Answer\Step-by-step explanation:
0≤(x − y)^2 ⟹ 0≤x^2−2xy+y^2
⟹ 2xy≤x^2+y^2
⟹ xy≤ x2+y2\2
⟹ xy≤ x^2+y^2
since the clearly nonnegative real x^2+y^2
clearly satisfies x^2+y^2\2 ≤x^2+y^2.
The proof of the quadratic equation (x-y)²=x²-2xy+y² is given.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
Quadratic equation
(x-y)²=x²-2xy+y²
To prove the equation:
We substitute the value and see if LHS = RHS.
In the LHS,
LHS = (x-y)²
LHS = (2-1)²
LHS = 1
In the RHS,
RHS = x²-2xy+y²
RHS = 4 - 4 + 1
RHS = 1
LHS = RHS
Therefore, the theorem (x-y)²=x²-2xy+y² is proved.
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Sara had fourteen peaches and forty pears left at her roadside fruit
stand. She went to the orchard and picked more peaches to stock up the
stand. There are now eighty-one peaches at the stand, how many did
she pick ?
Answer:
67
Step-by-step explanation:
she picked 67 because if you take how many she had at the end and subtract it from the starting number it gives you 67
Write the fraction in simplest form. *
8/12
Answer:
2/3
Explanation:
/////////////
Multiply the following complex numbers. Reduce terms and simplify. Explain how your simplified result and the first term in the pair below are related algebraically to each other and to the complex number (1 + i).
1 1 - i
_____ * _____
1 + i 1 - i
Answer:
= 1/2 - 1/2i
Step-by-step explanation:
(x-4)^2=25 by taking the square root
Answer:
x = -1, 9
Step-by-step explanation:
[tex](x-4)^2=25\\x-4=\sqrt{25}\\[/tex]
x - 4 = ±5 (positive or negative 5, because (-5)^2 = 25)
x - 4 = 5
x = 9
or
x - 4 = -5
x = -1
x = -1, 9
Find the vertex of the graph of the quadratic function f(x)=7x2+14x+10
Answer:
plazzz get lost bro fast
a town has a population of 70,230 in the year 2020. Over the next five years, 6556 people move into the town for work, but 4096
Answer:
63,674
Step-by-step explanation:
70,230-6556
=63,674
Find the missing side length. Round to the nearest tenth.
Can someone PLEASE HELP!!
Answer:
the answer is 17.0 or just 17
Step-by-step explanation:
you have to use the pythagorean theorem, a^2 + b^2 = c^2
a = 11 and b = 13
11^2 + 13^2 = c^2
121 + 169 = c^2
290 = c^2
square root each side, so you have to find the square root of 290 which is 17.0293864
round it to the nearest tenth which is 17.0 but you can just write 17
hope this helps you understand it and answer it :)
Answer:
[tex]\boxed {\boxed {\sf c \approx 17.0}}[/tex]
Step-by-step explanation:
This is a right triangle because of the small square in the corner. Therefore, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs and c is the hypotenuse.
In this triangle, 11 and 13 are the legs because they make up the right angle. The missing side is the hypotenuse because it is opposite the right angle.
[tex]a=11\\b= 13[/tex]
[tex](11)^2+(13)^2=c^2[/tex]
Solve the exponents.
11²= 11*11=12113²= 13*13=169[tex]121+169=c^2[/tex]
Add.
[tex]289=c^2[/tex]
We are trying to solve for c, so we must isolate the variable. It is being squared. The inverse of a square is the square root, so take the square root of both sides.
[tex]\sqrt {289}= \sqrt {c^2}[/tex]
[tex]17.0293864=c[/tex]
Round to the nearest tenth. The 2 in the hundredth place tells us to leave the 0 in the tenth place.
[tex]17.0 \approx c[/tex]
The missing side is approximately 17.0
Solve the equation x-20.7=9.5 for x
NEED HELP ASAP!!!!!!!
Step-by-step explanation:
It's must be -3 ...............
What is the first step in solving 5x-2=3
Answer:
5x-2=3
5x=3+2
5x=5
x=5÷5
x=1
Lightening Energy Drink has 15.2 calories per fluid ounce. If Jeremy drinks two 12 ounce of Lightening Energy Drinks, then how much calories Dias he consume? Must show work
Answer:
15.2*12=182.4
Step-by-step explanation:
write the following integers in ascending order (smallest to biggest).1._5,2,1,_8 2. _4,_3,_5,2 3._10,_15,-7
Answer:
1. -8 , -5 , 1 , 2
2: -5, -4 , -3 , 2
3: -15, -10, -7
Step-by-step explanation:
Given
1. -5, 2, 1, -8
2. -4, -3, -5, 2
3. -10, -15,-7
Required
Sort in ascending order
To write in ascending order, means that the number must increase from left to right.
So, we have:
1. -5, 2, 1, -8
From left to right, we have:
[tex]-8 < -5 < 1 < 2[/tex]
Hence, the sorted list: -8 , -5 , 1 , 2
2. -4, -3, -5, 2
From left to right, we have:
[tex]-5 < -4 < -3 < 2[/tex]
Hence, the sorted list: -5, -4 , -3 , 2
3. -10, -15,-7
From left to right, we have:
[tex]-15 < -10 < -7[/tex]
Hence, the sorted list: -15, -10, -7
The smallest angle of a triangle is measure x degrees. The second angle is 45 degrees more than the smallest angle. The third angle is three times larger as the smallest angle. Write algebraic expression to express measures of the second and third angles of the triangle.
Answer:
Smallest angle = 27°
Second angle = 72°
Third angle = 81°
Step-by-step explanation:
Given:
In triangle
Smallest angle = x
Second angle = x + 45
Third angle = 3x
Find:
All angle
Computation:
Using angle sum property
x + x + 45 + 3x = 180
5x + 45 = 180
x = 27
Smallest angle = 27°
Second angle = x + 45
Second angle = 27 + 45
Second angle = 72°
Third angle = 3x
Third angle = 3(27)
Third angle = 81°
Eight hundred fifty two thousand, six hundred seventy four and thirty five hundredths in numbers
Answer:
Number = 857674.35
Step-by-step explanation:
Translating the word problem into a numerical format;
Eight hundred and fifty two thousand = 852,000
Six hundred and seventy four = 674
Thirty five hundredths = 35/100 = 0.35
Now, we would add all of the values together.
Number = 852,000 + 674 + 0.35
Number = 857674.35
Solve this system using Substitution
y=5
y=-2x+3
Answer:
x = -1
Step-by-step explanation:
-2x+3 = 5
subtract 3 on both sides: -2x = 2
divide both sides by -2: x = -1
If y varies directly as x and y =6 when x =2 ... find y when x=9
Answer:
27
Step-by-step explanation:
y = kx, where k is the constant of proportionality. If x = 2 and y = 6, that constant is determined as follows:
6 = k(2), or k = 3. Then y = 3x. When x = 9, y = 27
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
First option
Step-by-step explanation:
Biotechnology contains genetic manipulation and agricultural purposes, so growing crops in areas they usually do not grow would be a positive use of biotechnology.
I hope you get the problem right.
Help plzzz!! Marking most Brainly;)
Answer:
D it
Step-by-step explanation:
We have two equations, A quadratic and a linear equation.
The domain of a linear equation and quadratic equation is all real numbers but since it dealing with time we must make sure the roots or x-intercepts is positive.
Looking at the quadratic equation, we can use the discramnt formula to see if all roots are positve.
[tex]b {}^{2} - 4ac [/tex]
[tex] { - 6}^{2} - 4(1)(8.75)[/tex]
[tex]36 - 35 = 1[/tex]
The discramnt is greater than zero so there is two distinct real roots. So let check if they are positve
If you graph the equation, it intercepts at two positve roots so it is D
Which equation is equivalent to
4
1
+x=-
? Select all that apply.
4
6
X
6
X=
4
3
--
4 4
3
2
3
4.
) Intro
Answer:
3 and 2 r equivalent i belive
A carpenter needs to cut a 5 foot, 8 inch piece of wood from an 8-foot board to make a repair to a door. How many inches of wood will he have left after he makes the cut and repairs the cut and repairs the door?
Answer:
Step-by-step explanation:
1 foot = 12 inches
length of board in inches = 8 ft × (12 in)/ft = 96 in
length of cut in inches = 5 ft + 8 in = 5 ft × (12 in)/ft + 8 in = 60 in + 8 in = 68 in.
96 - 68 = 28 inches left
Can someone please help me with my homework
Answer:
Do not use, there's still one more piece of the puzzle missing.
X =
Step-by-step explanation:
Lets look everything over and compare the corresponding parts of the 2 triangles.
One side of each is shared between the two triangles.
Another side of each triangle is 13 on each triangle.
The included angle of one triangle is 80 degrees and the other is 110 degrees.
Which is greater, 0.024 or 0.102? How did you get answer?
Answer:
0.102
Step-by-step explanation:
because 0.102-0.024>0, meaning it has more. also the second number has a . tenth while the first number has 2 hundreths, which is smaller
Answer:
0.102
Step-by-step explanation:
Because 0.024 and 0.102 is compared by digits first digit of THEM both is 0 and its equal second digit is 0 and 1 so 1 is greater than 0 because of the 1 on the 0.102 it is greater
A piece of paper has an area of 93.5 square inches. How many times does it need to be folded in half before the area is less than 1 square inch? Explain how you know.
Answer:
7 times.
Step-by-step explanation:
Keep dividing 93.5 by 2 until it becomes less than 1.
The sheet needs to be folded in half 7 times.
Since the area of the piece of paper is 93.5 square inches, and we need to fold the sheet in half it 'n' times to get an area less than 1 square inch. This is written mathematically as 93.5(1/2)ⁿ ≤ 1.
So, dividing through by 93.5, we have
(1/2)ⁿ ≤ 1/93.5
(1/2)ⁿ ≤ 0.0107
taking natural logarithm of both sides, we have
㏑(1/2)ⁿ ≤ ㏑0.0107
n㏑(1/2) ≤ ㏑(0.0107)
n ≤ ㏑(0.0107)/㏑(1/2)
n ≤ -4.538/-0.693
n ≤ 6.55
Rounding up to the nearest whole number,
n ≅ 7
So, the sheet needs to be folded in half 7 times.
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The expression below represents the vertical height above the ground, in meters, of a roller coaster when it is x meters away from the starting station.
x^2+6x=15
Which statement best describes the term 15?
the maximum height of the roller coaster
the horizontal distance from the station when the roller coaster is at its maximum height
the velocity of the roller coaster
the initial height of the roller coaster
Answer:
D.) the initial height of the roller coaster
Step-by-step explanation:
Answer:
the initial height of the roller coaster
Step-by-step explanation:
Solve the proportion:
-9/6 = 3/x
Answer:
-2
Step-by-step explanation:
1. The temperature of a body rises from -6°c to 5°c. By how much degrees does it rises?
Write the phrase as an algebraic expression: The product of a number m and three.
Answer:
3m
Step-by-step explanation:
Product means multiplication, so you're multiplying 3 with m.
Carla draws two rectangles.
One of the rectangles has an area of 35 square inches.
The other has a perimeter of 20 inches
Select the two rectangles that could be the rectangles Carla draws
A rectangle with a width of 2 inches and a length of 6 inches
A rectangle with a width of 2 inches and a length of 8 inches
A rectangle with a width of 4 inches and a length of 6 inches
A rectangle with a width of 5 inches and a length of 7 inches
A rectangle with a width of 6 inches and a length of 10 inches
Answer:
A rectangle with a width of 5 inches and a length of 7 inches.
A rectangle with a width of 4 inches and a length of 6 inches
Step-by-step explanation:
De acuerdo a la siguiente imagen, selecciona la opción que muestre la operación que permite llegar al número encerrado en color rojo.
Answer:
2?
Step-by-step explanation:
I think im wrong/ creo que estoy mal?!
A computer game designer uses the function f(x) = 4(x - 2)2 + 6 to model the path of the fish The horizontal path of
the squid intersects the path of the fish. At what other point does the squid's path intersect the path of the fish?
Answer:
(-1,42)
Step-by-step explanation:
ahaha i got it wrong then it told me the actual answer
At point (5, 42), the squid's path intersect the path of the fish
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given a computer game designer who uses the function;
f(x) = 4(x - 2)² + 6
Since the function f(x) = 4(x - 2)² + 6 to model the path of the fish The horizontal path of the squid intersects the path of the fish.
When x = 5
f(x) = 4(x - 2)² + 6
f(x) = 4(5 - 2)² + 6
f(x) = 36 + 6
f(x) = 42
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