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2 years ago

How to solve the word problem

Mathematics

1 answer:

goldfiish [28.3K]2 years ago

3 0

Your solution is correct. Kay is 18 and Liam is 12. Good Job!

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Prove that an = 4^n + 2(-1)^nis the solution to

olga nikolaevna [1]

Answer:

See proof below

Step-by-step explanation:

We have to verify that if we substitute $a_n=4^n+2(-1)^n$ in the equation $a_n=3a_{n-1}+4a_{n-2}$ the equality is true.

Let's substitute first in the right hand side:

$3a_{n-1}+4a_{n-2}=3(4^{n-1}+2(-1)^{n-1})+4(4^{n-2}+2(-1)^{n-2})$

Now we use the distributive laws. Also, note that $(-1)^{n-1}=\frac{1}{-1}(-1)^n=(-1)(-1)^{n}$ (this also works when the power is n-2).

$=3(4^{n-1})+6(-1)^{n-1}+4(4^{n-2})+8(-1)^{n-2}$

$=3(4^{n-1})+(-1)(6)(-1)^{n}+4^{n-1}+(-1)^2(8)(-1)^{n}$

$=4(4^{n-1})-6(-1)^{n}+8(-1)^{n}=4^n+2(-1)^n=a_n$

then the sequence solves the recurrence relation.

4 0

3 years ago

Find the Circumference of a circle with a Diameter of 9 inches Group of answer choices 9 pi inches 9 pi inches^2 9 pi inches^3 1

katen-ka-za [31]

Answer: $9\pi\ in.$

Step-by-step explanation:

Given

The diameter of a circle is $d=9\ in.$

So, the radius is $r=\frac{d}{2}=4.5\ in.$

The circumference is given by $2\pi r$

Insert the values

$\Rightarrow 2\pi \cdot 4.5\\\Rightarrow 9\pi \ in.$

Thus, the circumference of the circle is $9\pi\ in.$

8 0

3 years ago

Question 5 (1 point)<br><br> Write an equivalent expression for (m + 4n) - 2.5m

aliina [53]

Answer:

-1.5m + 4n is the equivalent expression

Step-by-step explanation:

To find the equivalent expression, we combine the like terms.

We are given the following expression:

m + 4n - 2.5m

Combining the like terms:

m - 2.5m + 4n

-1.5m + 4n is the equivalent expression

4 0

3 years ago

Simplify the expression below, I really just need the steps I have the answer (also can someone tell me how to edit points on th

Sloan [31]

Answer: $3x^2y\sqrt[3]{y}\\\\$

Work Shown:

$\sqrt[3]{27x^{6}y^{4}}\\\\\sqrt[3]{3^3x^{3+3}y^{3+1}}\\\\\sqrt[3]{3^3x^{3}*x^{3}*y^{3}*y^{1}}\\\\\sqrt[3]{3^3x^{2*3}*y^{3}*y}\\\\\sqrt[3]{\left(3x^2y\right)^3*y}\\\\\sqrt[3]{\left(3x^2y\right)^3}*\sqrt[3]{y}\\\\3x^2y\sqrt[3]{y}\\\\$

Explanation:

As the steps above show, the goal is to factor the expression under the root in terms of pulling out cubed terms. That way when we apply the cube root to them, the exponents cancel. We cannot factor the y term completely, so we have a bit of leftovers.

4 0

3 years ago

Easy slope question need answer FAST

mars1129 [50]

Answer:

Assuming that the scale is 1, x int: (-4,0), y int: (0,-3)

Step-by-step explanation:

Hope this helps :)

5 0

2 years ago

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