In the adjoining figure, AB//CD. Show that, AC//BD.
Learn
for

A
70°
C
50%
B
60%D
T

The value of a if HL is perpendicular to HJ is 20

From the information given, we have that;

It is important to note that perpendicular lines always intersect each other and the angle between perpendicular lines is equivalent to 90 degrees.

Then, we have that;

Angle 2 + angle 3 =  90 degrees

Substitute the values

a + 15 + a + 35 = 90

collect like terms

2a + 50 = 90

2a = 90 - 50

subtract like terms

2a = 40

Make 'a' the subject

Divide both sides by 2

2a/2 = 40/2

a = 20

Thus, the value of a if HL is perpendicular to HJ is 20

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The area of the regular pentagon is 60 square units

The given parameters are

Radius, r = 5 units

Side length, l = 6 units

The area of the pentagon is calculated as

A = 1/4√[25 + 10√5] * l^2

Substitute 6 for l in the above equation

So, we have

A = 1/4√[25 + 10√5] * 6^2

Evaluate the product

A = 60 (approximated)

Hence, the area of the regular pentagon is 60 square units

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Answer:

[tex]{ \tt{5y = y ln( {x}^{2} ) }} \\ { \tt{impossible}}[/tex]

Answer:

  (d)  519

Step-by-step explanation:

You want the ratio of (7.785×10^10) to (1.5×10^8) expressed in standard form.

Since you want the result in standard form, it can work well to make the numerator and denominator powers of ten be the same.

  [tex]\dfrac{7.785\times10^{10}}{1.5\times10^8}=\dfrac{7785\times10^7}{15\times10^7}=\dfrac{7785}{15}=\boxed{519}[/tex]

The cost to rent a canoe for 4 hours is $57.

It should be noted that the equation given is illustrated as equation C= 8h+25 represents the cost in dollars, C, to rent a canoe.

C = 8h + 25.

where h = number of hours

C = 8h + 25

When h = 4..

C = 8h + 25

C = 8(4) + 25

C = 32 + 25

C = 57

Therefore, the cost to rent a canoe for 4 hours is $57.

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The linear equation with  the given information is

2y+2 = 3x+18

Given :

The slope of Parallel Lines:

Slopes of parallel lines are equal. The parallel lines are equally inclined with the positive x-axis and hence the slope of parallel lines is equal. If the slopes of two parallel lines are represented as m1, m2 then we have

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

The slope of the line can also be represented by

tan θ = Δy/Δx

So, tan θ to be the slope of a line.

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’

m1 = m2.

y 2/3 = x + 1 ...1

2y = 3x+3

y = 3/2x +3/2

m1= 3/2

x,y = -6,-1

y = mx +b

(y-y1 ) =m (x-x1) +b

m1=m2

m2= 3/2

(y +1) = 3/2 (x+6)

2(y+1 )= 3x+18

the equation of the line that is parallel to y 2/3 = x + 1 and passes through the point (–6, –1) = 2y+2 = 3x+18

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Answer:

Kinetic energy

Step-by-step explanation:

because when something is in motion it gains kinetic energy

With the help of the volume of cube it is concluded that Beth should buy 4 bags of beans.

The volume of a cube is the total three-dimensional space that it occupy. A cube's volume is expressed as cubic units. The SI unit of volume is the cubic meter [tex](m^3)[/tex], which is the volume occupied by a cube with each side measuring 1 m.

The first thing to do in this case is to find the volume of the cube, which will be given by:

V = [tex]L ^ 3[/tex]

where, L = sides of the cube.

Substituting we have:

V = [tex](2) ^ 3[/tex]

V = [tex](8) ^ 3[/tex]

Since, beans are sold in bags that hold two cubic feet of beans.

Now, to find the number of bags, we calculate

n = 8/(2)

n = 4

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a. The weight of a particular crate such that the probability of randomly selecting a heavier crate is 0.05 is 16.30kg.

b. The probability that a randomly selected crate will weigh more than 16kg is 0.0764.

c. The probability that.at least 2 of them will weigh more than 16kg is 0.4584.

a. From the information, there is a mean of 14 kg and a standard deviation of 1.4 kg. The weight will be:

Let the weight = x

X = (Z × mean × standard deviation)

= (1.645 × 1.4 ×14)

= 16.30kg

b. The probability that a randomly selected crate will weigh more than 16kg will be:

P(z > 16)

= P(Z > 16-14/1.40)

= P(Z > 1.43)

Looking under the normal distribution table, the value is 0.0764.

c. The probability that at least 2 of them will weigh more than 16kg when 20 crates are randomly and independently selected will be through binomial distribution where n = 20 and p = 0.0764.

This will give a value of:

= 1 - 0.5416

= 0.4584

Therefore, the probability that.at least 2 of them will weigh more than 16kg is 0.4584.

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6 inches more than 2 times the height, 54 square inches the base and height is

b=13.8 inches

h=3.9 inches

Let base and height be b and h respectively,

So ,

b=2h+6

Area = b*h= 54 square inches

So,

(2h+6)(h)=54

2h²+6h=54

h²+3h=27

h²+3h-27=0

h= [tex]\frac{-3 +\sqrt{3^{2}-4(-27)(1) } \\}{2}[/tex]

h=[tex]\frac{-3 +\sqrt{9+108} \\}{2}[/tex]

h=[tex]\frac{-3 +\sqrt{117} \\}{2}[/tex]

h=[tex]\frac{-3 +10.8\\}{2}[/tex]

h=3.9 inches

b=2h+6=13.8 inches

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The quantity of unit squares necessary to completely cover a shape is its area. As a result, it is stated and measured in square units.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

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The correct answer answers will vary

Students should apply their findings to the calculation to determine a distance.

S=D÷T. The speed would be equal to the time and the speed from the 5-meter trial of walking backwards.

ought should be 15 minutes. To calculate the distance, students must multiply the speed by the time.

The distance that an item travels in relation to the amount of time it takes to do so may be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.

The speed formula, which was developed by scientists, is used to determine different types of speed. The speed equation is:

Speed=Distance/Time

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The value when it was purchased is  $160,000 in linear equation.

What in mathematics is a linear equation?

Let the original price be = x

Decreased value  = 0.35

Current value = 104000

x - 0.35x  = 104000

0.65x = 104000

x = 104000/0.65

x = 160,000

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Answer:

BC to ∆A''

Step-by-step explanation:

in order to find the shorter side of a golden rectangle we need to divide 13

by 1.6180.

A golden rectangle is a rectangle in geometry whose side lengths are in the golden ratio, or display style 1:tfrac 1+sqrt 5 2 which is display style 1:varphi 1:varphi (the Greek letter phi), where display style var phi var phi is roughly 1.618.

All rectangles made by including or excluding a square from one end are also golden rectangle, which is a unique example of self-similarity.

Length of longer side a = 13

let the length of shorter side is b.

them by the property of golden rectangle,

a : b = 1: (1+sqrt 5)/2

by substitution method

13 : b = 1 : (1+sqrt 5)/2

b = 8.034

so to get the length of shorter side we need to divide by 1.6180

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Answer:

A

Step-by-step explanation:

He paid $376.20

Answer: Aniela took 2.5 pages of notes per class

Step-by-step explanation: If you take the total amount of pages of notes taken and divide it by the number of classes you get the rate of pages of notes per class. So 10 pages/4 classes = 2.5 pages/class

Answer:

18.64% discount

Step-by-step explanation:

If she had a $22 discount and bought the radio for $96, then the original cost was $118.

discount = (22 * 100) / 118

Answer:

-7+5 >2

-7+5=2

collect like terms

-7 =2-5

-7 = -3

Answer:

Given y = 0,

[tex]\sf 4(6y+1)\\4(6* 0+1)\\(6 * 0 + 1)\\(6 * 0)\\= 0\\= 0 + 1\\= 1\\= 1 * 4\\= 4[/tex]

Thus, the answer is 4.

Answer:

1-13 and 2-13 and 4-13 because if you add them that is the answer

Answer:

46.2%

Step-by-step explanation:

6 divided by 13 multiplied by 100. rounded up

Answer:

6 x 10^18

Step-by-step explanation:

u multiply numbers as normal and add exponents when they are being multiplied to each other

Answer:

C. 6 x 10^18

Step-by-step explanation:

Hope it helped :)
(Ik it was already answer but I just wanted to answer)

Answer:

9, 18, 27, 36, 45

Step-by-step explanation:

multiples is like finding the factors. like 1*9=9 and 2*9=18, 9*3=27, 4*9=36, 9*5=45

Answer:

3.9 x [tex]10^{8}[/tex]

Step-by-step explanation:

0.39 is not in scientific notation.  For a number to be in scientific notation the first factor has to be 1 or greater, but less then 10.  0.39 is less than one.

First we must write 0.39 in scientific notation.  We need to move the decimal so that the number is greater than 1, but less than ten.  If we move the decimal one place to the right, we get 3.9.  The standard number is smaller than 3.9.  How much smaller?  [tex]10^{-1}[/tex] smaller.

0.39 in scientific notation would be 3.9 x [tex]10^{-1}[/tex].  We cannot forget the [tex]10^{9}[/tex], so our number looks like this now:

3.9 x [tex]10^{-1}[/tex] x [tex]10^{9}[/tex]  The product of powers principle tells us that if we have powers with the same bases, we can add the exponents.

3.9 x [tex]10^{-1+9}[/tex]

or 3.9 x [tex]10^{8}[/tex]

Answer:

6 people

Step-by-step explanation:

To figure this out, let's set up an equation.

We know 30 people went last year to Universal, and that this is 5 times as many people as who went the year before

So to figure out how many went the year before, we divide 30 by 5

30/5 = 6

So 6 people went to Universal the year before.

I hope this helps :)

Han produced hot chocolate by combining 6 tablespoons of cocoa with 4 cups of milk. For every spoonful of cocoa, 0.67 glasses of milk are required.

The relationship between two values is described by a ratio. It displays how frequently one value appears in another. The answer to this question will depend on how many cups of milk there are to every tablespoon of chocolate.

Divide the provided cups of coffee by the cost of the tablespoon of coffee to get the required quantity of milk per tablespoon of chocolate.

Cups per tablespoon of coffee equal cups of milk divided by tablespoons of cocoa.

Given that,

Number of cups of milk = 4

Tablespoons of cocoa = 6

4/6=0.67 cups

Therefore, for every spoonful of cocoa, 0.67 glasses of milk are required.

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