Graph parallelogram ABCD on a coordinate plane with vertices A(3,4) B(6,1) C(0,-2) and D(-3,1).
Find the slope of each side.
What do you notice about the slopes?

Answers

Answer 1
SLOPES

AB = (1 - 4) / (6 - 3) = -3 / 3 = -1
BC = (-2 - 1) / (0 - 6) = -3 / -6 = 1/2
CD = (1 - (-2)) / (-3 - 0) = 3 / -3 = -1
DA = (4 - 1) / (3 - (-3)) = 3 / 6 = 1/2

EXPLANATION

Every line has one side parallel to it and I know this because the slope is equal.
Answer 2

A parallelogram, the opposite sides have equal slopes.

To graph the parallelogram ABCD on a coordinate plane, we can plot the given points A(3,4), B(6,1), C(0,-2), and D(-3,1), and then connect them in order to form the parallelogram.

Here are the steps to find the slope of each side:

Plot the Points:

Plot the points A(3,4), B(6,1), C(0,-2), and D(-3,1) on the coordinate plane.

Connect the Points:

Connect the points in order (A to B to C to D to A) to form the parallelogram.

Find the Slope:

The slope of a line passing through two points

(x_1 ,y_1 ) and (x_2 ,y_2 ) is given by the formula m= y_2 -y_1/ x_2- x_1

​Calculate the slope for each pair of consecutive points:

Slope of AB: mAB​ = 1−4/6−3

​Slope of BC: mBC = −2−1/0−6

​Slope of CD: mCD = 1−(−2)/−3−0

​Slope of DA: mDA = 4−1/ 3−(−3)

​Now, observe the slopes:

mAB  and mCD

​are the slopes of opposite sides. They should be equal for a parallelogram.

mBC and mDA are the slopes of the other pair of opposite sides. They should also be equal for a parallelogram.

So, for a parallelogram, the opposite sides have equal slopes.


Related Questions

Jane can pack 48 shirts into each box. round to the nearest compatible numbers to estimate how many boxes she will need to box 1,453 shirts

Answers

1400 would be the answer i belive 

Answer: There are 30 boxes for 1453 shirts.

Step-by-step explanation:

Since we have given that

Number of shirts = 48

Number of box for 48 shirts = 1

We need to adjust number of boxes she will need to box 1453 shirts.

So, number of boxes would be

[tex]\dfrac{1453}{48}\\\\=30.27\\\\\approx 30[/tex]

Hence, there are 30 boxes for 1453 shirts.

Doors for a small cabinets are 11.5 inches long. Doors for the large cabinets are 2.3 times as long as the doors for the small cabinets. How many large doors can be cut from a board that is 10.5 feet long?

Answers

Hello!

1 ft = 12 inches.
10.5 ft = 126 inches.
11.5 × 2.3 = 26.45
126/26.45 = 4.76 (About)

4.76 large doors can be cut from a 10.5 ft long board.

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

Answers

(-2,6) this is the coordinates of the vertex

Answer:

The coordinates of the vertex are [tex] (-2, -6)[/tex]

Step-by-step explanation:

The graph of this function is a parabola that opens up in the Cartesian plane. We can find like this:

[tex]y = (x ^ 2 + 4x +4) +6 = (x + 2) ^ 2 +6[/tex], where,  [tex](y - 6) = (x + 2) ^ 2[/tex]

In the canonical equation of the parabola:

[tex](y - k) = (x + h) ^ 2[/tex], with the point (h, k) as the vertex, [tex]h = -2[/tex] and [tex]k = 6[/tex].

Conclusion: the coordinates of the vertex are [tex](-2, -6)[/tex]

In the game of blackjack played with one​ deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. a winning​ "blackjack" hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. the two cards can be in any order. find the probability of being dealt a blackjack hand. what approximate percentage of hands are winning blackjack​ hands?

Answers

We are given here that a blackjack hand consists of:

1 of the 4 aces = 4 / 52

1 of the 16 cards worth 10 points (10, jack, queen, king) = 16 / 52

 

So assuming that cards are dealt without replacement, therefore the probability of getting a blackjack hand is:

P = 1st is ace * 2nd is 10 pt card + 1st is 10 pt card * 2nd is ace

P = (4 / 52) * (16 / 51) + (16 / 52) * (4 / 51)

P = 0.04827 = 4.83%

 

Therefore there is a 4.83% probability to get a blackjack hand.

 

Final answer:

The probability of being dealt a blackjack hand with a single deck is approximately 0.0483, which translates to about 4.83% of the hands.

Explanation:

To find the probability of being dealt a blackjack hand in a single-deck game, we need to calculate the chances of drawing an ace and a 10-point card (10, Jack, Queen, or King) in any order. There are 4 aces and 16 cards worth 10 points in a deck of 52 cards. The probability of drawing an ace first is 4/52, and then drawing a 10-point card is 16/51, giving us (4/52)*(16/51). Conversely, if a 10-point card is drawn first (16/52) followed by an ace (4/51), the probability is (16/52)*(4/51). Adding the two probabilities gives us the chance of a blackjack in either order:

P(Blackjack) = (4/52)*(16/51) + (16/52)*(4/51) = (64/2652) + (64/2652) = 128/2652 ≈ 0.0483

The approximate percentage of hands that are winning blackjack hands is about 4.83%.

3x-2=x
show work and check

Answers

Solving for the variable x boils down to isolating it, so we need to collect all of our x's on one side of the equation and "undo" any operations being performed on it.

First, we'll move the 2 over to the right side ("undoing" the subtraction on the left side by adding 2 to both sides):

(3x-2)+2=x+2
3x=x+2

Next, we'll subtract x from both sides to collect all of the terms on the left side of the equation:

3x-x=(x+2)-x
2x=2

Finally, "undo" the multiplication being performed on x by dividing both sides of the equation by 2:

(2x)/2=2/2
(2/2)x=2/2

2/2 is, of course, another form of 1, so simplifying, we get:

x=1

A person standing 20 feet from a street light casts a 10 foot shadow. How many times taller is the streetlight than the person? Assume the triangles are similar.

Answers

check the picture below.

they're at a 3:1 ratio, thus, 3 times.

Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable

Answers

multiply 365 by 8

365 * 8 = 2920

so yes it is reasonable

2,920”divided”by 8 = 365so yes

A TV has a listed price of $607.95 before tax. If the sales tax rate is 8.75% , find the total cost of the TV with sales tax included.

Answers

Answer:

  $661.15

Step-by-step explanation:

The addition of tax causes the price to be multiplied by (1+0.0875), so the final price is ...

  $607.95×1.0875 ≈ $661.15

In 34 pound of a spice mix, there is 5/6 cup of cinnamon. How much cinnamon does the spice mix contain per pound? a 5/8 cup b ​ 9/10 ​ cup c ​ 1 1/9 ​ cups d ​ 1 3/5 ​ cups

Answers

Answer:

c. 1 1/9 cups

Step-by-step explanation:

To find cups per pound, divide cups by pounds.

  (5/6 cup)/(3/4 pound) = (5/6)/(3/4) cup/pound

  = (5/6)×(4/3) cup/pound . . . . . . . invert the denominator and multiply

  = 20/18 cup/pound = 10/9 cup/pound = 1 1/9 cup/pound

Will Reward Brainliest!

Answers

Hey there!

So, I solved it for you but I couldn't type it here because they don't have everything I need :) . Please see the pictures below  for the answer.

Best of luck!

If you need help in the future, just send me a message then I'll help you out :)

Garebear~


What are fissures and how are theu created by land subsidence?

Answers

as the land above subsides due to gaps in the soil underneath due to tectonic activity, the area above that sinks to a lower level, requires soil to cover that horizontal hole.

as soil is pulled in to this location, it has to come from somewhere and it comes from the nearby land mass, whilst covering that sink-hole made by this one gap underneath, the land mass splits on other parts where the extra soil came from, causing the fissure.

so the fissure is made from the extra soil used to cover the sink-hole, whilst covering the sink-hole made by the underneath gap, making another gap on the surface above, and that is what the fissure ends up as.

in a sense, the gap underneath kinda tranferred to above at the surface.

When converted to speeds, which list is in order from slowest to fastest?
17 miles in 2 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes;
60 miles in 8 minutes
17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
33 miles in 6 minutes;
26 miles in 4 minutes;
60 miles in 8 minutes;
17 miles in 2 minutes
60 miles in 8 minutes;
33 miles in 6 minutes;
26 miles in 4 minutes;
17 miles in 2 minutes

Answers

speed = distance / time

17 miles in 2 minutes ....17/2 = 8.5 miles per minute
26 miles in 4 minutes.....26/4 = 6.5 miles per minute
33 miles in 6 minutes.....33/6 = 5.5 miles per minute
60 miles in 8 minutes.....60/8 = 7.5 miles per minute

slowest to fastest : 
(1) 33 miles in 6 minutes
(2) 26 miles in 4 minutes
(3) 60 miles in 8 minutes
(4) 17 miles in 2 minutes
I believe that is answer C

Answer:

When converted to speeds, the list which is in order from  slowest to fastest is:

  1)      33 miles in 6 minutes

  2)      26 miles in 4 minutes

  3)      60 miles in 8 minutes

  4)       17 miles in 2 minutes

Step-by-step explanation:

We know that speed is defined as the ratio of distance and time.

Here we are given distance and time in each of the options and we will check the speed of each and arrange them in increasing order.

1)

33 miles in 6 minutes

The speed is:

[tex]\dfrac{33\ \text{miles}}{6\ \text{minutes}}=5.5\ \text{miles\ per\ minute}[/tex]

2)

26 miles in 4 minutes

The speed is:

[tex]\dfrac{26\ \text{miles}}{4\ \text{minutes}}=6.5\ \text{miles\ per\ minute}[/tex]

3)

60 miles in 8 minutes

The speed is:

[tex]\dfrac{60\ \text{miles}}{8\ \text{minutes}}=7.5\ \text{miles\ per\ minute}[/tex]

4)

17 miles in 2 minutes

The speed is:

[tex]\dfrac{17\ \text{miles}}{2\ \text{minutes}}=8.5\ \text{miles\ per\ minute}[/tex]

Since,

[tex]5.5\ \text{miles\ per\ minute}<6.5\ \text{miles\ per\ minute}<7.5\ \text{miles\ per\ minute}<8.5\ \text{miles\ per\ minute}[/tex]

Hence, the increasing order of speed is:

           1→2→3→4

Can someone help me with this?

Answers

check the picture below.

notice, the figure is really just a triangle on top of a semi-circle.

now, the triangle has a base and height of 3 each, and the semi-circle has a diameter of 3√(2), so its radius is half that.

[tex]\bf \begin{array}{llll} \textit{area of a circle}\\\\ A=\pi r^2 \end{array}\qquad \begin{array}{llll} \textit{area of a semi-circle}\\\\ A=\cfrac{\pi r^2}{2} \end{array}\qquad \begin{array}{llll} \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf d=3\sqrt{2}\qquad r=\cfrac{3\sqrt{2}}{2}\impliedby \textit{radius of the semi-circle}\\\\ -------------------------------\\\\ \stackrel{\textit{area of triangle}}{\cfrac{3\cdot 3}{2}}+\stackrel{\textit{area of semi-circle}}{\cfrac{\pi \left( \frac{3\sqrt{2}}{2} \right)^2}{2}}\implies \cfrac{9}{2}+\cfrac{\frac{\pi \cdot 3^2\cdot 2}{2}}{2}\implies \cfrac{9}{2}+\cfrac{9\pi }{2} \\\\\\ \cfrac{9+9\pi }{2}[/tex]

Round 10,386.145 to the nearest tenth

Answers

Rounded to the nearest tenth would be one since the four isn't higher. So the answer would be 10,386.1. You did mean the tenths place right?? because could have also meant tenth(8)

3.1666666667 as a fraction

Answers

31666666667/10000000000
Recognize that 0.16666666..... is equivalent to 1/6.  Try dividing 6 into 1 on your calculator and see what y ou get.

Then 3.166666666666 ...  = 3 1/6   =>  19/6 (as a fraction).

circle P had a circumference of approximately 75 inches. what is the approximate of the radius ,r? use 3.14 for

Answers

circumference=2πr=75
2×3.14×r=75
6.28 r=75
r=75/6.28=11.943=12 inch (nearly)

Answer:

1)  12in

Step-by-step explanation:

The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.

at a school pep rally, the ratio of students who wore red to those who wore yellow is 7 to 3. There are 300 students at the pep rally, and each student wore either red or yellow. How many more students wore red?

Answers

300 total, divided by 10 is 30. 30 x each part of ratio gives:
30 x 7 = 210 - red
30 x 3 = 90 - yellow
210 - 90 = 120 more students
120 more students


I hope this helps and have a wonderful day filled with joy!!

What is the matter with this number: .000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
Is it real?

Answers

possibly. its prob like 1trillion
yes, it is just a really really small fraction of 1

The average person lives for about 78 years. Does the average person live for at least 1,000,000 minutes? (Hint: There are 365 days in each year, 24 hours in each day, and 60 minutes in each hour.)

Answers

Okay. so, there are 1,440 minutes in one day. 1,440 * 365 is 525,600. There are 525,600 minutes in one year. 525,600 * 78 is 40,996,800. The average person lives 40,996,800, which is without a doubt way over 1 million minutes, so yes. The average person lives over 1 million minutes. Living 1 million minutes or less would mean that you would live less than 2 years. That's just barely starting to enter the toddler years.

Answer:

cool kkdkdkkdkkfkkfkfkd

a recipe makes a total of 5 cups a serving of pudding is 3/4 cup how many servings of pudding does the recipe make?

Answers

Final answer:

To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. The recipe makes approximately 6.67 servings of pudding.

Explanation:

To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. In this case, the recipe makes 5 cups and each serving is 3/4 cup. So, to find the number of servings, divide 5 cups by 3/4 cup: 5 cups ÷ (3/4 cup) = 5 cups × (4/3 cup) = 20/3 servings

Therefore, the recipe makes approximately 6.67 servings of pudding.

The manager of a plant nursery bought 120 lb of soil to use for potting plants. The manager can put 5 lb into each of the small pots and 12 lb into each of the large pots. The manager made a sketch to show the line representing the different combinations of pots that can be used. The x-axis represented the number of small pots and the y-axis represented the number of large pots. The manager labeled only the intercepts.

Which points did the manager label?



(0, 12) and (5, 0)
(0, 10) and (24, 0)
(0, 24) and (10, 0)

(0, 5) and (12, 0)

Answers

Set up the equation. The equation is: 5x + 12y = 120. Solve for both variables (x and y). The answer will give you the intercepts.

(0,10) and (24,0) is the final answer.
Yeah the answer is C.

The photography club has 28 members .there are 12 boys in the club . What is the ratio of boys to girls in simplest form?

Answers

First, find the # of girls.  28 total members, less 12 boys, leaves 16 girls.
Write the ratio boys/girls as 12/16.  Reduce this to 3/4.

Karen is riding her bike at 4 miles per hour she wants to show this on a graph what should she draw

Answers

Graph needs to be labeled. I labeled it as shown on picture. It also needs a title. The title can be up to you. :) you can title it “Karen riding her bike”

a garden table and a bench cost $1,000 combined the cost of a garden table is three times the cost of the bench what is the cost of the bench.

Answers

it shold be something like 834 or something liek that

20 randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions - all on the same material. the professor was interested in determining which type of questions the students scored higher. this experiment is an example of a one sample test of means. a two sample test of means. a paired t-test. a test of proportions.

Answers

I think that this an example of a paired t test. Since each student (subject) is given 2 treatments of the same material. 

Solving Equations with Variables on Both Sides

1. (g+4) - 3g = 1 + g

g = 1
g = 4
no solution
identity

2. -6a + 3 = -3(2a - 1)

a=5
a=10
no solution
identity

3. 0.5b + 4 = 2(b+2)

b=0
b=0.5
no solution
identity

4. 8 -(3 + b) = b - 9

7
8
no solution
identity

Answers

1)
g+4-3g=1+g
subtracting g from both sides
4-3g=1
subtracting 4 from both sides
-3g=-3
g=1
2)
-6a+3=-3(2a-1)
extending the right side
-6a+3=-6a+3
adding 6a to both sides
3=3
which is an identity
3)
0.5b+4=2(b+2)
extending the right side
0.5b+4=2b+4
subtracting 0.5 b from both sides
4=1.5b+4
subtracting 4 from both sides
0=1.5b
b=0
4)
8-(3+b)=b-9
subtracting 8 from both sides
-(3+b)=b-17
extending the left side
-3-b=b-17
adding b to both sides
-3=2b-17
adding 17 to both sides
14=2b
b=7

One of the angles formed by two intersecting lines is 42°. What is the measure of the other three angles?

Answers

okay, so first lets think about the angle next to the 42 degree angle.
we know that those two angles must add to 180 degrees, so lets form an equation to figure out the other angle
42 + x = 180
subtract 42 from both sides
x = 138
so 138 degrees is the first AND the 3rd angle
the opposite angle from the 42 degree angle also happens to be 42 degrees

this is because there are two lines in total right?? if you draw out the 42 degree angle and the 138 degree angle, flip that upside down, the angles are the same!!

i hope this helps!! 

Answer:

42, 138, 138

Step-by-step explanation:

Let c be parametrized by x = et sin (10t) and y = et cos (10t) for 0 ≤ t ≤ 2. find the length l of
c. l = 2 correct: your answer is correct.

Answers

Final answer:

To find the length of the curve c parameterized by given equations, we differentiate these equations with respect to t, find the magnitude of the derivative vector, and integrate this magnitude from t = 0 to t = 2.

Explanation:Finding the Length of Parametrized Curve

To find the length L of a curve c parametrized by x = et sin(10t) and y = et cos(10t) for 0 ≤ t ≤ 2, we use the formula for the arc length of a curve given in parametric form. The formula is L = ∫ |c'(t)| dt, where |c'(t)| represents the magnitude of the derivative of the parametric equations. The integral is evaluated over the given interval of t.

Step-by-step Explanation

First, compute the derivatives of the parametric equations: dx/dt and dy/dt.Next, find the magnitude of the velocity vector |c'(t)| = sqrt((dx/dt)^2 + (dy/dt)^2).Finally, integrate |c'(t)| from t = 0 to t = 2.

Using this approach, we find that the length L of the curve c over the interval from 0 to 2 is indeed 2, as verified by the calculus of parametric functions.

−2 is less than or equal to w , and 8 is greater than or equal to w Use w only once in your inequality.

Answers

Attached the solution.

For a circle of radius 3 feet, find the arc lengths subtended by a central angle of 57 degrees.

Answers

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=3\\ \theta = 57 \end{cases}\implies s=\cfrac{57\cdot \pi \cdot 3}{180}[/tex]

Answer: The length of an arc is 2.98 feet.

Step-by-step explanation:

Since we have given that

Radius of a circle = 3 feet

Angle subtended at the centre = 57°

We need to find the length of an arc:

As we know the formula for "Length of an arc":

[tex]Length=\dfrac{\theta}{360^\circ}\times 2\pi r\\\\Length=\dfrac{57}{360}\times 2\times \dfrac{22}{7}\times 3\\\\Length=2.98\ feet[/tex]

Hence, the length of an arc is 2.98 feet.

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