Kira is using the figure shown to prove the Pythagorean theorem. She starts by writing the
equation (a + b)2 – 2 = 4( ab) because she knows two equal ways to represent the area
of the shaded region. Which best describes the next steps Kira should take to complete her
proof?
Answer:
B. Simplify both sides of the equation to get [tex]a^2 + 2ab + b^2 - c^2 = 2ab[/tex]; then subtract 2ab and add [tex]c^2[/tex] to both sides of the equation
Step-by-step explanation:
Given
[tex](a + b)^2 - c^2 = 4(\frac{1}{2}ab)[/tex]
Required
Describe the next steps to
First, we open all brackets
[tex](a + b)^2 - c^2 = 4(\frac{1}{2}ab)[/tex]
[tex](a + b)(a + b) - c^2 = 4(\frac{1}{2}ab)[/tex]
[tex]a^2 + 2ab + b^2 - c^2 = 4 * (\frac{1}{2}ab)[/tex]
[tex]a^2 + 2ab + b^2 - c^2 = 2ab[/tex]
At this point, options A and C are incorrect because they didn't present the right result of the expression.
So, we have options B and D to consider
The next step is to subtract 2ab from both sides
[tex]a^2 + 2ab + b^2 - c^2 - 2ab = 2ab - 2ab[/tex]
Collect like terms
[tex]a^2 + b^2 - c^2 +2ab - 2ab = 2ab - 2ab[/tex]
[tex]a^2 + b^2 - c^2 = 0[/tex]
Lastly, to prove the Pythagoras theorem, the equation has to be in form of[tex]a^2 + b^2 = c^2[/tex]; meaning the [tex]c^2[/tex] is added to both sides; See below
[tex]a^2 + b^2 - c^2 = 0[/tex]
Add [tex]c^2[/tex] to both sides
[tex]a^2 + b^2 - c^2 + c^2= 0 + c^2[/tex]
[tex]a^2 + b^2 = c^2[/tex]
At this point, only option B completes Kira's proof
Answer:
It’s B
Step-by-step explanation:
I did the test
14 is 12 1/2% of what number?
Answer:
112
Step-by-step explanation:
Determine whether 90.5m .92m is equivalent to each of the following expressions.
Equivalent
Not equivalent
ვნm
81m
92.5m
Answer:i think it is 92.5
The measure of an angle is 15⁰. What is the measure of a complementary angle?
Answer:
75
Step-by-step explanation:
Because to find a complementary angle you take 90 and subtract it from the angle you already have, then that would be your answer. Complimentary angles are a pair of angles that add up to 90.
A manager samples the receipts of every fifth person who goes through the line. Out of 50 people, 4 had a mispriced item. If 1,600 people go to this store each day, how many people would you expect to have a mispriced item?
Answer:
128
Step-by-step explanation:
There are 32 50's in 1600.
So 32x4=128
PLEASE HELP - Select the TWO sets of points that CANNOT belong to a linear function.
We see for each row the x coordinates are in arithmetic progression, with a constant difference between successive points. For example in A x coordinates 3-5=1-3. So for this to be a line, the same has to be true of the y coordinates; they have to be in arithmetic progression.
A. 5/2, 3/2, 1/2 is just 5,3,1 (constant factors don't matter) so those are in arithmetic progression like the x coordinates so we have a line.
B. 1/2, 1, 3/2. In AP, a line
C. -1/2, -1/3, -1/4 multiplying by common denominator -12 makes 6, 4, 3. Those aren't in arithmetic progression. Not a line.
D. 2,3,4 in AP, a line.
E. 3/4, 1 3/4, 2 3/4 mixed numbers but obvious AP.
Answer: C
i need your help please asap
Step-by-step explanation:
First we will calculate the total amount spent on each website so
Website A = 49.95 + 4.39 = 54.34
Website B = 47.68 + 6.95 = 54. 63
So website A is cheaper by €0.29
?????HELPPPP PLEASE
Answer: choices 1 and 4
Step-by-step explanation:
A central angle is the angle that forms when two radii meet at the center of a circle. So the answers are the ones with point D in the middle.
Simple Probability - Item 20781
Question 4
Which of the following events has a probability closest to 1?
CLEAR
CHECK
It will snow in July in Phoenix, Arizona.
If you roll a die, it will come up with an even number.
If you flip a coin, it will come up either heads or tails.
The next child born in the United States will be a girl.
O
Answer:
C. If you flip a coin, it will come up either heads or tails.
Step-by-step explanation:
A. My guess is it doesn't rain much in Phoenix in July. A probability of 1 means it will happen for sure, so this is not it.
B. A die has 3 even numbers and 3 odd numbers. The probability of rolling an even number is 3/6 = 0.5. This is not it.
C. If you flip a coin, you either get heads or tails. The probability of heads or tails is 1 since one of the two outcomes will always happen. This is the answer.
D. The probability of the birth of a girl is 1 out of 2, so it is 0.5. This is not it.
Answer:
If you flip a coin, it will come up either heads or tails. It either will fall on heads or tails everytime so that is closest to one.
Step-by-step explanation:
HELP ASAP FIRST CORRECT GETS BRAINLIEST
Answer:
Right
Step-by-step explanation:
Answer: the first one is x less than 468 and the second one is and open circle at 468 and the third one is go left
Step-by-step explanation:
it would be a open circle if it wasnt a line under it and it would move the oppisite which is the left
WILL MARK BRAINLIEST! A bag has 4 blue marbles, 6 green marble and 3 red marbles in it. What is the ratio proportion of pulling a red or green marble from the bag ? *
Answer:
9:13
Step-by-step explanation:
need help with this question it’s a mastery grade!
Which number is divisible by 3?
A 137
B 136
C 138
D 41
Answer:
C (148)
Step-by-step explanation:
All numbers divisible by 3:
The numbers equal to something divisible by 3
ex:
138=
1+3+8= 12 which is divisible by 3, so 138 is divisible by 3
Answer:
138
Step-by-step explanation:
We know that if the sum of the numbers that make up 138 is divisible by 3, then 138 is divisible by 3. Note: If you divide 138 by 3, you get 46 which is a whole number.
Arial says that, for any pair of linear relations, if the coefficients of the y-terms are equal and the coefficients of the x-terms are equal, the graphs of the two lines will be parallel.
a. Give an example for which Arial's claim is true.
b. Give an example for which Arial's claim is false.
c. Suggest an improvement to Arial's claim.
Answer:
a. Give an example for which Arial's claim is true.If linear relations have equal coefficient about the independent variable, then those linear relations are parallel. For example, [tex]y=3x+4[/tex] and [tex]y=3x-5[/tex].
Notice that the coefficient of the dependent variable must be also equal, otherwise it would change the slope of the expression and they wouldn't be parallel.
b. Give an example for which Arial's claim is false.The statement is not false.
c. Suggest an improvement to Arial's claim.An improvemente would be that the constant term no need to be equal too, between linear relations, because they can be at "differecent heights", sort of speak.
Find the area. Will mark brainliest.
Answer:
98... BTW Google has a calculator to figure this out :) brainliest pls
Answer: why dont you find your own, we have same brain capacity, or you have less?
Step-by-step explanation: brainiest
PLEASE HELP I WILL MARK BRAINLIEST
Right to expressions that are equivalent to the expression below.
(9-c) + (9-c) + (9-c) + (9-c)
Answer:
36-4c
plz mark brainliest
What is the surface area of the cylinder with height 5 m and radius 8 m?
Round your answer to the nearest thousandth.
Answer: 653.45m²
I got it right thats why
Find the difference. Write your answer in standard form.
(5x3−3x+6)−(2x2−4x+8)
The difference is _______
Answer: 5x^3 + x-6
Step-by-step explanation:
which value makes the equation
3x - 6 = 36 true?
a) 10
b)12
c)14
d)16
Answer:
C) 14
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, add 6 to both sides:
3x - 6 (+6) = 36 (+6)
3x = 36 + 6
3x = 42
Next, divide 3 from both sides:
(3x)/3 = (42)/3
x = 42/3
x = 14
c) 14 is your answer.
~
The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How
much interest would Daniel have received if he had deposited $2000 into
his account? *
A. $1,285.35
B. $34.04
C. $90.00
D. $44,444.44
Answer:
90.00
Step-by-step explanation:
because all they did was add a couple of hundred that would not boost the 55.35 all the way to the thousands so A is not right It's not B because 55.35 is more than 34.04 so it's not B it's not D because 44,444.44 is just way too high it's even higher than option A.
What is the value of g?
The image is of a circle with a tangent and a secant, which are intersecting at an angle 38 degrees. Measure of smaller arc cut by them is g degrees and that of bigger arc is 119 degrees.
A. 124
B. 43
C. 100
D. 86
We have been given a circle with a tangent and a secant, which are intersecting at an angle 38 degrees. We are asked to find the measure of arc g.
We can see that angle with 38 degrees measure is a secant tangent angle outside the circle.
We know that measure of an angle formed by intersection tangent and secant outside circle is half the difference of intercepted arcs.
[tex]38^{\circ}=\frac{1}{2}(119^{\circ}-g^{\circ})[/tex]
[tex]38^{\circ}\cdot 2=\frac{1}{2}\cdot 2(119^{\circ}-g^{\circ})[/tex]
[tex]76^{\circ}=119^{\circ}-g^{\circ}[/tex]
[tex]76^{\circ}+g^{\circ}=119^{\circ}-g^{\circ}+g^{\circ}[/tex]
[tex]76^{\circ}+g^{\circ}=119^{\circ}[/tex]
[tex]76^{\circ}-76^{\circ}+g^{\circ}=119^{\circ}-76^{\circ}[/tex]
[tex]g^{\circ}=43^{\circ}[/tex]
Therefore, the measure of smaller arc is 43 and option B is the correct choice.
Jake received a student loan for $12,000. He plans on paying off the loan in five years. At the end of five years, J. Cole have paid $3600 in interest. What is a simple interest rate on the student loan?
Answer:
The simple interest rate on the student loan is 6%.
Step-by-step explanation:
To solve for the simple interest rate, use the formula for total simple interest:
[tex]I = Prt[/tex]
[tex]I[/tex] = total interest paid
P = principal, or starting value
r = interest rate in decimal form
t = time in years
State known values
P = 12,000
t = 5
[tex]I[/tex] = 3,600
Substitute known values and isolate "r"
[tex]I = Prt[/tex]
3,600 = (12,000) (r) (5)
3,600 = (60,000) r
r = 0.06
Since "r" is given as a decimal, convert this to a percentage by multiplying by 100.
0.06 = 6%
∴ The simple interest rate on the student loan is 6%.
Answer=6%
Step-by-step explanation:
Principal(P)=12000
Time(T)=5 yrs
Interest(I)=3600
We have,
I=PTR/100
3600=(12000*5*R)/100
3600*100=60000*R
R=360000/60000
R=6%
15 points for this!! ( btw d is 90 it got cut off)
Answer:
The value of x is D) 90°
Step-by-step explanation:
The sum of interior angles in a quadrilateral is 360°
As the total interior angles in a quadrilateral is 360 to work this out you would first need to work out the total of the angles given You can do this by adding 101 and 75 and 94, this gives you 270. This is because it tells us how much of that 360 degree total has been used.
The next step is to work out the angle of x. You can do this by subtracting the total angles gives of 270 from the total of 360, this gives you 90 degrees. This is because by subtracting it we are isolating the value of x.
1) Add the values of 94, 101, 75.
[tex]101+94+75=270[/tex]
2) Minus 270 from 360.
[tex]360-270=90degrees[/tex]
obtain all the zeros of the polynomial f[x]=x^4-3x^2-x^2+9x-6 if two of its zeros are-√3 and√3
Answer:woah
Step-by-step explanation:
What is the slope of a line that is parallel to the line shown?
Question and options in images below.
Answer: m= 2/3
Step-by-step explanation:
4/6 simplify into 2/3
Solve for y: 4.0
2y + 16 = 0
Answer:
y=-8
Step-by-step explanation:
2y+16=0
2y=-16
y=-8
sandra cut her sandwich into 3 equal parts. she ate 1 part for lunch. what fraction of the sandwich did sandra eat for lunch?
17. Which of the following forces is not a
long-range force?
A) gravitational force
B) friction
() electric force
D) magnetic force
Answer: D. Magnetic Force
Step-by-step explanation:
The range isn't compatible from a long distance. Only when close to contact.
Answer:
the answer is magnetic force
hope this helps u
Find the distance between (6, −2) and (1, −2).
Question 14 options:
5 units
6 units
7 units
4 units
Answer:
5 units
Step-by-step explanation:
the formula is delta y over delta x.
The distance between -2 and -2 is 0
The distance between 6 and 1 is 5
So, it's 5 units.
Hope this helps :)
PLS HELP NEED TO PASS TEST :)))))
Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale.
351 m^2
415 m^2
542 m^2
790 m^2
