Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to indicate exponents. For example, type a2 as a∧2. (Hint: Let s be a length of each side and x be the angle measure; then use these variables in the law of cosines.)
The algebraic proof shows that the angles in an equilateral triangle must equal 60° each
What is trigonometry?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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Cooking oil is sold 250ml packets. How much money would Joshua pay for 1litre of cooking oil,if the market price of 1/2litre is 1700
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
can anyone tell me what points I plot these two at ? ty
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
PLEASE HELP WILL MARK BRSINLIEST!!!!!pleaseeee
Answer:
[tex]x(3x-7)=3x^2-7x[/tex]
Step-by-step explanation:
[tex]\Large \begin{array}{| c | c | c |}\cline{1-3} \textsf{x} & 3x & -7\\\cline{1-3} x & 3x^2 & -7x\\\cline{1-3}\end{array}[/tex]
[tex]\textsf{Therefore,}\quad x(3x-7)=3x^2-7x[/tex]
During which year(s) did Henry collect more coins than Chris?
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
This window is designed in the shape of a right trapezoid.
Answer: 128°
Step-by-step explanation:
There are 360° in a trapezoid. Since this is a right trapezoid, two of those angles will be equal to 90°. We will set up the following equation, and solve.
360° = 90° + 90° + 52° + x°
360° = 90° + 90° + 52° + x°
360° = 232° + x°
128° = x
x = 128°
The obtuse angle has a measure of 128°.
As a single logarithm, 2log2 6- log29+ 1/3log2 27 = log2 12.
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.
Which of these numbers are relatively prime to 51? Select all that apply. da) 84 Ob) 70 Oc) 62 0d) 30
Answer:
b) 70
c) 62
Step-by-step explanation:
Numbers are relatively prime when they have no factors in common.
__
The factors of 51 are ...
51 = 3×17
The factors of the other numbers are ...
84 = 2²×3×7 . . . . . has a factor of 3 in common with 51
70 = 2×5×7 . . . . . . no factors in common
62 = 2×31 . . . . . . . no factors in common
30 = 2×3×5 . . . . . has a factor of 3 in common with 51
The numbers 70 and 62 are relatively prime to 51.
HELP ASAP PLEASE!!!!!!!
i need this answer quickly
5. Find the equation of the line that is perpendicular to the given line and passes through the given point. y = 5x-1; (-1, 1)
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
simplify 15a^z * 4c * 5ab
[tex]300a {}^{z + 1} bc[/tex]
Sandy baked two dozen cookies. She gave ten cookies to the neighbours and ate three cookies.
How many cookies are left?
Answer:
11
Step-by-step explanation:
2 dozen = 24
24-10=14
14-3=11
Answer:
11
Step-by-step explanation:
two dozens is 24 because one dozen is 12. 24-10=14-3=11
Help me with the 2 problems
Answer:
9) Vincent will not get the correct answer because the + 484 is unneccesary, as he already subtracted it.
10a) 310,000 + x = 465,000; so x = 155,000
10b) 930,000/310,000 = 3 times more
Step-by-step explanation:
can anyone help plssss??
Answer:
42 degrees
Step-by-step explanation:
48+90=138
180-138=42
Need help thank you
Answer: [tex]i\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{-5}=\sqrt{(-1)(5)}=\sqrt{-1} \sqrt{5}=\boxed{i\sqrt{5}}[/tex]
Select the correct answer.
Consider this quadratic equation.
X^2+ 1 = 2x-3
Which expression correctly sets up the quadratic formula?
OA. -(-2) + 2)2 - 4(1)(4)
2(1)
OB.-(-2) + VE-2)2 – (1)(4)
2(2)
OC -2 + (-2)2 - 4(1)(4)
2(1)
OD. -2 + (2)2 – 4(1)(-2)
2(1)
Find the values a, b, and c to substitute into the quadratic formula.
Remember:Standard formNotice how there are a, b, and c. Everything is left of the equal sign, leaving 0 on the right.
ax² + bx + c = 0
Quadratic formulaNotice 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]
Step-by-step solutionHere are the steps we will follow:
Rearrange the equation from the question into standard form.Determine the values for a, b, and c.Substitute a, b, and c into the quadratic formula.Compare options and simplify as needed.Rearrange into standard formMove 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.
Determine a, b, and c valuesFind 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 into the quadratic formulaSubstitute 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]
Compare answer optionsLet'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.
SimplifyBefore 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,
an odd exponent results in a negative product, and;an even exponent results in a positive product.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.
Simplify: (5 + i)(5 − i)
A) −12
B) 24i
C) 26
D) 8i
Answer:
C) 26
Simplify using the FOIL method--used to multiply binomials--and then combine real and imaginary parts of the problem.
5 × 5 = 25 + positive 1(i) = 26
Answer:
option c, 26
Step-by-step explanation:
(5 + i)(5 - i)
Apply complex arithmetic rule: (a + bi)(a - bi) = a^2 + b^2
a = 5, b =1
(5)^2 + (1)^2
(5)^2 = 25
(1)^2 = 1
25 + 1
Given the function f(x) = (1/4)^x , how will g(x) = (1/4) ^x-3 + 5 be translated
See
x is decreased by 3 .
and y is increased by 5
So translation is
f(x)=(1/4)^xHence
f(x)=(1/4)^x-3+5So
x will go 3 units right
y will go 5units up
Graph attached
Answer:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=\left(\dfrac{1}{4}\right)^x[/tex]
Translated 3 units to the right:
[tex]f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}[/tex]
Translated 5 units up:
[tex]f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5[/tex]
[tex]\implies g(x)=f(x-3)+5[/tex]
Therefore:
[tex]\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)[/tex]
Ali and Mo share a sum of money in the ratio Ali:Mo = 9:7 . Ali recieves $600 more than Mo. Calculate how much each recieves.
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
On a recent survey, 35% of those surveyed indicated that they preferred running. If 540 people were surveyed, how many people preferred running?
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!
Complete the long division problem on your own sheet of paper. Then, fill in the digits. 2 ÷ 694
Answer:
Here!! Hope i helped.
Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of PQ. P(1,4), Q(3,-2)
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]
Find the factor of each ff.
6z²+12z+18
Answer:
Step-by-step explanation:
6z² + 12z +1 8
= 6(z^2 + 2z + 3).
That's it.
What is the surface of the area of the composite figure
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
Sort these in either Combination or Permutation PLEASE HELP!!!! 100 POINTS
If order matters then that's permutation else that's combination
So
Here the answers are
#1
Teams cannot be repeated
Permutation#2
Teachers also can't be repeated
Permutation#3
Can't repeat
Permutation#4
Already mentioned
Permutation#5
Repeating allowed
Combination#6
Can be repeated
Combination#7
Can't be repeated
Permutation#8
Can be repeated
Combination#9
CombinationIs q = 5 a solution to the inequality below? q ≤ 8
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)
May I please get help to this question.
Answer: 3
Step-by-step explanation:
Rahul drives 10 miles in 20 minutes. If he drove three hours in total at the same rate, how far did he go?
Before you try that problem, answer the question below.
How many minutes did Rahul drive in total?
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
one last question! so i am doing this equation 6x-5=8x+2 but as I am doing it I got 7/-2 but in my answer key both are negative? what am I doing wrong?
this is what I have so far
6x-5=8x+2
6x-8x=5+2
-2x=7
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:)
