The straight line L has the equation 4y=5x+3
The point A has coordinates (3,-2)
Find the equation of the straight line that is perpendicular to L and passes through A
Write your answer in the form y=Mx+c

Answer:

b

Step-by-step explanation:

The third quartile is the upper quartile whose value is the value on the right side of the box, that is

third quartile = 23 → b

Answer: B 23

Step-by-step explanation:

The third quartile comes after the median.

Answer:

1 + root 5, 1 - root 5

Step-by-step explanation:

I assume you mean 3x^2-6x-12=0.

First, note that you can divide both sides by 3. You get:

x^2-2x-4=0

Use the quadratic equation.

[tex]x=\frac{2\pm\sqrt{4+16}}{2}=\frac{2\pm2\sqrt{5}}{2}=1\pm\sqrt{5}[/tex]

Therefore, x=1 + root 5, 1 - root 5

Answer:

As Sophie has just taken the medicine, the quantity of drug present in her body is 500mg

Amount left from 1st dose = 4.5/100 × 500 = 22.5mg

Amount of Drug after 2nd dose = Amount left from 1st dose + 2nd dose taken.

Amount of Drug after 2nd dose = 22.5mg + 500mg

Amount of Drug after 2nd dose = 522.5mg

Amount left from 2nd dose = 4.5/100 × 522.5 = 23.513 mg

Amount of Drug after 3rd dose = Amount left from 2nd dose + 3rd dose taken.

Amount of Drug after 3rd dose = 23.513mg + 500mg

Amount of Drug after 3rd dose = 523.513 mg

Amount left from 3rd dose = 4.5/100 × 523.513 = 23.558mg

Amount of Drug after 4rth dose = Amount left from 3rd dose + 4rth dose taken.

Amount of Drug after 4rth dose = 23.558mg + 500mg

Amount of Drug after 4rth dose = 523.558 mg

The pattern formed above can be written in the form of sum of finite geometric series:

Sₙ = 500 + 500(0.045) +500(0.045)² + ........................500(0.045)ⁿ

Sₙ = 500(1 + 0.045 + 0.045² ........................0.045ⁿ)

Where

Sₙ = Sum till nth term

a = 500

r = 0.045

As Sophia takes medicines 2 times a day, she takes medicine 20 times in 10 days. So substitute n=20 in the formula for the sum of finite geometric series

[tex]S_n=a\frac{(1-r^n)}{1-r}\\S_{20}=500(\frac{1-0.045^{20}}{1-0.045})\\S_{20}=523.5602~\text{mg}[/tex]

Greatest amount of antibiotic present = 523.5602 mg

This amount is almost constant after 3rd dose, so it will occur after every dose after 3rd dose

After 1st dose = 500mg

After 2nd dose = 522,5mg

After 3rd dose = 523.513 mg

After the the amount left in the body almost remains constant.

Which means that after each dose, the amount in body is maximum, at the end of the 12 hours, the amount reduces to 4.5%, which reaches almost the same maximum after taking another dose.

Answer:

1715 metros

Step-by-step explanation:

Lo que debemos hacer es calcular la distancia del primer y del segundo eco.

Debemos conocer la velocidad del sonido que en términos generales es 343 m/s, por lo tanto, la distancia sería igual a:

v = d/t => d = v*t

d1 = 343*2 = 686 metros

d2 = 343*3 = 1029 metros

La separación sería la suma de ambas distancias así:

686 + 1029 = 1715

1715 metros sería la distancia de separación entre ambas montañas.

Answer:

nth term = 2n^2 - 3n - 6.

Step-by-step explanation:

                      n   =  1   2    3    4     5     6    7  

                             - 7   -4   3   14   29   48   71  

Differences                3    7   11    15   19    23

Differences                   4   4     4    4     4

So the first term in the Rule is 2n^2

Subtracting  the values of 2n^2 from the original terms:

                  - 7   -4   3      14   29   48   71  

2n^2           2     8  18    32   50   72   98

Subtrct       -9   -12 -15  -18   -21   -24   -27

                       -3     -3    -3   -3    -3     -3

So we have -3n  and the last  term is  -6 because    -7 = 2(1)^2 -3 - 6  and the other terms fit this pattern as well.

The nth term rule of the provided quadratic sequence to find the n'th term of the sequence is 2n²-3n-6.

The quadratic sequence is the series of the numbers in which the rule for the n'th term included an n squared term (n²). The quadratic equation for n can be given as,

[tex]an^2+bn+c[/tex]

Here, (2a) is equal to the second difference, (3a+b) is equal to the first difference and (a+b+c) is equal to the first term.

The sequence given in the problem is

[tex]-7, -4, 3, 14, 29, 48, 71[/tex]

Thus, (a+b+c) is,

[tex]a+b+c=-7[/tex]                ......1

The first difference between the sequence is,

[tex]3,7,11,15,19,23[/tex]

Thus, the value of (3a+b) is,

[tex]3a+b=3\\b=3-3a[/tex]                      ......2

The second difference between the sequence is,

[tex]4,4,4,4,4[/tex]

Thus, the value of 2a is,

[tex]2a=4\\a=\dfrac{4}{2}=2[/tex]

Put this value in equation 2 as,

[tex]b=3-3\times2\\b=-3[/tex]

Put the value of a and b in equation 1 as,

[tex]2-3+c=-7\\c=-7+1\\c=-6[/tex]

Put these values in the above formula as,

[tex]2n^2-3n-6[/tex]

The nth term rule of the provided quadratic sequence to find the n'th term of the sequence is,

[tex]2n^2-3n-6[/tex]

Learn more about the quadratic sequence here;

https://brainly.com/question/26373760

Answer:

0.83?

Step-by-step explanation:

Step-by-step explanation:

1/6 or 1÷6 =

0.1666666r

Answer:

The  recursive formula for the given sequence

                 [tex]t_{n}= (2)^{n+2}[/tex]

Step-by-step explanation:

Explanation:-

Given sequence is 8 , 16, 32, 64 ,.....

First term is   a = 8

common ratio   [tex]r = \frac{16}{8} =2[/tex]

                       [tex]r = \frac{32}{16} =2[/tex]

                      [tex]r = \frac{64}{32} =2[/tex]   and so on..

Given sequence of the common ratio 'r' is equal

The [tex]n^{th}[/tex] term of the sequence

                   [tex]t_{n} = a r^{n-1}[/tex]

                   [tex]t_{n}= 8 (2)^{n-1}[/tex]

                   [tex]t_{n}= (2)^{(3+n-1)}[/tex]

                  [tex]t_{n}= (2)^{n+2}[/tex]

This is  recursive formula for the given sequence

                 [tex]t_{n}= (2)^{n+2}[/tex]

Verification:-

           [tex]t_{n}= (2)^{n+2}[/tex]

put n=1   ⇒ t₁ = 8

put n=2   ⇒ t₂ = 16

put n=3   ⇒ t₃ = 32

put n=4   ⇒ t₄= 64    

and so on..

The sequence  8 ,16 , 32 , 64 ....

Answer:

x = -5 or x = -4/3

Step-by-step explanation:

First possibility.

|2x − 1| = |4x + 9|

2x - 1 = 4x + 9

2x - 4x = 9 + 1

-2x = 10

x = 10/-2

x = -5

Second possibility.

2x - 1 = - (4x+9)

2x - 1 = -4x - 9

2x + 4x = -9 + 1

6x = -8

x = -8/6

x = -4/3

Answer:

[tex] |2x - 1| = |4x + 9| [/tex]

this equation can be separated into 2 possible cases :

[tex]2x - 1 = 4x + 9[/tex]

and

[tex]2x - 1 = - (4x + 9)[/tex]

solve the 1st possible case:

[tex]2x - 1 = 4x + 9[/tex]

[tex]2x - 4x = 9 + 1[/tex]

[tex] - 2x = 10[/tex]

[tex]x = - \frac{10}{2} [/tex]

[tex]x = - 5[/tex]

solve the 2nd possible case:

[tex]2x - 1 = - (4x + 9)[/tex]

[tex]2x - 1 = - 4x - 9[/tex]

[tex]2x + 4x = - 9 + 1[/tex]

[tex]6x = - 8[/tex]

[tex]x = \frac{ - 8}{6} [/tex]

[tex]x = - \frac{4}{3} [/tex]

so the x value for this equation is:

x = -5 or x = -1.333

Answer:

10 x squared minus 4 y + 2 x squared minus y

Step-by-step explanation:

9x^2-2y+3x^2-3y

Collect like terms

9x^2+3x^2-2y-3y

=12x^2-5y

10 x squared minus 4 y + 2 x squared minus y

10x^2-4y+2x^2-y

Collect like terms

10x^2+2x^2-4y-y

=12x^2-5y

9x^2-2y+3x^2-3y is equivalent to

10x^2-4y+2x^2-y

Check all the options

6 x squared minus y + 6 x squared minus 5 y

6x^2-y+6x2-5y

12x^2-6y

6 x squared minus y + 3 x squared minus 4 y

6x^2-y+3x^2-4y

9x^2-5y

10 x squared minus 4 y + 2 x squared minus y

10x^2-4y+2x^2-y

12x^2-5y

11 x squared + 2 y + x squared minus 3 y

11x^2+2y+x^2-3y

12x^2-y

Answer:

C.) 12x squared- 2y- 3y

Step-by-step explanation:

i'm not 100 percent on this but it is the only logical answer, i will comment if i am right or not :) good luck luvs

Answer:

A

Step-by-step explanation:

The base angles L and N are congruent.

Thus the triangle is isosceles and ML = MN, that is

3x = x + 8 ( subtract x from both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Thus

MN = x + 8 = 4 + 8 = 12 → A

Answer:

x=74

Step-by-step explanation:

If two tangent segments are drawn from the same external point, then the segments are equal.

Answer:

As we know that the theorm says that tangents drawn from external points of circle are equal so

AB = BC

X - 24 = 50

x = 50 - 24

x = 26

Hooe it helps u

Answer:

x = -2/3

Step-by-step explanation:

Step 1: Convert signs

f(x) = -(-3x) + 4

f(x) = 3x + 4

Step 2: Set f(x) and g(x) equal to each other and solve for x

3x + 4 = 2

3x = -2

x = -2/3

And we have our final answer!

Answer:

-450

Step-by-step explanation:

Say the first number is x to get the idea.

The first 150 terms are 150x - 5 * 150

15x - 750

300 - 750 = -450

Answer:

Step-by-step explanation:

first lets find the total # of portions:

3+4+13=16+4=20

To make 4kg of this alloy you have to use:

nickel: (4/20)*3=12/20=6/10=0.6 kg

zinc: (4/20)*4=16/20=8/10=0.8 kg

copper: (4/20)*13=52/20=26/10=2.6 kg

Answer:

Option 3.

Step-by-step explanation:

Angle E and angle A are corresponding angles, therefore they are congruent angles. Corresponding angles have the same angle.

Answer:

14.5 =x

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opposite side/ hypotenuse

sin A = BC / AB

sin 65 = x /16

Multiply each side by 16

16 sin 65 =x

14.50092459 =x

14.5 =x

Answer:

C on edge

Step-by-step explanation:

Answer:

y = -7/3x + 10

Step-by-step explanation:

Step 1: Find the slope of the perpendicular line

Do this by taking the negative inverse of the first line

m = -7/3

Step 2: Find b

y = mx + b

y = -7/3x + b

3 = -7/3(3) + b

3 = -7 + b

b = 10

You should get y = -7/3x + 10 as your final answer.

Answer:

1/26

Step-by-step explanation:

In a standard pack of cards, there are 52 total cards and 4 aces, two black aces and two red aces.

The probability of selecting an ace is therefore:

4/52 = 1/13

The probability of flipping a coin and it landing on tails is:

1/2

Therefore, the probability of selecting an Ace and the coin landing on tails is:

1/13 * 1/2 = 1/26

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

"Mr. Anderson cuts a piece of metal in the shape of the triangle shown. The piece of metal has an area of 7 1/2 square feet. What is the base of the piece of metal? triangle 5ft high"

Area of the triangle = 1/2 * base * height

Given the area of the piece metal = 7 1/2 ft² and its height = 5ft (since the triangle is 5ft high). On substituting the values in the formula;

7 1/2 = 1/2* base * 5

15/2 = 5/2 * base

15 = 5 * base

base = 15/5

base = 3ft

The base of the piece of metal is 3ft

Answer:

y = -(3/4)x + 19

Step-by-step explanation:

If you look at the line, you have the y intercept already. so there is less work to do.

The equation for a linear line is y=mx+b (or c depending on which country you are from) where m is the gradient and b is the y intercept

b = 19 from the diagram

To find the gradient, it is y2-y1/x2-x1, so pick any 2 points, let say  (16,7) and (0,19)

m = 19-7/0-16

= 12/-16

=3/-4

Sub the required numbers back into the equation

y = -(3/4)x + 19

Answer:

its D

Step-by-step explanation:

Answer:

a) y = 5x

b) y = 60

Step-by-step explanation:

y ∝ x

So, y = kx      -----(1)

Where k is the constant of proportionality

Now, y = 30, x = 6

Putting in (1)

30 = k(6)

Dividing both sides by 6, we get

k = 5

Now, Putting k=5 in (1)

So,

a) The equation connecting x and y is :

y = 5x

b) x = 12, Putting in (1)

y = (5)(12)

y = 60

Answer:

a)y=5x

b)60

Step-by-step explanation:

it just is

Answer:

£3.80

Step-by-step explanation:

£1.76 + £2.04

Add the both terms.

= £3.80

Answer:

£66

Step-by-step explanation:

1/5 times £495

2/3 times £495

Rent =£99

Food =£330

99+330=429

495-429=£66

I hope that help you and you learned how to do it for next time.

Answer:

£66 Left

Step-by-step explanation:

Total Money = £495

Rent:

=> [tex]\frac{1}{5} * 495[/tex]

=> £99

Food:

=>[tex]\frac{2}{3} * 495[/tex]

=> 2 * 165

=> £330

Left:

=> £495-£99-£330 = £66

Answer:

A slope of zero means a horizontal line (parallel to the x axis). So the line is y=-6, which is the y intercept. There is no x term because y=-6 for all x.

Step-by-step explanation:

Answer: y + 10 = -9(x - 6)

Step-by-step explanation:

Use this formula to solve for point-slope form: y - y1 = m(x - x1)

m would be the slope and the given slope is -9

y1 refers to the given y coordinate and x1 refers to the given x coordinate.

y + 10 = -9(x - 6)

Answer:

it is 50 :)

Step-by-step explanation:

im taking the review on edg and i got it right

Answer:

The answer is 50. Edge 2022

Step-by-step explanation:

If you trace the way the points move you can find out it is 50.

Answer: D √234

Step-by-step explanation:

a^2 + b^2 = c^2

3^2 + 15^2 = c^2

9 + 225 = c^2

c = √234

Answer:

B

Step-by-step explanation:

In B, the oranges is always 3 times the cups of juice. So it always follows the ratio 3:1.

Answer:

7/12

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

12-5=7

7/12

Answer:

1.053

Step-by-step explanation:

1.053(100)=105.3

Answer:

D. Between the ladder and the ground

Step-by-step explanation:

The 75° is made by the ladder leaning on the tree. So the angle would be from the ground up to the ladder.