 2121 meters. The height of 44 fir trees stacked on top of each other is 2424 meters taller than one pine tree. How tall are the types of trees that Logan genetically engineered? Each fir tree is meters tall and each pine tree is meters tall.

1 answer:

Maru [420]4 years ago

5 0

Answer:

Fir trees are 9 meters and the pine trees are 12 meters tall.

Step-by-step explanation:

Let the height of the fir tree = x and the height of the pine tree = y (in meters).

It is given that the combined height of both the trees is 21 meters.

That is, $x+y=21$

Also, the height of 4 fir trees is 24 meters more than that of the pine tree.

That is, $4x=y+24$ i.e. $4x-y=24$

So, we get the system of equations,

x+y=21

4x-y=24

Adding both the equations, gives us,

5x = 45 i.e. x= 9.

So, x+y=21 ⇒ y= 21 - x ⇒ y= 21 - 9 ⇒ y= 12.

Thus, the fir trees are 9 meters tall and the pine trees are 12 meters tall.

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Find the lateral and total surface area for the cone. If necessary, round to the nearest tenth and leave the

bija089 [108]

9514 1404 393

Answer:

262.2π cm²
392.16π cm²

Step-by-step explanation:

The lateral surface area is the product of half the circumference, and the slant height:

LA = πrh = π(11.4 cm)(23 cm) = 262.2π cm²

The total surface area adds the area of the base to that:

A = πr² +LA = π(11.4 cm)² +262.2π cm² = (129.96 +262.2)π cm²

A = 392.16π cm²

3 0

3 years ago

15/30 = n/34 round to the nearest tenth.

avanturin [10]

The equation given in the question has to be answered to the nearest tenth. The only thing that one should be careful about is the cross multiplication part. Other than that there is no difficulty in the given problem. Now let us get down to the equation in the question.
15/30 = n/34
30 * n = 15 * 34
30n = 510
n = 510/30
= 51/3
= 17
So the value of the unknown variable "n" comes out to be 17.

6 0

3 years ago

Read 2 more answers

How many ounces are equivalent to 6 pounds?

Dima020 [189]

Answer:

96

Step-by-step explanation:

1 pound is 16 ounces

6 pounds=x ounces

So we use the X to signal it's presence

1x16 is 16,

That means 16 ounces

6xP=Q

6x16 will give us our answer

Because it will tell us how many pounds there are since ounces is multiplied to get ounces.

6x16=96

P=16

Q=96

96 is our answer.

I hope this helps!!!!

If you need help, don't hesitate to ask!

I'm here until 2:30

May I please have brainliest?

5 0

3 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

PLEASE HELP PRE CAL!!

Len [333]

Answer:

Width = 2x²

Length = 7x² + 3

Step-by-step explanation:

∵ The area of a rectangle is $14x^{4}+6x^{2}$

∵ Its width is the greatest common monomial factor of $14x^{4}$ and 6x²

- Let us find the greatest common factor of 14 , 6 and $x^{4}$ , x²

∵ The factors of 14 are 1, 2, 7, 14

∵ The factors of 6 are 1, 2, 3, 6

∵ The common factors of 14 and 6 are 1, 2

∵ The greatest one is 2

∴ The greatest common factor of 14 and 6 is 2

- The greatest common factor of monomials is the variable with

the smallest power

∴ The greatest common factor of $x^{4}$ and x² is x²

∴ The greatest common monomial factor of $14x^{4}$ and 6x² is 2x²

∴ The width of the rectangle is 2x²

To find the length divide the area by the width

∵ The area = $14x^{4}+6x^{2}$

∵ The width = 2x²

∴ The length = ( $14x^{4}+6x^{2}$ ) ÷ (2x²)

∵ $14x^{4}$ ÷ 2x² = 7x²

∵ 6x² ÷ 2x² = 3

∴ ( $14x^{4}+6x^{2}$ ) ÷ (2x²) = 7x² + 3

∴ The length of the rectangle is 7x² + 3

8 0

3 years ago