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3 years ago

The point-slope form of the equation of the line that passes through (-9, -2) and (1, 3) is y – 3 = {(x - 1). What is the

Mathematics

1 answer:

Marina86 [1]3 years ago

4 0

Option A is the correct answer, y = x + 2

y - 3 = x-1

If you bring the 3 to the R.H.S, it becomes y = x + 2

If you substitute the values,

3 = 1 + 2

3 = 3

Thus, e equation is correct

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The sum of three consecutive even numbers is 114. what is the smallest of the three numbers?

saul85 [17]

Answer:

Step-by-step explanation:

Let's let n be any number.

If we multiply n by 2, we get 2n. Since anything multiplied by 2 is even, 2n <em>must</em> be even. Therefore, let 2n be our first number.

So, the consecutive even number will be (2n+2) followed by (2n+4).

We know that their sum must be 114. Therefore, we can write the following equation:

$(2n)+(2n+2)+(2n+4)=114$

Solve for n. Combine like terms on the left:

$6n+6=114$

Subtract 6 from both sides:

$6n=108$

Finally, divide both sides by 6. Therefore, the value of n is:

$n=108/6=18$

Therefore, our first even number is 2n or 2(18) which equates to 36.

And the consecutive even numbers will be 38 and 40.

So, the smallest of them, the first term, is 36.

4 0

3 years ago

Read 2 more answers

Find (a) arc length and (b) Area of a sector.

barxatty [35]

Answer:

a) 29.45 cm (2 dp)

b) 220.89 cm² (2 dp)

Step-by-step explanation:

<u>Formula</u>

$\textsf{Arc length}=r \theta$

$\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta$

$\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}$

<u>Calculation</u>

Given:

$\theta=\dfrac{5 \pi}{8}$
r = 15 cm

$\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 15\left(\dfrac{5 \pi}{8}\right)\\& = \dfrac{75}{8} \pi \\& = 29.45\: \sf cm\:(2\:dp)\end{aligned}$

$\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(15^2) \left(\dfrac{5 \pi}{8}\right)\\\\& = \dfrac{225}{2}\left(\dfrac{5 \pi}{8}\right)\\\\ & = \dfrac{1125}{16} \pi \\\\& = 220.89 \: \sf cm^2\:(2\:dp)\end{aligned}$

5 0

2 years ago

Which of the statements is also true in Spherical geometry?

Rus_ich [418]

I think all of them are true

3 0

4 years ago

Interpret the meaning of each term in the expression 14(22x)+350

Mrrafil [7]

308x+350 is the answer simplified or interpreted

7 0

3 years ago

A car travels 87 miles north and 114 miles west. what is the magnitude of the cars resultant vector

anyanavicka [17]

The magnitude of the resultant vector is 27 miles

<h3>How to determine the vector magnitude</h3>

Resultant vector = Distance of A - Distance of B

This is so because of the opposite direction of the car's movement

A = 87 miles

B = 114 miles

Resultant vector = 114 - 87

Resultant vector = 27 miles

Thus, the magnitude of the resultant vector is 27 miles

Learn more about resultant vector here:

brainly.com/question/3184914

#SPJ1

8 0

2 years ago