Answer:
a²-7ab+7b²-2
Step-by-step explanation:
3a²-5ab+7b²+3 - ( 2a²+2ab+5 ) = 3a²-5ab+7b²+3 - 2a²-2ab-5 = a²-7ab+7b²-2
Please help me on this math problem
WILL GIVE BRAINLIEST! Given: ∆ABC, AB =√2. M ∈ AC, AM = 1. BM = 1, BC = 2. Find: m∠ABC
The measurement of ∠ ABC in [tex]\triangle ABC[/tex], When AB =√2, AM = 1. BM = 1, BC = 2 will be [tex](\cos^{-1}{5)[/tex].
The measures of angle ∠ ABC can be calculated as:
The Law of Cosines, states that:
[tex]c^2 = a^2+ b^2 - 2ab \cos (C)[/tex]
Where, c is the side opposite angle C, and a and b are the other two sides of the triangle.
The sides of ∆ ABC will be :
AB = [tex]\sqrt{2}[/tex] (given)
BC = 2 (given)
[tex]AC = 1 + \sqrt{MC}[/tex]
∆ ABC is a triangle and according to the triangle inequality theorem, the The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So:
BC+AB > AC
[tex]2+\sqrt 2 > 1 + {\overline{MC}}[/tex]
[tex]\sqrt 2 +1 > \overline{MC}[/tex]
The law of cosines for [tex]\angle ABC[/tex] can be calculated as:
[tex]{BC}^2 = {AB}^2 + {AC}^2 - 2.AB.AC.cos(\angle ABC)[/tex]
The values can be obtained by the substitution.
[tex]2^2 = (\sqrt2)^2 + (1+{\overline {MC)}^2 - 2.\sqrt2 > (1 +{\overline{MC}).cos (\angle ABC)[/tex]
[tex]4 = 3 +2.\overline{MC} + \overline{(MC})^2 - 2. (\sqrt2. (1+ \overline{MC}).cos (\angle ABC)[/tex]
This can be simplified as:
[tex]0 = 3 + 2.\overline{MC} + \overline{MC})^2 - 2. (\sqrt2. (1+ \overline{MC}).cos (\angle ABC)[/tex]
The value of [tex]\overline{MC}[/tex] can be calculated as:
[tex]\sqrt 2+1 > \overline{MC}[/tex]
Substitute the value in the equation,
[tex]0 = 3+2.(\sqrt2+1) + (\sqrt2+1)^2 - 2.\sqrt2. (1+ \sqrt2+ 1).cos (\angle ABC)[/tex]
[tex]0 = 3+2 \sqrt2+4+2\sqrt2+1-2\sqrt2-2-2\sqrt2-2\sqrt2- 2.cos (\angle ABC)[/tex]
[tex]0 = 10 - 2.cos (\angle ABC)[/tex]
Thus, the value of cos [tex](\angle ABC)[/tex] is calculated as:
[tex]cos (\angle ABC) = \dfrac{10}{2}[/tex]
[tex]cos(\angle ABC) = 5[/tex]
Thus, the value of[tex](\angle ABC)[/tex] is [tex](\cos^{-1}{5)[/tex].
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#SPJ12
Factors that are greater than 1/2 but less than one
6/8
Step-by-step explanation:
1/2 = 0.5
6/8 = 0.75
therefore, 0.75 > 0.5
Please help me on this math problem
Find the degree of this polynomial
z − 2
Answer:
1
Step-by-step explanation:
What is the exact value of sin(-5 π/3)
Answer:
√3/2 is the correct answer. I hope this helps ^^
Step-by-step explanation:
Evaluate 6/8×4/5 Give your answer in its simplest form.
Answer: 3/8
Step-by-step explanation:
Answer:
your answer is
its 3.5
Are the equations m+3=-5 and m-4=-12$ equivalent?
Answer:
Yes They Are Equivalent
Step-by-step explanation:
I checked by multiplying them.
Answer: yes, because they both equal x= -8
Step-by-step explanation:
m= -5 -3
calculate
= -8
m= -12+4
calculate
m= - 8
help pls the image below represents ____
Answer:
I think it's a Box Plot, hope this helps
Rebah and her twin brother are planning a birthday party at Pizza Pete's. There is a S64.75 charge to reserve a party room plus $4.95 per person charge for lunch
Explain how to find the greatest number of people that can attend the party for $175.00. Show your work, and state the number of people.
QUICKKK PLZZ
Answer:
22 people
Step-by-step explanation:
Step 1: I first subtracted $64.75 from $175.00 so that I knew how much would be leftover after the charge of the room, because you can't count that cost. When I did this, I got $110.25. So then I knew how much was paid other then for the room.
Step 2: I then divided $110.25 by $4.95, so I would get the amount of people who went to the party, since each person costs $4.95. When I divided, I got 22.
So that would be my answer. I hope that helps. :)
Help help help help math math
Answer:
A = 192
Step-by-step explanation:
3 x 8^2
3 x 64 = 192
Algebra 2 How many Real solutions does the equation have? X-1 squared = x-4
The solutions are where the lines cross each other.
The lines only cross each other once so there is 1 real solution.
Answer: 1
deacrease 250 by 15%
Answer:
212.5
Step-by-step explanation:
help pls please hmmmm
Graph 7x+y=10x-4.
Show your work and explain the method used to determine the graph.
The graph must pass through the y-axis at y = -4 with a positive slope of 3
Given the expression
7x+y=10x-4.Write the given equation in standard form to have:
7x+y=10x-4.
y = 10x - 7x - 4
y = 3x - 4
From the equation, the slope is 3 and the y-intercept is -4
The graph must pass through the y-axis at y = -4 with a positive slope of 3.
Learn more on equation of a line here: https://brainly.com/question/13763238
fill in the table of values for y=2x+3
Answer:
2 4 2 y-3
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Yan po answer
Describe the following change as both an absolute change in terms of Percentage Points, and as a relative change in terms of a percentage.
The annual interest rate for Jack's savings account increased from 2.3% to 2.8%.
Answer:
0.5%
Step-by-step explanation:
I need help with this math help please!
Answer: R= 7
Step-by-step explanation:
Answer:
[tex]\huge\boxed{\sf t = 7}[/tex]
Step-by-step explanation:
-8 (4 - t) = 24
-32 + 8t = 24
Add 32 to both sides
8t = 24 + 32
8t = 56
Divide both sides by 8
t = 7
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807The Kicking Cacti and the Sprinting Stingrays met in their town's annual kickball
championship this year. They were so evenly matched that the game lasted 11 innings! The
Stingrays had 3 pitchers, and each of them pitched for the same number of innings.
How long did each of the pitchers for the Stingrays pitch?
Write your answer as a proper fraction or mixed number.
innings
Using proportions, it is found that each of the pitchers for the Stingrays pitched for [tex]\mathbf{\frac{11}{3} = 3\frac{2}{3}}[/tex] innings.
This question is solved by proportions, using a rule of three.In total, the Stingrays pitched 11 innings, with 3 pitchers. Each pitcher pitched the same amount of innings, hence, 1 pitcher pitched x innings.The rule of three is:
3 pitchers - 11 innings
1 pitcher - x innings
Applying cross multiplication:
[tex]3x = 11[/tex]
[tex]x = \frac{11}{3}[/tex]
11 divided by 3 has result 3 with remainder 2, hence, also considering the answer as a mixed number:
Each of the pitchers for the Stingrays pitched for [tex]\mathbf{\frac{11}{3} = 3\frac{2}{3}}[/tex] innings.You can learn more about proportions at https://brainly.com/question/24372153
I really need help! Please, please, PLEASE do not give me a link.
Last year, Kristen read a total of 30 fiction and non-fiction books. The number of non-fiction books was 5 less than 4 times the number of fiction books.
What is the total number of FICTION books that Kristen read last year?
A. 5
B. 7
C. 23
D. 25
Answer:
7 fiction and 23 non- fiction
Step-by-step explanation:
The number of non-fiction read was 5 less than 4 times the number of fiction books.
Assume fiction books are x.
An equation representing this would be:
x + (4x - 5) = 30
5x - 5 = 30
5x = 30 + 5
x = 35 / 5
x = 7 fiction books
Non-fiction books:
= 4x - 5
= 4 * 7 - 5
= 23 non - fiction books
What is the slope of the line
Answer:
Slope: 1/2
Step-by-step explanation:
Look at the file.
write an equation for the line that gose through the points (-2,6) and (2, 12)
Answer:
y = [tex]\frac{3}{2}[/tex] x + 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 6 ) and (x₂, y₂ ) = (2, 12 )
m = [tex]\frac{12-6}{2-(-2)}[/tex] = [tex]\frac{6}{2+2}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex] , then
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation.
Using (2, 12 ) , then
12 = 3 + c ⇒ c = 12 - 3 = 9
y = [tex]\frac{3}{2}[/tex] x + 9 ← equation of line
Which system of equations is equivalent to the following system? 3x 5y = 29 x 4y = 16 3x 5y = 29 â’x â’ 4y = 16 3x 5y = 29 â’3x â’ 12y = â’48 â’3x â’ 5y = 29 x 4y = 16 â’9x â’ 15y = 87 x 4y = 16.
The correct option is (B). [tex]3x+5y=29[/tex] And [tex]-3x-12y=-48[/tex].
Given Equations,
[tex]3x + 5y = 29......(1)[/tex]
[tex]x + 4y = 16.......(2)[/tex]
We have to find out Which system of equations is equivalent to the Given system of Equations.
1). System of equation are,
[tex]3x+5y=29\\-x-4y=16[/tex]
taking - common and transposing to R.H.S we get,
[tex]x+4y=-16[/tex]
This equation is not equal to equal (2), so the option (1) is not the system of equation equivalent to given Equations.
Similarly, on checking other options,
2. system of equation,
[tex]3x+5y=29\\-3x-12y=-48[/tex]
Taking -3 common from L.H.S. we get,
[tex]-3(x+4y)=-48\\\\x+4y=\dfrac{-48}{-3}[/tex]
[tex]x+4y=16[/tex].
Hence the Above system of equation is equivalent to the given system of equation.
So, there is no need to check option (3) and option (4).
Hence the correct option is (B).
For more details on Equations follow the link:
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Calvin works at a facility which processes apples. It costs the facility $0. 68 to make either a jar of applesauce or a bottle of apple juice. Due to the nature of the process and contractual agreements, Calvin’s facility must make and sell three jars of applesauce for every two bottles of apple juice. A jar of applesauce sells for $2. 20, and a bottle of apple juice sells for $3. 15. If the facility has annual overhead costs of $368,500, not including production costs, how many bottles of apple juice will the facility have sold when it breaks even every year? Round to the nearest whole bottle, if necessary. A. 38,789 b. 77,579 c. 116,368 d. 167,500.
The number of bottles the facility requires to sell when it breaks is given by
a system of two simultaneous equations.
When the facility breaks even, it would have sold 77,579 bottles of apples juice.Reasons:
The cost to make a jar of applesauce or a bottle of apple juice = $0.68
Number of jars of applesauce to be sold foe every 2 bottles of apple juice = 3 jars
The selling price for a jar of applesauce = $2.20
Selling price for a bottle of apple juice = $3.15
Annual overhead cost excluding production cost = $368,500
Required: Number of bottles of apple juice sold by the facility when it breaks even annually.
Solution:
Let J represent the number of bottles of apple juice sold, and let S represent the number of jars of apple sauce, by excluding the production cost, we have;
(3.15 - 0.68)·J + (2.2 - 0.68)·S = 368,500
S : J = 3 : 2
Which gives;
[tex]\displaystyle \frac{S}{J} = \mathbf{ \frac{3}{2}}[/tex]
[tex]\displaystyle S= \frac{3}{2} \cdot J[/tex]
Therefore;
[tex]\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot S = (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot \frac{3}{2} \cdot J = \mathbf{368,500}[/tex]
Which gives;
[tex]\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot \frac{3}{2} \cdot J = \mathbf{ \frac{19 \cdot J }{4} } = 368,500[/tex]
[tex]\displaystyle J = \frac{368,500 \times 4}{19} = \frac{1474000}{19}=77578\frac{18}{19} \approx 77,579[/tex]
The number of bottles of apple juice sold, J ≈ 77,579 bottles
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y = {x-5?
Which equation describes a line parallel to the line described by y-
Your answer:
o y=-2x
o y=-3x+1
oy
-
Oy - 2x - 5
Clear answer
Back
NEW
Answer:
The third option, 1/2..
HELP PLEASE IS IMPORTANT!
Solve the equation by using the Quadratic Formula.
2x 92-5
See attachment for answer and math work.
Select the correct answer.
You're trying to determine how much money it would cost to hire a lawn mowing company to cut your grass. Your yard
measures 8,712 square feet. The lawn mowing company charges a base rate of $30, plus $20 for every tenth of an
acre. You determine that it will cost $70 to hire the lawn mowing company. Which sentence best describes this price
estimate?
A. The price should be $50 because you have a 0.1 acre yard.
B. The price should be $50 because you have a 0.2 acre yard.
C. The price should be $90 because you have a 0.3 acre yard.
D.
The price estimate is accurate,
B1
F
Ayesha plays hockey.
Last year Ayesha scored 8 goals.
This year Ayesha scored 13 goals.
Calculate the percentage increase
in for the number of goals
scored.
Answer:
60% Increase
Step-by-step explanation:
Ayesha scored 5 more goals over her previous goal count of 8. That means:
(5/8) = 0.60 or 60% increase.
A 60% increase means a factor of 1.6 (1 + 0.6)
(8 goals)*(1.6) = 13 goals
Answer:
13 _18= 5
5/13×100%=38.46%
How can I solve this?
Answer:
This is not possible with 2 equal symbols
What type of angles are these?
Answer:
7. Consecutive Interior Angles that are Supplementary
8. Alternate Exterior Angles that are Congruent
9. Alternate Exterior Angles that are Congruent
10. Alternate Exterior Angles that are Congruent
11. Same Side Exterior Angles that are Supplementary
12. Consecutive Interior Angles that are Supplementary
Step-by-step explanation:
Not sure if I even got them in the correct order, my apologies. The picture provided was a bit hard to read.
Correct me if I am incorrect.
