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2 years ago

Find the equation of a line parallel to y - 5 = 6x - 10 that passes through the point (4, 10). (answer in slope-intercept form)

1 answer:

3 0

A.

This is because we start with the slope of 6. This is because it is the slope of the original equation (the number attached to x) and parallel lines have the same slope. Then you can use that along with the point to find the y intercept using slope intercept form (y = mx + b)

y = mx + b
10 = 6(4) + b
10 = 24 + b
-14 = b

So -24 must be the number at the end of the equation, making a the right answer.

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Read the following poem:

pentagon [3]

Answer:

7, I believe. I have to fill in the extra character space, so I hope you have a nice day :)

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2 years ago

Tic is an isosceles triangle with a vertex angle I. if the angle of I is 70. find the measure of t.

Colt1911 [192]

Angles of a triangle = 180 degrees
T + C = 110 degrees, and T=C (according to the definition of an isosceles triangle).
measure of T is 110/2 which equals 55 degrees

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3 years ago

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Find the longer leg of the triangle.

Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship $\sin{\theta} < \cos{\theta}$ holds for all acute angles? (That is, $0^{\circ} < \theta$ ?) It turns out that:

$\sin{\theta} < \cos{\theta}$ if $0^{\circ} < \theta$ ;
$\sin{\theta} > \cos{\theta}$ if $45^{\circ} < \theta$ ;
$\sin{\theta} = \cos{\theta}$ if $\theta = 45^{\circ}$ .

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2 years ago

Read 2 more answers

A water cup is shaped like a cone. It has a diameter of 3 inches and a slant height of 5 inches. About how many square inches of

daser333 [38]

Options were missing in the question;

A water cup is shaped like a cone. It has a diameter of 3 inches and a slant height of 5 inches. About how many square inches of paper do you need to make a cup? Use 3.14 to approximate pi.

24 square inches

31 square inches

47 square inches

52 square inches

Answer:

24 square inches

Step-by-step explanation:

Given:

Diameter = 3 in

So we can say that;

Radius is half of diameter.

radius (r) = $\frac{3}{2}=1.5\ in$

Slant height (l) = 5 in

We need to find how many square inches of paper do you need to make a cup.

Solution:

Now according to question we required to find the amount of paper used to make cup.

Also Water cup is shaped liked cone.

Hence we can say that the base of cone is not covered since it will remain open.

So we will use Lateral surface area of the cone to find the paper requirement.

Now we know that;

Lateral surface area of cone is equal to π times radius times slant height.

framing in equation form we get;

$A_L = \pi rl=3.14\times1.5\times5 = 23.55 in^2 \approx 24\ in^2$

Hence We can say that 24 square inches of paper will be needed to make the cup.

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2 years ago

What is the slope of the line passing through the points (2, 5) and (0, –4)?

iragen [17]

In order to find the slope of line that passes through 2 points, use the equation slope=rise/run
rise = 5-(-4) =9
run = 2- 0 =2
slope = rise/run = 9/2

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2 years ago

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