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3 years ago

Find the GCF 15 and 33

Mathematics

2 answers:

kicyunya [14]3 years ago

7 0

Answer: The GCF of 15 and 33 is 3

scoundrel [369]3 years ago

3 0

Answer:

Step-by-step explanation:

Greatest comment factor (gcf) basically means what is one greatest common number that divides both of the given numbers.

In our example:

15=3x5

33=11x3

3 is common b/w the factors of both the numbers and it divides both 15, and 33. Which is why gcf if 3.

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Find the general term of sequence defined by these conditions.

disa [49]

Answer:

$\displaystyle a_{n} = (2)^{2n -1} - (3) ^{n-1 }$

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

$\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0 \: \: where : \: \:a_1 = 1 \: ,a_2 = 5,$

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

${x}^{n} = c_{1} {x}^{n - 1} + c_{2} {x}^{n - 2} + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}$

the steps for solving a linear homogeneous recurrence relation are as follows:

Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
Solve the polynomial by factoring or the quadratic formula.
Determine the form for each solution: distinct roots, repeated roots, or complex roots.
Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

${x}^{2} - 7x+ 12= 0$

Step-2:Solve the polynomial by factoring

factor the quadratic:

$( {x}^{} - 4)(x - 3) = 0$

solve for x:

$x = \rm 4 \:and \: 3$

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

$\displaystyle a_{n} = c_{1} {x} _{1} ^{n } + c_{2} {x} _{2} ^{n }$

so substitute the roots we got:

$\displaystyle a_{n} = c_{1} (4)^{n } + c_{2} (3) ^{n }$

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

$\begin{cases}\displaystyle 4c_{1} +3 c_{2} = 1 \\ 16c_{1} + 9c_{2} = 5\end{cases}$

solve the system of equation which yields:

$\displaystyle c_{1} = \frac{1}{2} \\ c_{2} = - \frac{1}{3}$

finally substitute:

$\displaystyle a_{n} = \frac{1}{2} (4)^{n } - \frac{1}{3} (3) ^{n }$

$\displaystyle \boxed{ a_{n} = (2)^{2n-1 } - (3) ^{n -1}}$

and we're done!

7 0

3 years ago

For my homework i dont understand this: the sale price on an item is $160 after a 20% discount.what is the origonal price of the

mr_godi [17]

The original price is $200 because if you did 200 * 0.2, it would equal $160 which is the discounted price.

5 0

3 years ago

Write the fraction 13/25 as a decimal. Show work

iragen [17]

$0.52$ ✅

Step-by-step explanation:

$\frac{13}{25} = 0.52$

$\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘$

7 0

2 years ago

Read 2 more answers

A rectangle is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse, and two other on th

Ronch [10]

Refer to the attachment for the diagram of the problem.

Let us call the two identical sides of the isosceles triangle with s. Since we know that the hypotenuse measures 45 inches, we can find s by using the Pythagorean Theorem:
$45^{2} = s^{2}+ s^{2}$
$45^{2} = 2s^{2}$
$45^{2} = 2s^{2}$
$1012.5 = s^{2}$
$s=31.82$

We can notice that the figure will have similar triangles with the smaller triangle having one length equal to 5x. We then compute for the equivalent hypotenuse of the smaller triangle (denoted as y).
$\frac{31.82}{5x} = \frac{45}{y}$
$y=7.07x$

We can then solve for the value of x by applying the Pythagorean Theorem in the smaller triangle.
$(7.07x)^{2} = (5x)^{2}+ (31.82-2x)^{2}$
$50x^{2} = 25x^{2}+ 1012.5-127.28x+4x^{2}$
$0= -21x^{2}-127.28x+1012.5$
$x=4.55,-10.61$

We ignore the negative value since there is no negative side. x is therefore 4.55 thus the dimensions of the rectangle would be 22.75 and 9.1. For the other case, the dimensions would simply be inverted since we would be dealing with a rectangle with its width longer than its length.

6 0

3 years ago

Four more than three times a number is thirteen. What is this number?

Ostrovityanka [42]

Answer:

Step-by-step explanation:

13-4=9

9/3=3

4 0

2 years ago

Read 2 more answers