Given: AE ≅ CE ; DE ≅ BE Prove: ABCD is a parallelogram. Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E. Line segments A E and E C are congruent. Line segments D E and E B are congruent. We have that AB || DC. By a similar argument used to prove that △AEB ≅ △CED, we can show that △ ≅ △CEB by. So, ∠CAD ≅ ∠ by CPCTC. Therefore, AD || BC by the converse of the theorem. Since both pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

Answer:

Step-by-step explanation:

Given:

height of pole = 50 ft

angle of depression = 75°

to find:

how much wire is used

Solution:

Let x be the wire used

sin 75° = 50/x

x = 50/sin 75°

  = 50 / 0.9659

  = 51.765

x = 51.8 ft

Answer:

Step-by-step explanation:

If you are asking how much money were the drinks?

Then, the answer is $6.75. This is because 19.25 - 12.50 = 6.75

If you are asking how much money per drink, then the answer is $1.35

Answer:

27

Step-by-step explanation:

If you substitute the two give numbers and follow BEDMAS, you can calculate the answer.

n+5m

n = 7 and m = 4

=(7)+(5(4))

=7+20

=27

Answer: Standard Deviation.

Step-by-step explanation:

DescriptionIn insights, the standard deviation is a proportion of the measure of variety or scattering of a lot of qualities. A low standard deviation demonstrates that the qualities will in general be near the mean of the set, while an elevated expectation deviation shows that the qualities are spread out over a more extensive territory.

Answer:

Total calories eat = 107,520 calories

Step-by-step explanation:

Given:

Number of calories everyday = 5120 calories

Number of days = 21

Find:

Total calories eat

Computation:

Total calories eat = Number of calories everyday × Number of days

Total calories eat = 5120 × 21

Total calories eat = 107,520 calories

Answer:

Identity Property of Multiplication

Step-by-step explanation:

Required

State with property that describes the question

I'll answer this question using the following instances;

[tex]1.\ \frac{x}{3} = 1[/tex]

[tex]2.\ 3x = 1[/tex]

For the first expression, we multiply both sides by 3

[tex]3 * \frac{x}{3} = 1 * 3[/tex]

[tex]x = 1 * 3[/tex]

[tex]x = 3[/tex]

For the second; divide both sides by 2

[tex]\frac{3x}{3} = \frac{1}{3}[/tex]

[tex]x = \frac{1}{3}[/tex]

The property applied in both expressions is the identity property of multiplication

Answer:

the minimum is 771 erasers while the maximum is 789 erasers

Step-by-step explanation:

=====================================================

Explanation:

The blue parent function has a positive coefficient of 1. The purple g(x) function is a reflection of f(x) over the x axis, so everything is now negative. The coefficient must be negative as well.

But the answer is simply not g(x) = -x^2 because plugging x = 3 does not lead to y = -6 as the point (3,-6) shows.

Let's say the coefficient is k for now. So we have y = kx^2

Plug in x = 3 and y = -6. Solve for k

y = kx^2

-6 = k(3)^2

-6 = k*9

9k = -6

k = -6/9

k = -2/3

So we update y = kx^2 into y = (-2/3)x^2

Meaning that g(x) = (-2/3)x^2 is the equation of the purple curve.

Plug x = 3 into g(x) to find that

g(x) = (-2/3)x^2

g(3) = (-2/3)(3)^2

g(3) = (-2/3)(9)

g(3) = -6

which is the output we want, so this confirms we have the correct coefficient.

Answer:

y=(-2/3)x^2

Step-by-step explanation:

Answer:

The natural numbers from 1 to 30:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Prime Numbers can only divide by themselves and 1.

Prime Numbers From 1 to 30: 2,3,5,7,11,13,17,19,23,29.... ( 10 )

Answer:

144/6 = 24

24 x 20 = 480

480 is the answer

Answer:

80 MINS  to bike 144 miles

Step-by-step explanation:

20=6 miles

144 divided by 6 = 24  

24 more miles to go

6 times 4 = 24 miles

20+20+20+20= 80

Answer: The  length of a rectangle is 5 more than two times the width. If the width of the rectangle  is represent by x  then what is the area of the rectangle?  

Step-by-step explanation:

Answer: 3 feet

Step-by-step explanation: The area of a rectangular garden can be represented by the function

f(x) = x(2x + 5)

Find the area if the length, x, is 3 feet.

Answer:

D prominent is spelled wrong that's how you spell it

Step-by-step explanation:

Step-by-step explanation:

so, x+4/x-1=11/16

16x+64=11x-11

16x-11x=-11-64

5x=-75

x = -15

also, x+1 = -14

x =first number

x+1 = second number

(x) + 4 = x + 4 = 1 ^ new number [first number + 4]

(x + 1) -2 = x - 1 = 2 ^ new number [second number - 2]

[tex]\frac{x+4}{x-1}=\frac{11}{16}[/tex]

now, we resolve it:

[tex]\frac{16(x+4)-11(x-1)}{16(x-1)}=0[/tex]

[tex]\frac{16x+64-11x+11}{16x-16}=0[/tex]

[tex]\frac{5x+75}{16x-16}=0[/tex]

we eliminate the denominator and do c.e.: 16x - 16 ≠ 0; 16x ≠ 16; x ≠ 1

5x + 75 = 0

x = - 15

so x + 1 = - 14

But what you ask are two positive numbers! Are you sure that you write correctly the question? Thank you

Answer:

A. 48.9'

C. 48.9663'

Answer:

5+7i

Step-by-step explanation:

associative prop of addition

then simply add

Answer: Choice A) z = -3

====================================

Work Shown:

-2z + 3 + 7z= -12

5z+3 = -12

5z = -12-3 .... subtract 3 from both sides

5z = -15

z = -15/5 .... divide both sides by 5

z = -3

Answer:

A. z = -3

Step-by-step explanation:

B, C, and D have the wrong variable in the answer

-2z + 3 + 7z = -12

5z + 3 = -12

5z = -15

z = -3

Answer:

a line

Step-by-step explanation:

Answer:

40b

Step-by-step explanation:

25 + 15 = 40

Answer:

40b

Step-by-step explanation:

We are given the expression:

25b+15b

and asked to simplify.

To simplify, we must combine like terms. Let's analyze the terms.

25b ⇒ has a variable "b"

15b ⇒ also has a variable "b"

The like terms in this expression are the terms with a variable, b.

To combine like terms, add the coefficients and leave a b on the end.

(25+15)*b

(40)*b

40b

The expression 25b+15b simplified is 40b.

Answer:  multiplied together or divided, the answer is positive. If two negative numbers are multiplied together or divided, the answer is positive.

Step-by-step explanation:

The result of adding a negative number and a positive number will depend on the magnitude of the two numbers and which one is larger.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

In mathematics, adding a negative number and a positive number involves combining two quantities with opposite signs. When we add a negative number and a positive number, we can think of it as "subtracting the absolute value of the negative number from the positive number."

For example, if we have -3 + 5, we can rewrite it as 5 - 3, which equals 2. In this case, we are subtracting the absolute value of the negative number (3) from the positive number (5).

Similarly, if we have -7 + 2, we can rewrite it as 2 - 7, which equals -5. In this case, we are subtracting the absolute value of the negative number (7) from the positive number (2), but since the negative number has a larger absolute value, the result is negative.

So, the result of adding a negative number and a positive number will depend on the magnitude of the two numbers and which one is larger.

Learn more about subtraction here:

https://brainly.com/question/1927340

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The complete question is as follows:

What is a negative plus a positive?

Answer:

The answer is 280

Step-by-step explanation:

Because, the formula of volume of rectangular prism is Volume = length•width• height

Answer:

66

Step-by-step explanation:

The height of the person in inches by unit conversion will be 66 inches.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

It is known that,

1 feet = 12 inches

Multiply both sides by 5.5

5.5 feet = 12 x 5.5 = 66 inches

Hence "The height of the person in inches by unit conversion will be 66 inches".

To learn more about unit conversion,

brainly.com/question/11543684

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Answer:

3 : 1

Step-by-step explanation:

[tex] \huge7.5 : 2.5 = \frac{7.5}{2.5} = \frac{3}{1} = 3 : 1 [/tex]

The equivalent ratio to 7.5 : 2.5 is given by dividing both elements by 2.5, the ratio is: 3 : 1

Remember that in a ratio A : B we can always multiply or divide both numbers by the same number, and the ratio does not change.

So, for the ratio:

7.5 : 2.5

To be in the form of:

n : 1

We can just divide both elements by 2.5, so we get:

7.5/2.5 = 3

2.5/2.5 = 1

Then we conclude that:

7.5 : 2.5 is equivalent to 3 : 1

If you want to learn more about ratios:

https://brainly.com/question/2328454

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Answer:

The answer is C. 76.53

Answer:

4cm        10mm         1year

         x               x                             its fractions

1 year       1cm        365days

Step-by-step explanation:

its all fractions

Answer:

1.6448 * 10^4.

Step-by-step explanation:

16448

There are 4 digits after the first so the exponent is 4.

1.6448 * 10^4.

Answer:

28 = x

Step-by-step explanation:

62 =  angle BAC  since they are vertical angles

angle ABC is a right angle since KL is perpendicular to FG

Adding the angles in triangle ABC

BAC + ABC + BCA = 180

62 + 90 + BCA = 180

152 + BCA = 180

BCA = 180-152

BCA = 28

BCA = x since they are vertical angles

28 = x

Answer:

ok he has $40 left

Step-by-step explanation:

1000-500 = 500

500 - 400 = 100

100-60 = 40

Answer:

Money with Peter = $ 40

Step-by-step explanation:

Let 'x' be the money left with Peter

Money left with Peter after fixing his car = 1000 - 500 = 500

500 is divided into 5 equal parts and 4 parts he gave away. 500 - 400 = 100

x = (1000 - 500) - 400 - 60

= 500 - 400 - 60

= 100 - 60

x =$  40

Answer:

  x = 28/(3y -15)

Step-by-step explanation:

Put the x-terms on the same side of the equal sign and everything else on the other side. Divide by the coefficient of x.

  3xy -28 = 15x . . . . . . given

  -28 = 15x -3xy . . . . . subtract 3xy

  -28 = x(15 -3y) . . . . . factor out x

  -28/(15 -3y) = x . . . . . . divide by the coefficient of x

We prefer to have a positive sign where possible, so we can multiply this by -1/-1 to get ...

  x = 28/(3y -15)

Answer:

x < -8

Step-by-step explanation:

3 - (2x - 5) < -4(x + 2)

3 - 2x + 5 < -4*x -4*2

-2x + 8 < -4x - 8

-2x + 4x < -8 -8

2x < -16

x < -16/2

x < -8