factorize the following numbers by Factor tree method
20

Answers

Answer 1

Answer:

tara specimen!

Step-by-step explanation:

1+2=3 ok


Related Questions

Let the lengths of each side of △ABC having area equal to 1 be as follows: AB = 2, BC = a and CA = b. Let CD be a perpendicular line from point C to AB. Answer the following questions.
(1) Given AD = x, write a²+(2√3-1)b² in the form of x.
(2) Find the value of x at which a²+(2√3 - 1)b² is the lowest and the magnitude of ∠BAC.
Need help! Please show your work too. Thanks!

Answers

Answer:

Part 1)

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

Or simplified:

[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]

Part 2)

The value of x for which the given expression will be the lowest is:

[tex]\displaystyle x = \frac{\sqrt{3}}{3}\approx 0.5774[/tex]

And the magnitude of ∠BAC is 60°.

Step-by-step explanation:

We are given a ΔABC with an area of one. We are also given that AB = 2, BC = a, and CA = b. CD is a perpendicular line from C to AB.

Please refer to the diagram below.

Part 1)

Since we know that the area of the triangle is one:

[tex]\displaystyle \frac{1}{2} (2)(CD) = 1[/tex]

Simplify:

[tex]\displaystyle CD = 1[/tex]

From the Pythagorean Theorem:

[tex]\displaystyle x^2 + CD^2 = b^2[/tex]

Substitute:

[tex]x^2 + 1 = b^2[/tex]

BD will simply be (2 - x). From the Pythagorean Theorem:

[tex]\displaystyle (2-x)^2 + CD^2 = a^2[/tex]

Substitute:  

[tex]\displaystyle (2-x)^2+ 1 = a^2[/tex]

We have the expression:

[tex]\displaystyle a^2 + (2\sqrt{3} - 1) b^2[/tex]

Substitute:

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

Part 2)

We can simplify the expression. Expand and distribute:

[tex]\displaystyle (4 - 4x + x^2 + 1)+ (2\sqrt{3} -1)x^2 + 2\sqrt{3} - 1[/tex]

Simplify:

[tex]\displaystyle = ((2\sqrt{3} -1 )x^2 + x^2) + (-4x) + (4+1-1+2\sqrt{3})[/tex]

Simplify:

[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]

Since this is a quadratic with a positive leading coefficient, it will have a minimum value. Recall that the minimum value of a quadratic always occur at its vertex. The vertex is given by the formulas:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 2√3, b = -4, and c = (4 + 2√3).

Therefore, the x-coordinate of the vertex is:

[tex]\displaystyle x = -\frac{(-4)}{2(2\sqrt{3})} = \frac{1}{\sqrt{3}} =\boxed{ \frac{\sqrt{3}}{3}}[/tex]

Hence, the value of x at which our expression will be the lowest is at √3/3.

To find ∠BAC, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

Substitute:

[tex]\displaystyle \tan \angle BAC = \frac{CD}{x}[/tex]

Substitute:

[tex]\displaystyle \tan \angle BAC = \frac{1}{\dfrac{\sqrt{3}}{3}} = \sqrt{3}[/tex]

Therefore:

[tex]\displaystyle\boxed{ m\angle BAC = \arctan\sqrt{3} = 60^\circ}[/tex]

Determine the center and radius of the following circle equation:

Answers

Answer:

Hello,

Step-by-step explanation:

[tex]x^2+y^2+6x+18y-10=0\\\\x^2+6x+9+y^2+18y+81-9-81-10=0\\\\(x+3)^2+(y+9)^2=10^2\\\\\\center=(-3,-9)\\radius=10\\[/tex]

The price of a hamburger is 3 dollars. what is the price of 90 hamburgers?

Answers

Cost of each Hamburger = $3

Cost of 90 Hamburgers = 3×90

= $270

Therefore cost of 90 hamburgers is $270

Must click thanks and mark brainliest

Write and algebraic expression:
The tens digit of a number is b and the units digit is twice as big. What is the value of the number in terms of b if the digits are reversed?

Answers

Answer:

21b

Step-by-step explanation:

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNKW THE ANSWER!!

Answers

Answer: will be D

Step-by-step explanation:

a student walks 50m on a bearing 0.25 degrees and then 200m due east how far is she from her starting point.​

Answers

Answer:

Step-by-step explanation:

I'm going to use Physics here for this concept of vectors. Here are some stipulations I have set for the problem (aka rules I set and then followed throughout the problem):

** I am counting the 50 m as 2 significant digits even though it is only 1, and I am counting 200 as 3 significant digits even though it is only 1. 1 sig dig doesn't really give us enough accuracy, in my opinion.

** A bearing of .25 degrees is measured from the North and goes clockwise; that means that measured from the x axis, the angle is 89.75 degrees. This is the angle that is used in place of the bearing of .25 degrees.

** Due east has an angle measure of 0 degrees

Now let's begin.

We need to find the x and y components of both of these vectors. I am going to call the first vector A and the second B, while the resultant vector will be C. Starting with the x components of A and B:

[tex]A_x=50cos(89.75)[/tex] so

[tex]A_x=.22[/tex]

[tex]B_x=200cos(0)[/tex] so

[tex]B_x=200[/tex] and we need to add those results together. Due to the rules for adding significant digits properly, the answer is

[tex]C_x=200[/tex] (and remember I am counting that as 3 sig fig's even though it's only 1).

Now for the y components:

[tex]A_y=50sin(89.75)[/tex] so

[tex]A_y=50[/tex] (which I'm counting as 2 sig fig's)

[tex]B_y=200sin(0)[/tex] so

[tex]B_y=0[/tex] and we need to add those results together.

[tex]C_y=50[/tex]

Now for the resultant magnitude:

[tex]C_{mag}=\sqrt{(200)^2+(50)^2}[/tex]  and that gives us a final magnitude of

[tex]C_{mag}=206[/tex] m

Now for the angle:

Since both the x and y components of the resultant vector are in quadrant 1, we don't need to add anything to the angle to get it right, so

[tex]tan^{-1}(\frac{50}{200})=14[/tex]

The girl is 206 meters from her starting point at an angle of 14 degrees

pls help and explain. I will give brainliest

Answers

Answer:

4 2/3 hours

Step-by-step explanation:

There are 7 days in a week

2/3 of an hour per day * 7 days

2/3 *7 = 14/3 hours

Changing to a mixed number

4 2/3 hours

Answer:

4.667

Step-by-step explanation:

2/3*7=4.667 (if you need decimal notation)

If you need a mixed number:

4+2/3:-)

I hope this helps!

[tex]- RosalindCordelia[/tex]

Enter the location of the point as an ordered pair.
5
-5
-6

Answers

Answer:

(4,1)

Step-by-step explanation:

(4,1) is the correct answer. Answered by Gauthmath


Water scarcity is increasing for all of the following reasons except
A. demand is increasing
B. the population of the globe is increasing
C. the amount of freshwater on Earth is decreasing
D. more land is being farmed
Please select the best answer from the choices provided
B
Ο Ο Ο Ο
С
D

Answers

Answer:

The Answer is C .............

Answer:

D

Step-by-step explanation:

You could see this both ways but I think this is the best answer because land is not saying the specifics for water

Hope this helps <3

Need more thanks? Comment /hearts

What is the midpoint of segment AB?

Answers

Answer:

(-1, -3.5)

Step-by-step explanation:

Use the midpoint formula by finding the points of A and B.

A = (-5, -4)

B = (3, -3)

Add the x-values of both coordinates to get the following:

[tex]3_{1} + -5_{2} = -2\\-2/2 = -1[/tex]

Midpoint = (-1, y)

Now we find the y-value by doing the same as we did to the x-coordinates of A and B.

[tex]-3_{1} + -4_{2} = -7\\-7/2 = -3.5[/tex]

Midpoint = (-1, -3.5)

Answer the question

Answers

Answer:

1,041,958.5, or 104,195 1/2

Step-by-step explanation:

All you have to do is 15787.25 times 66, because 15787.25 is the price for on acre, so 66 acres will be 15787.25 times 66. If you want to put it in fraction form, you can do 15787 1/4 times 66. I hoped you liked this answer!

Change 300mm into cm​

Answers

Answer:

30 centimeters

Step-by-step explanation:

true

It’s going to be 30 Cm

which of the following represents…

Answers

The correct answer is the first option

What is the volume of the solid? Let π=3.14
.

Answers

The volume of the solid as shown in the task content is; 2786.2cm³.

What is the volume of the solid?

It can be obtained from the task content that the solid given is a Cone.

On this note, the volume of the cone can be evaluated by means of the formula;

V = (1/3)π r²h where(r =22/2 = 11 and h=22).

Hence, Volume, V = (1/3) ×3.14× (11)²×22 = 2786.2cm³.

Read more on volume;

https://brainly.com/question/13677400

#SPJ1

What is an equation of the line that passes through the points (0, 8) and (-8, -4)?

Answers

Answer:

y = 1.2x + 2

Step-by-step explanation:

slope = (8 - 2)/(5 - 0) = 6/5y-intercept = (0, 2)y = (6/5)x + 2y = 1.2x + 2

Answer:

y=1.5x +8

Step-by-step explanation:

In the circle below, if arc AC = 66°, and arc BD = 146, find the measure of Select one:
a. 146
b. 212
C. 66
d. 106

Answers

Answer:

D. 106°

Step-by-step explanation:

m∠BPD = m∠APC = 1/2(mAC + mBD) = 1/2(66° + 146°) = 1/2(212°) = 106°

Answer:

By applying intersecting chords angle theorem:-

[tex]m\angle BPD= 106[/tex]° [tex]=1/2(BD+AC)[/tex]

[tex]=1/2(146+66)[/tex]

[tex]=1/2\time(212)[/tex]°

[tex]m\angle BPD=106[/tex]°

Answer:- D) 106°

OAmalOHopeO

please help me by answering this?

Answers

Answer:

180

Step-by-step explanation:

[tex]\frac{6}{2} x^{2} | \frac{8}{2}[/tex]

192-12=180

ASAP!!! PLEASE

A pair of equations is shown below: y = 2x − 1 y = 4x − 5 Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points) Part B: What is the solution to the pair of equations? (4 points)

Answers

Step-by-step explanation:

526 133 3821

P: 12345

j _o _I _n g _I _r l

o. n z-oo-o-m

1. thực hiện phép nhân
a) (2x-1)(x-8)
b) (x^2-3)(2x+4)
c) (2x-1)x+x^2-2(x-3)
d) x(2x-6).(-3x)+9x(x-1)
e) 2x(x^2-3x)-(x+1)(x^2-2)
f)3x(x-1)+x^2(x-2)+3(x-1)(x+1)

Answers

Answer:

Hey I'm sorry I didn't get to answer your question it's just that I need the points because I don't have enough to get help with my question. I hope you get the answer that you need for you question. Good Luck :).................

Step-by-step explanation:

what is the equation of the line written in general form?

Answers

Answer:

option 2 or y + x -2 = 0

Step-by-step explanation:

Given a line on a graph, it is easiest to start with point-slope form.

y = mx + b

where m is the slope (rise/run) and b is the y-axis intercept.

From the plot m = -2/2 = -1 and b = 2 SO

y = mx + b

y = -x  + 2

Then the general form is

y + x -2 = 0

below are properties of a square which one is not a all sides are equal b all angles are right angles C has five interior angles d diagonals are equal​

Answers

Answer:

has five interior angles

a square is a quadrant meaning it has four interior angles

What is the value of the expression below when z=10z=10 and w=4w=4? 2z-3w 2z−3w

Answers

Answer:

8

Step-by-step explanation:

more details

2(10)-3(4)

20-12

8


[tex] \frac{5}{5 \sqrt{6 + 2 \sqrt{3} } } \times ( \frac{1}{5 \sqrt{3} } + \frac{3 \sqrt{2} }{2 \sqrt{3} } - \frac{2 \sqrt{3} }{3 \sqrt{2} } ) = [/tex] ....................​

Answers

Decimal form = 0.1702

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

the length of each Edge of a cube is X centimeters. if x is an integer, why can't the volume of the cube equal 15 cm3.​

Answers

Answer:

see explanation

Step-by-step explanation:

The volume cannot be 15 cm³ because it is not a perfect cube.

V = x³

let x = 4 then x³ = 4³ = 64 ← a perfect cube

There is not an integer when cubed gives 15

I need help on this asap please!

Answers

Answer:

-8 5/20 , 4/25 , 9/20

Step-by-step explanation:

If there are negative numbers, those are the least. Let's say the number was -2 and -1. With a positive integer, 2 would be greater, but since it's negative, it's the least. SO -8 and 5/20 would be the least. Then putting the other two fractions into decimal form, or you can find the greatest common denominator, you'll find that 9/20 is greater than 4/25.

Can someone answer this pls

Answers

Answer:

maximum/minimum value for f(x) = ax2 + bx + c: Put the quadratic in standard form f(x) = a(x − h)2 + k, and the absolute

Step-by-step explanation:

maximum/minimum value is k and it occurs at x = h. If a > 0, then the parabola opens up, and it is a minimum functional value of f.

Sishsisbsushansjnsnsisjsbabajsuhsbshia

The lengths of the sides of a triangle are 4,5 and 6 if the length of the longest side of a similar triangle is 15,what is the length of the shortest side of the triangle

Answers

Answer:

The length of the shortest side of the triangle is 10.

Step-by-step explanation:

Given that the lengths of the sides of a triangle are 4, 5 and 6, if the length of the longest side of a similar triangle is 15, to determine what is the length of the shortest side of the triangle, the following calculation must be performed :

6 = 15

4 = X

4 x 15/6 = X

10 = X

Therefore, the length of the shortest side of the triangle is 10.

Can anyone help me with this please and maybe explain it?.. I need working please
I'll mark as brainlist

Q. A factory uses 800 watts of electricity in 40 minutes. How many watts does it uses in 3 hours?​​

Answers

Answer:

it uses 3,600 watts of electricity in 3 hours

Electricity used in 40 minutes = 800 watts

So, electricity used in 1 minute

= 800watts/40

= 20 watts

Electricity used in 3 hours

= electricity used in 180 minutes

= electricity used in 1 minute × 180

= 20 watts × 180

= 3600 watts

help solve for b it is for trigonometry

Answers

Answer:

[tex]b\approx 21.435332[/tex]

Step-by-step explanation:

The Law of Sines is a property that relates the sides and angles of any triangle. This property states the following:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Where (A), (B), and (C) are the angles of the triangles. The sides (a), (b), and (c) are the sides opposite their respective angles, (side (a) is the opposite angle (<A); side (b) is the opposite angle (<B); and side (c) is the opposite angle (<C)). Substitute the given information into the formula and solve for the unknown:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

[tex]\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]

Remove the parts of the equation that are not relevant to the problem,

[tex]\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]

[tex]\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]

Take the cross product of the proportion,

[tex]\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]

[tex]18(sin(72))=b(sin(53))[/tex]

Inverse operations,

[tex]18(sin(72))=b(sin(53))[/tex]

[tex]b=\frac{18(sin(72)}{sin(53)}[/tex]

[tex]b\approx 21.435332[/tex]

simplify. 5+ 8y^2- 12y^2+ 3y

Answers

Answer:

The answer simplified would be:

-4y^2+3y+5

If you combine the like terms, you will get this answer.

You have to add 8y^2 to -12y^2 and you get -4y^2.

Hope this helps you! :)

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