Solve this systematically and snap it for me

A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What

ivann1987 [24]

Step-by-step explanation:

We have to find the measures of other two angles of triangle.

$\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}$

We know that,

The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.

Angle sum property,

The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.

$\rule{200}{3}$

$\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}$

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

$\rule{200}{3}$

Second AnglE :

3x
3 × 10
30°

∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

$\rule{200}{3}$

Third AnglE :

14x
14 × 10
140°

∴ Hence, the measure of the third angle of the triangle is 140°.

5 0

3 years ago

The standard form of a linear equation is Ax + By = C. Rewrite this equation in slope-slope-intercept form. What is the slope? W

myrzilka [38]

Standard form is Ax + By = C, or By = C - Ax.

Dividing both sides by B, we get y = C/B - (A/B)x

Here the y intercept is C/B, and the slope is -A/B.

4 0

4 years ago

The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater

LenaWriter [7]

Answer:

Function 1 has the larger maximum at (4, 1)

Explanation:

After observation, graph of function 1 has vertex at Maximum (4, 1)

In order to find vertex of function 2, complete square the equation.

f(x) = -x² + 2x - 3

f(x) = -(x² - 2x) - 3

f(x) = -(x - 1)² - 3 + (-1)²

f(x) = -(x - 1)² - 2

Vertex form: y = a(x - h)² + k where (h, k) is the vertex

So, here for function 2 vertex: Maximum (1, -2)

<h3>Conclusion:</h3>

Function 1 = Maximum (4, 1), Function 2 = Maximum (1, -2)

Function 1 has greater maximum value of (4, 1) as "1 is greater than -2"

5 0

2 years ago

Which unit of measurement would Guatemalans typically use to measure milk for a recipe? a) milliliters b) grams c) ounces d) gal

oksian1 [2.3K]

Guatemalans would use milliliters because they use the metric system which is common throughout Latin America and which is basically easier to use than the Imperial system because it is all divisible by 10 whether it be millitres,litres,meters, kilometers etc.

6 0

4 years ago

Read 2 more answers

What is the y-intercept of the line perpendicular to (1,1) and (-3,-1) and passes through (-3,-2)

marin [14]

Answer:

-8

Step-by-step explanation:

Let's first establish the reference line (the one that the second line will be perpendicular to). We are told that this line passes through two points:

(1,1) and (-3,-1).

We'll find a line equation using the point slope form format to start:

(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.

(x,y) = (1,1)

(x1,y1) = (-3,-1)

Rearrange the equation:

(y - y1) = m * (x - x1)

m = (y - y1)/ (x - x1)

m = (1-(-1))/(1-(-3))

m = 2/4, or 1/2: The slope is 1/2. [<u>This is "m."]</u>

We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:

y = (1/2)x + b

Use either of the two given points. I'll use (1,1) since I have memorized the "1" math tables.

y = (1/2)x + b

1 = (1/2)(1) + b for (1,1)

b = 1/2

This makes the reference line: y = (1/2)x+(1/2)

===

The line perpendicular must have a slope that is the negative inverse of (1/2). This would be -(2/1), or -2.

We can then write y = -2x + b

To find be, enter the one given point for this line: (-3,-2)

y = -2x + b

-2 = -2(-3) + b

-2 = 6 + b

b = -8

The perpendicular line is thus:

y = -2x - 8

It has a y-intercept of -8

5 0

2 years ago

Solve this systematically and snap it for me​

Solve this systematically and snap it for me