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a line and a line segment are given. Construct a line parallel to the given line on a distance equal to the given segment.

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Answer:

A. 36°

Step-by-step explanation:

Given:

m<NST = 15x - 4

m<RSN = 6x

m<RST = 122°

Required:

m<RSN

Solution:

First we need to create an equation to determine the value of x.

Thus:

m<NST + m<RSN = 122° => angle addition postulate

15x - 4 + 6x = 122 (substitution)

Add like terms

21x - 4 = 122

21x - 4 + 4 = 122 + 4

21x = 126

21x/21 = 126/21

x = 6

✔️m<RSN = 6x

Plug in the value of x

m<RSN = 6(6) = 36°

The value of u is given by the equation u = 37°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the sum of total internal angles of a triangle be = 180°

Now , the triangle be ΔABC

The measure of ∠A = u + 4°

The measure of ∠B = u

The measure of ∠C = ( 180° - ( u + 41° ) ) ( angles on a straight line = 180° )

From the triangle theorem ,

u + 4° + u + ( 180° - ( u + 41° ) ) = 180°   be equation (1)

On simplifying the equation , we get

2u + 184° - u - 41° = 180°

u + 143° = 180°

Subtracting 143° on both sides of the equation , we get

u = 37°

Therefore , the value of u is 37°

Hence , the value of u in the triangle is 37°

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The solution to the inequality is (-∞, 4.05) .An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

Both equations and inequalities are mathematical phrases created by connecting two expressions.

The equal sign (=) in an equation denotes that the two expressions are regarded as equal.

In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.

Given the inequality:

-3(4 – x) 6 < 9 – 2x

Solving the inequality:

(-12 + 3x)6 < 9 - 2x

-72 + 18x < 9 - 2x

20x < 81

x < 4.05

Therefore the solution to the inequality is (-∞, 4.05)

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Answer:

x=8

Step-by-step explanation

Vertical angles are always congruent which means they are equal

Since we know this we can simply set the two angle equal to each other so...

5x-5=2x+19

Now what we do is add five to 19 and subtract 2x from 5x to get

3x=24

simply divide 24 by 3 to isolate x and now we have

x=8

Hope this was helpful!

Answer:

24

Step-by-step explanation:

You just do 6 / 1/4 = 24

Answer:

38.13m²

Step-by-step explanation:

We find the area of ;

Rectangule and semicircle

Area of rectangle :

Length * width

Length = 8m ; width = 3m

Area = 8 * 3 = 24m²

Area of semicircle = 1/2 πr²

Radius, r = 3m

A = 1/2 * 3.14 * 3²

A = 1/2 * 3.14 * 9

A = 14.13 m²

Area of patio :

(24 + 14.13)m²

= 38.13m²

Answer: 889.909090909

Step-by-step explanation:

divide

Answer:

S= 76, T= 76, U= 104, R= 104

Y=104, V= 104, X= 76, W= 76

Step-by-step explanation:

Opposite Angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent (equal in measure).

U and V are alternating angles

so U and  are 104

i d k the last one am so sorry

Answer:

He travelled: 1728 miles

Step-by-step explanation:

20.75 * 4 = 83 (Route A miles a week)

33.25 * 4 = 133  (Route B miles a week)

83 + 133 = 216 (Route A + Route B)

216 * 8 = 1728

Comparing the parabola's equation to the formula [tex]y = ax^2 + bx + c[/tex] in standard form is the first step. In step 2 Apply the formula h = -b/2a to find the vertex's x-coordinate. In step 3 Substitute x = h in the expression [tex]y = ax^2 + bx + c[/tex]  to obtain the vertex's y-coordinate (k).

The equation of the parabola's axis of symmetry is the vertex's x-coordinate. The axis of symmetry for a quadratic function in standard form, [tex]y = ax^2 + bx + c[/tex] is a vertical line, [tex]x=b^2a[/tex].

The intersection of two lines or rays that create an angle is known as the vertex of the angle.

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The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Advantages include:

Disadvantages:

Additional expenses include

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Answer:

t is the independent variable of time

Step-by-step explanation:

t is the independent variable of time

Answer:

Based on the given equation, the function g is an exponential function with base 2. The y-intercept of the function g is at (0, 4).

The graph of function f is not described, so it is not possible to accurately compare the two functions. In order to accurately compare the two functions, it would be helpful to have more information about the graph of function f, such as the vertex and any other points that the graph passes through.

Answer:

x = 12

Step-by-step explanation:

i. 29 = 2x + 5 [The length of two tangents to a circle at the point of contact from the same external point are equal]

ii. 29 - 5 = 2x

iii. 24 = 2x

iv. x = 24/2

v. x = 12

Answer:

So the side with the red square is 90 degrees. Anytime you see that that's what it will be. The inside of the triangle should equal 180 so 90 + 60 is 150. 180-150 = 30

Two side lengths are 90 and 30.

Step-by-step explanation:

If the x and y are pythagorean theorem then a2+b2=c2

If not then y= 120

and x= 150

the outside should equal 360

Answer:

136in^2

Step-by-step explanation:

According to the information the amount of insurance would be $66,160, the amount of coverage for personal property would be $41,350, the amount of coverage for loss of use would be $16,540 and the amount of coverage for garage would be $8,270.

To calculate the amount of each insurance we have to take into account the main value ($82,700) and the percentage of each insurance. Then, we have to calculate every percentage value as shown.

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The prime factorization of 72 using exponential notation is 2³ x 3².

Prime factorization is a process of writing all numbers as a product of primes.

Given:

Prime factorization is representing a number in form of products of its primes.

Consider the given number 72

72 = 2 x 2 x 2 x 3 x 3

So, 72 can be written as 2 × 2 x 2 × 3 × 3.

Thus, exponential notation it can be written as 2³ x 3².

Also, Simplifying 12 /16 as

= 12/16

= 3/4

and, the equivalent fraction whose denominator is 32.

Then, 3/4 = x/32

4x = 96

x = 24

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Answer:

12 bananas

9 apples

18 pears

Step-by-step explanation:

You are tripling the recipe.

10 x 3 = 3

4 x 3 = 12

3 x 3 = 9

6 x 3 = 18

9514 1404 393

Answer:

  (b)  y = -5x

Step-by-step explanation:

When "y varies directly as x" the equation for that is ...

  y = kx . . . . . . . for some constant k

The value of k can be found by solving for it:

  k = y/x . . . . . . divide by x

So, the given point (x, y) = (2, -10) tells you the value of k is ...

  k = -10/2 = -5

and the direct variation equation is ...

  y = -5x

_____

Additional comments

There are a couple of other useful facts about direct variation. When you compare the equation to the slope-intercept form equation for a line, ...

  y = mx + b

you see that b=0 and the slope, or rate of change, (m) is the same as k.

The y-intercept of 0 means that the graph of any direct-variation equation must go through the origin. (If it does not, then the variation is not direct.)

Answer:

The answer is 7/9

Step-by-step explanation:

Had this on my quiz one time

Answer:

7-9

Step-by-step explanation:

Answer:

[tex]m = 10\sqrt 3[/tex]

[tex]n = 10[/tex]

Step-by-step explanation:

Required

Find m and n

Considering the given angle, we have:

[tex]\sin(60) = \frac{Opposite}{Hypotenuse}[/tex]

This gives:

[tex]\sin(60) = \frac{m}{20}[/tex]

Make m ths subject

[tex]m = 20 * \sin(60)[/tex]

[tex]\sin(60) =\frac{\sqrt 3}{2}[/tex]

So, we have:

[tex]m = 20 *\frac{\sqrt 3}{2}[/tex]

[tex]m = 10\sqrt 3[/tex]

Considering the given angle again, we have:

[tex]\cos(60) = \frac{Adjacent}{Hypotenuse}[/tex]

This gives:

[tex]\cos(60) = \frac{n}{20}[/tex]

Make n the subject

[tex]n = 20 * \cos(60)[/tex]

[tex]\sin(60) =\frac{1}{2}[/tex]

So, we have:

[tex]n = 20 *\frac{1}{2}[/tex]

[tex]n = 10[/tex]

Answer:

A = 0.5 × [ sqrt(17^2 - 15^2) ] × 15 + 0.5 × [ sqrt(25^2 - 15^2) ] × 15 = 210 in^2

Answer:

.45

Step-by-step explanation:

it wants u to divide 5.40 by 12

HOPE THIS HELPS CHU (≧w≦)

Answer:

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