Find the cardinal number for the following set A.
A= {x | x is a letter in the word aftershock}
The cardinal number of set A is

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:

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:

9360

Step-by-step explanation:

2/5 is 40%

40% of 23400 is 9360

Answer:

A, Yes because each t value is paired with exactly one number of gallons.

Step-by-step explanation:

Simply perform the vertical line test. On a graph, draw a vertical line, and if the line crosses the graph exactly once, it is a function. See the diagram below. Hope it helps, have a fantastic day.

Answer:

a

Step-by-step explanation:

because i am built diffrent thats why

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: 27

Step-by-step explanation:

6 is the 1st

13 is the 2nd

20 is the 3rd

27 is the 4th

34 is the 5th

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: 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:

Step-by-step explanation

the answer is A.

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!

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

[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:

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:

A)

Step-by-step explanation:

2005: 118000000000

2011: 2357000000000

Option A) = 20

118000000000 * 20 = 2360000000000

2360000000000 is approximately close to 2357000000000

If the triangle ABC is enlarged using the point P as a center, then the point of the dilated triangle will be A'(-3, 2), B'(1, 2), and C'(-1, -2).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The coordinate of point P will be (5, 4).

Let shift the origin at P, then the coordinate of ABC will be

A(-4, -1), B(-2, -1), and C(-3, -3)

If the scale factor is 2. Then the coordinate of the triangle A'B'C' will be

A'(-8, -2), B'(-4, -2), and C'(-6, -6)

Then shift the origin at (0, 0), then the coordinate of A'B'C' will be

A'(-3, 2), B'(1, 2), and C'(-1, -2)

The graph is shown below.

More about the dilation link is given below.

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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:

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≈32[tex]\frac{3}{10}[/tex]ft²

--

To find the surface area of a right rectangular prism you must use this formula A=2(wl+hl+hw)

Then plug in your variebles

A=2( 1.33*1.5+5+1.5+5+1.33)

This comes out to be A≈32 [tex]\frac{3}{10}[/tex]

Answer:

32 1/3 ft² for K12

Answer:

See below ~

Step-by-step explanation:

3. coordinate proof

4. exterior

5. included angle

Answer:

coordinate proof

exterior

included angle

By using the information given on the graph, we can see that a = 3.

Here we have an exponential of the form:

[tex]y = p*a^x[/tex]

And by looking at the graph, it passes through (0, 4) and (2, 36), so we can write:

[tex]4 = p*a^0\\\\36 = p*a^2[/tex]

From the first equation we get that p = 4, replacing that on the second one we get:

[tex]36 = 4*a^2\\\\36/4 = 9 = a^2\\\\\sqrt{9} = 3 = a[/tex]

So we conclude that a = 3.

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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

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Answer:

21 minutes

Step-by-step explanation:

hope it helps you

Answer:

Step-by-step explanation:

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

Answer:

  B)  192 pi

Step-by-step explanation:

The volume of a cylinder is found from the formula ...

  V = πr²h

where the radius is r and the height is h. The radius is half the diameter.

__

  V = π(8/2)²(12) = 192π . . . . . . using the given values

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

Using the Empirical Rule, it is found that 95% of the employees will have a travel time within the following range:

B. 8 minutes to 28 minutes.

It states that, for a normally distributed random variable:

Considering that the mean time is 18 minutes and the standard deviation is 5 minutes, the the bounds of the 95% range are given by:

Hence option B is correct.

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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)

Step-by-step explanation:

2 things to remember :

1. the sum of all angles in a triangle is always 180°.

2. the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

triangle 1 :

angle B = 180 - 62.2 - 43.8 = 74°.

a/sin(62.2) = 15.8/sin(74)

a = 15.8 × sin(62.2)/sin(74) = 14.53961961... in

c/sin(43.8) = 15.8/sin(74)

c = 15.8 × sin(43.8)/sin(74) = 11.37657122... in

triangle 2 :

14.9/sin(49) = 11.6/sin(A)

sin(A) = 11.6 × sin(49)/14.9 = 0.587559136...

angle A = 35.98398776...° ≈ 36°

angle C = 180 - 49 - 35.98398776... = 95.01601224...° ≈

≈ 95°

c/sin(95) = 14.9/sin(49)

c = 14.9 × sin(95)/sin(49) = 19.66708505...

newly weds triangle :

let's call the 2 sides a and b (25 m and 30 m).

the angle between them is 60°.

here we should use the extended Pythagoras for general triangles :

c² = a² + b² - 2×a×b×cos(C)

with c being the side opposite to the angle C.

so, we have in our case

c² = 25² + 30² - 2×25×30×cos(60) = 625 + 900 - 750 =

= 775

c = sqrt(775) = sqrt(25×31) = 5×sqrt(31) = 27.83882181... m

the area of the triangle we get via Heron's formula :

s = (a+b+c)/2 = (25+30+c)/2 = 41.41941091...

area = sqrt(s(s-a)(s-b)(s-c)) = sqrt(s(s-25)(s-30)(s-c)) =

= sqrt(105,468.75) = 324.7595264... m²

with Php 2000 per m² this would cost

324.7595264... × 2000 = Php 649,519.0528...

Answer:

20.11 °

Step-by-step explanation:

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