The coordinates of three points are A(- 1, - 3) , B(2, 3) and C(6, k) . If AB is perpendicular to BC find (i) the value of k, (ii) the gradient of AC (iii) the acute angle that AC makes with the x-axis.​

Answer:

17 units

Step-by-step explanation:

Use the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Plug in the points and simplify:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(-8 - 7)^2 + (0-8)^2}[/tex]

[tex]d = \sqrt{(-15)^2 + (-8)^2}[/tex]

[tex]d = \sqrt{225 + 64[/tex]

[tex]d = \sqrt{289[/tex]

[tex]d = 17[/tex]

So, the distance between the points is 17 units

Answer:

242.7 dB

Step-by-step explanation:

Answer:

B. 13 units

Step-by-step explanation:

let

(x1 , y1) = (-4 , -6)

(x2 , y2) = (1 , 6)

distance between CD = root (x2 - x1)^3 + (y2 - y1)

= root {1 - ( -4)}^2 + {6 - ( -6)}^2

= root {1 +4}^2 + {6+6}^2

= root 5^2 + 12^2

= root 25 + 144

= root 169

= 13 units ans

Answer: 50.2 is it  

Step-by-step explanation: thats easy

Probability helps us to know the chances of an event occurring. The probability of selecting a heart and then selecting a diamond is 144/2652.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that Two cards are selected with replacement from a standard deck of 52 cards. Therefore, the probability of selecting a heart and then selecting a diamond is,

Probability = (12/52) × (12/51)

Probability = 144/2652

Hence, The probability of selecting a heart and then selecting a diamond is 144/2652.

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Answer:

A,D,E,F

1,4.5,6

The experimental units are subjects.

There are three treatments.

One treatment is a circuit training class.

The factor is the type of class.

ED2021

Answer:

56

Step-by-step explanation:

[2 ÷ (4 - 2) + 8^2] - [2 - (-1) ] ^2

Brackets first

Then parentheses in the brackets

[2 ÷ 2 + 8^2] - [2 - (-1) ] ^2

Exponents in the brackets

[2 ÷ 2 + 64] - [2 - (-1) ] ^2

Divide

[1+64] - [2 - (-1) ] ^2

Add and subtract in the brackets

[65] - [3 ] ^2

Exponents

[65] - [9 ]

Subtract

56

Answer:

Step-by-step explanation:

A) 26*26*26 =17576

B)26*25*24=15600

C)26*26=676

D) 26

Answer:

288 ft³

Step-by-step explanation:

Volume of the pyramid,

base area × height × (1/3)

= (9×8)×12/3

= 72×4

= 288 ft³

Answer:

Simply because x=y2 doesn't imply that y=

√

x

.

The area of the larger circle is 81π square units.

Congruent circles are circles that are similar in pattern.

The formula for calculating the area of a circle is expressed as:

[tex]A = \dfrac{\pi d^2}{4}[/tex]

Given that the area of each of the small circles is 9π, then:

[tex]9 \pi =\frac{\pi d^2}{4}\\9 = \frac{d^2}{4}\\d^2=9*4\\d^2=36\\d=\sqrt{36}\\d=6units[/tex]

This shows that the diameter of one of the small circles is 6units.

Since the diameter of the three circles will be equivalent to the diameter of the larger circle, hence;

Diameter of the larger circle = 3(6) = 18units

Get the area of the larger circle:

[tex]A=\frac{\pi D^2}{4}\\A=\frac{\pi \times 18^2}{4}\\A =\frac{324\pi}{4}\\A= 81\pi[/tex]

Hence the area of the larger circle is 81π square units.

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Answer:

$3735

Step-by-step explanation:

2/5 = 8/20

8/20 + 7/20 = 15/20 = 3/4

3/4*4980 = 3735

Answer:

2110

Step-by-step explanation:

4100-1990=2110

Answer:

392

Step-by-step explanation:

1.49×10⁸/3.8×10⁵ = 392

Answer:

14 nickels

Step-by-step explanation:

One nickel is worth 5 cents, so find the value of 14 nickels by multiplying 14 by 5:

14(5)

= 70

So, 14 nickels is equal to the 70 cents that she has in her purse.

The correct answer is 14 nickels.

angle G

sin inverse (21/29) = 46.4

GH

c^2 - b^2 = a^2

29^2 - 21^2 = a^2

a = √(29^2 - 21^2)

GH = 20

therefore ans is B) <G = 46.4º, <I = 43.6º, GH = 20

9514 1404 393

Answer:

  92°

Step-by-step explanation:

The "givens" tell you the E and F are midpoints of their respective segments. That means EF ║ AB and angles DBF and EFC are "corresponding" angles with respect to transversal BC and those parallel lines. Corresponding angles are congruent, so ...

  m∠DBF = m∠EFC = 92°

Answer: 996 ft2

Step-by-step explanation:

Add up the area of all 6 sides of the prism:

(10 · 13) + (10 · 13) + (10 · 16) + (10 · 16) + (16 · 13) + (16 · 13)

= 130 + 130 + 160 + 160 + 208 + 208

=996 ft²

Answer:

B) 996 ft2

Step-by-step explanation:

Answer:

Nên sử dụng số răng lẻ cho đĩa xích dẫn động kết hợp với số lượng mắt xích chẵn để mài mòn đồng đều trên răng và trục lăn. Trong trường hợp này, một răng cụ thể của bánh xích không tiếp xúc với một mắt xích cụ thể của xích trong mỗi lần quay.

Step-by-step explanation:

Translated

It is preferable to use an odd number of teeth for the driving sprocket in combination with an even number of chain links for uniform wear and tear on the teeth and rollers. In this case, a particular tooth of the sprocket wheel does not come in contact with a particular link of the chain for every rotation.

Answer:

A

Step-by-step explanation:

The volume of prism is b*h, base area is (2.5)*(3.24*(1.1)=8.91. Hence volume is 8.91*6.17=54.97

Answer:

x=4

Step-by-step explanation:

log5(x+1)=1, (x+1)=5, x=4

Answer:

x= -6

Step-by-step explanation:

i got it wrong and the answer is -6

Answer:

Step-by-step explanation:

2x + 3y = 6

2x = 6-3y

x = (6-3y)/2

x - 3y = 9

(6-3y)/2 -3y = 9

(6-3y)/2 -6y/2 = 9

(6-9y)/2 = 9

6 - 9y = 9×2

-9y = 18-6

y = 12/-9

y = -4/3

2x + 3y = 6

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

2x -4 = 6

2x = 6+4

2x = 10

x = 10/2

x = 5

Therefore x = 5 and y = (-4/3)

I used subsitution method

please click thanks and mark brainliest if you like :)

Answer:

x = 5; y = -4/3

Step-by-step explanation:

One equation has 3y. The other equation has -3y. Add the equations to eliminate y and solve for x.

     2x + 3y = 6

(+)     x - 3y = 9

---------------------

      3x        = 15

x = 5

2x + 3y = 6

2(5) + 3y = 6

3y + 10 = 6

3y = -4

y = -4/3

Answer: x = 5; y = -4/3

the answer is on the photo

Answer:

50.854 seconds

Step-by-step explanation:

24.98 + 25.874 = 50.854 seconds

Answer:

175731 is one of the answers of the 6 digit number

some others are:

275732

375733

475734

575735

675735

775734

875732

The 6-digit number is 175731.

The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.

Let the number would be ABCDEF

Given the condition that the value of its thousands of digits is 5,000.

So C = 5

Given the condition that the value of its hundreds of digits is 700.

So D = 7

Given the condition that Its tens digit is 2 less than the thousand digits.

So E = 5-2 = 3

Given the condition that Its hundred thousand digits is the same as the hundred digits.

So B = 7

Therefore, all possible answers:

275732

375733

475734

575735

675735

775734

875732

Hence, the 6-digit number is 175731

Learn more about the place value strategy here:

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Answer:

11.2

Step-by-step explanation:

yz = 11.2

since the corresponding arc of yz and xy are same, their measures will ba same too

Answered by GAUTHMATH

Answer:

11.2

Step-by-step explanation:

good luck!

9514 1404 393

Answer:

  (a)  M = 0.25n +100

Step-by-step explanation:

The distance between the dots on the graph is a rise of 1 grid square and a run of 2 grid squares. If we extend the sequence of dots to the left, we expect to place one at (0, 100). That is, the y-intercept of this function is 100 (eliminates choices C and D).

The rise of 1 grid square represents 25 kg, and the run of 2 grid squares represents 100 CDs. Then the slope of the function (rate of change) is ...

  slope = rise/run = 25/100 kg/CD = 0.25

Then the equation describing the points on the graph will be ...

  M = 0.25n +100

Answer:

the answer to this equation is c (10)

Answer:

14.7

Step-by-step explanation:

tan(73)=48/x

or, x=48/tan(73)

or, x=14.7 (rounded to the nearest tenth)

Answered by GAUTHMATH