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.​

Answers

Answer 1

9514 1404 393

Answer:

  (i) k = 1

  (ii) 4/7

  (iii) arctan(4/7) ≈ 29.7°

Step-by-step explanation:

(i) A graph of the given points is helpful. It shows us the slope of AB is ...

  mAB = rise/run = 2/1 = 2

so the slope of BC must be the opposite reciprocal, -1/2.

Point C is 6-2 = 4 units to the right of point B, so will be (-1/2)(4) = -2 units from point B in the vertical direction. That is, ...

  k = 3 -2

  k = 1

__

(ii) The gradient of AC is found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-3))/(6 -(-1))

  mAC = 4/7

__

(iii) The angle that line AC makes with the +x axis is the arctangent of the slope:

  arctan(4/7) ≈ 29.7° . . . angle between AC and +x axis

The Coordinates Of Three Points Are A(- 1, - 3) , B(2, 3) And C(6, K) . If AB Is Perpendicular To BC

Related Questions

A speed training service wants to explore the effectiveness of some of the classes offered to their clients. They randomly select 300 high school athletes and record their 50-meter dash time. The 300 high school athletes are then randomly assigned to three groups with 100 in each. One hundred athletes will take a circuit training class, 100 athletes will take an interval training class, and 100 athletes will take a plyometrics training class. At the end of 10 weeks of taking these classes, their 50-meter dash time will be recorded a second time. Their times will be analyzed to see which class showed the greatest overall improvement in times.


Select all the sentences that correctly identify the components of the experiment.


The experimental units are subjects.

The subjects are the 50 athletes.

There is one treatment, the 50-meter dash.

There are three treatments.

One treatment is a circuit training class.

The factor is the type of class.

There are 10 levels of the factor.

Answers

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

Tại sao số mắt xích không được là bội số của số răng đĩa xích

Answers

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.

What is the solution to the system of equations below?

2x+3y=6
x-3y=9

Answers

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

Which of the following shows the extraneous solution to the logarithmic equation below?

2 log Subscript 5 Baseline (x + 1) = 2

Answers

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

Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a heart and then selecting a diamond.

Answers

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.

What is Probability?

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.

Learn more about Probability:

https://brainly.com/question/795909

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50% of 80
50% of 48
50% of 15
25% of 120
25% of 90

Answers

1. 40
2. 24
3. 7.5
4. 30
5. 22.5

Given the linear function f(x) 2/3x + 6 evaluate f(-6)

Answers

the answer is on the photo

During a​ one-month promotional​ campaign, Fran's Flix gave either a free DVD rental or a​ 12-serving box of microwave popcorn to new members. It cost the store ​$1 for each free rental and ​$2 for each box of popcorn. In​ all,46 new members were signed up and the​ store's cost for the incentives was ​$86. How many of each incentive were given​ away?

Answers

43 for popcorn or 86 for rental dvds

What is the distance between point C and point D?

Question 5 options:


A)


17 units


B)


13 units


C)


12 units


D)


√85 units

Answers

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

12 units is the answer for ur question

the image is located below

Answers

Answer:

288 ft³

Step-by-step explanation:

Volume of the pyramid,

base area × height × (1/3)

= (9×8)×12/3

= 72×4

= 288 ft³

what represent the relationship between the total mass of a crate

Answers

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

Can someone please help
Me

Answers

Answer:

$3735

Step-by-step explanation:

2/5 = 8/20

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

3/4*4980 = 3735

Help
Plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

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

please help me with this

Answers

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°

Y=square root of x compare to y= - square root of x how they differ and why

Answers

Answer:

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

x

.

Mariah swam her leg of the race in 24.98 seconds and Janet swam her leg of the relay race in 25.874 seconds. What was their combined time for their part of the relay?

Answers

Answer:

50.854 seconds

Step-by-step explanation:

24.98 + 25.874 = 50.854 seconds

Hey I need helping with solving thank you

Answers

Answer:

the answer to this equation is c (10)

Write a 6-digit number that fits the description.

1. The value of its thousands digit is 5,000.
2. The value of its hundreds digit is 700.
3. Its tens digit is 2 less than the thousands digit.
4. Its hundred thousands digit is the same as the hundreds digit.

The number is?​

Answers

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.

What is the place value strategy?

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:

brainly.com/question/654419

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What is the volume of this regular prism?

54.97 cubic inches
8.91 cubic inches
109.95 cubic inches
21.99 cubic inches

Answers

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

Find the surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet.
988 ft2
996 ft2
980 ft2
1000 ft2

Answers

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:

Please help‼️
Given O below, if XY and YZ are congruent, what is the measure of chord XY?

Answers

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!

Joes bait shop brought in a gross profit in sales of $4,100.00 in the month of June. During the same month their operating expenses totaled $1990.00. Calculate the net income of the bait shop for the month of June

Answers

Answer:

2110

Step-by-step explanation:

4100-1990=2110

please help me asap!!!!!

Answers

Answer:

392

Step-by-step explanation:

1.49×10⁸/3.8×10⁵ = 392

What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid?

Answers

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

(a) How many different three-letter initials can people have: , (b) How many different three-letter initials with none of the letters repeated can people have: , (c) How many different three-letter initials with letters repeated begin with an X: , (d) How many different three-letter initials begin with a F and end in a D: .

Answers

Answer:

Step-by-step explanation:

A) 26*26*26 =17576

B)26*25*24=15600

C)26*26=676

D) 26

Laura makes a sound that 80.9 dB loud. Sarah makes a sound that is 3 time as intense. What is the loudness of Sarah's sound (in dB)

Answers

Answer:

242.7 dB

Step-by-step explanation:

llana has 70¢ in her purse. All the coins have the same value. What could describe all the coins she has in her
purse?
71 pennies
8 dimes
1 0 0
14 nickels
3 quarters

Answers

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.

[2 ÷ (4 - 2) + 8^2] - [2 - (-1) ] ^2

A. 62
B.60
C.56

Answers

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

in the figure above, three congruent circles are tangent to eachother and have centers that lie on the diameter of a larger circle. if the area of each of these small circles is 9pi, what is the area of the larger circle?
a) 36pi
b) 49pi
c) 64pi
d) 81pi

Answers

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.

Learn more on the area of circles here: https://brainly.com/question/12298717

Find the missing side. Round your answer to the nearest tenth

Answers

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

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