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3 years ago

What is the value of x? Justify each step.

Mathematics

1 answer:

coldgirl [10]3 years ago

7 0

a) Addition of line segments

b) Substitution rule

c) Simplification by addition of like terms

d) Collecting lie terms

e) Dividing both sides by 8

AB = 2x

BC = 6x + 8

AC = 32

AB + BC = AC (Addition rule)

Addition of the component segments of a line

2x + 6x + 8 = 32 (Substitution rule)

Substituting for AB, BC, and AC in the equation AB + BC = AC

8x + 8 = 32 (Simplification)

Simplifying 2x + 6x + 8 = 32 by adding like terms

8x = 24 (Collecting like terms)

8x = 32 - 8

8x = 24

x = 3 (Divide both sides by 8)

8x / 8 = 24/8

x = 3

Learn more here: brainly.com/question/19253676

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What equation represents the line that is perpendicular to y=1/2x - 3 and passes through the point (4,-6)?

zmey [24]

Answer:

The equation of line perpendicular to given line and passing through point (4 , - 6) is y = - 2 x - 2

Step-by-step explanation:

Given as :

The equation of line is

y = $\dfrac{1}{2}$ x - 3

Now, standard equation of line is

y = m x + c

where m is the slope of line and c is the y-intercept

So, comparing with standard line equation with given line equation

∴ slope of given line = m = $\dfrac{1}{2}$

Again

other line is perpendicular to given line and passes through point (4 , - 6)

Let The slope of other line = M

∵ Two lines are perpendicular

∴ <u>From perpendicular lines property , the product of lines = - 1</u>

i.e m × M = -1

Or, $\dfrac{1}{2}$ × M = -1

Or M = $\frac{-1}{\frac{1}{2}}$

∴ M = - 2

So, The slope of other line = M = - 2

<u>Now, equation of line with slope - 2 and points (4 , - 6) in slope-point form</u>

y - $y_1$ = M (x - $x_1$ )

Or, y - ( - 6) = ( -2) × (x - 4)

Or, y + 6 = - 2 x + 4

Or, y = - 2 x + 4 - 6

∴ y = - 2 x - 2

So, The equation of other line is y = - 2 x - 2

Hence, The equation of line perpendicular to given line and passing through point (4 , - 6) is y = - 2 x - 2 Answer

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3 years ago

Find the values of x and y using trig

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

The triangle is a right angle triangle. This is because one of its angles is 90 degrees.

Let us determine x

Taking 47 degrees as the reference angle,

x = adjacent side

11 = hypotenuse

Applying trigonometric ratio,

Cos # = adjacent side / hypotenuse

# = 47 degrees

Cos 47 = x/11

x = 11cos47

x = 11 × 0.6820

x = 7.502

Let us determine y

Taking 47 degrees as the reference angle,

y = opposite side

11 = hypotenuse

Applying trigonometric ratio,

Sin # = opposite side / hypotenuse

# = 47 degrees

Sin 47 = y/11

x = 11Sin47

x = 11 × 0.7314

x = 8.0454

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Angie is wrapping a present for her best friend. The box is 16 inches long, 12 inches wide, and 3 inches high. How many square i

defon

Alright, you will need to find the areas of 3 of the sides(i.e. Top/Bottom, Left/Right, Front/Back), to do so let's go through multiplying these:

Since we're not looking for the Volume, we'd just multiply one variable by another, for instance:

Bottom = Length * Width
x = 16 * 12 | 16 * 12 = 192

Left = Length * Height
x = 16 * 3 | 16 * 3 = 48

Front = Width * Height
x = 12 * 3 | 12 * 3 = 36

Now that we know 3 of the sides, we then multiply each by 2 since there's another side to this box(in other words, we'd be adding both sides together, multiplying it by 2 still gives you the same answer though).

Bottom + Top, or Bottom * 2
192 + 192 = 384 | or | 192 * 2 = 384

Left + Right, or Left * 2
48 + 48 = 96 | or | 48 * 2 = 96

Front + Back, or Front * 2
36 + 36 = 72 | or | 36 * 2 = 72

Adding these together gives you the answer you're looking for. ^ ^
384 + 96 + 72 = 552

So, the answer should be that Angie needs 552 square inches of wrapping paper for her present. I hope that helped, have a great rest of your day!
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3 years ago