Can anyone please solve this for me right now?

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b² + c² - a²)/2bc

cos B= (a² + c²- b²)/2ac

cos C = (a²+ b²- c²)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s² + s² - s²)/(2s×s)

cos A = (s² )/(2s²)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s² + s² - s²)/(2s×s)

cos B = (s²)/(2s²)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s² + s² - s²)/(2s×s)

cos C = (s² )/(2s²)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

Learn more on The law of cosines here:

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          [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

        What is the number sentence for "1 less than n is the sum of z and 2?"

         [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

  ❖ First, Notice it says "1 less than n". This expression indicates that

        we subtract 1 from n, which  looks as follows:-

                                                     [tex]\Large\textit{n-1}[/tex]

❖ Now, It also says "the sum of z and 2". This indicates that we add z and

     2:-

                                       [tex]\Large\textit{z+2}[/tex]

❖ Now, Combine these two little expressions into one equation:-

[tex]\implies\sf{n-1=z+2}[/tex]

#TogetherWeGoFar

[tex]\rule{300}{1}[/tex]

Answer:

y = -0.2x+ 0.8

Step-by-step explanation:

If a line is perpendicular to another line then the slope of the line = the negative reciprocal of the other line

Here Line AB has the equation y = 5x - 1. Here slope = 5
This comes from the fact that if a line has the equation y= mx + c then the slope = m and the y intercept = c

If XY is the line perpendicular to AB then its slope = -1/5. Let the y intercept of XY be c

Then equation of line XY is: y = (-1/5)x + c = -0.2x + c (1)

Since it passes through (-1, 1) ie through x = -1, y=1, substitution these values into the above equation (1), we get

1 = (-0.2)(-1) + c or

1 = 0.2 + c or  

c = 0.8

Answer:

Both graphs in 2 separate attachments--placed in order

Hope it helps.

Hello ~

My name is Sxnnysoul, and I will be answering your question today! :D

Let's solve for x ~

⇢ [tex]\sf{x^2 \: + \: y^2 \: = \: 4}[/tex]

⇢  [tex]\sf{Step \: 1: \: Add \: -y^2 \: to \: both \: sides.}[/tex]

⇢  [tex]\sf{x^2 \: + \: y^2 \: + \: -y^2 \: + \: = \: 4 \: + \: -y^2}[/tex]

⇢  [tex]\sf{x^2 \: + \: -y^2 \: + \: 4}[/tex]

⇢  [tex]\sf{Step \: 2: \: Take \: square \: root.}[/tex]

⇢  [tex]\sf{x \: = \sqrt{-y^2 \: + \: 4} \: or \: = - \sqrt{-y^2 \: + \: 4}[/tex]

P.S here's the graph that might help you!

Let's solve of x ~

⇢  [tex]\sf{x^2 \: + \: y^2 \: = \: 32}[/tex]

⇢  [tex]\sf{Step \: 1: \: Add \: -y^2 \: to \: both \: sides.}[/tex]

⇢  [tex]\sf{x^2 \: + \: y^2 \: + \: -y^2 \: + \: = \: 32 \: + \: -y^2}[/tex]

⇢  [tex]\sf{x^2 \: + \: -y^2 \: + \: 32}[/tex]

⇢  [tex]\sf{Step \: 2: \: Take \: square \: root.}[/tex]

⇢  [tex]\sf{x \: = \sqrt{-y^2 \: + \: 32} \: or \: x \: = - \sqrt{-y^2 \: + \: 32}[/tex]

P.S here's the second image of the graph. so, you won't get confused.

Hope It Helps! ~

~ Learn With Sxnnysoul ~

[tex]\underline{Answer :}[/tex]

ꜱ x ɴ ɴ ʏ ꜱ ᴏ ᴜ ʟ

Answer:

Answer:-6x^2 -11x - 3

Step-by-step explanation:

(f.g)(x)=(-2x-3)(3x + 1)

= -6x^2 -11x - 3

Answer:

[tex]m <U = 80°[/tex]

Step-by-step explanation:

Before we start calculating we have to first note that the angles in a triangle always add up to 180°. Therefore in order to find the missing angle U we have to add both the angles we know, 37° and 63°, then subtract the sum from 180°

[tex]m < U = 180- (37 + 63) \\ \\ m < U = 180 - 100 \\ \\ m< U = 80[/tex]

Answer: 180 minutes

90 miles in 3 hours

Step-by-step explanation:

60 minutes = 1 hour

60 mins/20 mins = 3

60*3 = 180

30 miles per hour for 3 hours is 90 miles

Answer:

a) 6.3; b) (2;1).

Step-by-step explanation:

[tex]a) \ |PQ|=\sqrt{(X_P-X_Q)^2+(Y_P-Y_Q)^2}=\sqrt{4+36}=\sqrt{40} =6.3;[/tex]

[tex]b) \ (\frac{X_P+X_Q}{2};\frac{Y_P+Y_Q}{2}); \ = > \ (2;1).[/tex]

If order matters then that's permutation else that's combination

So

Here the answers are

#1

Teams cannot be repeated

#2

Teachers also can't be repeated

#3

Can't repeat

#4

Already mentioned

#5

Repeating allowed

#6

Can be repeated

#7

Can't be repeated

#8

Can be repeated

#9

Answer:

6x - 5 = 8x + 2

or -5-2 = 8x-6x

or -7 = 2x

or -7 / 2 = x

this is correct answer because in fraction form if one number is negative whole fraction is negative

Hey there!

IF YOUR EQUATION IS:

6x - 5 = 8x + 2
THEN:

SUBTRACT 8x to BOTH SIDES

6x - 5 - 8x = 8x + 2 - 8x

SIMPLIFY IT!

-2x - 5 = 2

ADD 5 to BOTH SIDES

-2x - 5 + 5 = 2 + 5

SIMPLIFY IT!
-2x = 2 + 5

-2x = 7

DIVIDE -2 to BOTH SIDES

-2x/-2 = 7/-2

SIMPLIFY IT!
x = -7/2

The step you had a partial mistake was step 2 because that’s not what had to simplify to get the 7/-2. You should’ve converted your equation to: -2x - 5 = 2 (as I put for STEP 1.1) but your overall result is correct x DOES equal to 7/-2.

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

brainly please

Step-by-step explanation:

yes because 5 is less than 8

Answer:

No, the correct solution is q < 8 because 5 can not be equal to 8 but rather less than 8 (only)

Answer:

true

Step-by-step explanation:

2log2 6- log2 9+ 1/3log2 27 =

= log2 6² - log2 9 + log2 27^(1/3)

= log2 36 - log2 9 + log2 3

= log2 [(36 × 3)/9]

= log2 12

The statement is true.

Answer:

w represents the width

w + 2 represents the length

2(w + w +2) = 76     formula for perimeter

w + w + 2 = 38        divide both sides by 2

2w + 2 = 38             combine like terms

2w = 36                    subtract 2 from both sides

w = 18                      divide both sides by 2

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6z² + 12z +1 8​

= 6(z^2 + 2z + 3).

That's it.

Answer:

3400

Step-by-step explanation:

1L=1000ml

½L=500ml price = 1700

2(500)=2(1700)

1000L= 3400

hence Joshua will pay R3400 for 1L of cooking oil

[tex]300a {}^{z + 1} bc[/tex]

Answer:

Step-by-step explanation:

1. Henry - 800. Chris - 600. 800 + 600 = 1,400 coins · 2. henry - 600. Chris - 400. 600 - 400 = 200 coins · 3. because henry has 800 chris

Answer:

y=3x+12

Step-by-step explanation:

Use this formula: y-y1=m(x-x1)
(y-Your y point=slope(x-Your x point)

Point= (-2, 6), Slope= 3

(Anything negative, you add. Anything positive, you subtract.)

Plug in your values: y-6=3(x+2)
distribute: y-6=3x+6
Add six to both sides of the equation:y-6(+6)=3x+6(+6)
We get our answer: y=3x+12
Hope this helps!! :)

Answer:

1744.4

First, remove 13

13 and use length times width times height to get the surface area. 14 x 14 x 8.9

Answer: 189 people preferred running.

Step-by-step explanation: 35% is equal to 35/100. Since 540 people were surveyed, we can multiply 35/100 by 540 to find that 189 people out of 540 preferred running. Hope this helps!

Using it's concept, it is found that the probability that the lawyer will flip to a page number that is not a multiple of 4 is given by:

[tex]p = \frac{19}{25}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 50 numbers, of which 50 - (48/4) = 38 are not multiples of 4, hence the probability is given by:

[tex]p = \frac{38}{50} = \frac{19}{25}[/tex]

More can be learned about probabilities at https://brainly.com/question/14398287

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Answer:

1-nonlinear it is not consistant

2- a increasing, b constant, c decreasing

3- 'a' walking away from hole, 'b' rests, 'c' goes back to hole (b could also be gather, as in food)

4- 8cm per second

work 16cm/2sec=8cm/1sec

Step-by-step explanation:

Find the values a, b, and c to substitute into the quadratic formula.

Notice how there are a, b, and c. Everything is left of the equal sign, leaving 0 on the right.

ax² + bx + c = 0

Notice how there are a, b, and c too, just like in standard form. After we find standard form, we can substitute a, b and c values into the quadratic formula.

[tex]\displaystyle{x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a} }[/tex]

Here are the steps we will follow:

Move everything to the left while keeping both sides equal.

x² + 1 = 2x – 3                 Equation from the question

x² + 1 + 3 = 2x – 3 + 3     Add three to both sides.

x² + 1 + 3 = 2x                 -3 + 3 cancels out to 0.

x² + 4 = 2x                      Simplify.

x² + 4 – 2x = 2x – 2x     Subtract 2x from both sides.

x² + 4 – 2x = 0                No numbers on the right side is the same as 0.

x² – 2x + 4 = 0                Rearrange to follow ax² + bx + c = 0.

Find a, b, and c from standard form.

ax² + bx + c = 0         Standard form

x² – 2x + 4 = 0           No number attached to x² means a = 1.

a = 1,  b = –2,  and  c = 4

Substitute a = 1, b = –2, and c = 4 into the quadratic formula.

[tex]\displaystyle{x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a} }[/tex]    

Here is how our formula set up should look:

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

Let's compare formula set up to the options in the question.

The denominator is 2(1). So, the answer is not option B.

Inside the square root, it says –4(1)(4). So, the answer is not option D.

This leaves us with either option A or option C.

Before the ±, it says –(–2). When simplified, –(–2) is 2.

Option C has –2. So, the answer is not option C.

Inside the square root, it says (–2)², which is equal to 2².

When solving exponents of negative numbers,

The exponent 2 is even.

(–2)² = 4

∵ (–2)² = 4 and 2² = 4

∴ (–2)² = 2²

(–2)² is the same as 2².

Therefore, the answer is option A.

Answer: 3

Step-by-step explanation:

Answer:

79.2 yards per minute

Step-by-step explanation:

First you 440 times 0.9. which equals 396. Then you divide the answer by 5 to get 79.2.

Answer:

A = 2700   M = 2100 dollars

Step-by-step explanation:

9 + 7 = 16 shares

  2 shares more = 600

       1 share = 300

9 shares * 300 = 2700

7 shares x 300 = 2100