Square root of -1 = 1. Math test

The exterior angle of a triangle is equal to the sum of the two interior opposite angles, so : f° = a° + b° .

A triangle is a polygon which has 3 sides. The triangles can be divided into 3 types based on the value of the angles: Equilateral, isosceles ,scalene and right angled.

One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs. Right triangles adhere to the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

We know when we add all the angles of any given triangle it is 180°

∴ a° + b° + c° = 180°

or, a° + b° = 180° - c°

Now we know that a linear pair the sum of the angles is 180°.

∴c° + f° = 180°

or, f° = 180° - c°

So from the above two equations we can say that

f° = a° + b°

Therefore in the triangle the exterior angle of the triangle is equal to the sum of the two interior opposite angles.

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Answer:

Step-by-step explanation:

N sei

Answer:

c = 11

Step-by-step explanation:

2c+8+6c-6 = 90 ( the angle measure of the two angles)

8c+2 = 90

8c = 88

c = 11

Answer:

9

Step-by-step explanation:

12 / 4 = 3

3 x 3 = 9

Answer:

L = 18,4 ft

Step-by-step explanation:

The building, the ground, and the ladder make up a right triangle, with legs:

The distance (a) between the bottom of the ladder and the building 12 ft

The distance (b) between the gound and the window 14 ft up

The hypothenuse is the length of the ladder (L)

According to Pythagoras theorem

L²  = a²  + b²

L  = √  (12)²  +  (14)²

L = √ 144 + 196

L = √ 340

L = 18,4 ft

Answer:

42 ft

Step-by-step explanation:

4.2/1=4.2

4.2*10=42 ft

PLS GIVE BRAINLIEST

Answer:

42

Step-by-step explanation:

1 cm=10ft on the diagram

so the only thing we have to do is multiply.

4.2x10=42 make sure your answer is in FT not CM

so for example

42ft. Units are important XD

Answer:

The area of given figure is: 179.3

Step-by-step explanation:

The figure consists of a rectangle and a semi-circle

The length of rectangle is 14 and width is 10.

The width of rectangle is also the diameter of the semi-circle.

So,

d = 10

[tex]r = \frac{d}{2} = \frac{10}{2} = 5[/tex]

Area of Semi-Circle:

[tex]C =\frac{ \pi r^2}{2}\\= \frac{3.14 * (5)^2}{2}\\=\frac{3.14*25}{2}\\=\frac{78.5}{2}\\= 39.25[/tex]

Area of Rectangle:

[tex]R = Length * Width\\R = 10*14\\R = 140[/tex]

The total area will be the sum of area of rectangle and the area of semi-circle

So,

[tex]Total\ Area = C + R\\= 39.25 + 140\\=179.25[/tex]

Rounding off to nearest tenth

The total area is: 179.3

Answer:

-log_4

Step-by-step explanation:

The value of log1/4 rounded to the nearest hundredth is -0.60

Given the parameter which is needed for our Calculation:

Using a calculator, the value of log1/4 is -0.602059

Rounding to the nearest hundredth, is two digits after the decimal point.

Hence, we have ;

Therefore, log1/4 is -0.60

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Answer:

$324,870.00

Step-by-step explanation:

357,000.00 x .09 = $32,130.00

357,000.00  - $$32,130.00 = $324,870.00

Answer:

D. 50º

Step-by-step explanation:

According to the image below attached, blue lines represents line segments [tex]DB[/tex] and [tex]DB'[/tex], the red line creates a right angle regarding [tex]DB[/tex] (90º), where green line creates a flat angle with the same respect (180º). The angle between [tex]DB[/tex] and [tex]DB'[/tex] is less than 90º and 180º, meaning an acute angle. Therefore, the right answer is D.

Answer:

7/3

Step-by-step explanation:

If I solved it correctly, you use  y2-y1 / x2-x1. From here you get -3-4/1-4=-7/-3 which when you divide equals 7/3. LMK IF its wrong and ill figure it out champ!

Answer:

5

Step-by-step explanation:

the points is also given on graph

(6,5)

Answer:

y = -2x + 5

Step-by-step explanation:

Given:

Passes through point (1, 3)

Perpendicular to x – 2y = -8

Solve:

x – 2y = -8

y = 1/2x + 4

The slope is m = 1/2

The slope of the perpendicular line is the inverse of the slope of the original equation.

The slope of the inverse equation is m = -2.

Making an inverse equation of y = -2x + a

Find a:

Use point, (1, 3) where (x, y):

3 = (-2)*(1) + a

a = 5

y = -2x + 5

Answer:

y=½x+5

Step-by-step explanation:

Passes through, (1,3)

Perpendicular to x-2y=-8.

Step 1

write the equation in form of y=mx+c

x-2y=8

-2y=-x+8

Dividing both sides of the equation by -2 we get;

y=-x/2+8

y=-½x+8

Thus the gradient is -½. Call it M1

Recall, The product of the gradients(slopes) of perpendicular lines is -1 i.e

M1 × M2= -1

Solve for M2

-½×M2=-1.

Dividing both sides by -½ we get

M2=-1×-2

Now, use this slope(M2) with the points (1,3) to find the new equation that is perpendicular to x-2y=-8

Note: Given two points (x1,y1) and (x2,y2) the the slope would be ∆x/∆y i.e (x1-x2)/(y1-y2).

Therefore, identify new point (x,y). Use this new point with point (1,3) and the slope M2 to get the new equation.

Slope=∆x/∆y

M2=(x-1)/(y-3)

but M2 is 2

2=(x-1)/(y-3)

2/1=(x-1)/(y-3) Note: 2= 2/1

Cross multiplying we get:

2(y-3)=1(x-1)

Open the brackets

2y-6=x-1

Solve for y so as to write the equation in form of y=mx+c

2y=x-1 +6

2y=x+5

Divide both sides of the equation by 2

y=x/2+5

Answer:

ummm did you need help or....

Step-by-step explanation:

cause you got the answer right....

Answer:

260?

Step-by-step explanation:

I used the equation (4)13+(16)13 and plugged it into my calculator and got 260.

The sum of 4 thirteens and 16 thirteens is 260.

What is the meaning of sum?

You add up all the numbers to arrive at the sum. When you summarise something, you pay attention to all of its crucial components. A specific sum of money can also be referred to using the word sum. You might have to spend a sizable sum of money on a new car. However, you might be able to justify spending so much if you add up or total all of its advantages. When you add up the costs of everything you ordered, the total on a restaurant bill is determined. Sum need not be restricted to numbers. When you summarise something, you're providing a summary or overarching statement about it.

Here, 4 thirteens = 4 × 13 = 52

16 thirteens = 16 × 13 = 208

Sum of 4 thirteens and 16 thirteens = 52 + 208 = 260

Hence, 260 is the correct answer.

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Answer:

y=x+2

y=-x+8

Step-by-step explanation:

Answer:

Step-by-step explanation:

SOH - CAH - TOA

Since the opposite side is given and we need to find the length of the adjacent side, we can use tangent to solve for x.

[tex]tan 21=\frac{opposite}{adjacent} \\tan 21 =\frac{8}{x} \\0.384 =\frac{8}{x} \\0.384x =8 \\x=\frac{8}{0.384} \\x=20.84[/tex]

Since the opposite side is given and we need to find the length of the hypotenuse, we can use sine to solve for y.

[tex]sin 21=\frac{opposite}{hypotenuse} \\sin21 =\frac{8}{y} \\0.358 =\frac{8}{y} \\0.358y=8 \\y=\frac{8}{0.358} \\y=22.32[/tex]

Answer:

6042915 balls.

Step-by-step explanation:

Volume of a ping pong ball is;

V = (4/3)πr³

diameter of ping pong ball is given 4cm = 0.04 m

Radius; r = 0.04/2 = 0.02 m

V = (4/3)π(0.02³)

V = 0.00003351032 m³

Room is 9.5 meters long, 7.5 meters wide, and 3 meters high.

Volume; V = 9 × 7.5 × 3 = 202.5 m³

Number of ping pong balls that will fit into the room = volume of room/volume of ping pong balls = 202.5/0.00003351032 = 6042914.540956151

Approximately 6042915 balls.

Answer:d

D. 9 and 46/180

Step-by-step explanation:

Answer:

Ok thank you for your efforts

Step-by-step explanation:

The answer is D 9 46/180

Answer:

The rate of change of function is: 2

Step-by-step explanation:

Using the given table we have to exclude two pairs of input and output.

The rate of change or slope of function is given as:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

We take first two pairs of input/output from the table

(x1,y1) = (1,11)

(x2,y2) = (2,13)

Putting the values

[tex]m = \frac{13-11}{2-1}\\m =\frac{2}{1}\\m = 2[/tex]

Hence,

The rate of change of function is: 2

Answer:

[tex] \boxed{Maria \: got \: \$11} \\ \boxed{Bill \: has \: \$21} \\ \boxed{ Eric \: has \: \$63}[/tex]

Step-by-step explanation:

[tex]let \: maria \: be \to \: m \\ let \: eric \: be \to \: e \\let \: bill \: be \to \: b \\then : m =b - 10 \: and \: e = 3b \\ but : m + b + e = 95 \\ hence \to \: (b - 10) + b + (3b) = 95 \\ 2b - 10 + 3b = 95 \\ 5b = 95 + 10 \\ 5b = 105 \\ \boxed{b = 21} \\ m = b - 10 = 21 - 10 \\ \boxed{ m = 11} \\ e = 3b = 3(21) \\ \boxed{e= 63}[/tex]

♨Rage♨

Answer:

Last option is the correct answer.

[tex] m\angle A = 61°, m\angle B = 57°, m\angle C = 61°[/tex]

Step-by-step explanation:

Since, 61° + 57° + 61° = 179° < 180°

Therefore,

[tex] m\angle A = 61°, m\angle B = 57°, m\angle C = 61°[/tex] cannot be the measurements of triangle ABC.

Answer:

Step-by-step explanation:

1/2 + b + h

Okay so we know that b is 6 and that h is 10 so we can change the question to this : 1/2 + 6 + 10. We know that 1/2 is also writen as 0.5 , now all you need to do is 0.5 + 6 + 10 = 16.5 . The question asks to round to the nearest 10th so you need to add a 0 after the 5 so you can round up or down.

16.50

Now you need to look at the 10th number which is 5 and to round it up you need to look at the number after that which would be 0, we know that anything that is 4 or below gets rounded down so your answer for this question is simply 16.5.

I hope that helped you and good luck!

Answer:

Step-by-step explanation:

2x² + 6x - 5 = 0

D = 36 + 40 = 76 = (2√19)²

[tex]x_{1}[/tex] = ( - 6 - 2√19) / 4 = ( - 3 - √19) / 2

[tex]x_{2}[/tex] = ( - 3 + √19) / 2

Answer:

0.7142857

Step-by-step explanation:

Let wholesale price = x

Retail price = 40% Markup of wholesale price

Retail price = (100 + 40)% of x

Retail price = 140% of x

Retail price = 140/100 * x

Retail price = 1.4x

Hence,

Wholesale price / retail price

x / 1.4x

= 0.7142857

Hence, wholesale price is 0.7142857 of the retailer price

Answer:

Step-by-step explanation:

b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.

You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive

Answer:

-125

Step-by-step explanation:

Answer: 4. Transporting quests to and from the airport and sightseeing trips.

Step-by-step explanation:

Substantial services in regards to this question, are those described as being done outside the normal scope of business for the convenience of the customers or guests in this scenario.

Transporting guests to and from the airport and taking them on sightseeing trips is outside the scope of the rental business and so they are considered to be substantial services.