Given: Line segment A B is parallel to line segment D C and Measure of angle 2 equals measure of angle 4
Prove: Line segment A D is parallel to line segment B C

A parallelogram has points A B C D. Angle D A B is angle 1, Angle A B C is angle 2, Angle B C D is angle 3, and angle C D A is angle 4.

A 2-column table with 7 rows. Column 1 is labeled statements and has entries line segment A B is parallel to line segment D C, measure of angle 2 = measure of angle 4, angle 1 and angle 4 are supplements, question mark, measure of angle 1 + measure of angle 2 = 180 degrees, angle 1 and angle 2 are supplements, line segment A D is parallel to line segment B C. Column 2 is labeled reasons with entries given, given, same side interior angles theorem, definition of supplementary angles, substitution, definition of supplementary angles, converse same side interior angles theorem.



m∠1 = m∠4
m∠2 = m∠3
m∠1 + m∠4 = 180°
m∠2 + m∠3 = 180°

Answer:

=>A. -6x - 4

Step-by-step explanation:

=>-4(x + 2) - 2x + 4

=> -4x-8-2x+4

=> -6x-4

Using the normal distribution, it is found that there is a 0.0571 = 5.71% probability that the total weight exceeds the maximum weight.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, we have that the parameters are given as follows:

[tex]\mu = 60, \sigma = 10, n = 10, s = \frac{10}{\sqrt{10}} = 3.1623[/tex]

The probability that the total weight exceeds the maximum weight is the probability of a sample mean above 650/10 = 65 kg, which is one subtracted by the p-value of Z when X = 65.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{65 - 60}{3.1622}[/tex]

Z = 1.58.

Z = 1.58 has a p-value of 0.9429.

1 - 0.9429 = 0.0571.

0.0571 = 5.71% probability that the total weight exceeds the maximum weight.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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The relationship that describes the measure of the inscribed angle and the measure of the intercepted arc is: 2(m∠JKL) = m(JL)

The inscribed angle theorem states in a circle, the measure of the angle that is inscribed is always half of the arc that is intercepted. Which means that the intercepted arc is twice the measure of the inscribed angle.

In the image given:

Therefore, the relationship that describes the measure of the inscribed angle and the measure of the intercepted arc is: 2(m∠JKL) = m(JL)

Learn more about the inscribed angle theorem on:

https://brainly.com/question/5436956

Answer:

2(m∠JKL)=mJL

Step-by-step explanation:

I took the test :)

Answer:

42 ft²

Step-by-step explanation:

Rectangle Area: L * W

[tex]\bf A=(8ft)(6ft)[/tex]

[tex]\bf 48 \; ft^2[/tex]

[tex]\bf A= (3ft)(2ft)[/tex]

[tex]\bf 6\;ft^2[/tex]

[tex]\bf 48ft^2-6ft^2[/tex]

[tex]\boxed{\bf 42\; ft^2}[/tex]

Answer:

42

Step-by-step explanation:

6 x 6 is 36. 3 x 2 is 6. 36 + 6 is 42.

Answer:

never.

Step-by-step explanation:

Answer: (x-4)

Step-by-step explanation:

x^2 + 8x +15 is the area

x+5 is the length

x+3 is the width

(x+5)(x+3)=

x^2 + 3x +5x +15

x^2 +8x + 15

Answer:

(x-4)

Step-by-step explanation:

Region A is the region that represents the graph of the feasible region

For the given constraints

y ≥ 2x x y ≤ 14 y ≥ 1 5x y ≥ 14 x y ≥ 9

Let's look to the graph to answer the question

y ≥ 2x represented by the line shown in figure

The sign of inequality is greater than, then the shaded part will

be over the line

The solution is in the A region

x + y ≤ 14 represented by the line shown in figure

The sign of inequality is smaller than, then the shaded part will

be under the line

The solution is in A or B or C regions

y ≥ 1 represented by the line shown in figure

The sign of inequality is greater than, then the shaded part will

be over the line.

The statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

inequality means in the equation

The solution is in A or B or C regions

5x + y ≥ 14 represented by the line shown in figure

The sign of inequality is greater than, then the shaded part will

be over the line

The solution is in A or B or C regions

x + y ≥ 9 represented by the line shown in figure

The sign of inequality is greater than, then the shaded part will

be over the line

The solution is in A or B regions

From all the above the common region in the five inequalities is A

Region A is the region that represents the graph of the feasible region

for the given constraints.

To learn more about the inequality visit:

https://brainly.com/question/24372553

Answer:

A

Step-by-step explanation:

The Answer is A on Edge as of 2022

Answer:

12/25

Step-by-step explanation:

48%   is the same as 48/100 = 12/25

Check the picture below.

[tex]\textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=29\\ h=48\\ V=5568 \end{cases}\implies \begin{array}{llll} 5568=(29)w(48)\implies \cfrac{5568}{(29)(48)}=w \\\\\\ 4=w \end{array}[/tex]

Answer:

75

Step-by-step explanation:

15/12

there are 1.25 boys for every girl in the gaming club

60*1.25=75

Answer:

Step-by-step explanation:

Use pythogeream theroem:

Explanation in image attached :)

Answer:

5 : 7

Step-by-step explanation:

First figure  surface    a * a * 6  = 6 a^2

  now scale the dimesion by x

      ax * ax * 6 =  6 a^2 x^2

                        =  150 x^2   = 294

                           x^2 = 294/150

                            x = 7 : 5      is th ratio of the larger to the smaller

The product of the two equation in which one is binomial equation another quadratic equation,  is 12a³+2a²+23a+18.

To multiply the two equation, each term of the first equation is multiples from the second term.

The first equation given in the problem is,

[tex]3a+ 2[/tex]

The second equation given in the problem is,

[tex]4a^2 -2a+ 9[/tex]

The product of these two equations are,

[tex]p=(3a+2)\times (4a^2 -2a+ 9)\\p=12a^3-6a^2+27a+8a^2-4a+18\\p=12a^3+2a^2+23a+18[/tex]

Hence, the product of the two equation in which one is binomial equation another quadratic equation,  is 12a³+2a²+23a+18.

Learn more about the multiplication of two equation here;

https://brainly.com/question/69383

Answer: D:   12a^3 + 2a^2 + 23a + 18

Step-by-step explanation: got it right :)

Answer:

t = 2

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{4}[/tex] (7t + 2) = 2 , then

7t + 2 = 4² = 16 ( subtract 2 from both sides )

7t = 14 ( divide both sides by 7 )

t = 2

Answer:

t = - 4/13

Step-by-step explanation:

Answer:

45 degree angle

Step-by-step explanation:

Let's say that the line crossing the middle of quadrant four was on the y-axis, that would be known as a 90 degree angle.  Since it was cut in half, that would become a 45 degree angle.

Answer:

The answer to 30*120 is 3,600

Answer:

30 times 120 equals 3600

Step-by-step explanation:

One thing that is really easy to use to multiply is a calculator (either online or a hand-held one). But here is how you can multiply without a calculator...

Set up an equation on a piece of paper like how it is shown right below...

  30

x 120

Then, times the last digit (so the zero) of the bottom number. (But it doesn't really matter what order you put them in). Then, times it by the last digit of the top number. So that would equal 0! So as shown below, you would put the answer like so...

  30

x 120

      0

Then, you do 0 (last digit of bottom number) times 3 (you keep going left of the top number's digits). So that would also equal 0.

   30

x 120

   00

     0

Then you add a zero below, since we are now moving on to the next number to the left of the last digit of the bottom number (hopefully this is making sense). Then you do the exact same thing.

   30

x 120

   00

 600

Now that we're done with that, we add two zeros this time, since we are in the hundreds now. So it is to the next number now! (1) And then we do the exact same thing again!

   30

x 120

   00

 600

3000

Alright, that's done! Now we add all those answers together (0+600+3000)

And that gives us our answer! 3600!

Hopefully that made sense! :)

Answer:

cylinder

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

The range for the given function is ~

[tex]\qquad \tt \dashrightarrow \: - 6 \leqslant y \leqslant 9[/tex]

Because, maximum value of y is 9 and minimum value is -6. so range lies between these two points (including them).

Step-by-step explanation:

Match in the given pattern

1-->F

2-->A

3-->E

4-->C

5-->B

6-->D

I hope it helps you

Answer:

f(8)= -16 + 6

Step-by-step explanation:

f(x) = -2x + 6(4-3)

f is a function. In this case, a function of variable x. So wherever x is written, swap it by the variable of a number which is 8.

Answer:

I think

Step-by-step explanation:

25x9

is 225

which should be it

The rule for a rotation by 270 ° about the origin is (x,y) ⇒ (y,-x)

Rotating the triangle PQR to create an image of the triangle involves moving the triangle PQR in a circular direction.

The coordinates of the given triangle are:

Using the rule, the coordinates now are:

In the attatchment, the answer is in pictoral form.

Answer:

a_n = 9n - 11

Step-by-step explanation:

Explicit rule for an arithmetic sequence is a_n = a_1 + (n-1) d

a_1 is the first term of the sequence

d is the common difference. To find d you pick a number in the sequence and subtract it by the previous number. For example, 7 - (-2) = 9

16 - 7 = 9 so, d = 9

a_1 = -2 since it is the first term. Now substitute these numbers into the formula.
a_n = -2 + (n-1)(9)

And then we simplify.
9 • n = 9n

9 • -1 = -9
Then we’ll have a_n = -2 + 9n -9 and well simplify even further.
-2 -9 = -11

So we get

a_n= 9n -11

hope that helped! God bless you!!

x=2

Hope it helps.

Do comment if you have any query.

Add 12 to the current age:

Y = 15 + 12

Answer:

y=15x12

Step-by-step explanation:

Answer:

33.

Step-by-step explanation:

Arithmetic sequence with a1 = 5 and d = 2.

nth term = a1 + d(n - 1), so

15th term = 5 + 2(15 - 1)

=  5 + 2*14

= 33.