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3 years ago

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Mathematics

1 answer:

zhuklara [117]3 years ago

3 0

Ths number that goes beneath the radical symbol is 29.

Explanation:

If we form a triangle using the given points, we drop a vertical line from (1, 1) and a horizontal line to the left of (3, -4). The point where both the lines intersect is the third point. The other point is (1, -4).

The vertical distance from (1, 1) and (1, -4) is 1 - (-4) = 1 + 4 = 5 units, the horizontal distance from (1, -4) and (3, -4) is 3 -1 = 2 units.

The opposite side of the triangle measures 5 units while the adjacent side measures 3 units. The line joining (1, 1) and (3, -4) is the hypotenuse. Assume the hypotenuse measures x units.

According to Pythagoras theorem, x = √(5² + 2²), x = √25 + 4 = √29. So the number under the radical symbol is 29.

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Heeelp

alukav5142 [94]

Answer: see below

Step-by-step explanation

Let 2 + a = 11 x

Let 35 - b = 11 y

Where x and y are any unknown integer

subtract the two equations

- 33 + a + b = 11 (x+y)

a+ b = 11 (x+ y) +33

a+ b = 11 (x+y) + 3 (11)

a+ b = 11(x+ y+3)

Which proves that a+b is a factor of 11

6 0

3 years ago

Find the distance d (P1,P2) between the given points P1 and P2 P1= (5,4) P2=(-4,5)

oee [108]

Answer:

$\sqrt{82 }$

Step-by-step explanation:

d = $\sqrt{(x_{1} - x_2)^2+(y_1-y_2)^2 }$

d = $\sqrt{(5 - (-4))^2+(4-5)^2 }$

d = $\sqrt{(9)^2+(-1)^2 }$

d = $\sqrt{81+1 }$ = $\sqrt{82 }$

5 0

3 years ago

The graph of a function f(x) passes through the following points:

Alex

The function is f(x) = -2x² + 2 if the function f(x) passes through the following points:(0,2), (1, 0), (-1,0)

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

The graph of a function f(x) passes through the following points: (0,2), (1, 0), (-1,0)

Let

f(x) = ax² + bx + c

Plug x = 0, and y = 2

c = 2 ...(1)

Plug x = 1 and y = 0

a + b + c = 0 ..(2)

Plug x = -1 and y = 0

a - b + c = 0 ...(3)

After solving (1), (2), and (3)

a = -2

b = 0

c = 2

f(x) = -2x² + 2

Thus, the function is f(x) = -2x² + 2 if the function f(x) passes through the following points:(0,2), (1, 0), (-1,0)

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

5 0

2 years ago

Given the third-order differential equation z′′′+2z′′−4z′−8z=0, find the general solution. Enter your solution as z(x)=... . In

Scorpion4ik [409]

Answer: $z(x) = c_{1} e^{2x} +c_{2} e^{-2x} + c_{3} xe^{-2x}$

Step-by-step explanation:

This is a <em>homogeneous linear third-order differential equation</em>

z′′′+2z′′−4z′−8z=0 so the

FIRST STEP is to find the characteristic equation and its roots

Using the method of finding roots of a polynomial (using m = 2) would provide the solution below

(m-2)(m+2)(m+2)=0; m = 2 and m = -2 (repeated twice)

SECOND STEP is to write the general solution with the arbitrary constants.

The general solution based on the roots and the using x as the independent variable would provide

$z(x) = c_{1} e^{2x} +c_{2} e^{-2x} + c_{3} xe^{-2x}$

<em>*It should be noted that when the characteristic equation has a repeated root, the general equation form becomes similar to the last part of the answer*</em>

6 0

3 years ago

16.43 in word form math

astraxan [27]

Answer:

Sixteen and forty-three hundredths

Step-by-step explanation:

6 0

4 years ago