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1 year ago

If a line is vertical then the slope is... need help

Mathematics

2 answers:

alisha [4.7K]1 year ago

8 0

The slope-intercept form of a line is:

$\begin{gathered} y=mx+b \\ \text{Where m is the slope and b is the y-intercept} \end{gathered}$

For a vertical line the equation is:

$\begin{gathered} x=c \\ \text{Where c is a constant} \end{gathered}$

If we compare the two form equations, we can say that the slope is undefined for vertical lines.

Rus_ich [418]1 year ago

5 0

If the line is vertical then the slope is undefined.

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Graph the following lines and using the graph determine several values of x for which the graph is positive (negative): y=−4x+3

True [87]

Answer:

Step-by-step explanation:

Given line is,

y=-4x+3

when, x=-1 , y=-4(-1)+3=4+3=7

when, x=0 , y=-4(0)+3=0+3=3

when, x=1 , y=-4(1)+3=-4+3=-1

So, we got the points (-1,7) , (0,3) , (1,-1)

Now, putting the points in the graph and adding them , we will get the graph of given line.

Please check image for the graph.

Now for the second part-

The graph is positive means- it will be above the x-axis, that is y value will be positive.

From the graph we can see that, if x<0 , then y is positive.

So, any value of x which is less than 0 , will give the positive graph here.

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3 years ago

The letter w represents a whole number such that 2021 + w is a multiple of 7. What is the smallest possible value of w?

7nadin3 [17]

Answer:

Step-by-step explanation:

2021/7 leaves a remainder of 5 so add 2 and that's the answer

7 0

3 years ago

Find the equation of the line tangent to the graph of

garik1379 [7]

Answer:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

$\displaystyle y=\sin^{-1}\big(\frac{x}{5}\big)\text{ at } x=\frac{5}{2}$

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

$\displaystyle y^\prime=\frac{1}{\sqrt{1-(\frac{x}{5})^2}}\cdot\frac{1}{5}$

Simplify:

$\displaystyle y^\prime=\frac{1}{5\sqrt{1-\frac{x^2}{25}}}$

We can factor out the denominator within the square root:

$\displaystyle y^\prime =\frac{1}{5\sqrt{\frac{1}{25}\big(25-x^2)}}$

Simplify:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}$

So, we can find the slope of the tangent line at <em>x</em> = 5/2. By substitution:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}$

Evaluate:

$\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\frac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}$

We will also need the point at <em>x</em> = 5/2. Using our original equation, we acquire that:

$\displaystyle y=\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}$

So, a point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}(x-\frac{5}{2})$

Distribute:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}$

Isolate. Hence, our equation is:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

7 0

3 years ago

Ed needed to extend the string on his kite. The current string was eight and three fourths feet. He cut a piece of string that m

Pani-rosa [81]

The new length of the string is (13 + 1/4) feet, then the correct option is the last one (counting from the top)

<h3> What is the new length of the string?</h3>

We know that the current string was (8 + 3/4) feet in length. Then they add another piece that measures 4.5 feet.

The new length of the string is given by the addition of the above two lengths, we will get:

L = (8 + 3/4) feet + 4.5 feet

We can rewrite the second length as a mixed number:

4.5 = 4 + 1/2 = 4 + 2/4

Replacing that we get:

L = (8 + 3/4) ft + 4.5 ft

= (8 + 3/4) ft + (4 + 2/4) ft

= (8 + 4) ft + (3/4 + 2/4) ft

= 12ft + 5/4ft = 12ft + (4/4 + 1/4)ft = (13 + 1/4)ft

The new length of the string is (13 + 1/4) feet, then the correct option is the last one (counting from the top).

If you want to learn more about mixed numbers:

brainly.com/question/1746829

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6 0

2 years ago

Answer correctly please !!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!

irina [24]

Answer:

x=70

Step-by-step explanation:

If we extend the lines we can create an imaginary angle that is directly vertically opposite angle x (see picture for visualisation).

Then, using the rule that alternate interior angles are equal, we can deduct that this new angle is 30+40=70 degrees.

Finally, we know that vertically opposite angles are also equal meaning that x=70 degrees.

Hope this helped!

3 0

3 years ago