What is the relationship between the measures of alternate interior angles?

Helpp its for a test and I don’t know how to do it

lozanna [386]

X f(x)
1 -12
0 -9
-1 -6

5 0

2 years ago

(5,1); m=2 write an equation of the line

gtnhenbr [62]

Hey there! :)

To find an equation of a line that passes through (5, 1) and has a slope of 2, we'll need to plug our known variables into the slope-intercept equation.

Slope-intercept equation : y = mx + b ; where m=slope, b=y-intercept

Since we're already given the slope, all we really need to do is find the y-intercept.

We can do this by plugging our known values into the slope-intercept equation.

y = mx + b

Since we're trying to find "b," we need to plug in "y, m, x" into our formula.

(1) = (2)(5) + b

Simplify.

1 = 10 + b

Subtract 10 from both sides.

1 - 10 = b

Simplify.

-9 = b

So, our y-intercept is 9!

Now, we can very simply plug our known values into slope-intercept form.

y = mx + b

y = 2x - 9 → final answer

~Hope I helped!~

3 0

3 years ago

How does the measure of the pink inscribed angle compare with the measure of the blue intercepted arc? How do you know?

Goryan [66]

Answer:

The pink angle is half the angle subtended by the blue arc.

Step-by-step explanation:

Given

See attachment for circle

Required

Compare the pink angle to the blue arc

Let the pink angle be x and the angle subtended by the blue arc be y.

So, we have:

$x \to$ angle at circumference

$y \to$ angle subtended by arc

The relationship between x and y is:

$y =2x$

Make x the subject

$x = \frac{1}{2}y$

7 0

2 years ago

Please help me with this

Len [333]

Answer:

60 degrees

Step-by-step explanation:

To first solve this problem, we need to figure out the size of an interior angle for a regular hexagon.

This can be done with the formula :

$angle = \frac{(n-2)*180}{n}$ , with n being the number of sides

A hexagon has 6 sides so here is how we would solve for the interior angle:

$\frac{(6-2)*180}{6}=120$ , with n= 6 sides

Now that we know that each interior angle in the hexagon is 120 degrees, we can now turn our attention to the rhombus.

The opposite angles of the rhombus are congruent, so the two larger obtuse angles are congruent, and so are the two smaller acute angles.

It is also important to note that a rhombus is a quadrilateral, so all of its interior angles add up to 360 degrees.

Looking at the rhombus, we already know one of the angles because it is shared by the interior angle of the hexagon, so the two larger angles in the rhombus are both 120 degrees.

But what about the smaller angles? All we need to do is subtract the two larger angles form 360 and divide by 2 to find the angle.

$\frac{360-2(120)}{2} = 60$ , so the smaller angle in the rhombus is 60 degrees.

Now that we know both the interior angle and smaller angle of the rhombus, we can find x.

Together, angle x and the angle adjacent to it makes up an interior angle of the hexagon, so x plus that angle is going to equal to 120 degrees.

All we need to do is solve for x:

$x+60=120$

$x=120-60$

x = 60 degrees

3 0

2 years ago

The length of a rectangular garden is 8m greater than twice the width the area of the garden is 280m^2 what is the width of the

yarga [219]

Step-by-step explanation:

Given :-

The length of the garden 8m greater than 2 times the width.

Area of the garden is 280 m²

Let us consider the length as x and width as y.

Sp, we can day length as :-

x = 8 + 2y ---(1)

Now, we know that:-

Area of Rectangle = Length × Breadth

280 = x * y

We can replace the value of x now,

280 = y × ( 8 + 2y)

280 = 8y + 2y²

2y² + 8y - 280 = 0

y² + 4y - 140 = 0

Factorise it.

(y -10)(y + 14)

Cancelling -ve value, we get the width as 10 metres.

Hope it helps :)

5 0

3 years ago

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