factorize completely the expression(h+2k)²+4k²-h²
Answers
Answer:
\(\rm 4k(2k+ h)\)
Step-by-step explanation:
A expression is given to us and we need to factorise it . The given expression is ,
\(\rm\implies (h+2k)^2+4k^2-h^2\)
Open the brackets using the identity, (a +b)² = a² + b² + 2ab , we have ;
\(\rm\implies h^2+4k^2+4hk + 4k^2 - h^2 \)
Simplify ,
\(\rm\implies 8k^2+4hk \)
In the above expression 4k is common in both the terms , so that ,
\(\rm\implies \boxed{\pink{\frak{ 4k(2k+h) }}}\)
The expression factorized completely is (h +2k)[(h+2k) + (2k-h)]
From the question,
We are to factorize the expression (h+2k)²+4k²-h² completely
The expression can be factorized as shown below
(h+2k)²+4k²-h² becomes
(h+2k)² + 2²k²-h²
(h+2k)² + (2k)²-h²
Using difference of two squares
The expression (2k)²-h² = (2k+h)(2k-h)
Then,
(h+2k)² + (2k)²-h² becomes
(h+2k)² + (2k +h)(2k-h)
This can be written as
(h+2k)² + (h +2k)(2k-h)
Now,
Factorizing, we get
(h +2k)[(h+2k) + (2k-h)]
Hence, the expression factorized completely is (h +2k)[(h+2k) + (2k-h)]
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Related Questions
choose the graph of the function f(x)=1/2 times -2.
click on the graph until the correct graph appears.
Answers
Answer:
ur correct u got it.
Step-by-step explanation:
What is the area of a rectangle with a length of Four and two-fourths meters and a width of Seven and five-sixths meters?
Answers
Answer:
the area of the rectangle is 35.25 square meters.
Step-by-step explanation:
To find the area of a rectangle, we multiply the length by the width.
First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:
4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4
7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6
Now we can multiply the length and width:
Area = (18/4) * (47/6)
Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)
Area = (9 * 47) / (2 * 6)
Area = 423/12
Area = 35.25
Therefore, the area of the rectangle is 35.25 square meters.
7. Calculate the Perimeter AND Area of triangle
ABC
B
24 m
40 m
14 m
А
с
20 m
37 m
Answers
9514 1404 393
Answer:
perimeter: 121 marea: 399 m²Step-by-step explanation:
The perimeter is the sum of the side lengths. Here, the bottom side is broken into two parts, so that side length is the sum of the parts. The area is given by the formula for the area of a triangle.
perimeter = 24 m +40 m + 37 m + 20 m = 121 m
area = 1/2bh = 1/2(20 m +37 m)(14 m) = 399 m²
Evaluate the expression when b = 4 and y = -59b-y
Answers
We have to evaluate the expression 9b-y when b = 4 and y = -5.
We replace b with 4 and y with -5 and calculate:
\(\begin{gathered} 9b-y \\ 9(4)-(-5) \\ 36+5 \\ 41 \end{gathered}\)Answer: 41
help ASAP Which expressions have a value equal to or greater than 13?
A. five sixths x 13
B. 4 x 13
C. three fourths x 13
D. ten tenths x 13
Answers
Answer:
D. ten tenths x 13
Step-by-step explanation:
ten tenths are equal to one meaning that expression is equal to 13
1 x 13=13
If f(x) = 2x - 3, find f(-2).
Answers
Answer:
f(-2) is -7
Step-by-step explanation:
input -2 as x
2(-2)-3
-4-4
-7
If a ball is thrown straight up into the air with an initial velocity of 95 ft/s, it's height in feet after t second is given by y=95t−16t^2. Find the average velocity for the time period beginning when t=2 and lasting
(i) 0.1seconds
(ii) 0.01 seconds
(iii) 0.001 seconds
Finally based on the above results, guess what the instantaneous velocity of the ball is when t=2.
Answers
The instantaneous velocity must be v= 265 at t=2
The height in feet after t second is given by y(t)=95t−16t^2.
Average velocity is defined by:
\(v_{ave} = \frac{x_{f} -x_{i} }{t_{f} -t_{i} }\)
i)
\(t_{i}\) = 2
\(x_{i}\)=y(2)=174
\(t_{f}\)=2+0.1
\(x_{f}\) = y(2+0.1) = 365.4
\(v_{ave}\) = 280.54
ii)
\(t_{i}\) = 2
\(x_{i}\)=y(2)=174
\(t_{f}\)=2+0.01
\(x_{f}\) = y(2+0.01) = 349.74
\(v_{ave}\) = 264.88
iii)
\(t_{i}\) = 2
\(x_{i}\)=y(2)=174
\(t_{f}\)=2+0.001
\(x_{f}\) = y(2+0.001) = 348.174
\(v_{ave}\) = 263.316
Instantaneous velocity is defined by: \(v= lim_{t-0} \frac{delta x}{delta t}\)
When, delta t = 0, v = 265
So instantaneous velocity must be v= 265 at t=2
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Write the equation of the line that passes through the points (2,8) and(2,9). Put your answer in fully reduced point-slope form, unless it is avertical or horizontal line.
Answers
Concept
Use the equation of a line for two-point forms below to find the equation of a line.
\(\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}\)Step 1: Represent each value of the coordinate.
Point (2 , 8) and (2, 9)
\(\begin{gathered} x_1\text{ = 2} \\ y_1\text{ = 8} \\ x_2\text{ = 2} \\ y_2\text{ = 9} \end{gathered}\)Step 2: Substitute all the value in the equation
\(\begin{gathered} \frac{y\text{ - 8}}{x\text{ - 2}}\text{ = }\frac{9\text{ - 8}}{2\text{ - 2}} \\ \frac{y\text{ - 8}}{x\text{ - 2}}\text{ = }\frac{1}{0} \\ \text{Cross multiply} \\ (x\text{ - 2) x 1 = (y - 8) x 0} \\ x\text{ - 2 = 0} \\ x\text{ = 2} \end{gathered}\)Step 3: Final answer
x = 2 and it is vertical
\(\frac{2}{2+\sqrt{7} }\)
Answers
Answer:
\(\huge\boxed{\sf \frac{2\sqrt{7}-4 }{3}}\)
Step-by-step explanation:
This is a rationalizing denominator question.
Given expression:\(= \displaystyle \frac{2}{2+\sqrt{7} } \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - \sqrt{7} \\\\= \frac{2}{2+\sqrt{7} } \times \frac{2-\sqrt{7} }{2-\sqrt{7} } \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= \frac{2(2-\sqrt{7}) }{(2)^2-(\sqrt{7})^2 } \\\\= \frac{4-2\sqrt{7} }{4-7} \\\\= \frac{4-2\sqrt{7} }{-3} \\\\= \frac{-(4-2\sqrt{7}) }{3} \\\\= \frac{2\sqrt{7}-4 }{3} \\\\\rule[225]{225}{2}\)
A câmera is capable of snapping 1/2 of a picture per second how long will it take the camera to snap 6 pictures
Answers
So if you count by 2: 2,4,6,8,10,12
You can see that it would take 12 seconds
Hope this was helpful :)
Answer: 12 seconds
Step-by-step explanation:
Step 1: Find the unit rate
1÷0.5=2
1 picture takes 2 seconds
Step 2: Find amount of time taken to snap 6 pictures
2*6= 12
Help me please thank you so much I appreciate it thank you
Answers
Answer:
(-2,-1)
Step-by-step explanation:
1 is x -2 is y
y is -2 so the point so far is (-2, -x)
-x is -1 so the point is (-2, -1)
By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0
Answers
By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.
To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.
Let's start by graphing the constraints:
1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.
2. Plot the line -x + 3y = 6 using a similar process.
3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.
Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.
Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.
Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.
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88.98 to the nearest tenth
Answers
Answer:
89 is the answer
Step-by-step explanation:
88.98
= 89
9514 1404 393
Answer:
89.0
Step-by-step explanation:
One way to round a number is to add half the place value you're rounding to, then truncate at the desired place value.
Here, we want to round to a tenth (0.1), so we first add half that value:
88.98 + 0.05 = 89.03
Now, we throw away all digits after the tenths place.
89.0 . . . . our rounded value
We would like to know the velocity of the block when it reaches some position x. Finding this requires an integration. However, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. To get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx.
Answers
Answer:
An alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\) is \(a_x=v_x \frac{dv_x}{dx}\)
Step-by-step explanation:
We know that :
\(a_x=\frac{dv_x}{dt}\)
Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\)
So, We will use chain rule over here :
\(a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}\)
Hence an alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\) is \(a_x=v_x \frac{dv_x}{dx}\)
The alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx is \(a_x = v_x \frac{dv_x}{dx}\)
Chain rule:Here we used the chain rule:
It is the basic method for differentiating a composite function. Here the first factor on the right, Df(g(x)), represents that the derivative of f(x) is first found and then x, wherever it arises, is replaced by the function g(x).
So,
\(a_x = \frac{dv_x}{dt}\\\\ = \frac{dv_x}{dt} \times \frac{dx}{dx}\\\\= \frac{dv_x}{dx} \times \frac{dx}{dt}\\\\ = \frac{dv_x}{dx} \times \frac{dx}{dt} (\frac{dx}{dt} = v_x)\\\\ = \frac{dv_x}{dx} \times v_x\\\\= v_x\frac{dv_x}{dx}\)
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65%. persent of 120 students ate pizza for lunch how many student's ate pizza
Answers
0.65 of 120 is the same as
0.65 x 120.
0.65 x 120 = 78.
So, 78 students ate pizza.
.65 * 120 = 6.5 * 12 = 65 * 1.2 = 65 + 13 = 78 students ate pizza
double check
78 / 120 = 0.65
please give brainliest
write the number pattern by writing the next number of 100, 90, 80, 70
Answers
Answer:
60
Step-by-step explanation:
Goes down by ten everytime.
Answer: 60
Step-by-step explanation:
You are taking away 10 each time.
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
1. If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest?
Answers
Answer:
Age difference between oldest the youngest = 48 years
Step-by-step explanation:
Given: Ratio of ages of Kissi and Esinam is 3:5, ratios of ages of Esinam and Lariba is 3:5 and sum of the ages of all 3 is 147 years
To find: age difference between oldest the youngest
Solution:
Let age of Lariba be x years
As ratios of ages of Esinam and Lariba is 3:5,
Age of Esinam = \(\frac{3}{5}x\) years
As ratio of ages of Kissi and Esinam is 3:5,
Age of Kissi = \((\frac{3}{5}) (\frac{3}{5}x)=\frac{9}{25}x\) years
Sum of the ages of all 3 = 147 years
\(x+\frac{3}{5}x+\frac{9}{25}x=147\\ \frac{25x+15x+9x}{25}=147\\ x=\frac{147(25)}{49}=75\)
Age of Lariba = x = 75 years
Age of Esinam = \(\frac{3}{5}(75)=45\,\,years\)
Age of Kissi = \(\frac{9}{25}(75)=27\,\,years\)
So,
Age difference between oldest the youngest = 75 - 27 = 48 years
Determine whether or not the equations represent a direct variation. Sort the equation into appropriate category
Answers
Answer:
Direct V:
y=3x
y=(2/7)x
-0.5x=y
Not direct V:
y=2.2x+7
x=-1
y=4
Step-by-step explanation:
That was the answer on edge2020 :))
Direct variation usually conform to the general formula : \(y = kx \) where k is the proportionality constant. Hence sorting the equation into tbe appropriate category :
Direct variation :
y = 3x
Constant of proportionality, k = 3y = (2/7)x
Constant of proportionality, k = 2/7y = -0.5x
Constant of proportionality, k = -0.5Non - direct variation :
y = 2.2x + 7
Linear equation expressed in slope - intercept formy = 4 and x = - 1
These are variable declarations as the constants are only assigned to one variable and no unknown.Therefore, only three of the expressions exhibit direct variation while the other three do not.
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Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−15, 3), (−15, −6), and (25, −6)?
(−6, 25)
(−25, −3)
(6, −25)
(25, 3)
Answers
The missing fourth vertex needed to create a rectangle is (25, 3) option D.
Define the term vertices?Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.
Here, the width of one side of the rectangle;
⇒ +3 - (-6) = 9 unit (left side y-coordinates)
Similarly the length of the rectangle;
⇒ 25 - (-15) = 40 unit (up-side x-coordinates)
Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)
So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:
⇒ (25, -6+9) = (25, 3)
⇒ (-15+40, 3) = (25, 3)
Therefore, the missing fourth vertex is (25, 3)
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Identify the range of 2 ∣x − 4∣+ 6 .
Answers
Answer:
Range: [6, ∞), {y≥6}
Step-by-step explanation:
Hope this helps :)
Solve the inequality for x.
4 − 4x < 16
x < −3
x > −3
x > 3
x < 3
Answers
Answer:
x > -3
Step-by-step explanation:
4 - 4x < 16
- 4x < 16 - 4
- 4x < 12 (note that both can be divided by -4)
x > -3
That's the final answer.
AND if you're co fused about why the sign changed, you should always remember this
• ALWAYS change the inequality sign when you divide (÷) or multiply (×) by a negative numberBy negative num I mean any number that starts with a minus for example -2, -3, -5, -100
Choose as many answers as apply.
According to the lesson, things you can do to help you decide on a bank include:
compare interest rates
determine which bank has the most attractive buildings
ask friends where they bank
visit two or three branch office
Answers
Some things you can do to help you decide on a bank include:
Ask friends where they bankVisit two or three branch officesCompare interest ratesWhy are these important?When trying to locate a bank that offers competitive returns on savings and favorable borrowing costs, consider comparing interest rates.
To gather additional information about certain banks, why not solicit feedback from acquaintances? People who have personal experience with a particular bank can provide valuable insights into their satisfaction levels with regards to customer service, for example.
Finally, taking the time to visit branch offices can offer valuable clues regarding convenience level and overall atmosphere.
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can someone please help
Answers
Answer:
The measure of CD is 46
Step-by-step explanation:
From the midpoint theorem, we have,
FG = (1/2)CD
so,
\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)
Now,
\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)
What is
6/7 of 2/3.
Answers
Step-by-step explanation:
\( = \frac{6}{7} \times \frac{2}{3} \\ \)
\( = \frac{12}{21} \\ \)
Change into lowest term...
\( = \frac{4}{7} \\ \)
...
Explanation: 6/7 = .8572, 2/3 = .6667
.8572 x .6667 = .5714 = 4/7
I hope that this helped! :)
Please help me with this.
Answers
Here are the correct matches to the expressions to their solutions.
The GCF of 28 and 60 is 4.
(-3/8)+(-5/8) = -4/4 = -1.
-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.
The solution of 0.5 x = -1 is x = -2.
The solution of 1/2 m = 0 is m = 0.
-4 + 5/3 = -11/3.
-2 1/3 - 4 2/3 = -10/3.
4 is not a solution of -4 < x.
1. The GCF of 28 and 60 is 4.
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:
28 = 2 x 2 x 7
60 = 2 x 2 x 3 x 5
The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.
2. (-3/8)+(-5/8) = -1.
To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.
3. -1/6 DIVIDED BY 1/2 = -1/3.
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.
4. The solution of 0.5 x = -1 is x = -2.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.
5. The solution of 1 m = 0 is m = 0.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.
6. -4 + 5/3 = -11/3.
To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.
7. -2 1/3 - 4 2/3 = -10/3.
To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.
8. 4 is not a solution of -4 < x.
The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.
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Jamal's friends toss 12 balls to him at the same time. Three balls are red, 3 are green, 3 are blue, and 3 are white. Jamal manages to catch 5 of the balls.
What is the probability that he catches 2 red balls and 1 ball of each of the other colors?
Enter your answer as percentage, expressed to the nearest tenth of a percent, like this: 42.2%
Answers
Answer:
Step-by-step explanation:
1 white 1 green 1 blue + 2 reds = 5 balls
5 seen as a percentage
5%
1÷-½ aswer please!!
Answers
Answer:
\(( - 2)\)
Step-by-step explanation:
\(1 \div - \frac{1}{2} \\ 1 \times - \frac{2}{1} \\( - 2)\)
Hope this helps you.
have a nice day!
the density of the copper is 9.86g/cm\(x^{3}\)
![the density of the copper is 9.86g/cm[tex]x^{3}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/kBdJoEKedYKgyZmbWgXrufRB5h52H33f.png)
Answers
The mass of the cubic cuboid is 1.479 kilograms.
What is the mass of a copper cuboid?
Dimensionally speaking, density (ρ), in kilograms per cubic meter, is mass (m), in kilograms, per unit volume (V), in cubic meters. By the assumption of uniform density within the copper cuboid, the mass of the solid is equal to:
m = ρ · V
Where V is the volume of cuboid, in cubic meters.
And the volume of cuboid is:
V = w · h · l
Where:
w - Width, in meters. h - Height, in meters.l - Length, in meters.Please notice that a kilogram equals 1000 grams and a meter equals 100 centimeters.
First, calculate the volume of the cuboid:
V = (0.05 m) · (0.03 m) · (0.10 m)
V = 1.5 × 10⁻⁴ m³
Second, determine the mass of the cuboid:
m = (9.86 g / cm³) · (1 kg / 1000 g) · (1000000 cm³ / m³) · (1.5 × 10⁻⁴ m³)
m = 1.479 kg
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Suppose there is a simple index of two stocks, stock A and stock B. Stock A opens on Monday with 5000 shares at $2.75 per share. Stock B opens on Monday with 3000 shares at $4.30 per share. Stock A opens on Tuesday at $3.10 per share, and stock B opens on Tuesday at $4.85 per share. Both stocks have the same number of shares that they opened with on Monday. What is the rate of change of this simple index over 1 day?
Answers
The rate of change of the simple index over one day is approximately 12.78%.
To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.
On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:
Total value of Stock A on Monday = 5000 * $2.75 = $13,750
Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:
Total value of Stock B on Monday = 3000 * $4.30 = $12,900
The total value of the index on Monday is the sum of the values of Stock A and Stock B:
Total value of the index on Monday = $13,750 + $12,900 = $26,650
On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.
The total value of Stock A on Tuesday is:
Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500
The total value of Stock B on Tuesday is:
Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550
The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:
Total value of the index on Tuesday = $15,500 + $14,550 = $30,050
To calculate the percent change in the index, we use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%
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