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3 years ago

Ajutați va rog și spuneti. va dau 20 de puncte

Mathematics

1 answer:

andreev551 [17]3 years ago

4 0

Answer:

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Step-by-step explanation:

what language do you speak

You might be interested in

Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago

Write an equation for each linear function described. Show your work. The graph of the function passes through the point (2,1),

svp [43]

Step-by-step explanation:

The graph of the function passes through the point (2,1), and

y increases by 4 when x increases by 1.

x y

2 1

3 5

4 9

5 13

6 17

and so on

From the table:

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(2,\:1\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)$

$m=\frac{5-1}{3-2}$

$m=4$

As the slope-intercept form of the line is

$y=mx+b$

putting m=4 and any point, let say (2, 1) to find y-intercept 'b'.

$1=\left(4\right)2+b$

$8+b=1$

$8+b-8=1-8$

$b=-7$

So putting $b=-7$ and $m=4$ in the slope-intercept form of the line

$y=\left(4\right)x+\left(-7\right)$

$y=4x-7$

Therefore, the equation for the linear function will be:

$y=4x-7$

8 0

2 years ago

Given the function g(x) = 4(3)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.

LenaWriter [7]

Easy peasy

the average rate of change in section A is the slope from (1,g(1)) to (2,g(2))
the average rate of chagne in section B is the slope from (3,g(3)) to (4,g(4))

A.

section A
g(1)=4(3)^1=12
g(2)=4(3)^2=4(9)=36
slope=(36-12)/(2-1)=24/1=24

section B
g(3)=4(3)^3=4(27)=108
g(4)=4(3)^4=4(81)=324
slope=(324-108)/(4-3)=216/1=216

section A has an average rate of change of 24
section B has an average rate of change of 216

3 0

3 years ago

Here is the histogram of a data distribution. All class widths are 1.

stich3 [128]

The median of the data is 5 if the all class widths are 1, option (C) is correct.

<h3>What is the median?</h3>

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

In the histogram, 15 data values are given:

1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 8, 9

The mid-value is 5 which is on the 8th place

Thus, the median of the data is 5 if the all class widths are 1, option (C) is correct.

Learn more about the median here:

brainly.com/question/21396105

#SPJ1

8 0

1 year ago

Solve the problem using the guess-and-check method.

ehidna [41]

Answer is 14 lightbulbs

8 0

2 years ago

Ajutați va rog și spuneti. va dau 20 de puncte​

Ajutați va rog și spuneti. va dau 20 de puncte