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3 years ago

Complete the Square and express the quadratic as a square.

Mathematics

1 answer:

Shtirlitz [24]3 years ago

6 0

Answer:

Step-by-step explanation:

x² - 6x + 13 = 0

x² - 2(x)(3) + 3² - 3² + 13 = 0

(x - 3)² = -4

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A band can play as much as 8 minutes of music in a competition. If the band plays a 2.33 minute song and a 4.25 minute song, how

dsp73

2.42 minutes will be left

8 0

3 years ago

What is true of the graph of two lines 3y-8=-5x and 6y=-10x+16

Murljashka [212]

Answer:

Both lines are equal (they are the same)

Step-by-step explanation:

Given

$3y - 8 = -5x$

$6y = -10x + 16$

Required

What is true about graph of both lines

Questions like this are better solved when there's option(s) to select from. However, some of the properties of line equation that I'll consider are to check if both lines are either parallel or perpendicular

To do this,

The first thing to do is to calculate the slope of both lines

$3y - 8 = -5x$

Add 8 to both sides

$3y - 8 + 8 = -5x + 8$

$3y = -5x + 8$

Divide both sided by 3

$\frac{3y}{3} = -\frac{5x}{3} + \frac{8}{3}$

$y = -\frac{5x}{3} + \frac{8}{3}$

The slope of the line is the coefficient of x;

$Slope = -\frac{5}{3}$

Solve for the y intercept; Let x = 0

$y = -\frac{5 * 0}{3} + \frac{8}{3}$

$y = 0 + \frac{8}{3}$

$y = \frac{8}{3}$

Solve for the x intercept; Let y = 0

$0 = -\frac{5x}{3} + \frac{8}{3}$

Subtract $\frac{8}{3}$ from both sides

$0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}$

$- \frac{8}{3} = -\frac{5x}{3}$

Subtract both sides by $-\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = x$

$\frac{3}{5} * \frac{8}{3} = x$

$\frac{8}{5} = x$

$x = \frac{8}{5}$

------------------------------------------------------------------------------------------------------

$6y = -10x + 16$

Divide both sides by 6

$\frac{6y}{6} = -\frac{10x}{6} + \frac{16}{6}$

$y = -\frac{10x}{6} + \frac{16}{6}$

Simplify fractions to lowest term

$y = -\frac{5x}{3} + \frac{8}{3}$

The slope of the line is the coefficient of x;

$Slope = -\frac{5}{3}$

Solve for the y intercept; Let x = 0

$y = -\frac{5 * 0}{3} + \frac{8}{3}$

$y = 0 + \frac{8}{3}$

$y = \frac{8}{3}$

Solve for the x intercept; Let y = 0

$0 = -\frac{5x}{3} + \frac{8}{3}$

Subtract $\frac{8}{3}$ from both sides

$0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}$

$- \frac{8}{3} = -\frac{5x}{3}$

Subtract both sides by $-\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = x$

$\frac{3}{5} * \frac{8}{3} = x$

$\frac{8}{5} = x$

$x = \frac{8}{5}$

-------------------------------------------------------------------------------------------------------

By comparing the slope, x intercept and y intercept of both lines;

It'll be observed that they have the same slope, x intercept and y intercept

This implies that both lines are equal; in other words, they are the same.

6 0

2 years ago

A child's toy is in the shape of a cone on top of a

sammy [17]

Answer:

1. 167.55

2. 10.77

Step-by-step explanation:

For #1 use the formula for volume of cone: $V=\pi r^2\frac{h}{3}$ , and for #2 use the Pythagorean Theorem: $a^2+b^2=c^2$

7 0

3 years ago

Please can some help me in this?

tino4ka555 [31]

Answer:

n = 70

Step-by-step explanation:

14 * x < 80

x = 6 won't work

14 * 6 = 84 which beyond the boundry.

14 * 5 = 70 which is less than 80 and is divisible by 14

14 * 3 = 42

70 does not have a 3 in it.

So the largest number that has 14 in it and is less than 80 is 70

5 0

2 years ago

Please help !! I would really appreciate it. brainliest will be given for best answer

faltersainse [42]

Since A is (-7,-4) and C is (7,3) for the x value from a to c is 14 for the y value from a to c is 7

Do 14 x 2/7 which is 4

Do 7 x 2/7 which is 2

then add (-7+4,-4+2) which is (-3,-2)

7 0

3 years ago