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3 years ago

Find the sum 5/8 + 7/12 A) 1 5/24 B) 1/2 C) 12/20 D) 5/24

Mathematics

2 answers:

Kay [80]3 years ago

3 0

Are those your only choices?

KATRIN_1 [288]3 years ago

3 0

Hoi!

To add fractions with uncommon denominators, we must first find a common denominator of both fractions. To do this, we find the least common multiple.

The least common multiple of 8 and 12 is 24.

$\frac{x}{24} + \frac{x}{24}$

Now, how many times do you have to add the denominator of the first fraction to get to 24?

8 + 8 + 8 = 24

3 times. Put the number 3 for the first numerator.

$\frac{3}{24} + \frac{x}{24}$

How many times do you have to do the same for the denominator of the second fraction?

12 + 12 = 24

2 times. Put two for the second numerator.

$\frac{3}{24} + \frac{2}{24} = \frac{5}{24}$

$\frac{5}{24}$ is your answer. :)

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Use the WeierstrassM-test to show that each of the following series converges uniformly on the given domain:

ryzh [129]

Answer:

Step-by-step explanation:

Given a series $\sum_{k=1}^\infty f(z)$ , the Weierstrass M-test tell us that if we find a sequence of positive numbers $M_n$ such that $|f(z)|\leq M_n$ in a certain domain D, and the series $\sum_{n=1}^\infty M_k$ converges, then the series $\sum_{k=1}^\infty f_k(z)$ converges uniformly in the domain D.

So, our objective is to find the so called sequence $M_k$ . The main idea is to bound the sequence of functions $\frac{z^k}{z^k + 1}$ .

Now, notice that the values of z are always positive, so $z^k$ is always positive, so $z^k+1\geq 1$ for all values of z in $\overline{D}$ . Then,

$\Big| \frac{z^k}{z^k + 1}\Big| \leq z^k,$

because if we make the values of the denominator smaller, the whole fraction becomes larger.

Moreover, as z is in the interval [0,r], we have that $z\leq r$ and as consequence $|z^k|\leq r^k$ . With this in addition to the previous bound we obtain

$\Big| \frac{z^k}{z^k + 1}\Big| \leq |z^k|\leq r^k.$

With this, our sequence is $M_k = r^k$ and the corresponding series is $\sum_{k=1}^\infty r^k$ , which is a geometric series with ratio less than 1, hence it is convergent.

Then, as consequence of Weierstrass M-test we have the uniform convergence of the series in the given domain.

6 0

3 years ago

Identify the vertex, roots, and equation of the function below.

spayn [35]

The equation of a parabola in vertex form, is:

$y=a(x-h)^2+k$

Where <em>(h,k)</em> are the coordinates of the vertex.

From the given graph, notice that the coordinates of the vertex are:

$(5,6)$

The roots are the values of <em>x</em> where the graph crosses the x-axis. In this case, the graph crosses the x-axis at the points <em>(4,0)</em> and <em>(6,0).</em> Then, the roots are:

$\begin{gathered} x_1=4 \\ x_2=6_{}_{} \end{gathered}$

Substitute the values of the vertex into the equation of the parabola in vertex form:

$y=a(x-5)^2+6$

To find the value of <em>a</em>, substitute <em>(x,y)=(4,0)</em>:

$\begin{gathered} 0=a(4-5)^2+6 \\ \Rightarrow0=a(-1)^2+6 \\ \Rightarrow0=a+6 \\ \Rightarrow-6=a \\ \Rightarrow a=-6 \end{gathered}$

Therefore, the equation of the parabola is:

$y=-6(x-5)^2+6$

3 0

1 year ago

Solve for the indicated variable. Include all of your work in your answer. Submit your solution.

levacccp [35]

Answer:

The answer is $L=\frac{A}{W}$

Step-by-step explanation:

In order to determine the answer, we have to know about equation. In an equation, we have variables, some of them depend on the others. If we want to know the value of one variable ( the dependent variable), we have to free it in any side of the equation.

In this case, we want to know the value of "L" variable. So we free that variable to the right side of the equation.

$A=LW$

We divide each side by "W":

$\frac{A}{W}=\frac{LW}{W}$

We simplify the "W" in the right side:

$\frac{A}{W}=L$

Finally, the solution for "L" is :

$L=\frac{A}{W}$

6 0

3 years ago

Read 2 more answers

How many combinations of players can a coach have if he needs to pick 2 out of a total of 4?

Leto [7]

Answer:

the coach will have a combination of 2 players since there are initially 4 players on ground and he's picking two from them.

8 0

3 years ago

At a local movie theatre, sodas cost $4.50 and bags of popcorn cost $1.50. Kirk buys three times as many bags of popcorn as soda

BigorU [14]

Based on the calculations, Kirk bought 2.4 bags of popcorn and 7.2 sodas.

Let the number of sodas bought be s.

Let the number of bags of popcorn be p.

<u>Given the following data:</u>

Cost of soda = $4.50.

Cost of popcorn = $1.50.

Total price = $36.

a. To write a system of equations that models this scenario:

<h3>What is a system of equations?</h3>

A system of equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

<h3>For the soda and popcorn:</h3>

$4.5s+1.5p=36$ ...equation 1.