Find the slope between the
following points:
(-3,3), and (5, 10)

Answer:

a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus

b. The equation of the diagonal line AC is y = 5 - x

The equation of the diagonal line BD is y = 5 - x

c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other

Step-by-step explanation:

The vertices of the given quadrilateral are;

A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)

a. The length, l, of the sides of the given quadrilateral are given as follows;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

The length of side AB, with A = (1, 4) and B = (6, 6) gives;

[tex]l_{AB} = \sqrt{\left (6-4 \right )^{2}+\left (6-1 \right )^{2}} = \sqrt{29}[/tex]

The length of side BC, with B = (6, 6) and C = (4, 1) gives;

[tex]l_{BC} = \sqrt{\left (1-6 \right )^{2}+\left (4-6 \right )^{2}} = \sqrt{29}[/tex]

The length of side CD, with C = (4, 1) and D = (-1, -1) gives;

[tex]l_{CD} = \sqrt{\left (-1-1 \right )^{2}+\left (-1-4 \right )^{2}} = \sqrt{29}[/tex]

The length of side DA, with D = (-1, -1) and A = (1,4)   gives;

[tex]l_{DA} = \sqrt{\left (4-(-1) \right )^{2}+\left (1-(-1) \right )^{2}} = \sqrt{29}[/tex]

Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus

b. The diagonals are AC and BD

The slope, m, of AC is given by the formula for the slope of a straight line as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Therefore;

[tex]Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1[/tex]

The equation of the diagonal AC in point and slope form is given as follows;

y - 4 = -1×(x - 1)

y = -x + 1 + 4

The equation of the diagonal AC is y = 5 - x

[tex]Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1[/tex]

The equation of the diagonal BD in point and slope form is given as follows;

y - 6 = 1×(x - 6)

y = x - 6 + 6 = x

The equation of the diagonal BD is y = x

c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;

The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs

The point of intersection of the two diagonals is given as follows;

5 - x = x

∴ x = 5/2 = 2.5

y = x = 2.5

The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.

Answer:

20%

Step-by-step explanation:

Original cost = $46.25

Decreased cost = $37.00

Decrease in cost = 46.25 - 37.00 = $9.25

Percentage decrease

[tex] = \frac{9.25}{46.25} \times 100 \\ \\ = \frac{92500}{4625} \\ \\ = 20\% [/tex]

Answer:we can solve the problem by setting a simple proportion.

We know that 22 pancakes can feed 8 people, so we have to find the number x which corresponds to the number of people that can be feeded with 55 pancakes:

Solving the proportion, we find

So, 55 pancakes can feed 20 people.

Step-by-step explanation:

Answer: yes

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

First, put them in numerical order: 2, 4, 5, 7, 8, 9, 12

Then cross out one from each side until  you get to the middle

The median of the given data set  7,5, 12, 8, 2,9,4 is 7.

Mode is the highest frequency number while the median is the middle value of a data set after writing either increasing or decreasing manner.

For example;

Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.

Given the data set,

7,5, 12, 8, 2,9,4

If we write it in increasing order then,

2, 4, 5, 7, 8, 9, 12

Now median is middle value so here 7 is in between 3 - 3 from left and right.

Hence "The median of the given data set  7,5, 12, 8, 2,9,4 is 7".

To learn more about mode and median,

https://brainly.com/question/300591

#SPJ2

Answer:

Answer is 159

Step-by-step explanation:

Use PEMDAS

First, solve paranthesis

10² + 8² - 5

Then from left to right, solve the exponents

100 + 8² - 5

100 + 64 - 5

Then, add

164 - 5

Subtract

159

Answer:

=159

Step-by-step explanation:

10^2 + (3+5)^2 - 5

10^2 = 10 x 10 = 100

100+ (3+5) (3+5) - 5

100+(8)(8)-5

100+64-5

164-5

=159

Hope this helps! :)

Answer:

The ribbon cost is $77

Step-by-step explanation:

Firstly, we need to get the 3rd side of the triangle

This represents the hypotenuse since we have 2 legs, we need the side connecting the legs

To get this, we use Pythagoras’ theorem

This states that the square of the hypotenuse equals the sum of the squares of the two other sides

Let the hypotenuse be marked x

Thus;

x^2 = 56^2 + 33^2

x^2 = 3136 + 1089

x^2 = 4225

x = square root of 4225

x = 65 feet

So the length of all the sides will be;

56 + 33 + 65 = 154 feet

So the cost of the ribbon will be;

154 feet. * 0.5

= $77

Answer and Step-by-step explanation:

36 dollars minus 17.85 dollars equals $18.15, or 18 dollars and 15 cents.

All you have to do is subtract 36 by 17.85

36 - 17 = 19

100 - 85 = 15

1 is subtracted from 19 because of the decimal.

18.15

#teamtrees #WAP (Water And Plant)

Answer:

$24.95X.095=$2.37

Answer:

Step-by-step explanation: 3.27

Answer:

The first side is 11.5cm, the second is 11.5cm×2 = 23cm, the third is 11.5cm × 3 = 34.5cm,

and the fourth side is 11.5cm × 6 = 69cm.

Step-by-step explanation:

A quadrilateral is a 4 sided shape, while perimeter is the addition of all the sides of the quadrilateral. Since the sides of the quadrilateral is not stade, assume the sides of the quadrilateral is x, therefore 1:2:3:6 = x:2x:3x:6x. The total ratio is x+2x+3x+6x=12x, therefore 12x= 138 , x = 11.5cm, Therefore the first side is 11.5cm, the second is 11.5cm×2 = 23cm, the third is 11.5cm × 3 = 34.5cm, and the fourth is 11.5cm × 6 = 69cm.

Answer:

b

Step-by-step explanation:

to find the number of subscribtion sold we divide the money she made by the price of subscription

monday:

42.80/5.35=8 subscriptions sold

tuesday:

64.20/5.35=12 subscriptions sold

wednesday:

74.90/5.35=14 subscriptions sold

8+12+14=34 subscriptions sold in 3 days

Answer:

34 subscriptions she sold

Answer:

88$

Step-by-step explanation:

Answer:

63 degrees

Step-by-step explanation:

All angles add up to 180

(5x+6) + (4x-6) + (5x-2) = 180

put like terms together

5x+4x+5x + 6-6-2 = 180

14x -2 = 180

add 2 to both sides

14x = 182

divide both sides by 14

x=13

angle G is 5x-2, so if x=13, angle G is 5(13) -2

= 65  -2 = 63 degrees

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and crown if right

The approximate unit price for the juice is about $0.50

Step-by-step explanation:

To find the unit price of an item, you must divide the price ($1.35) by how many units the item has (64 ounces). So 64 divided by 1.35 would be 47, or 50 since it's asking for the approximate unit price. Convert it and you have your answer. $0.50. Hope this helps :) I apologize if it's not completely correct

Answer:

48.69

Step-by-step explanation:

Step-by-step explanation:

30% off $53.50

= 70% of $53.50

= $53.50 * (70/100) = $37.45.

Answer:

r = 0.1

Step-by-step explanation:

Constant proportionality or slope(rate of change) is found by Y divided by X.

1.4(y) ÷ 14(x) = 0.1(slope)

1.6(y) ÷ 16(x) = 0.1(slope)

2.1(y) ÷ 21(x) = 0.1(slope)

Check Work:

14 x 0.1 = 1.4

16 x 0.1 = 1.6

21 x 0.1 = 2.1

Answer:

1/10.

Step-by-step explanation:

The proportionality equation is given to you: [tex]y = rx[/tex]

Next, plug in the given [tex]x[/tex] and [tex]y[/tex] variables into the equation:

When: [tex]x = 14[/tex] & [tex]y = 1.4[/tex]

[tex]1.4 = r(14)\\1.4 = 14r\\(1.4)/14 = (14r)/14\\1.4/14 = r\\r = 0.1[/tex]

When: [tex]x = 16[/tex] & [tex]y = 1.6[/tex]

[tex]1.6 = r(16)\\1.6 = 16r\\(1.6)/16 = (16r)/16\\r = 1.6/16\\r = 0.1[/tex]

When: [tex]x = 21[/tex] & [tex]y = 2.1[/tex]

[tex]2.1 = r(21)\\[/tex]

[tex]21r = 2.1\\(21r)/21 = (2.1)/21\\r = 2.1/21\\r = 0.1[/tex]

r = 0.1 in all of the given, ∴ 0.1 is your answer. Change the decimal into a fraction:

0.1 = 1/10

1/10 is your answer.

~

Answer:

Cube root of 864 can be represented as 3√864.

Answer:

9.52441

Step-by-step explanation:

[tex] \sqrt[3]{864} [/tex]

[tex] = \sqrt[3]{(9.524 \times 9.524 \times 9.524)} [/tex]

[tex] = 9.52441[/tex]

Answer: 72

Step-by-step explanation:

y=6, z=12

yz=6 x 12=72

Answer:

y=-2x+5

Step-by-step explanation:

thats the equation because you use the formula, y=mx+b. b is the y intercept (the verticle straight line) and m is the slope. hope this helped!!

Answer:

X = 2

Step-by-step explanation:

2 x 2 x 2 = 8

Hope this helps. Pls give brainliest.

Answer:

2 :)

Step-by-step explanation:

Answer:

The equation x + 2y = -1 describes a line with a slope of -1/2 that contains the point (-5, 2) ⇒ D

Step-by-step explanation:

Let us use this rule to solve the question

The slope of the line is [tex]-\frac{1}{2}[/tex] and the line contains the point (-5, 2)

We want to find which equation has the same slope and contains the point

A.

∵ x + 2y = 1

∴ a = 1 and b = 2

→ Use the rule above to find m

∴ m = [tex]\frac{-1}{2}[/tex]

∴ The line has the same slope

→ Let us find if the line contains the point (-5, 2), by substituting x by -5

   and y by 2 in the left side of the equation if the answer equals

   the right side, then the line contains it

∵ L.S = -5 + 2(2) = -5 + 4 = -1

∵ R.S = 1

∴ L.S ≠ R.S

∴ The line does not contain the point (-5, 2)

B.

∵ x - 2y = -1

∴ a = 1 and b = -2

→ Use the rule above to find m

∴ m = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

∴ The line does not have the same slope

C.

∵ x - 2y = 1

∴ a = 1 and b = -2

→ Use the rule above to find m

∴ m = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

∴ The line does not have the same slope

D.

∵ x + 2y = -1

∴ a = 1 and b = 2

→ Use the rule above to find m

∴ m = [tex]\frac{-1}{2}[/tex]

∴ The line has the same slope

→ Substitute x by -5 and y by 2 in the left side

∵ L.S = -5 + 2(2) = -5 + 4 = -1

∵ R.S = -1

∴ L.S = R.S

∴ The line contains the point (-5, 2)

The equation x + 2y = -1 describes a line with a slope of -1/2 that contains the point (-5, 2)

Answer:

A and B are parallel to D and C

or

A and D to B and C

basically do a line and expand them if they touch they are not parralelogram but if they don't they are

Answer:

1/625

Step-by-step explanation:

simply

(-1/5)^4

1/625

Answer:

The answer is 1/625

Step-by-step explanation:

hope this helps

Answer:

$7.20

Step-by-step explanation:

The first step is to convert 1 1/4 to decimal form. 1/4=0.25, which when added to the 1 gives a total weight of 1.25 pounds. Dividing this by the price to find the unit price, you get 9/1.25=$7.20 per pound of turkey. Hope this helps!

Answer:

s = 4

Step-by-step explanation:

The equation for the line of best fit for the data is p=25s+40.

Where p is no. of points and s is no. fo strikes

We need to find the number of strikes made by a bowler with 140 points.

Put p = 140

p=25s+40

140 = 25s+40

Subtract 40 to both sides,

140-40 = 25s+40-40

100 = 25s

⇒ s = 4

So, there are 4 strikes made by a bowler with 140 points.