Ask question

Ask question

All categories

3 years ago

5

Jon has two trees in his yard. One is 29 feet taller than the other. If we let h be the height of the shorter tree, write an alg

ebraic expression for the sum of the two trees’ heights. Be sure to simplify your expression.

1 answer:

inessss [21]3 years ago

7 0

h + h + 29

This will be simplified into 2h + 29

The shorter tree's height is represented with the variable 'h'

Because the taller tree is 29 feet taller, the equation for the taller tree would be 'h + 29'

SInce we're looking for the sum, all you have to do is add 'h' and 'h + 29'

If you have any questions, just ask. Good luck! :))

-T.B.

You might be interested in

Find the perimeter of the isosceles triangle in simplest radical form.

neonofarm [45]

9514 1404 393

Answer:

6 +8√5

Step-by-step explanation:

The leg length can be reduced to simpler form:

3 +√45 = 3 +√(3²·5) = 3 +3√5

The perimeter is the sum of the side lengths, so is ...

(3 +3√5) +(3 +3√5) +(2√5) = 6 +8√5 . . . perimeter

4 0

3 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

3 years ago

There were 3 adults and 9 children on the bus. What was the ratio of adults to children? Enter your answer in reduced form.

stiks02 [169]

Answer:

1:3

Step-by-step explanation:

I think i am right but I might not be hope this helps

5 0

3 years ago

Read 2 more answers

How many more pairs of parallel sides does a regular octagon have than a

iVinArrow [24]

Answer:

A

Step-by-step explanation:

5 0

3 years ago

A.A fish is 12 meters below the surface of the ocean. What is its elevation?

dalvyx [7]

A. -12
b. +28
c. 40meters

5 0

2 years ago

Read 2 more answers