- The line AB has equation 5x – 2y = 7. The point A has coordinates (1, -1) and the point B has coordinates (3,k). (a) (i) Find the value of k. (ii) Find the gradient of AB. (b) Find an equation for the line through A which is perpendicular to AB. (c) The point C has coordinates (-6, -2). Show that AC has length pV2, stating the value of p. ​

Answers

Answer 1

Step-by-step explanation:

For finding k we'll have to plug in the x-value of the coordinate (3,k) into the equation, and solve for the y:

5(3) - 2y = 7

15 - 2y = 7

2y = 8

y = 4 => k =4

2) I assume the gradient is the slope of the line. If so, just isolate the y in the original equation and see what's the coefficient of the x:

-2y = -5x + 7

y = (5/2)x + 7/2 => the gradient is 5/2

3) the condition of perpendicularity is expressed by the following relation:

a * a' = -1

Where a is the slope of the first line and a' of the second line. We need to find a' that will be:

-1/a = -1/(5/2) = -2/5

The perpendicular line will be:

y = (-2/5)x + b

We need to find  b, and we know that this line passes through A (1,-1):

-1 = (-2/5)*1 + b

b = -1+(2/5) = -3/5

The equation will be:

y = (-2/5)x - 3/5.

4) I don't know what that symbol means (pV2).


Related Questions

M is the midpoint of the segment. Find the length of XM.

Answers

Answer:

x=2 and XM=11

Step-by-step explanation:

because M is the midpoint of the line, you know that both XM and ZM are equal and you know an expression for the lengths of both of these.

set these expressions equal and solve:

4x+3=3x+5 so by subtracting the 3x from the right side, moving it over to the left and subtracting 3 from the left side to move it over to the right, you get:

x=2

then to find XM, plug in this value of x to get XM=11

4(2)+3=11

100 POINTS WILL AWARD BRAINLIEST PLEASE HELP
(IMAGE INCLUDED)
In the image below, the m

Answers

Answer: 67°.

Step-by-step explanation:

1) m∠PMR=m∠LMN=3x+19°;

2) m∠LMN+m∠LMP=180°, it can be written as 3x+19+9x-31=180;

3) if to solve the equation 3x+19+9x-31=180, then x=16;

4) m∠PMR=3x+19=48+19=67°.

Find x

Linear pairs are supplementary

9x-31+3x+19=18012x-12=180x-1=15x=15+1=16

So

opposite angles are equal

m=9(16)-31=144-31=113°

Which of the following is a geometric sequence with a common ratio of 2?

A) 14, 28, 56, 112, ...
B) 64, 32, 16, 8, ...
C) 87, 85, 83, 81, ...
D) 14, 16, 18, 20, ...

Answers

Answer:

A

Step-by-step explanation:

Geometric sequences involve multiplication and the ratio of 2 means each number is multiplied by 2 to get the next number.

please help me in this question
3(x-2)=2x+10​

Answers

Answer:

[tex]3(x-2)=2x+10\\3x-6=2x+10 | +6\\3x=2x+16 | -2x\\x = 16[/tex]

30.

a) [tex]180^{0} - 134^0-22^0=24^0[/tex]

[tex]r=24^0[/tex]

b)

[tex]90^0=2x^0+3x^0\\90^0=5x^0 |:5\\x^0=18^0[/tex]

[tex]2x^0= 2* 18^0=36^0[/tex]

[tex]3x^0=3*18^0=54^0[/tex]

Take care!

Given the function f (x) = 3x — 2, what is the value of f (3)?

Answers

Answer:

7

Step-by-step explanation:

Simply plug in 3 for x. 3 times 3 is 9 and 9 minus 2 is 7.

Matthew had $12m. He spent 80¢ every day. How much did he have left
after 2 weeks? Give your answer in dollars.

Answers

Answer:

11999988.80 or .80

Step-by-step explanation:

12,000,000-(.80*14)=11999988.80

12-(.80*14)=.80

a recipe for one batch of Holliday cookies uses 6 tablespoons of frosting for every 16 cookies please awnser quick

Answers

What is the question?

Can someone help me plssssssssss

Answers

I think the answer is C.

It’s saying is 5 times the original number. 200/5=40

| 2n+2g = 5
3x + 3y = 7
How many solutions does the system of equations above have?

Answers

Answer:

The following equation has no / zero solution.

Step-by-step explanation:

The slope of both the equations is proportional which means that the lines are parallel to each other. Thus, the given equation has no solutions.

Please hurry!! This assignment is almost due!!

Answers

Answer:

x = 23

Step-by-step explanation:

8x-27 = 7x-4

8x-7x = -4+27

x = 23

I believe it would be 23

Determine if the two triangles are congruent. If they are, state how you know

Answers

Answer:

yes the two triangles are congruent by the SSS theorum.

Step-by-step explanation:

it is given that two of the sides are congruent. they also share a side making that side also congruent. so, all three sides are equal, making the two triangles congruent by SSS/side-side-side theorum.

For the trig function f(0)=sin(0) whats the input variable
For the trig function g(0)=cos(0) whats the input variable

Answers

For the function f(0)=sin(0), 0 is the input variable while f(0) is the output.

For the function g(0)=cos(0), 0 is the input variable while g(0) is the output.

The standard form of representing trigonometry functions is f(x) = sinx or f(x) = cos x

From the functions:

x is the input variable (also known as the domain)y is the output variable also known as the range;

Given the trig function f(0)=sin(0), compared with the general equation, we can see that 0 is the input variable while f(0) is the output.

Similarly for the function g(0)=cos(0), 0 is the input variable while g(0) is the output.

Learn more on input variables here: https://brainly.com/question/11451813

1038*472 please help

Answers

Answer:

443,226

Step-by-step explanation:

Compare the investment below to an investment of the same principal at the same rate compounded annually.

principal: $1,000, annual interest: 6%, interest periods: 6, number of years: 14 more than the investment compounded annually.

After 14 years, the investment compounded periodically will be worth $ ____(Round to two decimal places as needed.)​

Answers

After 14 years, the investment will be worth $ 2,306.72.

Given that an investment has a $ 1000 principal, 6% annual interest, 6 interest periods and 14 years of investment, to determine, after 14 years, how much the investment will be worth, the following calculation must be performed:

1000 x (1 + 0.06 / 6) ^ 14x6 = X 1000 x 1.01 ^ 84 = X 1000 x 2.3067 = X 2,306.72 = X

Therefore, after 14 years, the investment will be worth $ 2,306.72.

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Given f(x) = x + 2, describe how setting k = 4 affects the slope and y-intercept of the graph of g compared to the graph of f.
g(x) = (4x) + 2
g(x)=4(x+2)

Answers

Answer:

g(2)=(4x) +2=7y

g(3)=4(x+2)

How are the two triangles congruent? If not congruent, select not
congruent.
1 point
SSS
SAS
ASA
AAS
ОО
Not congruent

Answers

Answer:

SAS

Step-by-step explanation:

there are vertical angles in the middle and the sides are already marked

Solve system of equations y=3/4x+2 5x+4y=-24

Answers

Answer:

[tex]\left \{ {{y=-1} \atop {x=-4}} \right.[/tex]

Step-by-step explanation:

[tex]\left \{ {{y=\frac{3}{4} x+2} \atop {5x+4y=-24}} \right. <=> \left \{ {{y=\frac{3}{4}x+2 } \atop {5x+4*(\frac{3}{4}x+2)=-24 }} \right. <=>\left \{ {{y=\frac{3}{4}x+2 } \atop {5x+3x+8=-24}} \right. <=> \left \{ {{y=\frac{3}{4}x+2 } \atop {8x=-32}} \right. \\<=>\left \{ {{y=\frac{3}{4}x+2 } \atop {x=-4}} \right. <=> \left \{ {{y=\frac{3}{4}*(-4)+2 } \atop {x=-4}} \right. <=> \left \{ {{y=-3+2} \atop {x=-4}} \right. =>\left \{ {{y=-1} \atop {x=-4}} \right.[/tex]


An article when sold at a profit of 5% yields Rs 50 more than when sold at a loss of 5%. What was the cost price of the article?​

Answers

Answer:

  Rs 500

Step-by-step explanation:

For cost c, the price that gives a 5% profit is ...

  c + 5%·c = 1.05c

The price that gives a 5% loss is ...

  c -5%·c = 0.95c

The difference of these prices is Rs 50:

  1.05c -0.95c = 50

  0.10c = 50 . . . . simplify

  c = 500 . . . . . . . divide by 0.1

The cost price of the article is Rs 500.

PLS HELP PLEASSSS ILL MARK U AS BRAIN KING THINGY WTV U CALL IT

Answers

Answer:  infinitley many solutions

Step-by-step explanation:

Men to women working for a company is 2 to 3 if there are 80 employees total how many men work for the company

Answers

Answer:

48

Step-by-step explanation:

because if there is 48 men there is 32 women therefor making 80 employees

calculate the quotient below and give your answer in scientific notation

Answers

Answer:

the answer is 95

For what values of r will the area of the shaded region be greater than or equal to 12 square units? Write your answer as an inequality.

Answers

Answer:

r>=12

Step-by-step explanation:

help with this please

Answers

y=-2x+12 is your equation and you are given a table with your x values in them so your first value is 0 so you would put the 0 where the x is so your equation would then look like this:

y=-2*0+12 —> y=0+12 —> y=12

so you would put that 12 in the first box. that gives you the points (0,12) on the graph and that’s where you would put your first dot…
you repeat this process for all the other x values

Solve for x, y, and z

Answers

Step-by-step explanation:

[tex]x = 46.16 \\ y = 23.00 \\ z = 55.7[/tex]

Which inequality represents the phrase below? a number more than 72 A. x < 72 B. x > 72 C. x > 71 D. x = 72

Answers

Answer:

the answer is. C.i hope this helps sorry if im wrong

6^9+6^8)/(6^8*6^-9)
HELP PLS​

Answers

Step-by-step explanation:

Question:-To simplify the expression

Expression:-[tex] \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]Solution :-

[tex] = \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]

[In numerator we take 6^8 common]

[tex] = \frac{ {6}^{8} ( {6} + 1)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]

[On Simplification]

[tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]

[In denominator as we know, a^x × a^y = a^(x+y)]

[tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8 + ( -9)} )} [/tex]

[On Simplification]

[tex] = \frac{( {6}^{8} \times 7)}{( {6}^{ - 1} )} [/tex]

[As we know, 1/a^-1 = a ]

[tex] = {6}^{8} \times 7 \times 6[/tex]

[On further multiplying of 6]

[tex] = {6}^{9} \times 7[/tex]

Result:-

In exponential form:

[tex] = {6}^{9} \times {7}^{1} (ans)[/tex]

In numerical form:

70,543,872 (Ans)

[tex] \huge \: \bf \: Question:—[/tex]

[tex] \sf \longmapsto6^9+6^8)/(6^8 \times 6^{-9})[/tex]

[tex]\huge\bf Solution:—[/tex]

[tex]\sf \longmapsto \: \dfrac{ {6}^{9} + {6}^{8} }{ {6}^{8} \times {6}^{ - 9} } [/tex]

[tex]\sf \longmapsto \dfrac{10077696 + {6}^{8} } { {6}^{8} \times {6}^{ - 9} } [/tex]

[tex]\sf \longmapsto \dfrac{10077696+1679616}{ {6}^{8} \times {6}^{ - 9} } [/tex]

[tex]\sf \longmapsto \: \dfrac{11757312}{{6}^{8} \times {6}^{ - 9}} [/tex]

[tex]\sf \longmapsto \dfrac{11757312}{1679616(6 {}^{ - 9} )} [/tex]

[tex] \boxed{\bf \: As \: a^{-n} = 1/a(n) \: ,}[/tex]

[tex]\sf \longmapsto \dfrac{11757312}{1679616 \bigg(\dfrac{1}{10077696} \bigg )} [/tex]

[tex]\sf \longmapsto \dfrac{11757312}{ \dfrac{1}{6} } [/tex]

[tex]\sf \longmapsto \: \: 70543872[/tex]

[tex] \boxed{\bf \: \: \: Convert\: 70543872 \: to\: scientific \: notation}[/tex]

[tex] \sf \longmapsto \: 7.0543872 × 10 {}^{7} [/tex]

[tex]\boxed{ \bf \: \: Convert\: 70543872 \: to\: exponent}[/tex]

[tex]\sf\longmapsto {6}^{9} \times 7 [/tex]

_________________________________

[tex] \boxed{\bf \: Answer\: in\: Number}:—[/tex]

[tex] \boxed{\bf \: 70543872}[/tex]

[tex]\boxed{ \bf \: Answer\: in\: Exponent:—}[/tex]

[tex] \boxed{\bf \: {6}^{9} \times 7}[/tex]

[tex]\boxed{\bf Answer\: in\: Scientific\: Notation:—}[/tex]

[tex]\boxed{ \bf \: 7.0543872 × 10 {}^{7} }[/tex]

Recently, your parents read in the newspaper that American factory worker jobs have the lowest income ra
What is the best explanation for this fact?
A A factory worker does not need a lot of education
B Companies are relocating factories to other parts of the world.
C Factories are always in poor areas.
D A computer can do the work a factory worker currently does

Answers

Answer:

A. A factory worker does not need a lot of education.

Step-by-step explanation:

The answer is " A " which is a factory worker does not need a lot of education. since most people don't have a PHD degree or anything higher education, it results in a lot of people joining due to the benefit of the factory worker doesn't need a lot of worker which makes it low in demand too.

Suppose a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year. Is this event unusual? Specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year? Know the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009.

Answers

Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.

Given that a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year, to determine if this event is unusual, and specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year knowing that the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009, the following calculation must be performed:

0.009 x 0.009 x 0.009 x 0.009 x 0.009 = X 0.000000000059049 = X 0.000000000059049 x 100 = X 0.0000000059049% = X

Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.

Learn more about maths in https://brainly.com/question/14696440

In ΔABC, m∠1=70° and m∠4=35°. What is m∠3?

Answers

Answer:

75

Step-by-step explanation:

A triangle can only have 3 angles that add up to 180 degrees. Subtract 70 and 35 from 180 to get 75.

180=x+70+35

180-(70+35)=x

WILL GIVE BRAINLIEST

Answers

Answer:

the y intercept is 5/3

the y intercept is 3/5

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