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
Simplify the expression
Answer:
x^(3)y^(4)\sqrt(2)
Step-by-step explanation:
A letter L with a height of 9 inches is drawn on the actual flag. What should be the height and inches of a letter L in the scale drawing? Explain plzzz....
Answer:
0.5 inch on the drawing
Step-by-step explanation:
The following information is missing:
The scale factor of the drawing to the actual flag is represented by the ratio 1:18.
This scale factor means that 1 inch on the drawing are equivalent to 18 inches o n the actual flag. We want to know the height on the drawing, given that a height of 9 inches is drawn on the actual flag. The following proportion must be satisfied:
1 inch on the drawing / x inch on the drawing = 18 inches o n the actual flag / 9 inches o n the actual flag
x = 9/18 = 0.5 inch on the drawing
I need help finding the length of GH.
Answer:
length of arc=2r+teete ×2πr
360
2×13+155°×2×22×13
360. 7
26+155°×572
360. 7
26+88660
2520
88686
2520
35.404
What is the sum of 1-2 and V-18?
Answer:
v-19
Step-by-step explanation:
Answer:
It depends on what you mean.
Step-by-step explanation:
If its to separate questions,
1-2= 1
V-18= -13
If its one whole question then
1-2 - V-18= 14
1-2 / V-18= -0.07692307692
1-2 * V-18= -13
1-2 + V-18= -12
Hope this helps! :D
Find an explicit formula for the geometric sequence 3, 15, 75, 375...
Answer:
3 * 5 ^ (n-1)
Step-by-step explanation:
3 is the first term and it multiplies by 5
The explicit formula for the geometric sequence is [tex]T_n = 3(5)^{n-1}[/tex]
The standard explicit formula for a geometric sequence is expressed as:
[tex]T_n = ar^{n-1}\\[/tex]
a is the first term
r is the common ratio
n is the number of terms
Given the sequence of numbers 3, 15, 75, 375...
r = 15/3 = 75/15 = 5
a = 3
Substitute the given parameters into the formula to have:
[tex]T_n = ar^{n-1}\\T_n=3(5)^{n-1}[/tex]
Hence the explicit formula for the geometric sequence is [tex]T_n = 3(5)^{n-1}[/tex]
Learn more here: https://brainly.com/question/20548958
In the expression 16x + 2x – 5y + 17, which terms are “like terms”?
Also i didn't mean to say exam on last question, turns out it was a quiz, my bad it just has alot of questions over 4, it has 6.
Answer:
16x and 2x have like terms
Asphere and a cylinder have the same radius and height. The volume of the cylinder is 64 m3.
hl
.
Answer:
r=21.3 h=32
Step-by-step explanation:
Please, someone, help me quickly!!
Answer:
(B)
Step-by-step explanation:
The value of 9 is more than the value than 4.
Therefore,
9 > 4.
4 is not greater than 9, and nine is not less than four.
Brainilest Appreciated!
A running track is 1/4 of a kilometre. What is the
total distance a runner travels if he goes three
times round the track?
How many times would you have to go round the
track to run 2 kilometres?
Willow has read 1/7 of the books in the library.
Answer:
If a runner went around the track 3 times, he would have ran 3/4 of a kilometre. He would have to run around the track 8 times to run 2 kilometres.
Step-by-step explanation:
Answer:He would have to go around the track 8 times to get 2 kilometers
Step-by -step explanation:
13. A circle with radius x is shown below. The diagram is not drawn to scale. (1 point)
What is the value of x? Round the answer to the nearest tenth.
Answer: 16.1
Step-by-step explanation:
x^2 = 8^2 + (28/2)^2
x^2=64 + 196
x^2= 260
Take the square root of 260 and get 16.1!
The value of x is x=16.1
Chord
The perpendicular from the center of a circle bisects the chord
RadiusA line from the center of the circle to the circumference of the circle is the radius of the circle
Lets connect the center of the circle to the other end of the chord that is at the circumference of circle
The diagram attached below
The line OA from the center bisects the chord
AB= half of 28 = 14
the triangle AOB forms a right angle triangle
apply Pythagorean theorem to find out the value of x
[tex]x^2=8^2+14^2\\x^2= 64+196\\x^2=260\\\sqrt{x^2}=\sqrt{260} \\ x=16.1[/tex]
The value of x is 16.1
Learn more information about 'perpendicular line ' here
brainly.com/question/4234327
Tomas selects one of these garments at random. Let AAA be the event that he selects a blue garment and let BBB be the event that he chooses a shirt.
Please help!!!
Answer:
can u explain it more lol
Step-by-step explanation:
1)The probability of choosing a blue garment is 1/2
2)The probability of choosing a shirt is 1/3.
Thomas has 1 blue shirt
Thomas has 1 green shirt
Thomas has 1 blue hat
Thomas has 1 green scarf
Thomas has 1 blue pair of pants
Thomas has 1 green pair of pants
So, number of blue garments = 3
Number of shirts = 2
Total garments =6
What is probability?Probability is the measure of the likelihood of an occurrence.
P(event) = Favorable outcomes / Total outcomes
P(blue garment) = 3/6 =1/2
P(shirt) = 2/6 =1/3
Hence, 1)The probability of choosing a blue garment is 1/2
2)The probability of choosing a shirt is 1/3.
To get more about probability visit:
https://brainly.com/question/24756209
Find the slope of the line that passes through (10, 8) and (1, 16).
Simplify your answer and write it as a proper fraction, improper fraction, or integer
Answer:
-8/9 is the answer
The frequency table represents the results of a survey comparing the average age of household members to the way that they watch non-network television. A 4-column table with 3 rows titled Television Viewing Method. The first column has no label with entries internet, cable, total. The second column is labeled average household age under 40 with entries 54, 81, 135. the third column is labeled average household age 40 or older with entries 23, 92, 115. the fourth column is labeled total with entries 77, 173, 250. Madigan converts the frequency table to a conditional relative frequency table by row. Television Viewing Method A 4-column table with 3 rows titled Television Viewing Method. The first column has no label with entries internet, cable, total. The second column is labeled average household age under 40 with entries W, Y, 0.54. The third column is labeled average household age 40 or older with entries X, Z, 0.46. The fourth column is labeled total with entries 1.0, 1.0, 1.0. Which value should she use for X? Round to the nearest hundredth. 0.09 0.20 0.25 0.30
Answer:
For X they would have to divide the number from the first given chart for average household of the people that are ages 40 or under, which is 23, by the total internet, which is now 77.
Therefore, X = 23/77 = 0.2987, which would round to 0.30
Mark as brainliest please, I need a few more :)
Answer:
.30
Step-by-step explanation:
< 40 > 40 total
internet 54 23 77
cable 81 92 173
total 135 115 250
< 40 > 40 total
internet w x 1
cable y z 1
total .54 .46 1
x is 23 /77 =.29870
Find the 43rd term of each sequence.
1. 21,12,9,3,...
Answer:
-231
Step-by-step explanation:
21, 12, 9, 3,...
Below is image
Answer:
-357
Step-by-step explanation:
a + (n-1)d
21+(42)(-9)
21-378
If A = (0,0) and B = (6,3), what is the length of AB?
O A. 6.24 units
O B. 7.73 units
O C. 5.20 units
O D. 6.71 units
Answer:
D. 6.71 units
Step-by-step explanation:
In order to solve this, we need to use the distance formula, which states that for two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:
d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Here, we have (0, 0) and (6, 3), so:
d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
d = [tex]\sqrt{(3-0)^2+(6-0)^2}=\sqrt{9+36} =\sqrt{45} =3\sqrt{5}[/tex] ≈ 6.71
The answer is thus D.
Answer:
D 6.71 units
Step-by-step explanation:
AB² = (6 - 0)² + (3 - 0)²
AB² = 36 + 9
AB² = 45
AB = 3sqrt(5)
Approximately 6.71
What is the point-slope form of a line with slope -3 that contains the point
(10,-1)?
A. y+ 1 = 3(x + 10)
B. x + 1 = -3(y-10)
C. y + 1 = -3(x-10)
D. y + 1 = 3(x-10)
Answer:
C
Step-by-step explanation:
Since we have a point and a slope, we can use the point slope formula.
The point slope formula is:
[tex]y-y_{1} =m(x-x_{1})[/tex]
where m is the slope, and (x1, y1) is the point given.
We know that the slope is -3, and the point given is (10, -1)
Therefore, our m is -3, x1 is 10, and y1 is -1.
y- -1 = -3(x-10)
y--1 is the same as y+1
y+1= -3(x-10)
Therefore, choice C is correct.
I need help nothing is working for the answer p÷3> 2
Answer:
p > 6
Step-by-step explanation:
Given
[tex]\frac{p}{3}[/tex] > 2 ( in fractional form )
Multiply both sides by 3 to clear the fraction
p > 6
Answer:
honestly idk
Step-by-step explanation:
it may be p (1/3)
hope this is right:000
PLEASE HELP ASAP worth alot
Answer:
I believe it is C
Step-by-step explanation:
Hope this helps
and if it at all possible and you mark me brainlyest please
Answer:
5 pts isnt a lot but ok.. and yes it is c
Step-by-step explanation:
how to i find b in y=my+b if the slope is undefined?
Answer:
By finding the y- intercept in the graph.
Step-by-step explanation:
This is the only point in the graph that is on the y axis.
Melanie's bedroom floor has length equal to 6x + 5 and width equal to 9x – 2 points
4. What equation represents the area of the floor?
Answer:
(6x+5)(9x-2)
Step-by-step explanation:
Area = Length x Width
Answer:
54[tex]x^{2}[/tex] +33x - 10
Step-by-step explanation:
you have to use F.O.I.L. First Outter Inner Last
(6x + 5)(9x - 2)
First (6x)(9x) = 54 [tex]x^{2}[/tex]
Outter (6x)(-2) = -12x
Inner (5)(9x) = 45 x
Last (5)(-2) = -10
combine middle terms
54[tex]x^{2}[/tex] +33x - 10
Evaluate A^2 for A = -4. -16 -8 8 16
Answer:
The answer is 4^2 (-16)
Step-by-step explanation:
-1 3/7 • (-3 2/5)
Find the product simplify if possible
Answer:
6 4/5
Step-by-step explanation:
-1 3/7 • (-3 2/5)
Let's turn them both into fractions with no whole numbers to make this easier:
-10/7 • -17/5
Now we can multiply straight across much easier!
170/35 (the negatives canceled each other out)
34/5 (simplified)
6 4/5 (answer)
Hope this helps! Please mark Brainliest :)
If a cube has a volume of 27mm3,
what is the length of one side?
Answer:
Step-by-step explanation:
Answer:
9mm
Step-by-step explanation:
since volume is l x w x h, you have to divide 27 by 3. you can do this because it is a cube
The graph of Y = COS X+ż is the graph of the y = cos(x) shifted in which direction?
T
2 units to the left
2
units to the right
units up
2 units down
Answer:
2 units up
Step-by-step explanation:
You're just taking the entire graph of cos(x) and then adding 2 so it moves everything up. If you added 2 to x BEFORE taking the cosine
(like y = cos (x+2) ), then you would shift it left 2. Adding and subtracting from the x moves everything left or right. Adding or subtracting at the end just moves it up and down.
The graph of y = cos x + 2 is the graph of the y = cos(x) shifted in ''2 units up.''
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
To find the graph of y = cos x + 2 is the graph of the y = cos(x) shifted in which direction.
Here, The function is,
⇒ y = cos x
Now, After translate 2 units up, we get;
⇒ y = cos x + 2
Thus, The graph of y = cos x + 2 is the graph of the y = cos(x) shifted in ''2 units up.''
Learn more about the transformation visit:
https://brainly.com/question/30097107
#SPJ7
Math question down below
Answer:
314.961
Step-by-step explanation:
What is the volume of the right cone below?
Answer:
The answer is A.
Step-by-step explanation:
You have to use the formula of volume of cone,
[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
Given that the diameter of cone is 10 units so the radius is 5. Then substitute the followung values into the formula :
Let r = 5 units,
Let h = 45 units,
[tex]v = \frac{1}{3} \times \pi \times {5}^{2} \times 45[/tex]
[tex]v = \frac{1}{3} \times \pi \times 1125[/tex]
[tex]v = 375\pi \: \: {units}^{3} [/tex]
Answer:
[tex]375\pi \: \: units ^{3} [/tex]
Answer A is correct.Step-by-step explanation:
[tex]v = \pi {r}^{2} \frac{h}{3} \\ =\pi \times 5 \times 5 \times \frac{45}{3} \\ = \pi \times 25 \times 15 \\ = 375\pi \: \: units ^{3} [/tex]
Find the domain and range
Answer:
Domain: x = all reals
Range: y is less than or equal to -4
What is the length of the hypotenuse
Answer:
20
Step-by-step explanation:
To find Hypotenuse: Pythagorean Theroem
a^2+ b^2= c^2
The legs are A and B
The side that is directly across from the Right angle is C
12^2 + 16^2 =C^2
144+256=400
400 = c^2
Square root on both sides to get rid of c^2
The square root of 400 is 20
c=20
Answer:
20 feet
Step-by-step explanation:
c = (a² + b²)
c= (12^2 + 16^2)
c= square root (400)
c= 20
Solve for x.
x + 23 = -22
Enter your answer in the box.
Answer:
X= -45
Step-by-step explanation:
Subract 23 from both sides to solve for x.
Answer:
x = -45
Step-by-step explanation:
x + 23 = -22
x = -22-23
x = -45
Maria bought an SUV for 21,000 dollars. Nancy bought a sedan for 2/3 as much. How much less did Nancy spend on her sedan?
Answer:
7000
Step-by-step explanation:
21,000*(2/3)=14000
21,000-14,000=7000
Answer:
7,000 dollars
Step-by-step explanation:
21,000 divided by 3 is 7,000 = 1/3
So 2/3 = 7,000 x 2 = 14,000
To find how much less Nancy spent on her sedan you do 21,000 - 14,000 = 7,000