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2 years ago

What is the equation of the following line? Be sure to scroll down first to see

Mathematics

1 answer:

topjm [15]2 years ago

8 0

Answer: (f)

Step-by-step explanation:

Given

Line that passes through $(-\frac{1}{2},3)$ and $(0,0)$

Using two point form, equation of a line is given by

$\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}$

Insert the values

$\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x$

Thus, option (f) is correct

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A 10-foot board is cut into two pieces. If one piece is x feet long, express the other length in terms of x

OleMash [197]

Answer:

10-x ft long

Step-by-step explanation:

If it starts out 10ft long, and xft is taken away, then the remaining board would be 10-x ft long.

In terms of x, I believe it would just be 10-x ft long

7 0

3 years ago

F(x)=x^2. what is g(x)? point given is (4,1)

svetoff [14.1K]

Answer:

It is (a)

$g(x) = ( { \frac{1}{4} x})^{2}$

Step-by-step explanation:

I hope that is useful for you :)

6 0

2 years ago

Using binomial theorem, expand (x+6)^8 <br><br> edit: You could use the help of combinations too.

Pavlova-9 [17]

x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

<u>Explanation:</u>

We know

(x+y)ⁿ = ∑ ⁿCₐxⁿ⁻ᵃyᵃ

and ⁿCₐ = n! / ( a! ) . ( n-a )!

So,

(x+6)⁸ = ⁸C₀x⁸ + ⁸C₁(x)⁸⁻¹(6)¹ + ⁸C₂(x)⁸⁻²(6)² + ⁸C₃(x)⁸⁻³(6)³ + .......+ ⁸C₈(x)⁸⁻⁸(6)⁸

= ₓ⁸ + 8x⁷ₓ 6 + 28x⁶ₓ 36 + 56x⁵ₓ 216 + 70x⁴ₓ 1296 + 56x³ₓ 7776 + 28x²ₓ 46656 + 8x . 279936 + 1679616

= x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

Thus, the expansion of ( x+6)⁸ using binomial theorm is

x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

4 0

3 years ago

Can someone help me, please ?? im stuck

Tresset [83]

Part A

5x - 5 >= 10 or-3x + 1 > 13

1) This is a disjunction (OR)

5x - 5 >= 10

5x >= 15

x >= 3

-3x + 1 > 13

-3x > 12

x < -4

Answer

x <- 4 or x >= 3

Part C:

1) This is a conjunction (And)

5x+ 3 <= 18 and 4 - x < 6

5x <= 15 and - x < 2

x <= 3 and x > -2

Answer

-2 < x <= 3

8 0

3 years ago

A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is c

svetoff [14.1K]

1. Consider the pyramid ABCDE in the figure 1 attached:

Each side of the square base equals $\sqrt{20} = \sqrt{4*5} = \sqrt{4}* \sqrt{5}=2 \sqrt{5}$ (units)

Area of 1 lateral side of pyramid ABCDE is $\frac{1}{2}* 2 \sqrt{5}*x=\sqrt{5}x$

so the total lateral area is $4\sqrt{5}x$ (units squared)

and the total surface area is $20+4\sqrt{5}x$ (units squared)

2. Now consider the second figure KLMNP, Sydney's pyramid:

The lateral area is $4* \frac{1}{2}* 4 \sqrt{5} *2x=16 \sqrt{5}x$

so the total area of the second pyramid is $20+16 \sqrt{5}x$

So 2 things can be said about the areas:

i) the lateral area of Sydney's pyramid is $\frac{16 \sqrt{5}x}{4\sqrt{5}x} =4$ times larger than the lateral area of the original pyramid.

ii) The total area of Sydney's pyramid is $(20+16 \sqrt{5}x)-(20+4\sqrt{5}x)=12\sqrt{5}x$ units squared larger than the total area of the original pyramid.

5 0

3 years ago

Read 2 more answers