WILL GIVE BRAINLIEST! Determine the coordinates of the point on the straight line y=3x+1 that is equidistant from the origin and (−3, 4).

Answers

Answer 1

Answer:

[tex](\frac{17}{18}, \frac{23}{6})[/tex]

Step-by-step explanation:

D1 = [tex]\sqrt{(x+3)^2 + (y-4)^2}[/tex]

D2 = [tex]\sqrt{x^2 + y^2}[/tex]

Then set D1 = D2, and substitute in y = 3x+1

[tex]\sqrt{(x+3)^2 + (3x-3)^2}[/tex] = [tex]\sqrt{x^2 + (3x+1)^2}[/tex]

[tex]x^2 +6x +9 +9x^2 - 18x + 9 = x^2 + 9x^2 + 6x + 1[/tex]

[tex]18x = 17[/tex]

x = 17/18

Then to find y, substitute back in x for y = 3x + 1

[tex]y = \frac{17}{18} * 3 + 1[/tex]

y = 23/6

Answer 2

The coordinates of the point on the straight line y = 3x + 1 is [tex](\frac{17}{18} ,\frac{23}{6} )[/tex].

Here,

The equation of straight line is y = 3x + 1

And, it is equidistant from the origin and (-3, 4)

We have to find the coordinates of the point on the straight line.

What is the distance between the two points?

The length of the line segment that connects the two given points, is called distance between two points.

Now,

Let the point (x, y) on the line y = 3x + 1.

Distance between the points (x, y) and (0, 0) is;

[tex]D = \sqrt{(x-0)^2+(y-0)^2}[/tex]

[tex]D = \sqrt{x^{2} +y^{2} }[/tex]

And, Distance between the points (x, y) and (-3, 4) is;

[tex]D = \sqrt{(x+3)^2+(y-4)^2}[/tex]

[tex]D = \sqrt{x^{2} +6x+9+9x^{2} -18x+9}[/tex]

Equating both distance we get;

[tex]\sqrt{x^{2} +6x+9+9x^{2} -18x+9} = \sqrt{x^{2} +y^{2} }\\\\ {x^{2} +6x+9+9x^{2} -18x+9} = x^{2} + y^{2} \\\\18x = 17\\\\x = \frac{17}{18}[/tex]

And, To find y put the value of x in y = 3x + 1, we get;

[tex]y = 3 * \frac{17}{18} + 1\\\\y = \frac{23}{6}[/tex]

Hence, The coordinates of the point on the straight line y = 3x + 1 is [tex](\frac{17}{18} ,\frac{23}{6} )[/tex].

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Related Questions

Every line segment has a length ?

Answers

Answer:

A line segment has two endpoints. A line has no end point. A line-segment has a definite length. But a line does not have definite length.

Step-by-step explanation:

When cut into 16 equal slices, each slice is 1/16 of the pizza. Express how much of the plzza 8 of these slices would be in decimal form. ​

Answers

Answer:

the answer is 0.5, or about 50%

Step-by-step explanation:

If 8 slices are being take out of 16, divide the taken pieces by the total pieces, and it would be half or 0.5.

Hope this helps

Answer: 0.5

Step-by-step explanation: because if the pizza is 8 slices that would be the half of the original number of slices it was, so therefore, it would be rounded to 0.5, or 50%- half the pizza

8cm 10cm 10cm 12cm 34cm what’s the volume

Answers

If these are all the side lengths then just multiply all of them together
Answer) 326,400cm^5

!!!! I NEED HELP RIGHT NOW ITS DUE IM 5 MINUTES !!!!

Answers

Answer:

Step-by-step explanation:

A = h(a+b)/2 for h

2A = h(a + b)

h(a+b) = 2A

h = 2A/(a+b)

The size of the largest angle in a triangle is 3 times the size of the smallest angle.

The other angle is 35 more than the smallest angle.


Work out in degrees the size of each angle in the trianlge

You must show your working

Answers

Answer:

a = 29

b = 64

c = 87

Step-by-step explanation:

Let the angles be a (smallest), b, and c (largest).

We know that a triangle's angles must add up to 180 degrees, so we can construct the following equations.

a + b + c = 180

c = 3a

b = a +35

With some solving and substitution...

a + (a + 35) + c = 180

2a + c = 145

2a + (3a) = 145

5a = 145

a = 29

and therefore,

b = 29 + 35 = 64

c = 3(29) = 87

Answer:

Let smallest angle be :x

So, the largest angle will be:3x

And the other angle will be :x+35

According to angle sum property of triangle,

x+3x+x+35=180

5x+35=180

5x=180-35

5x=145

x=(145/5)

Therefore, x=29

So, the smallest angle =x=29

The largest angle=3x=87

And the other angle=x+35=64


Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks.
How many weeks does it take her to have $250 in her bank account?
O 15 weeks
O 4.6 weeks

O 10 weeks

O 5.4 weeks


Answers

Answer:

10 weeks

Step-by-step explanation:

20x+50=250

First subtract 50 from both sides, which gives you 20x=200

then divide 20 from both sides which gives you x=10


Identify the perimeter and area of a square with diagonal length 16 cm. Give your answer in simplest
radical form

Answers

Answer:

32r2, 128 cm ^2

The area and the perimeter of the square are 128 cm² and 32√2 cm, respectively.

What is a square?

A square is a parallelogram, whose all sides are congruent and all angles are right angle.

Given that,  a square with diagonal length 16 cm

Let the side of the square be a,

We know that, all sides of a square are congruent,

And, the diagonal divides it into two congruent right triangles,

Therefore, using Pythagoras theorem,

a²+a² = 16²

2a² = 256

a² = 128

a = 8√2

Area = side²

Therefore, area = 128 cm²

perimeter = 4×sides = 32√2 cm

Hence, the area and the perimeter of the square are 128 cm² and 32√2 cm, respectively.

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y is directly proportional to x when y=30, x=6
a) work out an equation connecting y and x
b) work out the value y when x=12

Answers

Answer:

a) y = 5x

b) y = 60

Step-by-step explanation:

Since, y is directly proportional to x when y=30, x=6

[tex] \therefore \: y \: \alpha \: \: x \\ \therefore \: y = kx ...(1) \\ plug \: y = 30 \: and \: x = 6 \: in \: eq \: (1)\\ 30 = k \times 6 \\ k = \frac{30}{6} \\ k = 5 \\ plug \: k = 5 \: in \: (1) \\ y = 5x....(2) \: (required \: equation) \\ plug \: x = 12 \: in \: eq \: (2) \\ y = 5 \times 12 \\ \huge \red{ \boxed{y = 60}}[/tex]

What is 442500 represented in scientific notation?

Answers

Answer:

4.425*10⁵

Step-by-step explanation:

442500 = 4.425 * 10 ⁵

If f(x) = 5x – 2 and g(x) = 2x+1, find (f+ g)(x).
A. 4x - 3
B. 3x - 1
O c. 7x-3
O D. 7x-1
SUD

Answers

Answer: 3x-3 apex

Step-by-step explanation:

(-12) +7
what’s the answer

A.-11
B.-17
C.4
D.-5
E.8

Answers

Answer: -5

1.) remove parenthesis

-12+7

2.) simplify

-5

Answer:

D) -5

Step-by-step explanation:

When two numbers have different sign, subtract and the answer will have the sign of the bigger number.

Here the sign of bigger number is negative. So, (-5)

Ben went to the hardware store and bought 7 pieces of rope of equal length. The total length of the ropes was 56 meters. How long was each rope?

Answers

Answer:

8 meters

Step-by-step explanation:

56 / 7 = 8

My answer is B im sure im wrong ;-;

Answers

The answer is I think it’s A. 60 degrees is 1/6 of 360 so the answer should be 1/6of the perimeter. The perimeter is 24 pi so it should be 4 pi or 12.something

Answer:

12.56

Step-by-step explanation:

find the circumference of the circle : 2πr

C=2(12)(3.14)

C=75.36

the length of the arc is: arc length will be (60/360) one 1/6 of the total circumference.

(60/360)(75.36)= 12.56

Write 5.12 x 10⁵ in standard form.

MATH​

Answers

10^5 = 100,000

5.12 × 10^5 in standard form = 5.12 × 100,000 = 512000

Answer: 512,000

Answer:

10^5 = 100,000

5.12 × 10^5 in standard form = 5.12 × 100,000 = 512000

Answer: 512,000

Step-by-step explanation:

I will give brainliest!!!! Which expressions are equivalent to j+j+2k? Choose all answers that apply: (Choice A) A 2jk (Choice B) B 2(j+j+k) (Choice C) C None of the above

Answers

Answer:

The Answer Is C

Answer:

CHOICE C.

Step-by-step explanation:

They are not like terms, so they can't be added up.

Solve |y-2|<10
please

Answers

Your answer would be
Y=(-8, 12)

Wouldnt the answer be anything above 12? Because if Y is unknown, and you're taking 2 away from it, and it still has to be greater than 10, then it should be anything above 12. Unless it's saying that the number is greater than 10, and you are just taking away 2 from a number and it doesn't have to be greater than 10.

The graph of the function B is shown below. Find B(2).





1
-1
2

Answers

Answer: 2

Step-by-step explanation:

Answer:

The answer is 2

Step-by-step explanation:

Don't forget to thank and vote

If 2* = 32
find the value of x.​

Answers

Answer:

2^x = 2*2*2*2*2

2^X = 2^5

x=5

Step-by-step explanation:

The only reason I don’t think I can make it I was gonna I wanna is the time to come home from work today bruh bruh is a time to get

a -42+(-17)
b 8-(-9)
c 8(-9)
D
E
F
G

Answers

Answer:

.A -42+(-17)

Step-by-step explanation:

Please does anyone know how to do this x

Answers

Step-by-step explanation:

Weight before diet: 208 pounds

After diet: 192 pounds

Difference in weight: 16 pounds

(16÷208)*100= 7.7%

pls help i need help 20 points

Answers

Answer:

[tex]63 \ cm^2[/tex]

Step-by-step explanation:

The area of a triangle is found using the following formula:

[tex]A = \frac{base * height}{2}[/tex]

The base of our triangle is 21 cm.

The height of our triangle is 6 cm.

[tex]A= \frac{6*21}{2} =3 * 21 = 63[/tex]

Our distance unit is cm, so our area will be in cm squared.

Answer: [tex]63 \ cm^2[/tex]

Answer:

63

Step-by-step explanation:

21 times 6, then divide by 2.

solve for a.

-6a = -18​

Answers

Answer:

A=3

Step-by-step explanation:

Step 1: Divide both sides by -6/

-6a/-6= -18/-6

a=3

What value of x makes this equation true?
3(x + 4) = 7x - 18
O x = 5
O x = 4.5
O x = 34.5
0 x = 75.

Answers

Answer:

x = 15/2 or x = 7.5

Step-by-step explanation:

Step 1: Write equation

3(x + 4) = 7x - 18

Step 2: Solve for x

Distribute 3: 3x + 12 = 7x - 18

Subtract 3x on both sides: 12 = 4x - 18

Add 18 on both sides: 30 = 4x

Divide both sides by 4: x = 15/2 or x = 7.5

A package of floor tiles contains 22 one-foot-square tiles. Find how many packages
should be bought to cover a square ballroom floor whose side measures 66 feet Note:
Partial packages cannot be bought

Answers

3 Packages of 22 on foot square tiles because if you multiply 22 by 3 you get 66
So therefore your answer would be 3 packages!

Answer:

Step-by-step explanation:

66 times 66  for area is 4356 then 4356 divided by 22 is 217.8 so 218

Which number has a 3 that is 10 times greater than the 3 in 513?

Answers

Answer:

30

Step-by-step explanation:

The 3 in "513" is only 3. it's 1, 2, 3. If we do 3 x 10 it's 30.

3 x 10 = 30.

"times greater" means multiplication if you were confused about it.

Hope this helps! Have a nice day!

Place values are used to represent the value of digits in a given number. The number that has a 3 that is 10 times greater is 30.

Given that:

[tex]Number = 513[/tex]

We make the following observations in 513

513 does not have decimalsThe 3 in 513 is the rightmost digit.

The rightmost digit in a non-decimal number is the unit digit. So, the value of 3 in 513 is:

[tex]Value = 3 \times unit[/tex]

Unit means 1. So:

[tex]Value = 3 \times 1[/tex]

[tex]Value = 3[/tex]

So, the value of 3 in 513 is 3.

Let the other number be x.

x is 10 times greater than 3 means that:

[tex]x = 10 \times 3[/tex]

[tex]x = 30[/tex]

Hence, the number is 30

Read more about place values at:

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Find two consecutive even integers such that six times the first equals five times the second.

Answers

Answer:

4 and 6 are the two consecutive even integers

Step-by-step explanation:

Hi,

Let x represent the smaller of the two consecutive even integers, (x+2) the other

Write as we Read***

6x = 4(x+2)

solve for x

6x = 4x + 8

2x = 8

x = 4

checking our answer

6*4 = 4*6 = 24

i'm over this please

Answers

Answer:my answer is oooof

Step-by-step explanation:

x=127

since a triangle equals 180, subtract 180-37-90 to get the bottom angle of 53. that straight line is also 180 so 180-53=127

fd - m = 8
Solve for d
Please help!

Answers

Answer:

[tex]d=\frac{8+m}{f}[/tex]

Step-by-step explanation:

[tex]fd-m=8[/tex]

Add m to both sides:

[tex]fd-m+m=8+m[/tex]

[tex]fd=8+m[/tex]

Divide both sides by f:

[tex]\frac{fd}{f}=\frac{8+m}{f}[/tex]

[tex]d=\frac{8+m}{f}[/tex]

Find a general term an for the sequence whose first four terms are given.
2, 4, 8, 16, ...

Answers

Answer:

  an = 2·2^(n-1)

Step-by-step explanation:

There are simple tests to determine whether a sequence is arithmetic or geometric. The test for an arithmetic sequence is to check to see if the differences between terms are the same. Here the differences are 2, 4, 8, so are not the same.

The test for a geometric sequence is to check to see if the ratios of terms are the same. Here, the ratios are ...

  4/2 = 2

  8/4 = 2

  16/8 = 2

These ratios are all the same (they are "common"), so the sequence is geometric.

The general term of a geometric sequence with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

Filling in the values for this sequence, we find the general term to be ...

  an = 2·2^(n-1)

Fourteen less than the quotient of a number and 5

Answers

Answer:

Step-by-step explanation:

14-(a/5)

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