41. Write a proof of the theorem that states if an angle of a quadrilateral is supplementary to both of its consecutive angles, the quadrilateral is a parallelogram.
Given: m∠F + m∠G = 180, m∠F + m∠J = 180
Prove: FGHJ is a parallelogram

What statement proves the theorem?
A. By the Angle Addition Postulate m∠F = m∠J and m∠G = m∠H. So, by the definition of a parallelogram, FGHJ is a parallelogram.
B. By the Converse of the Same-Side Interior Angles Postulate, FJ|| GHand FG||JH. So, by the definition of a parallelogram, FGHJ is a parallelogram.
C. By the Polygon Interior Angle-Sum Theorem, m∠F + m∠G + m∠F + m∠J = 360. So, by the definition of a parallelogram, FGHJ is a parallelogram.
D. By the Converse of the Same-Side Interior Angles Postulate, FJ = JH andFG=JH. So, by the definition of a parallelogram, FGHJ is a parallelogram.

Using compound interest, it is found that Melanie would need to invest a value of $7,710.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In this problem, we have that:

Hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]11900 = P\left(1 + \frac{0.031}{365}\right)^{365(14)}[/tex]

[tex]1.54339P = 11900[/tex]

[tex]P = \frac{11900}{1.54339}[/tex]

[tex]P = 7710[/tex]

Melanie would need to invest a value of $7,710.

To learn more about compound interest, you can take a look at https://brainly.com/question/25781328

Step-by-step explanation:

Hey there!

Given eqautions are:

y = 2x + 1......... (i)

y = 4x - 3...........(ii)

Putting eqaution (ii) in eqaution (i), we get;

4x - 3 = 2x + 1

~ Keep like terms on same side.

4x - 2x = 1+3

~ Perform operations. ( +, -, *, /)

2x = 4

x= 4/2

Therefore, X= 2.

Putting the value of X in eqaution (i)

y = 2x+1

y = 2*2+1

Therefore, y= 5.

Therefore, the ordered pair is (2,5).

Hope it helps...

Which of the following ordered pairs are solutions to the system of equations below? y = 2x + 1 and y = 4x – 3 (1,4) (4,5) (2,5) (3,7)

Step-by-step explanation:

Hey there!

Given eqautions are:

y = 2x + 1......... (i)

y = 4x - 3...........(ii)

Putting eqaution (ii) in eqaution (i), we get;

4x - 3 = 2x + 1

~ Keep like terms on same side.

4x - 2x = 1+3

~ Perform operations. ( +, -, *, /)

2x = 4

x= 4/2

Therefore, X= 2.

Putting the value of X in eqaution (i)

y = 2x+1

y = 2*2+1

Therefore, y= 5.

Therefore, the ordered pair is (2,5).

Hope it helps...

Question:

A charter bus travels 225 miles in  4.5 hours. Assume the  distance travelled is directly  proportional to the time spent.

Write a direct variation equation.

Answer:

[tex]y = 50x[/tex]

Step-by-step explanation:

Let:

y =  distance

x = time

So:

[tex]y = 225[/tex]  and [tex]x = 4.5[/tex]

Since, they are directly proportional: The following relationship exists

[tex]y = kx[/tex]

Where

k = constant of variation

Substitute values for y and x

[tex]225 = 4.5 * k[/tex]

Make x the subject

[tex]k = \frac{225}{4.5}[/tex]

[tex]k = 50[/tex]

Substitute 50 for k in [tex]y = kx[/tex]

[tex]y = 50x[/tex]

Answer:

A=16

Step-by-step explanation:

6=A/4+2

-2       -2

4=A/4

x4  x4

16=A

Answer: The scale is 5cm/m  (5 cm in the drawing are equivalent to 1 meter on the actual pit)

Step-by-step explanation:

When we have an original measure M, and we redraw it with a new scale, where the new measure is m, the scale used is equal to:

scale = m/M.

In this case, we know that:

The pit is 3m, by 5m

and the drawing to scale is 15cm by 25cm

(15cm is the rescaled version of the 3m side, and 25cm is the rescaled version of the 5m side)

Using the equation above, we can find that the scale is:

Scale = 15cm/3m = 5cm/m

and, if we use the other side, we get:

Scale = 25cm/5m = 5cm/m

Both calculations give the same scale, as expected.

Then the scale is 5cm/m, which means that 5 centimeters in the drawing are equivalent to one meter in the real pit.

Answer:

the answer is A.

Step-by-step explanation:

to get the you would use the distributive property to multiple the 4 by the two term in the parentheses.

Answer:

It would be A

Step-by-step explanation:

The Key Skill is: Distribution Property

1) We have the expression 4(6-2x)

2) We have to use distribution property to expand this.

The way distribution property works is that we need to multiply the 6 by the 4 on the outside, and also the -2x by the 4 on the outside.

4 x 6 = 24

4 x -2x = -8x

Therefore, the final expression is 24-8x.  

The only answer that matches this is A.

Hope you understood & have a nice DAY!! :D

Answer:A

Step-by-step explanation:Product means to multiply and A is showing 3/4 is multiplying C.

Answer: p = 4

Step-by-step explanation:

For app one, you start with 140 points, and you lose 10 each time you check your phone.

Then, if you check your phone x times, you will have:

140 - x*10 points in total.

For app two, you start with 80 points, and you lose p points each time you check your phone.

Then, if you check your phone x times, you will have:

80 - x*p points left

We know that when x = 10, you have the same number of points in both apps, then we have the equation:

140 - (10)*10 = 80 - (10)*p

We can solve this for p

140 - 10*10 = 80 - 10*p

140 - 100 = 80 - 10*p

40 = 80 - 10*p

10*p = 80 - 40

10*p = 40

p = 40/10 = 4

Answer:

times 4 or multiply by 4each time

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

[tex] \sqrt{100} = 10[/tex]

Hope it helps you in your learning process.

Answer:

96.56 kilometers

Step-by-step explanation:

Find how many kilometers he will drive by multiplying 60 by 1.60934

60(1.60934)

= 96.56

So, John will drive 96.56 kilometers in one hour

Answer:

x = 36

Step-by-step explanation:

The total angles of a triangle is 180 degrees

(2x - 17) + (x + 53) + x = 180

2x - 17 + x + 53 + x = 180

4x + 36 = 180

Subtract 36 from both sides;

4x = 144

Divide both sides by 4;

x = 36

Answer:

80 cubic units

Step-by-step explanation:

Volume of rectangular pyramid = ⅓*L*W*H

L = 8 units

W = 5 units

H = OP = 6 units

Plug in the values into the equation

Volume = ⅓*8*5*6

Volume = 80 cubic units

Given:

Seeds planted = [tex]1\dfrac{2}{3}[/tex] rows

Crows ate = [tex]1\dfrac{1}{5}[/tex] rows

To find:

The remaining rows of seeds.

Solution:

According to the question,

Remaining rows of seeds = Seeds planted - Crows ate

                                          [tex]=1\dfrac{2}{3}-1\dfrac{1}{5}[/tex]

                                          [tex]=\dfrac{1(3)+2}{3}-\dfrac{1(5)+1}{5}[/tex]

                                          [tex]=\dfrac{3+2}{3}-\dfrac{5+1}{5}[/tex]

                                          [tex]=\dfrac{5}{3}-\dfrac{6}{5}[/tex]

Taking LCM, we get

[tex]=\dfrac{5(5)-3(6)}{15}[/tex]

[tex]=\dfrac{25-18}{15}[/tex]

[tex]=\dfrac{7}{15}[/tex]

Therefore, [tex]\dfrac{7}{15}[/tex] rows of seeds are left.

652.50

Step-by-step explanation:

1450 x .09 x 5 = 652.50

Step-by-step explanation:

It's a quadratic equation which simplifies to x²+2x-8

Now if you want to "solve" it then you must be a little more particular with your question because you can do many things with a quadratic equation, you can:

1. Factorise it

2. find the zeros

3. graph it

4. describe the nature of its roots,etc

but let me help you factorise it

x²+2x-8

x²+4x-2x-8

x(x+4)-2(x+4)

(x-2)(x+4)

Answer: Your answer is 61.25cm hope this helps!

Step-by-step explanation:

[tex]2x + 8 = 8x - 4 \\ 2x - 8x = - 8 - 4 \\ - 6x = - 12 \\ 6x = 12 \\ \\ x = {2} [/tex]

Answer:

JL = 8 m

KD = 8 m

Step-by-step explanation:

By 45° - 45° - 90° triangle theorem:

[tex]JK = \frac{1}{ \sqrt{2} } JD \\ \\JK = \frac{1}{ \sqrt{2} } \times 8 \sqrt{2} \\ \\ \red{JK = \boxed{8 }}\: m \\ \\ KD= \frac{1}{ \sqrt{2} } JD \\ \\KD = \frac{1}{ \sqrt{2} } \times 8 \sqrt{2} \\ \\ \purple{ KD = \boxed{8 } }\:m\\ \\[/tex]

Answer:

x = 5, ST = 45

Step-by-step explanation:

Given that m bisects SU, then

ST = TU , that is

9x = 4x + 25 ( subtract 4x from both sides )

5x = 25 ( divide both sides by 5 )

x = 5

Thus

ST = 9x = 9 × 5 = 45

Answer:

Equivalent fractions

3/10 = 6/20

1/4 = 5/20

4/5 = 16/20

Step-by-step explanation:

For

3/10

We Multiply numerator and Denominator by 2

= 3×2/10 × 2

= 6/20

For 1/4

We Multiply numerator and Denominator by 5

= 1×5/4× 5

= 5/20

For 4/5

We Multiply numerator and Denominator by 4

= 4×4/5× 4

4/5 = 16/20

Answer:

6 -6 -4

Step-by-step explanation:

Answer:

Income tax is money the government takes from your paycheck when you have a job

The government automatically takes income tax out of your paycheck every month