The prime factorisation of √169 is?

Answer:

Radians:Ф=0.46364... +π n

Degrees:Ф= 26.56505 + 180° n.

Step-by-step explanation:

Apply trig inverse properties

Ф= arccot(2) +π n

Ф=0.46364... +π n

Radians:Ф=0.46364... +π n

Degrees:Ф= 26.56505 + 180° n.

When we add two negative numbers, the result will be negative.

When we add a negative and a positive number, the result can be positive, negative, or equal to zero.

When we add two positive numbers, the result will be positive.

These are both negative numbers. We know this because they are both to the left of 0. When we add two negative numbers, we will get a result that is less than 0.

k is a negative number while n is a positive number.

Notice that on the number line, k and n appear to be at a equal distance away from 0. This means that if we were to take their absolute values, they would be equal.

This means that adding k and n would result in an answer of 0.

m is a negative number while n is a positive number.

Notice that on the number line, n appears to be further away from 0 than m is. m is very close to 0.

This means that the absolute value of n would be greater than that of m. The result would therefore be positive

Both these numbers are negative. Adding them would produce a negative result.

The area of room is 812 square feet, cost of carpet to cover the room is $6739.6 and the remaining square feet of carpet are covered by furniture is 203 square feet.

The area of the trapezoid is the space occupied by it on the two dimensional plane. The area of this figure is half of the product of height and sum of sides.

[tex]A=\dfrac{(a+b)h}{2}[/tex]

Here, (a and b) are the base sides of the trapezoid and (h) is the height.

A room is shaped like a trapezoid which has the height of 28 feet and the length of sides as 23 ft and 35 ft. Thus, the area of it is,

[tex]A=\dfrac{(a+b)h}{2}\\A=\dfrac{(23+35)28}{2}\\A=812\rm\; ft^2[/tex]

Carpet costs $8.30 per square foot. Thus, the cost of carpet with area 812 ft² is,

C=812×$8.30

C=$6739.6

Furniture covers 25% of the floor. Thus, the remaining square feet of carpet are covered by furniture is,

[tex]A=\dfrac{25}{100}\times812\\A=203\rm\; ft^2[/tex]

Thus, the area of room is 812 square feet, cost of carpet to cover the room is $6739.6 and the remaining square feet of carpet are covered by furniture is 203 square feet.

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Answer:

d =5

Step-by-step explanation:

d = [tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

at (1,5), (5,2)

d= [tex]\sqrt{(5-1)^2 +(2-5)^2}[/tex]

[tex]d = \sqrt{16 + 9} \\d=\sqrt{25}\\ d =5[/tex]

Therefore 5 is the distance.

Answer:

C

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (1, 5 ) and (x₂, y₂ ) = (5, 2 )

d = [tex]\sqrt{(5-1)^2+(2-5)^2}[/tex]

   = [tex]\sqrt{4^2+(-3)^2}[/tex]

    = [tex]\sqrt{16+9}[/tex]

    = [tex]\sqrt{25}[/tex]

    = 5

Answer: B, C

Step-by-step explanation:

All four sides are congruent, so it is both a rhombus and a parallelogram.

It is not a rectangle because we do not know if two of the sides are perpendicular. From this, we also cannot tell if it is a square.

Answer:

  A) transversal

Step-by-step explanation:

The vocabulary term you're looking for is "transversal."

A transversal crosses parallel lines (or ones that are nearly parallel in the vicinity of the transversal).

Answer:

x>-9

Step-by-step explanation:

1. bring x over to the other side to make it a positive (4+x>-5)

2. bring 4 to the other side (x>-5-4)

3. simplify (x>-9)

Answer:

x = 125º

Step-by-step explanation:

Angles in a triangle add to 180º so:

180 - 42 - 83 = 180 - 125 = 55º

Angles on a straight line also add to 180º so to find x:

180 - 55 = 125º

x = 125º

Hope this helps.

The exterior angle theorem states that one exterior angle of a triangle will always be equal to the sum of the two opposite interior angles.

x is an exterior angle of the triangle.

We are given two interior angles in the triangle. These are opposite of x.

According to the exterior angle theorem, we can solve for x by adding these two angles:

x = 125

Answer: a) 7mm  b) 18mm  c) 49mm

Step-by-step explanation:

There are 10 mm in 1 cm, so to find how many mm the measurements are, multiply the measurement in cm by 10.

a) 0.7 cm

0.7 cm x 10 mm per cm = 7 mm

b) 1.8 cm

1.8 cm x 10 mm per cm = 18 mm

c) 4.9 cm

4.9 cm x 10 mm per cm = 49 mm

Answer:

5/24

Step-by-step explanation:

Answer:

x = -2, -5

Step-by-step explanation:

x^2 + 7x + 10 = 0

The factors of 10 are as follows:

1, 10

2, 5

We can combine 2 and 5 to make 7

(x +2) (x + 5) = 0

One of these brackets must equal 0 to make the answer 0, as you are multiplying them together

If x + 2 = 0, x = -2

If x + 5 = 0, x = -5

Therefore, x = -2, -5

Hey there!

QUADRATIC EQUATION:

ax² + bx + c = 0 where a ≠ 0

The sign of the discrimant (b² - 4ac) determines the number of real-number solutions :

The solutions of the equation, also called roots, can be obtained with the QUADRATIC FORMULA :

[tex]x = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

---------------------------------------------------------------

▪️ x² + 7x + 10 = 0

(1) Substitute the letters in the general quadratic equation with their values in the given expression:

(2) Determine the sign of the discriminant:

[tex]{b}^{2} - 4ac \\ \\ \Longrightarrow {7}^{2} - 4(1)(10) \\ \\ \Longrightarrow 49 - 40 \: \: \: \: \: \: \: \: \: \\ \\ \Longrightarrow \red{9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

The discrimant is positive ; the equation has two real-number solutions.

(3) Determine the roots of the equation :

[tex]x_1 = \frac{ - b \: - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_1 = \frac{ - 7 - \sqrt{9} }{2(1)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = \frac{ - 7 - 3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = - \frac{10}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \green{ \boxed{ \red{x_1 = - 5}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 7 + \sqrt{9} }{2(1)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_2 = \frac{ - 7 + 3}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x_1 = - \frac{4}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \red{ \boxed{ \green{x_2 = - 2}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Therefore, x = -5 or x = -2

▪️ Learn more about quadratic equations :

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Answer:

i. No, Maurice statement is wrong

ii. Stephan does not have sufficient pieces of wood to make the tray because the square inches required is more than what he has.

Step-by-step explanation:

Stephan's piece of wood measures; 18 inches in length and 12 inches in width. Since the piece of wood has a shape of a rectangle,the area of the piece of wood = length × width                                                 = 18 × 12                                                = 216 square inchesAccording to Maurice's statement, he could make a tray that has a base of 1012 inches by 1012 inches. The base has the shape of a square, so that;     the area of the base = length × width =                                        = 1012 ×1012                                      = 1024144 squared inchesThis shows that Stephan does not have sufficient wood to make the tray because the square inches required is more than what he has.

Answer:

9360

Step-by-step explanation:

2/5 is 40%

40% of 23400 is 9360

Answer:

12

Step-by-step explanation:

Its 12 because when you do -16 + - 40.... then -12 you get =12 There you go

Step-by-step explanation:

Solution ,

Firstly we need to understand that

( - ) × ( - ) = ( + )

( + ) × ( + ) = ( - )

( - ) × ( + ) = ( - )

( + ) × ( - ) = ( - )

Question:

- 16 + ( - 12 ) - ( - 40 )

here ( + ) × ( - ) = ( - )

= - 16 - 12 - ( - 40 )

here ( - ) × ( - ) = ( + )

= - 28 + 40

here the ( + ) has greater variable so....

= + 12

hence 12 is the answer....

Answer:

20.11 °

Step-by-step explanation:

31.1 ° + 35.8 ° + 90m + 44.2 ° = 20.11 °

Answer:

20°

Step-by-step explanation:

Solution,

Here,

→(x+20°)+160°=180°[Sum of a straight line is 180°]

→x=180°-180°

→x=0°

Again,

→x+20°

→0°+20°

→20°

Answer:

I have the same problem as you and it told me that it’s 40

Step-by-step explanation:

Answer:

A. 44 (if unanswered questions do not deduct 1 point)

B. 40

Step-by-step explanation:

22 x 2 = 44

25 x 2 - 10 = 40

Answer:

7

Step-by-step explanation:

Because 2x-4 equals -8

Answer:

a:

1. ABC = 60°

2. BCA = 90°

3. CAB = 30°

b:

XVR = WVS = 125°

RVS = 55°

RST = VSU = 110°

RSV = UST= 70°

TUS = 39°

Step-by-step explanation:

a:

According this is a Right Triangle ( BCA = 90°) and the sum angles of a triangle is 180° :

90+5x+9x+6=180

14x=84

x=6

Then we have : ABC = 9(6)+6 =60

CBA = 5(6)=30

b :

Given that the size of the opposite angles to a vertex are equal and the sum of the interior angles of a triangle is 180 degrees, the size of all angles can be easily found.

Answer:

Step-by-step explanation:

Comment

The area of a right triangle is the product of the two smaller legs divided by  2.

Givens

Horizontal Leg =   4 units.

Vertical Leg      =   8 units

Note. you count units by calling the right angle 0,0. As you move to the next square, count 1 then 2 then 3 ...

Solution

Area = 4 * 8 / 2

Area = 32 / 2

Area = 16

Answer

Area  = 16

Answer:

21 minutes

Step-by-step explanation:

hope it helps you

Answer:

Step-by-step explanation

the answer is A.

Answer:

Ꮎ = 72.123°

Step-by-step explanation:

AC² = BC²+ AB² - 2BC AB x cos (ABC) 4.52 4.12 +3.52 - 2 x 4.1 x 3.5 x cos (8) =

Answer:

(3.5; 1.5).

Step-by-step explanation:

1) formula for midpoint:

[tex]x=\frac{X_A-X_B}{2}; \ y=\frac{Y_A-Y_B}{2};[/tex]

2) according to the formula above the required midpoint is:

x=0.5(5+2)=3.5; y=0.5(8-5)=1.5

Answer:

Step-by-step explanation:

{2, 3, 5, 7, 11, 13, 17, 19}

            - - - - - - -- - - - - - - - - - - - - -- -

[tex]\diamond\large\textsf{\textbf{\underline{Given\:question:-}}}[/tex]

          The backyard is 20 inches long and 37 inches wide. What is the area of the backyard?

[tex]\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

We are given the backyard's length (20 inches long) and the backyard's width (37 inches wide).

We are asked to find the area of the backyard, which can be found using the following formula:-

      [tex]\boxed{\bold{A_{(rectangle)}=LW}}[/tex]

Where:-

Substitute the values:-

[tex]\boxed{\bold{A=20*37}}[/tex]

On simplification,

✳︎ [tex]\boxed{\bold{A=740\:in^2}}[/tex], which is our final answer.

        - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - -

Answer: 37·20=740

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

2005: 118000000000

2011: 2357000000000

Option A) = 20

118000000000 * 20 = 2360000000000

2360000000000 is approximately close to 2357000000000

Both functions are increasing, but function g increases at a faster average rate.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

Let f(x) = abˣ + c

At x = 0, f(0) = -10. Then we have

a + c = -10

Then similarly, by satisfying the above table in f(x) will be

[tex]\rm f(x) = - \dfrac{33}{5} \left ( \dfrac{1}{11} \right )^x - \dfrac{17 }{5} \\\\f'(x ) > 0[/tex]

Then we can say f(x) is an increasing function.

[tex]\rm g(x) = - 18 \left ( \dfrac{1}{3} \right )^x +2 \\\\g'(x ) > 0[/tex]

Then we can say g(x) is an increasing function.

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Answer:

The correct answer would be option D- Both functions are increasing, but function g increases at a faster average rate.

Hope this helps and good luck!