(e) If a² + b² = 13 and ab = 6, find the value of (i) (a+b)² (ii) (a−b)²
Answers
Answer: Given a² + b² = 13 and ab = 6, we need to find (i) (a+b)² and (ii) (a−b)².
(i) (a+b)²
We can use the identity:
(a+b)² = a² + 2ab + b²
We know that a² + b² = 13 and ab = 6, so we can substitute these values into the identity to get:
(a+b)² = a² + 2ab + b²
= 13 + 2(6)
= 25
Therefore, (a+b)² = 25.
(ii) (a−b)²
We can use the identity:
(a-b)² = a² - 2ab + b²
Again, we know that a² + b² = 13 and ab = 6, so we can substitute these values into the identity to get:
(a-b)² = a² - 2ab + b²
= 13 - 2(6)
= 1
Therefore, (a−b)² = 1.
To summarize:
(a+b)² = 25
(a−b)² = 1
Step-by-step explanation:
Related Questions
Mel took out a loan of $40,000 at 14 percent on March 16, 2015 which will be due on January 9, 2016. Using exact interest the amount of Mel's interest cost is:
Answers
Answer:
the interest cost is $4,679.45
Step-by-step explanation:
The computation of the interest cost is shown below:
= Loan amount × rate of interest × given no of days ÷ total no of days in a year
= $40,000 × 14% × 305 days ÷ 365 days
= $4,679.45
hence, the interest cost is $4,679.45
((2016^2016)-(2016^2015))
/2015^2015
Answers
Answer:
2015(2016/2015)^2015
Step-by-step explanation:
\(\dfrac{2016^{2016}-2016^{2015}}{2015^{2015}}=\dfrac{2016^{2015}(2016-1)}{2015^{2015}}\\\\=2015\cdot\left(\dfrac{2016}{2015}\right)^{2015}\approx5475.9794\)
a candy maker produces 465 pounds of chocolate bites
Answers
Answer:
yes
Step-by-step explanation:
How do you model equations?
Answers
Answer: It basically it all depends on the type of equations you have.
Step-by-step explanation: For example: 1/2 x 2/5 = ?. We can use a modal to solve this problem. here is the modal that represents this equation. (Oh and I checked the answer, it was right)
Hope this helps you!
what is 3.75 as an improper fraction
Answers
answer may be this so my ans is right xxx
3 upon 75 = 1 /15
As a Mixed Number: \(3\frac{75}{100}\)
As an Improper Fraction: \(\frac{375}{100}\)
With steps:
3*100=300 plus 75 (the numerator) equals 375. The denominator does NOT change.
And we're done!
\(GraceRosalia\)
what is the length of ab
Answers
what is the graph of f(x) = 5(2)^x
Answers
The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.
The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.
As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:
When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).
As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.
For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.
The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.
Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.
The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.
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Jack needs 22 pirate for every two pirate ships he Manages
Answers
Answer:
Hi there! There is only one part of a question. I‘m not sure how to help you...
Sorry! Have a good day/night!
Step-by-step explanation:
what is LCM and WHAT is LCD?
Answers
a) In GeoGebra Links to an external site., construct a triangle (e.g. ABC), find the measure of all angles and all sides. Identify the type of your triangle (acute, right, obtuse/ scalene, isosceles, equilateral). Then construct a quadrilateral (e.g. DEFG), measure all angles and all sides. Identify the type of your quadrilateral (irregular, square, rectangle, etc.) Use the text command available in GeoGebra to describe the type.
b) Make a screenshot of your work in Geogebra and insert in the space provided below.
Answers
All angles are 90 degrees.Rhombus: All sides are of equal length.Square: All angles are 90 degrees and all sides are of equal length
a) To construct a triangle in GeoGebra, we can follow the steps below:
Step 1: Open GeoGebra and select the ‘Polygon’ tool.
Step 2: Select the ‘Triangle’ option.
Step 3: Click three points anywhere on the graph.
Step 4: Once you have drawn the triangle, you can use the ‘Angle’ tool to measure all the angles in the triangle. Similarly, use the ‘Length’ tool to measure the length of each side of the triangle.To identify the type of triangle, we can use the following properties:Acute Triangle: All angles of the triangle are less than 90 degrees.Right Triangle: One of the angles in the triangle is 90 degrees.Obtuse Triangle: One of the angles of the triangle is greater than 90 degrees.Scalene Triangle: All sides of the triangle are of different lengths.Isosceles Triangle: Two sides of the triangle are of the same length.Equilateral Triangle: All sides of the triangle are of the same length.To construct a quadrilateral in GeoGebra, we can follow the steps below:
Step 1: Open GeoGebra and select the ‘Polygon’ tool.
Step 2: Select the ‘Quadrilateral’ option.
Step 3: Click four points anywhere on the graph.
Step 4: Once you have drawn the quadrilateral, you can use the ‘Angle’ tool to measure all the angles in the quadrilateral. Similarly, use the ‘Length’ tool to measure the length of each side of the quadrilateral.To identify the type of quadrilateral, we can use the following properties:Irregular Quadrilateral: All sides and angles of the quadrilateral are of different lengths and measures.Trapezium: Only one pair of opposite sides is parallel.Parallelogram: Opposite sides are parallel.Rectangle:.b) Since we need to add a screenshot of the work done in GeoGebra, we cannot add it here. However, while you construct the triangle and the quadrilateral, you can keep adding the measure of angles and sides to find the properties of the figure. You can then use the Text command available in GeoGebra to describe the type of triangle or quadrilateral that you have constructed. To use the Text command in GeoGebra, follow the steps below:
Step 1: Select the ‘Text’ tool from the toolbar
.Step 2: Click anywhere on the graph to add the text box.
Step 3: Type the text in the text box.
Step 4: Customize the font, color, and size of the text as required.
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Decide whether a line with the given slope m=7/6 slants upward or downward from left to right, or whether its horizontal or vertical
Answers
When a bottle of milk replacer is made we add 1 cup of powdered milk to a 12 qt bottle. What is the ratio of powder to water?
Answers
Answer:
approximately 4 Tbsp. of powdered milk to 1 cup of water
Step-by-step explanation:
Answer:
....................
Find the arclength of the curve r(t) = ⟨ 10sqrt(2)t , e^(10t) , e^(−10t)⟩, 0≤t≤1
Answers
Answer:
\(\displaystyle AL = 2sinh(10)\)
General Formulas and Concepts:
Pre-Calculus
Hyperbolic FunctionsCalculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)
Derivative Rule [Chain Rule]: \(\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Exponential Differentiation
Integration
IntegralsIntegration Constant CDefinite IntegralsParametric Integration
Vector Value Functions
Vector IntegrationArc Length Formula [Vector]: \(\displaystyle AL = \int\limits^b_a {\sqrt{[i'(t)]^2 + [j'(t)]^2 + [k'(t)]^2}} \, dt\)
Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle \vec{r}(t) = <10\sqrt{2}t , e^{10t} , e^{-10t} >\)
Interval [0, 1]
Step 2: Find Arclength
Rewrite vector value function: \(\displaystyle r(t) = 10\sqrt{2}t \textbf i + e^{10t} \textbf j + e^{-10t} \textbf k\)Substitute in variables [Arc Length Formula - Vector]: \(\displaystyle AL = \int\limits^1_0 {\sqrt{\bigg[\frac{d}{dt}[10\sqrt{2}t \textbf i]\bigg]^2 + \bigg[\frac{d}{dt}[e^{10t} \textbf j]\bigg]^2 + \bigg[\frac{d}{dt}[e^{-10t} \textbf k ]\bigg]^2}} \, dt\)[Integrand] Differentiate [Respective Differentiation Rules]: \(\displaystyle AL = \int\limits^1_0 {\sqrt{[10\sqrt{2} \textbf i]^2 + [10e^{10t} \textbf j]^2 + [-10e^{-10t} \textbf k]^2}} \, dt\)[Integrand] Simplify: \(\displaystyle AL = \int\limits^1_0 {\sqrt{200 \textbf i + 100e^{20x} \textbf j + 100e^{-20x} \textbf k}} \, dt\)[Integral] Evaluate: \(\displaystyle AL = 2sinh(10)\)Topic: AP Calculus BC (Calculus I + II)
Unit: Vector Value Functions
Book: College Calculus 10e
The mean absolute deviation of Mr. Zimmerman's class is 0.46. What does this mean?
Answers
Answer:
is a measure of the average absolute distance between each data value and the mean of a data set.
9. Difference between the place values of "1" in 3116365 is
Answers
what's is 12+12x7+43?
Answers
Answer:
12x7+55
Step-by-step explanation:
Answer:
139
Step-by-step explanation:
12+43=
55
12x7=
84
84+55=
139
what type of number are associated with the word debt and why
Answers
The pyramid and prism above have the same triangular base and height. The volume of the pyramid is 18 cubic inches. What is the volume of the prism?
A. 36 cubic inches
B. 72 cubic inches
C. 6 cubic inches
D. 54 cubic inches
Answers
Since the volume of the pyramid is 18 cubic inches, then the volume of the prism is 3 times that amount which is 54 cubic inches 2.
Therefore, the answer is D. 54 cubic inches.
In a survey of 200 game lovers,it was found that 130 liked football, 90 liked cricket, and 20 didn't like both games.i) How many people were there who liked both football as well as cricket? ii)How many people like only cricket? A. 30,60 B. 40,50 C. 50,40
Answers
Step-by-step explanation:
Hey, there!!
Your required answer is:
i). = 40
ii). = 90
See explanation in picture..
Here, no(F) represents no. of people who just like football. and n (F intersection C) represents who like both games.
Hope it helps...
The question is in the picture. There is a 4th option you can't see and it is 14
Answers
At f(2) then function value is 2 so value of y is:
\(\begin{gathered} f(x) \\ at\text{ x=2} \\ f(2)=2 \\ \end{gathered}\)At x=2 given value y=2
Matemáticas resolver problemas
Answers
Sheena receives change of $7.55 after paying $20 bill.
How much is the change Sheena receives?Information is graphically represented in a bar graph. To represent value, it makes use of bars that stretch to various heights. Vertical bars, horizontal bars, grouped bars (multiple bars that compare values in a category), and stacked bars can all be used to create bar graphs.
Therefore,
Sheena buys three items, one sandwich and two pretzels.
Given the rate of sandwich = $6.95
Rate of pretzels = $2.75 each
So rate of two pretzels = $2.75 x 2 = $5.5
Total amount paid = $20
To find the change she receives ,
Total payment paid - total amount of items
Total amount for items = $6.95 + $5.5
= $12.45
Change receives = $20 - $12.45
= $7.55
Therefore the change Sheena receives is : $7.55.
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What are the coordinates of the terminal point determined by t = 10pi/3 ?
Answers
The correct option is- A: (-1/2 , -√3/2) are the coordinates found using the terminal points t = 10pi/3.
Explain about the terminal points?On the unit circle, the terminal point. To find any terminal point on the unit circle which start at (1, 0), and determine the angle in degree or radian on the circle that travel counter clockwise whereas if angle is positive as well as clockwise if the angle is negative. The terminal point is the coordinate of the endpoint.
Given values:
t = 10pi/3
convert to degrees
t = 10*pi/3
t = 10*180/3
t = 600 degrees
Find quadrant of 600 degrees.
600 = 360+240
240 comes in III quadrant
Thus, x-coordinate and y-coordinate are negative
Now,
240° = 180°+ 60°
60° is the angle for which terminal point are to be find.
Let ∅=60°
Consider unit circle
radius r = 1 units
Then,
x = -r*cos ∅
x = -cos 60
x = -(1/2)
And,
y = -r*sin ∅
y = -sin 60
y = -(√3)/2
Thus, the coordinates of the terminal point are found as (-1/2 , -√3/2) by
t = 10pi/3.
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Cameron has 468 trading card and for binders if each binder has the same amount how many will be in each binder
Answers
Is 5 inches bigger than 1/3 if a foot
Answers
Answer:
Yes
Step-by-step explanation:
1 foot= 12 inches
12÷3=4
This means that 1/3 of a foot is 4 inches
5 inches is larger than 4 inches
Answer:
Yes
Step-by-step explanation:
1/3 is 0.33333333333333 foot which = 4 inches.
Formula: multiply the value in feet by the conversion factor '12'.
So, 0.33333333333333 foot = 0.33333333333333 × 12 = 4 inches.
The other value is 5 inches.
5 inches is greater than 4 inches.
a tank truck holds 33.8 kl of oil. How many gallons does it hold
Answers
Sally owns a restaurant in Wooville. The city is trying to get a minor league team to move there in 2021, either to location A (near her restaurant) or location B. The team might stay in location C in another city. The probability of these events, and her estimated annual profit in 2021 are shown in the table below.
Answers
The standard deviation of the restaurant profits in 2021 is given by $71181.
Restaurant profit for outcome 'move to A' = $ 260000
Restaurant profit for outcome 'move to B' = $ 120000
Restaurant profit for outcome 'stay in C' = $ 100000
The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.
Standard deviation of the restaurant profits in 2021 is given by
= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)
= $ √(((100000)² + (40000)² + (60000)²)/3)
= $ √(15200000000/3)
= $ √5066666667
= $ 71181 (rounded to the nearest dollar)
Hence standard deviation of the restaurant profits in 2021 is given by $71181.
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The question is incomplete. The complete question will be -
2/3 X +9 equals -18 what is x?
Answers
____________________________
decimal form: x = -40.5
____________________________
mixed number form: x = -40 1/2
____________________________
(please give thanks if this was helpful)
Answer:
-81/2
Step-by-step explanation:
2/3x+9=-18
2/3=-27 Minus 9 from each side
2/3=-27 Divide 2/3 from each side
x=-81/2
5. Suppose the statement "even numbers are divisible by 2" is true. What is the truth value of
the statement "even numbers are not divisible by 2" ?
Answers
The truth value of the statement is false
What is the truth value of the statementGiven that
The statement "even numbers are divisible by 2" is true
The above statement is a conditional statement and we can calculate the following properties for the statement
ConverseContrapositiveInverse or NegationIn this case, we are to calculate the negation of the statement
When the statement "even numbers are divisible by 2" is negated, we have
The statement "even numbers are not divisible by 2" is not true
In logic expressions,
not true means false
So, the truth value of the statement is false
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The size of a rectangular television screen is usually given by its diagonal measurement. If a flat television screen is 20 inches high and 25 inches wide, what is its size rounded to the nearest inch?
Answers
Answer:
32 inches Aprox
Step-by-step explanation:
To find the size of a rectangular television screen given its height and width, we can use the Pythagorean theorem. The diagonal measurement (size) is the hypotenuse of a right triangle formed by the height and width.
Given:
Height of the television screen (h) = 20 inches
Width of the television screen (w) = 25 inches
Using the Pythagorean theorem:
diagonal² = height² + width²
diagonal² = 20² + 25²
diagonal² = 400 + 625
diagonal² = 1025
Taking the square root of both sides:
diagonal ≈ √1025
diagonal ≈ 32.02
Rounding to the nearest inch, the size of the television screen is approximately 32 inches.
Therefore, the size of the rectangular television screen, rounded to the nearest inch, is 32 inches.
Which graph shows the solution to the system of linear inequalities?
y≥ 2x + 1
y≤2x-2
Answers
Answer:
g
Step-by-step explanation:
jjnnkvigific and it's a boy f a horse y