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3 years ago

What is the slope of the line that has an equation of y=x-3?

Mathematics

2 answers:

Mrac [35]3 years ago

6 0

The slope is 1, because y=mx+b, where m is the slope.

aalyn [17]3 years ago

3 0

Slope intercept formula ; " y=mx+b"
"b" = y intercept , "m" = slope

Your line equation is " y= x-3" so the slope would be the coefficient next to the x. Since there is no coefficient next to the x , the slope would be 1 because one times x would equal x) .

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The length of a rectangle is 7 more than the width the area is 744 square centimeters find length and width of rectangle

andrezito [222]

Answer:

$l=31\ cm\\\\w=24\ cm$

Step-by-step explanation:

The formula that is used to calculate the area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

You know that the area of that rectangle is:

$A=744\ cm^2$

And, according to the exercise, its lenght is 7 more than its width; then:

$l=w+7$

Then, you can make the corresponding substitution into the formula $A=lw$ :

$744=(w+7)w$

Simplify:

$744=w^2+7w\\\\w^2+7w-744=0$

Factor the equation. Find two numbers whose sum is 7 and whose product is -744. These are 31 and -24.

Then, you get:

$(w-24)(w+31)=0\\\\w_1=24\\\\w_2=-31$

The width of the rectangle is the positive value:

$w=24\ cm$

Then, the lenght is:

$l=24+7\\\\l=31\ cm$

8 0

3 years ago

The answer choices are 11 1 2.48 6

Fudgin [204]

Answer:

The ball reached its maximum height of ( $11\ yards$ ) in ( $1\ second$ ).

Step-by-step explanation:

This question is essentially asking one to find the vertex of the parabola formed by the given equation. One could plot the equation, but it would be far more efficient to complete the square. Completing the square of an equation is a process by which a person converts the equation of a parabola from standard form to vertex form.

The first step in completing the square is to group the quadratic and linear term:

$h(t)=-5t^2 + 10t + 6\\\\h(t) = (-5t^2 + 10t) + 6$

Now factor out the coefficient of the quadratic term:

$h(t)=-5(t^2 -2t) + 6$

After doing so, add a constant such that the terms inside the parenthesis form a perfect square, don't forget to balance the equation by adding the inverse of the added constant term:

$h(t) = -5(t^2 -2t) + 6\\\\h(t) = -5(t^2 -2t + 1 -1 ) + 6$

Now take the balancing term out of the parenthesis:

$\\\\h(t)=-5(t^2 -2t + 1) + 6 + ((-1)(-5))$

Simplify:

$h(t) = -5(t^2 -2t + 1) + 6 + 5\\\\h(t) = -5(t-1)^2 + 11$

The x-coordinate of the vertex of the parabola is equal to the additive inverse of the numerical part of the quadratic term. The y-coordinate of the vertex is the constant term outside of the parenthesis. Thus, the vertex of the parabola is:

$(1, 11)$