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2 years ago

Write the equation of a line in slope intercept form of a line that has a slope of 1/2 and contains (-4,1)

1 answer:

6 0

The general form of the line is:
y = mx + c where:
m is the slope
c is the y-intercept

Now, we are given that the slope = 1/2.
The equation now became:
y = (1/2) x + c

Now, we need to get the y-intercept. We are given that (-4 ,1) belongs to the line. Therefore, this point satisfies the equation of the line. Based on this, we will substitute with this point in the equation above and solve for c as follows:
y = (1/2) x + c
1 = (1/2)(-4) + c
1 = -2 + c
c = 1+2
c = 3

Based on the above, the equation of the line is:
y = (1/2) x + 3

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2 years ago

What is the approximate area of the shaded sector in the circle shown below

saul85 [17]

Answer:

D) 191

Step-by-step explanation:

The entire circle is 254.5, calculated by using this formula

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Only 3/4 of the circle is needed for the area, however, so you multiply your area by 0.75

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2 years ago

What is the number of diagonals that intersect at a given vertex of a hexagon, heptagon, 30-gon and n-gon?

DENIUS [597]

Answer:

i. 9

ii. 14

iii. 405

iv. $\frac{n(n-3)}{2}$

Step-by-step explanation:

The number of diagonals in a polygon of n sides can be determined by:

$\frac{n(n-3)}{2}$

where n is the number of its sides.

i. For a hexagon which has 6 sides,

number of diagonals = $\frac{6(6-3)}{2}$

= $\frac{18}{2}$

= 9

The number of diagonals in a hexagon is 9.

ii. For a heptagon which has 7 sides,

number of diagonals = $\frac{7(7-3)}{2}$

= $\frac{28}{2}$

= 14

The number of diagonals in a heptagon is 14.

iii. For a 30-gon;

number of diagonals = $\frac{30(30-3)}{2}$

= $\frac{810}{2}$

= 405

The number of diagonals in a 30-gon is 405.

iv. For a n-gon,

number of diagonals = $\frac{n(n-3)}{2}$

The number of diagonals in a n-gon is $\frac{n(n-3)}{2}$

7 0

2 years ago

A right angled triangle has two shorter sides and one is twice as long as the other. The hypotenuse is 25cm long. What are the l

Bas_tet [7]

Answer: x = 14.43

Step-by-step explanation:

The Pythagorean Theorem states the following:

a^2 + b^2 = c^2

Make one side of the triangle x

Make the second side of the triangle 2x

Now, you can plug the values into the equation, right?

x^2 + 2x^2 = 25^2 or 625

3x^2 = 625

Divide each side by 3 and you are left with:

x^2 = 208.33

Now, take the square root of 208.33

x = 14.43

That is the shorter side. The longer side is twice that value: Therefore, 14.43 x 2 = 28.86 14.43 is one side of the triangle. The other is that same value times two. Therefore, the sides of your triangle are: 14.43 Shorter side 28.86 Longer side

5 0

3 years ago

Read 2 more answers