1. ABCD is a quadrilateral in which angle A = angle C and angle B = angle D
Prove that, if the opposite angles of a quadrilateral are equal, then the quadrilateral is a
parallelogram.

Answer:

6/6.71

Step-by-step explanation:

If you are given a 6-meter pole that is supported by guy wires that are anchored to the ground, you can create a relationship with respect to sin theta. sin theta is equal to the 6 meters over the slant line supported by the pole. as shown.  

Answer:

The missing letter is ( J )

There are four pairs (m,n) that work: (5,10), (6,6), (8,4), and (12,3).

Answer:

Step-by-step explanation:

Hello,

First term is 2 * 3 * x * x * x

Second term is 2 * 2 * 2 * x * x

Last term is 2 * 2 * x

So we can factorise it as below.

[tex]\boxed{6x^3+8x^2-4x=2x(3x^2+4x-2)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The factor should be [tex]2x ( 3x^2 +4x -2 )[/tex]

Given that,

Based on the above information, the calculation is as follows:

[tex] 6x^3+8x^2-4x[/tex]

[tex]2x ( 3x^2 +4x -2 )[/tex]

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Answer:

42 = 8x + 13x

42 = 21x

x = 2

8 = 8c -4(c + 8)

8 = 8c - 4c - 32

8 = 4c - 32

40 = 4c

c = 10

Answer:

42 = 21x

42/21 = x

x = 2

check:

42 = 8*2 + 13*2

42 = 16 + 26

8 = 8c -4*c -4*8

8 = 8c - 4c - 32

8 + 32 = 4c

40 = 4c

40/4 = c

c = 10

Check:

8 = 8*10 - 4(10+8)

8 = 80 - 4*18

8 = 80 - 72

Answer:

The answer is $40.

Step-by-step explanation:

According to the equation given in the question, we can assume that 550 is constant and was there when Mai started saving into a checking account.

Then as x gets increased by 1 each week, the amount of change in the account per week is $40.

I hope this answer helps.

2/3 of the job was completed in 4 minutes. the job left will be completed in 2 minutes

Answer:

Domain= time

Range= temperature

Step-by-step explanation:

Initially hot water cools down over time.

This can be expressed as a function of a temperature by a time. It takes 25 minutes for water to cooled down from 100°F to body temperature.

For any value of the time (from zero to 25 minutes), the temperature has certain value (from 100°F to body temperature). As time value increases, temperature value decreases accordingly.

In this example, time is the domain and temperature is the range.

Answer:

9

Step-by-step explanation:

Plug in 2 for x

You should get f(2)=(2+1)^2

Add 2+1 inside the parenthesis to get 3

Finally do (3)^2 to get 9

Answer:

11

Step-by-step explanation:

4=1

14=2

24=3

34=4

40=5

41=6

42=7

43=8

44=9

45=10

46=11

You will encounter 11 4s.

[tex] \LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}[/tex]

☃️ Refer to the trigonometric table....

Then, proceeding

⇛ tan 60 ° = √3

⇛ tan 60° = tan (a + b)

⇛ 60° = a + b

Flipping it,

⇛ a + b = 60° --------(1)

And,

⇛ tan 30° = 1 / √3

⇛ tan 30° = tan (a - b)

⇛ 30° = a - b

Flipping it,

⇛ a - b = 30° ---------(2)

Now adding eq.(1) and eq.(2),

⇛ a + b + a - b = 60° + 30°

⇛ 2a = 90°

⇛ a = 90° / 2

⇛ a = 45°

Putting value of a in eq.(1),

⇛ 45° + b = 60°

⇛ b = 15°

☄ So, Our Required answers:

━━━━━━━━━━━━━━━━━━━━

Answer:

19 x 97 = 1843

Answer:

4.6225

Step-by-step explanation: It would be too long to get an exact

Answer:

Step-by-step explanation:

Area of square = 18.49 square yards

side² = 18.49

side = √18.49

side = 4.3 yards

Answer and Step-by-step explanation:

1.  slope intercept

2.  point-slope form

3.  standard

Explanation:

1.   A slope intercept form equation is when it's set up as y = m x + b

m = slope  

b = y-intercept

2.   A point-slope form is when a line passes through a point

and the equation is set up as  y −b = m ( x−a)

m = slope

(a, b) A point that the line passes through

3. standard lope form is when the equation is set up as

Ax + By = C

Answer:

u should put this also in English then type it in so it will translate

Answer:

(0, -2)

Step-by-step explanation:

a point on the y-axis. that means x=0.

so, the distance of (5, -2) to (0, y) is the same as the distance from (-3, 2) to (0, y).

the distance between (5, -2) and (0, y) is based on Pythagoras (the differences in x and y directions are the sides of a right-angled triangle, and the distance is its Hypotenuse, its baseline) :

distance² = (5-0)² + (-2 - y)² = 25 + 4 + 4y + y² = 29+4y+y²

but it is also

distance² = (-3-0)² + (2 - y)² = 9 + 4 - 4y + y² = 13 - 4y + y²

so, we get

29 + 4y + y² = 13 - 4y + y²

29 + 4y = 13 - 4y

16 = -8y

y = -16/8 = -2

their, the point on the y-axis being equidistant to both points is (0, -2)

Answer:

There are 3 numbers that are not whole numbers.

3/4, 3.7, and sqrt 3 are not whole numbers

Answer:

3

Step-by-step explanation:

There are only 3 that aren't whole numbers. The whole numbers are: 32, 1,265, 3000, and 1. The numbers that aren't whole are: 3/4, 3.7, and √3

Answer:

i think its very interesting and pretty cool,  because there is so much to learn  and so much to explore

i wouldn't like the fact that you have to study so much though

Step-by-step explanation:

Answer:

To make only 12% profit, the discount should be increased to 16%

Step-by-step explanation:

The given information are;

The percentage discount on goods = 10%

The profit made from the sale of the watch = 20%

The amount the watch was sold = Rs.10,710

The percentage VAT included = 13%

Let the recommended selling price of the watch = X

Therefore, we have;

The price after 10% discount = 0.9×X

Which gives;

The amount the watch was sold = Price after 10% discount + Price after 10% discount ×VAT

The amount the watch was sold = 0.9×X + 0.9×X×13% = 0.9×X + 0.9×X×0.13

Rs.10,710 = 0.9×X + 0.9×X×0.13 = 1.017×X

X = Rs.10,170/1.017 = Rs. 10,000

The recommended selling price of the watch = Rs. 10,000

The profit was 20% of selling price which gives;

Profit = Selling price - Cost price = Rs. 9,000  - Rs. X = 0.2 × Rs. X

9000 - X = 0.2×X

9000 = X + 0.2×X  = 1.2×X

X = 9000/1.2 = Rs. 7,500

To make only 12% profit, we have;

12% of Rs. 7,500 = 0.12 × Rs.7,500 = Rs. 900

Selling price = Cost price + Profit = Rs. 7,500 + Rs. 900 = Rs. 8,400

Percentage discount from Rs.10,000 to get Rs. 8,400 is given as follows;

Percentage discount = Y%

Therefore;

Y = (10,000 - 8,400)/10000 × 100 = 0.16 × 100 = 16%

Y = 16%

Therefore, to make only 12% profit, the discount should be increased to 16%.

Answer:

D { -1,0,3,5}

R { -3,-1,1,7}

Step-by-step explanation:

The domain is the input values

3,-1,5,0

We normally put them from smallest to largest

D { -1,0,3,5}

The range is the output values

1,-3,7, -1

We normally put them from smallest to largest

R { -3,-1,1,7}

Answer:

[tex]28.07^{\circ}[/tex]

Step-by-step explanation:

We can use basic trig. for a right triangle to solve this problem. In any right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse (longest side) of the triangle.

The right triangle we're looking at involves the two dotted lines and an edge of the prism.

The bottom dotted line is a diagonal of the rectangular base of the prism. We can use the Pythagorean Theorem to find its length.

The Pythagorean Theorem states that for any right triangle, [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle and [tex]c[/tex] is the hypotenuse.

In this case, the two legs are 9 and 12 and we are solving for [tex]c[/tex]:

[tex]9^2+12^2=c^2,\\81+144=c^2,\\225=c^2,\\c=15[/tex]

This is theta's adjacent side. Its opposite side is an edge of the prism labelled as 8 inches. Therefore, we have the following equation:

[tex]\tan \theta = \frac{8}{15}[/tex]

Take the inverse tangent of both sides:

[tex]\arctan(\tan \theta)=\arctan(\frac{8}{15})[/tex]

Simplify using [tex]\arctan(\tan\theta)=\theta, \theta \in (-90^{\circ}, 90^{\circ})[/tex]:

[tex]\theta=\arctan(\frac{8}{15}),\\\theta=28.07248694\approx \boxed{28.07^{\circ}}[/tex]

Answer:

(-3 ÷ 4)x^2 + 6x

Step-by-step explanation:

Data mentioned in the question

Maximum height = 12m

Number of seconds = 8

Height = 3m

Depend on the above information, the quadratic equation is shown below:

As it took 8 seconds to hit the maximum altitude and it reverted to the ground floor, this graph also reflects the motion in parabola after 4 seconds, so that the a must be negative

Now it is given that

a × x ^ 2 + bx + c =0

We can considered that

x = 0

x = 8

As {0.8} are intercepts of x

When x = 0, then it is

a × 0 ^ 2 + b(0)  + c = 0 .................... (i)

Hence 0 = 0

Now x = 8, it is

a × 8 ^ 2 + b(8)  + c = 0

Hence a(8)^2 + b(8) + c =  0 ..................(ii)

As it can be seen that in the first equation c must be zero

Whereas the second equation is

64a + 8b = 0

i.e.

8a = -b or a = -b ÷ 8

Now according to the quadratic function, it presented

(-b ÷8)x^2 + bx + 0

So, the parabola vertex is (4, 12)

Now place this in the place of a

(-b ÷ 8)(4)^2 + b(4) = 12

And for calculating this b, all terms must be multiplied by 8

That appears

-b(16) + 32b = 96

16b = 96

So, b = 6.  

As a = -b ÷8

a = -6 ÷ 8

a = -3 ÷4

So, the equation is

= (-3 ÷ 4)x^2 + 6x

Hence, this is the equation

Answer:

A

For something to be a function every x value bust have at most 1 y value and in A 9 has 2 y values so it cant be a function

Answer:

∠ P ≈ 46.9°

Step-by-step explanation:

The area (A) of Δ PST is calculated as

A = [tex]\frac{1}{2}[/tex] × PS × PT × sinP

Here A = 71.24 , then

[tex]\frac{1}{2}[/tex] × 15 × 13 × sinP= 71.24 , that is

97.5 × sinP = 71.24 ( divide both sides by 97.5 )

sinP = [tex]\frac{71.24}{97.5}[/tex] , then

∠ P = [tex]sin^{-1}[/tex] ([tex]\frac{71.24}{97.5}[/tex] ) ≈ 46.9° ( to the nearest tenth )

Answer:

B.

Step-by-step explanation:

All the possible outcomes are listed on choice B.

The event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have three coins.

As we know, in a coin there are two sides head and a tail.

If we flip three coins then the set of all the possible outcomes:

O = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

The set of outcomes has more tails than heads.

E = {ttt, tth, tht, htt}

We can find the probability, the probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Probability = 4/8 = 1/2

Thus, the event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.

Learn more about the set here:

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frustum of a cone is: = pi * l(R + r)

(l) = slant height of the frustum.

from 2929.645714 - 506.1257143

= 2423.52

= 2423.5cm

Answer:

from 2929.645714 - 506.1257143

= 2423.52

= 2423.5cm