Solve (x – 3)² =5 give your answers to the correct 3 significant figures

Hello,

We need first to know what's a gradient. The Gradient (also called Slope) of a straight line shows how steep a straight line is.

But how do we find the slope (or Gradient) from two points ?

For exemple, let's find the gradient of the two points PQ...

Method

1. We need the coordinates of the point P, and the point Q :

P = (6 ; -11)

Q = (k ; -9)

2. The slope is the change in height divided by the change in horizontal distance.

In other words we :

a) subtract the x values

b) subtract the y values

c) divide

Application for PQ

subtract x values : xQ - xP = k - 6

subtract the y values : yQ - yP = -9 - (-11) = -9 + 11 = 2

divide : (k-6) / 2

That is the gradient of PQ.. Now let us find the gradient of PR

Application for PR

subtract x values : xR - xP = 2k - 6

subtract the y values : yR - yP = -3 - (-11) = -3 + 11 = 8

divide : (2k-6)/8

That is the gradient of PR.

We know that by assumption, gradient of PQ = gradient of PR, what is the value of k ? Well, we simply need to solve an equation here :

gradient of PQ = gradient of PR

(k-6) / 2 = (2k - 6) / 8

k-6 = (4k - 12)/8 (we have multiplied by 2 on each sides of the equation)

8k - 48 = 4k - 12 (we have multiplied by 8 on each sides of the equation)

8k - 4k = - 12 + 48

4k = 36

k = 36 / 4 = 9

So the value of k in order for the two gradients to be equals needs to be equal to 9

Good luck

Answer:

A part of a wall that Melinda paints in 1 minute is: x = 1/80

Answer:

You Need the angle GEF in order to find DEF and DGE

Step-by-step explanation:

Triangle = 180 degrees

EFD = 60 degrees

180 degrees - (GEF + 60 degrees) = EGF

DEG = 60 degrees

180 - (DEG + GEF + EFD) = EDF

180 - EGF = EGD

DEG + EGD + EDG = 180 degrees

FEG + GFE + EGF = 180 degrees

Answer:

[tex]f'(4)=16[/tex]

Step-by-step explanation:

First, we need to find the derivative:

[tex]f'(x)=(2)(2)x^(^2^-^1^)-0[/tex]

[tex]f'(x)=4x[/tex]

Now, we need to plug in 4 for x:

[tex]f'(4)=(4)(4)=16[/tex]

Answer:

x = 12

9x = 108º

6x = 72º

Step-by-step explanation:

The angles sum to 180º

9x + 6x = 180

15x = 180

x = 12

9x = 9 * 12 = 108

6x = 6 * 12 = 72

In the given parallelogram, we can see that 9x° & 6x° are adjacent angles.  2 adjacent angles in a parallelogram sum up to 180°. So,

9x° + 6x° = 180°

15x° = 180°

x = 180/15

x = 12

Now,

6x° = 6 × 12 = 72°

9x° = 9 × 12 = 108°.

=》The value of 'x' is 12 & the measure of each labelled angle is 72° & 108°.

________

Hope it helps ⚜

Answers:

=================================================

Explanation:

The diagram is below.

Draw two triangles that are identical copies of each other. This is exactly what the term "congruent" means. Congruent items are identical items.

The order is very important when it comes to figuring out congruent triangles. Triangle ABC has A first, B next, C last. For triangle DEF, we have D first, E next, F last.

This means we have this pairing:

Because the triangles are congruent, we know that:

So if we could find out angle B, then we automatically will find out angle E as well.

Use the idea that for any triangle, the angles always add to 180

A+B+C = 180

34+B+124 = 180

B+158 = 180

B = 180-158

B = 22

Angle B is 22 degrees, and so is angle E.

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

Everything in the previous section handled how to find angle E.

In this section, we'll find how long side DE is.

Since the angles pair up in the way mentioned earlier, we can further extend that idea to have these three pairs

The pairs are formed directly based on how the angles pair up. For instance, AB and DE are both the first two letters of ABC and DEF respectively. In the diagram, AB and DE are both the left slanted side. However, the diagram can sometimes be misleading because it's perfectly possible to rotate triangle DEF to not have it line up with ABC. I drew the diagram to help make the pairings as clear as possible.

Anyways, we have AB pair up with DE. Both of those pieces must be congruent if we want the overall triangles to be identical. We're told that AB = 24, which means DE = 24.

Answer:

the slope is

2/3x+2

Hope This Helps!!!

Answer: It’s C

Step-by-step explanation:

Answer:

OC. 5:17 compares the amount og goldfish he has to the amount of total animals he has

Answer:

Cylinder and cube are three dimensional shape

Answer:

triangular prism

rectangular prism

Step-by-step explanation:

Answer:

where is questions asking

Gustavo used 8 round tables and 6 rectangular tables.

Since Gustavo sets up tables for a caterer on weekends, and each round table can seat 8 people while each rectangular table can seat 10 people, and one weekend, his boss asked him to set up tables for 124 people, and he uses 2 more round tables than rectangular tables, to find the number of round tables and rectangular tables Gustavo used the following calculation must be performed:

Therefore, Gustavo used 8 round tables and 6 rectangular tables.

Learn more in https://brainly.com/question/25443927

Answer:

Ms. Brown needs 0.18 more cents to afford the pounds of granola and cranberry mix.

Step-by-step explanation:

Ms. Brown = $10 limit

Purchases 1.75 lbs of granola and 2.9 lbs of cranberry mix

Cranberry per lb = $3.25

Granola per lb = $2.19

1.75 x 2.19 = 3.8325 (Cost of granola)

2.9 x 2.19 = 6.351 (Cost of cranberry)

3.8325 + 6.351 = 10.1835 (Total cost of both cranberry and granola)

10.1835 rounded to nearest cent = 10.18

10 < 10.18

Ms. Brown doesn't have enough money to buy the pounds of granola and cranberry mix.

Answer:

[tex]\frac{1}{9}[/tex] , 3 , 10

Step-by-step explanation:

Using the rules of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^m}[/tex]

[tex]a^{0}[/tex] = 1

(a)

[tex]6^{-x}[/tex] = [tex]\frac{1}{6^{x} }[/tex] = [tex]\frac{1}{9}[/tex]

(b)

[tex]6^{\frac{x}{2} }[/tex] = [tex]\sqrt{6^{x} }[/tex] = [tex]\sqrt{9}[/tex] = 3

(c)

[tex]6^{0}[/tex] + [tex]6^{x}[/tex] = 1 + 9 = 10

Answer:

option 3

Step-by-step explanation:

The translation [tex]T_{3, - 4}[/tex] means add 3 to the x- coordinate and subtract 4 from the y- coordinate, then

(- 5, 2 ) → (- 5 + 3, 2 - 4 ) → (- 2, - 2 )

[tex]-5x = 78 + 25 <=> -5x = 103 <=> x = -103/5[/tex]

Answer:

Osmosis is the diffusion of water to an area of high water concentration to an area of low water concentration.

Step-by-step explanation:

Answer:

the spontaneous passage or diffusion of water or other solvents through a semipermeable membrane

Step-by-step explanation:

a process by which molecules of a solvent tend to pass through a semipermeable membrane from a less concentrated solution into a more concentrated one, thus equalizing the concentrations on each side of the membrane.

Option D is correct, the value of the rational expression when x = –3 is undefined.

An expression is combination of variables, numbers and operators.

The given expression is x/x²-9

x divided by x square minus nine.

Now let us find the value of the expression when x is minus three,

Plug in x as -3 in the above expression.

-3/(-3)²-9

-3/9-9

-3/0

Anything divided by zero then the value is undefined.

Hence, Option D is correct, the value of the rational expression when x = –3 is undefined.

To learn more on Expressions click:

https://brainly.com/question/14083225

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What is the value of the rational expression x/x2-9 when x = –3?

A. -1/12

B. 0

C. 1/6

D. Undefined

Answer:

if the units is in m/s

Step-by-step explanation:

first work out using this triangle.

distance= speed x by time

so if we're trying to find out the speed we reaarange the triangle to :

   distance

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

speed x   time

so speed = distance divided by time

distance = 45cm

divided by time = 90 seconds

But the units are cm and should be metres per second

change 45cm to m

that is 45cm = 45/ 100 = 0.45

0.45/ 90= 0.005cm

answer = 0.005 metres per second( m/s)

plz say thanks + rate !

Answer:

4

Step-by-step explanation:

I think if not sorry

Answer:

B-at the second line

Step-by-step explanation:

hope it can help you lovelots

#LEARN WITH BRAINLY

[tex]x^2 +6x +18 =0\\\\\implies x^2 + 2 \cdot 3 \cdot x + 3^2 -3^2 +18 =0\\\\\implies (x+3)^2 -9 +18 =0\\\\\implies (x+3)^2 +9 =0\\\\\implies (x+3)^2 =-9[/tex]

Answer: b > 16

Step-by-step explanation:

Because a > -25, b must be at least greater than 16, as if a is -25.1, for example, b must be 16.11.  

we have 9x - 7 ≤ 28 + 4x

⇔9x - 4x ≤ 28 +7

⇔5x ≤ 35

⇔x ≤ 7

ok done. Thank to me :>

Answer:

x=-1

y=-3

Step-by-step explanation:

3x-2y=3(1)

5.(1) <=> 15x-10y=15 (2)

15x-4y=-3 (3)

(2)-(3) <=> -6y=18

Answer:

d

Step-by-step explanation:

po ang tamang sagon po

Answer:

8

Step-by-step explanation:

1/2(4)-(-6)                  BODMAS method

2-(-6)

2+6

8

h = 2 + 32t - 16t^2 is the function given to model the balls flight and we want to know what time the ball is at 15 feet in the air, which is at 2 points in time since the ball takes a parabolic trajectory.

15 = 2 + 32t - 16t^2

0 = -16t^2 + 32t -13

since the equation isn't factorable we will use the quadratic formula.

(-b +- sqrt(b^2 - 4ac))/2a

=

we end up with t = (4+-sqrt(3))/4 which is t = 1.43 seconds and t = 0.57 seconds when approximated.

Answer:

The last one is the answer.