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3 years ago

What is the vertex of y = - | x + 3 | + 5

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

7 0

Answer:

vertex = (- 3, 5 )

Step-by-step explanation:

The general form of the absolute value function is

y = a | x - h | + k

where (h, k) are the coordinates of the vertex

Given

y = - | x + 3 | + 5 ← in general form, then

vertex = (- 3, 5 )

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Which of the following is the best estimate of 31% of 15? 7.5 3 5 4

Alex777 [14]

Th answer is 5 because 31% of 15 is 4.65

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3 years ago

Read 2 more answers

What are the exact solutions of x2 + 5x + 1 = 0? (5 points)

Rus_ich [418]

Answer:

$x=\frac{-5\pm\sqrt{21} }{2}$

Step-by-step explanation:

We use the quadratic formula here which says for a quadratic equation $ax^2+bx+c=0$ .

$x= \frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Now in our case

$a=1\\b=5\\c=1$

so we have:

$x=\frac{-5\pm\sqrt{5^2-4(1)(1)} }{2(1)} =\frac{-5\pm\sqrt{21} }{2}$

$\boxed{x=\frac{-5\pm\sqrt{21} }{2} }$

Which are our solutions.

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3 years ago

Find the radius of convergence and the internval of convergence:

o-na [289]

You can use the root test here. The series will converge if

$L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}$

You have

$L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}=|4-x|\lim_{n\to\infty}\frac1{\sqrt[n]{4^n+9^n}}$

Notice that

$\dfrac1{\sqrt[n]{4^n+9^n}}=\dfrac1{\sqrt[n]{9^n}\sqrt[n]{1+\left(\frac49\right)^n}}=\dfrac1{9\sqrt[n]{1+\left(\frac49\right)^n}}$

so as $n\to\infty$ , you have $\left(\dfrac49\right)^n\to0$ , which means you end up with

$L=\dfrac{|4x-1|}9$

This is the interval of convergence. The radius of convergence can be determined by finding the half-length of the interval, or by solving the inequality in terms of $|x-c|$ so that $R$ is the ROC. You get

$|4x-1|$

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3 years ago

Bottom left Angle: Top Angle: Bottom right Angle:

Arturiano [62]

Angles in a triangle always add up to 180 degrees

Here, we add up all the angles given to equal it to 180 degrees:

X + X + 10 + X + 5 = 180

Collect like terms -> 3X + 10 + 5 = 180

Add the whole numbers -> 3X + 15 = 180

Take 15 from to the other side (then make it negative) to isolate the X:
3X = 180 - 15

The subtract -> 3X = 165

Take 3 over to the other side (and it it should divide 165) and isolate the X -> X = 165/3

Finally, X = 55

Now wherever you see X in the triangle, replace it with 55.

With that, the top angle = 55 + 10 = 65 degrees
The bottom left angle = 55 + 5 = 60 degrees
The bottom right angle = 55 degrees

8 0

3 years ago

Rhea is writing a paper, and she notices that she can write 1.25 pages every 2 hours.

Ymorist [56]

Answer:

Rhea's estimation is unreasonable.

Step-by-step explanation:

Identify what you know:

1) Rhea calculates that she can write 1.25 pages every 2 hours

2) Rhea is calculating how long it would take her to write 6 pages.

Using Rhea's initial calculation, we can figure out roughly, how long it would take her to finish 6 pages.

First we need to divide 6 by 1.25, to figure out how many "2 hour" periods it would take Rhea.

6/1.25 = 4.8

4.8 x 2 = 9.6

It would take Rhea roughly 9.6 hours to finish 6 pages, which is 3.6 hours more than her original estimation. Thus, her estimate is unreasonable.

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3 years ago