Can you prove that DEF is congruent to HGF.!? Justify your answer.

Answer:

1)  ∠DCE = (180  - x)°

2)   x  = 60°

Step-by-step explanation:

Here, given :  Lines AD and BE intersect at point C

(a)  Now, as we know, c BE is a straight line.

⇒∠BCD + ∠DCE = 180 °  (LINEAR PAIR)

⇒x °  + ∠DCE = 180 °

or, ∠DCE = (180  - x)° ....... (1)

(b) ∠DCE  = 120°

Putting the value in the equation (1), we get:

120°  = (180  - x)°

or, x =  180 - 120° = 60°

or, x  = 60°

y=3x+38 is the expression for Sidney's weekly salary.

Step-by-step explanation:

Given,

Casey's weekly salary = x

Let,

y be the weekly salary of Sidney's.

According to given statement;

Sidney makes $38 more than 3 times Casey's weekly salary.

Sidney's weekly salary = 3 times Casey's weekly salary + $38

[tex]y=3x+38[/tex]

y=3x+38 is the expression for Sidney's weekly salary.

Keywords: variable, addition

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Step-by-step explanation:

The complete question:

What is the value of y in the formula shown when x = [tex]\dfrac{4}{5}[/tex] ?

[tex]y=\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]

We have,

[tex]\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]       ...... (1)

To find, the value of y = ?

Put x = [tex]\dfrac{4}{5}[/tex] in equation (1), we get

[tex]y=\dfrac{4}{\dfrac{4}{5}}+\sqrt{\dfrac{4}{5}+0.2}-5(\dfrac{4}{5})[/tex]

[tex]=5+\sqrt{0.8+0.2}-4[/tex]

[tex]=1+\sqrt{1}[/tex]

= 1 + 1

= 2

Thus, the value of y is equal to 2.

Answer: The Fund last year was 19,860

Step-by-step explanation:

Just set up a ratio using 70 over 13902 and set it equal to 100 over x and cross multiply to get x = 19,860

Answer:

  m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9

Step-by-step explanation:

The given points are the y-intercept and the x-intercept, so they can be used directly in the intercept form of the equation of a line.

  x/(x-intercept) +y/(y-intercept) = 1

  x/3 +y/9 = 1

Multiplying by 9 gives ...

  3x +y = 9

This can be rearranged to the slope-intercept form ...

  y = -3x +9

_____

The answer selection shown above is the only one that matches the slope and y-intercept of the line through the given points.

Answer:

because m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9

Step-by-step explanation:

Answer:

15.7cm

Step-by-step explanation:

2 + 1.4 + 1.3 + 1.2 + 4.1 + 1.3 + 1.4 + 3

Answer: 5 + 25n

Explanation: Let's simplify this problem using the distributive property.

In this problem, the 5 "distributes" through the parentheses which means that it multiplies by each of the terms inside.

So we have 5(1) + 5(5n) which simplifies to 5 + 25n.

Answer:

the degree for the polynomial is 2

Answer:

Senior citizen tickets = 9

Student tickets = 10

Step-by-step explanation:

We begin by converting the question into simultaneous linear equations;

Senior citizen tickets = a

Student tickets = b

4a + 6b = 96

8a + 13b = 202

to find a,

if 4a +6b = 96

a = 96/4 - 6b/4

a = 24 - 1.5b

We now substitute this into the second equation

8(24 - 1.5b) + 13b = 202

192 - 12b + 13b = 202

b = 202 - 192

b = 10

We now put the value of b in either equation

4a + 6b = 96

4a + 6(10) = 96

4a + 60 = 96

4a = 96 - 60

4a = 36

a = 9

Answer:

-2x-3y

Step-by-step explanation:

-1/4(8x+12y)

-8/4x-12/4y

-2x-3y

Final answer:

The expression -1/4(8x+12y) is expanded by distributing -1/4 to both 8x and 12y, resulting in the equivalent expression -2x - 3y.

Explanation:

To expand the expression -1/4(8x+12y), you need to distribute the term outside the parenthesis (-1/4) to each term inside the parenthesis. This process is known as the distributive property of multiplication over addition. Here's the step-by-step process:

In conclusion, the equivalent expression after expanding -1/4(8x+12y) is -2x - 3y.

Answer:

31.94 miles

Step-by-step explanation:

we know that

The circumference of a tire represents the distance traveled by the vehicle in one revolution

so

by proportion

Find out the distance traveled by the vehicle in 23,000 revolutions

[tex]\frac{88}{1}\ \frac{in}{rev}=\frac{x}{23,000}\ \frac{in}{rev}\\\\x=88(23,000)\\\\x=2,024,000\ in[/tex]

Convert inches to miles

Remember that

[tex]1\ mile=63,360\ inches[/tex]

To convert inches to miles divided by 63,360

therefore

[tex]2,024,000\ in=2,024,000/63,360=31.94\ miles[/tex]

Answer:

Therefore 6th year his income was $19,700.

Step-by-step explanation:

Given, Joe's annual income has been increasing in some dollar amount . The first year his income was $15,200 and 4th  year his income was $17,900.

A=$17900, P= $15,200 and n = 3 year

[tex]A= P(1+\frac{r}{100} )^n[/tex]

[tex]\Leftrightarrow 17900=15200(1+\frac{r}{100})^3[/tex]

[tex]\Leftrightarrow (1+\frac{r}{100})^3=\frac{17900}{15200}[/tex]

[tex]\Leftrightarrow (1+\frac{r}{100})=(\frac{17900}{15200})^{\frac{1}{3} }[/tex]

[tex]\Leftrightarrow \frac{r}{100}=(\frac{17900}{15200})^{\frac{1}{3} }-1[/tex]

[tex]\Leftrightarrow r=5.60[/tex]

Let  [tex]t^{th}[/tex] year Joe's income was $19,700.

[tex]\therefore 19700=15,200(1+\frac{5.60}{100} )^{t-1}[/tex]

[tex]\Leftrightarrow 1.296= (1+0.056)^{t-1}[/tex]

[tex]\Leftrightarrow 1.296= (1.056)^{t-1}[/tex]

[tex]\Leftrightarrow log(1.296)= (t-1)log(1.056)[/tex]

[tex]\Leftrightarrow \frac{log(1.296)}{log(1.056)}= (t-1)[/tex]

[tex]\Leftrightarrow t-1= 4.75[/tex]

[tex]\Leftrightarrow t= 4.75+1[/tex]

[tex]\Leftrightarrow t = 5.75[/tex] ≈6

Therefore 6th year his income was $19,700.

Answer:

480 tons

Step-by-step explanation: You have to figure out how many minutes are in 24 hours. (1440 min) Then, you multiply 1440 x 1/3.

Answer:

the answer is 480

Step-by-step explanation:

it is common sense but in your case it is uncommon sense

Answer:

Step 1: D for Divide. How many times will 5 go into 65? ...

Step 2: M for Multiply. You multiply your answer from step 1 and your divisor: 1 x 5 = 5. ...

Step 3: S for Subtract. Next you subtract. ...

Step 4: B for Bring down. ...

Step 1: D for Divide. ...

Step 2: M for Multiply. ...

Step 3: S for Subtract.

Step-by-step explanation:

It will need 864 meters³ of water to fill it completely

Step-by-step explanation:

The formula of the volume of a prism is V = B h, where

The swimming pool is shaped a prism

∵ The length of each side of the four sides is 12 meters

- That means its base is shaped a square with side length 12 meters

∵ Area of a square = (side)²

∴ The area of the base of the swimming pool = (12)² = 144 meters²

∴ B = 144

∵ The pool is 6 meters deep

- That means its height is 6 meters

∴ h = 6

The volume of the water in the swimming pool is equal to the volume of the swimming pool because it will be needed to fill completely

∴ The volume of the water = B h

∴ The volume of the water = 144(6)

∴ The volume of the water = 864 meters³

It will need 864 meters³ of water to fill it completely

Learn more:

You can learn more about the volume of solids in brainly.com/question/12497249

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Answer:

The system has infinitely many solutions

Step-by-step explanation:

we have

[tex]5x+3y=9[/tex] ----> equation A

[tex]-10x-6y=-18[/tex] ----> equation B

Multiply by -2 both sides equation A

[tex]-2(5x+3y)=-2(9)[/tex]

[tex]-10x-6y=-18[/tex] ----> equation C

Compare equation B and equation C

The equations are identical (is the same line)

therefore

The system has infinitely many solutions

Is a consistent dependent system

Answer:

The complement of 33 is the angle that when added to 33 forms a right angle

Step-by-step explanation:

it is un needed for a explanation

Answer:

160-153=7 dogs

you will need 1 more truck to hold 160 dogs

Step-by-step explanation:

1 truck=9 dogs

9x17=153 dogs

160-153=7 dogs

you will need 1 more truck to hold 160 dogs

Answer:

45 metres

Step-by-step explanation:

You have to get the base to answer the question.

Do this by dividing 315 by 15 then timesing by 2

You get 42.

Do 42^2 = 1764

Do 15 ^2 = 225

Because you want the hypotenuse you add them

1764 + 225 =1989

Do the square root of 1989 which is 45 to the nearest metre

Answer:

25.80

Step-by-step explanation:

Area = 315 [tex]m^{2}[/tex]

Area = l*b

315 = 15 *b

b= 315/15

b = 21

From Right angled Triangle ,

Hypotenuse square = side square + side square

[tex]x^{2}[/tex] = [tex]21^{2}[/tex] + [tex]15^{2}[/tex]

[tex]x^{2}[/tex] = 441 + 225

[tex]x^{2}[/tex] = 666

apply sq root on both sides, the we get

[tex]\sqrt{x^{2}} = \sqrt{666}[/tex]

x= 25.80

Answer:

The statement is true.

Step-by-step explanation:

Given : Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis.

To find : Is this statement true or false?

Solution:

Rules of reflection :

Along across y-axis if we have a point

So, y=sinx

The reflection across y-axis→ .......[1]

Along across x-axis if we have a point

so, y=sinx

The reflection across x-axis →  .....[2]

Hence, [1] and [2] both of them are equal

Therefore, the statement is true.

Answer:

The answer is true for A P E X

Step-by-step explanation:

Answer:

The bowling ball has only potential energy as it sits on top of a building.

The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.

The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.

Therefore the bowling ball will have more potential energy as it sits on top of the building.

Step-by-step explanation:

The bowling ball has only potential energy as it sits on top of a building.

The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.

The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.

Therefore the bowling ball will have more potential energy as it sits on top of the building.

Answer:

Before the ball hits the ground it has more potential energy but when is going down it looses potential energy and creates kinetic energy so when the ball hits the floor it would have more kinetic energy.

Step-by-step explanation:

Answer:

7 10/9 - 6 7/9

1 4/9

Step-by-step explanation:

the denominator stays the same

Change the FIRST fraction to an improper mixed fraction

then keep the denominators the same and subtract the numerators

subtract the whole numbers

We can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.

Given that, two pairs of corresponding sides and the corresponding included angles are congruent.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

If two pairs of corresponding sides are equal and corresponding included angles are equal.

By SAS congruence theorem, two triangles are congruent.

Therefore, we can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.

To learn more about the congruent theorem visit:

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Answer

wherever the decimal is, put it directly on top of the dividing line thing. Now that the decimal looks like a regular whole number you can divide like you usually would. Whenever you do regular long division, your answer is always going to be on the top of the line. Your answer should have a decimal in it ... and that should be your answer.

Answer:

16 fluid ounces=2 cups

Hope this helps!

Step-by-step explanation:

Answer:

16 fluid ounces

Step-by-step explanation:

1 cup is equal to 8 fluid ounces, so 2 cups is 16 fluid ounces.

Answer:66

Step-by-step explanation:

27.5x4.8/2

Answer:

66 meters squared

Step-by-step explanation:

You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.

Answer:

s = 32

Step-by-step explanation:

-5(s - 30) = -10

-5s + 150 = -10

-5s = -10 - 150

-5s = -160

s = -160/-5

s = 32

Answer:

46

Step-by-step explanation:

47.84 / 1.04, which is 46

The opening price of Company A's stock before the 4% increase to the closing price of $47.84 was $46.00.

To calculate the opening price of Company A's stock at the beginning of the day, before the 4% gain, we need to work backwards from the closing price. Since the stock closed at $47.84 after gaining 4%, we can represent the closing price as 104% of the opening price. Thus, the equation to find the opening price (OP) is:

OP x1.04 = $47.84

Now we solve for OP:

OP = $47.84 / 1.04

OP = $46.00

The opening price of Company A's stock at the beginning of the day was $46.00.

Therefore possible committees are [tex]^5C_3[/tex] =10

Step-by-step explanation:

Given , from a group of 5 candidates , an environmental committee of 3 people is selected.

Therefore possible committees are [tex]^5C_3[/tex] =10

Answer:

[tex]S =19P\\S-19P = 0[/tex]                              

Step-by-step explanation:

We are given the following in the question:

Let P be the number of professor and S be the student in a college.

According to the question:

There are 19 times as many students as professors.

We have to write an equation to show the given relationship between professors and students.

[tex]S =19P\\S-19P = 0[/tex]

The above situation is the situation that represents the given relationship.