Factorize the following function 36(3x-2)² - 25(2-x)²
Answers
The question is given to factorize the expression:
\(36\mleft(3x-2\mright)^2\: -\: 25\mleft(2-x\mright)^2\)Given that:
\(\begin{gathered} 36=6^2 \\ 15=5^2 \end{gathered}\)Therefore, the expression becomes:
\(\Rightarrow6^2(3x-2)^2\: -\: 5^2(2-x)^2\)Recall the rule of exponents:
\(m^x\cdot n^x=(m\cdot n)^x\)Hence, the expression can be rewritten to be:
\(\Rightarrow\lbrack6(3x-2)\rbrack^2\: -\: \lbrack5(2-x)\rbrack^2\)Expand the terms in the brackets:
\(\begin{gathered} 6(3x-2)=18x-12 \\ 5(2-x)=10-5x \end{gathered}\)Hence, we have the expression to be:
\(\Rightarrow(18x-12)^2-(10-5x)^2\)Recall the Difference of Two Squares Formula, defined as:
\(x^2-y^2=(x-y)(x+y)\)Hence, we have the expression to be:
\((18x-12)^2-(10-5x)^2=\lbrack(18x-12)-(10-5x)\rbrack\cdot\lbrack(18x-12)+(10-5x)\rbrack\)Simplifying, we have:
\(\Rightarrow(18x-12-10+5x)\cdot(18x-12+10-5x)=(23x-22)(13x-2)\)ANSWER:
\(36\mleft(3x-2\mright)^{2}-25\mleft(2-x\mright)^{2}=(23x-22)(13x-2)\)Related Questions
A trader starts with 80 mangoes. She
sells 36 during the day. What percentage
of mangoes are left at the end of the
day:
Answers
the trader sell 36 mangos.
so she has 44 mangos with her.
44÷88=0.55
0.55×100%=55%
use the table to write a proportion.
Answers
Answer:
22
Step-by-step explanation:
Find an expression for the volume of a rectangular prism with a length of (x + 5), width of (x - 4) and a height of (x-7)
Answers
Given:
The length of a rectangular prism is (x + 5), the width is (x - 4), and (x - 7).
To find:
The expression for the volume of the rectangular prism.
Solution:
It is known that the volume of the rectangular prism is given by:
\(V=l\times w\times h\)So, the volume of the given rectangular prism is:
\(\begin{gathered} V=(x+5)(x-4)(x-7) \\ =(x^2+5x-4x-20)(x-7) \\ =(x^2+x-20)(x-7) \\ =x^3+x^2-20x-7x^2-7x+140 \\ =x^3-6x^2-27x+140 \end{gathered}\)Thus, the expression for the volume of the rectangular prism is x^3 - 6x^2 - 27x + 140.
What are some combinations you can buy for lunch?
How much are you spending on your choice
Answers
Answer:
You can spend all of the money by getting 1 sandwich and 2 things of chips
Step-by-step explanation:
1 sandwich =4$
1 bag of chips =3$
4 + 3 =7
7+ 3= 10
) Write an expression to show the amount of
soup Marta has left. Let s equal the number
of ounces of soup Marta makes.
2
S
32
Answers
Answer:
s-32
Step-by-step explanation:
i got it correct:)
S-32 is the expression to show the amount of soup Marta has left
What is Expression?An expression is combination of variables, numbers and operators.
Given,
Marta makes S ounces of soaps.
She always freezes 32 of the soap for remaining.
We need to find the expression to show the amount of soup Marta has left.
This can be done by the expression
S-32
where S is the number of ounces.
Hence, S-32 is the expression to show the amount of soup Marta has left
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James wants to buy a gaming computer priced at $3,774, but he is not able to pay the amount in full.
The shop, though, offers purchase plans to help customers afford their products.
The annual interest rates on offer are below. Simple interest will be calculated on each loan.
Payment Period Interest Rate
12 months 14.8%
24 months 11.6%
James chooses to go with the 12-month plan.
How much will the shop earn in interest? (Answers to whole dollars)
$
What is the total amount that James will pay for the computer?
$
If the repayments are split evenly over the year, how much will James pay per month?
$
Answers
2nd answer) Total amount James payed is $3774+438= $4212
3rd answer) an year has 12 so to get the amount he paid per month divide $4212 by 12 to get $351
what are the next terms in the number pattern -11, -8, -5, -2, 1
Answers
Answer:
4, 7, 10, 13
Step-by-step explanation:
Hey there!
Well in the given pattern,
-11, -8, -5, -2, 1
we can conclude that the pattern is +3 every time.
-11 + 3 = -8
-8 + 3 = -5
-5 + 3 = -2
-2 + 3 = 1
And so on
4, 7, 10, 13Hope this helps :)
Jan went to the mall to buy 9 crop tops but she seen 201 other and she 1,000,000,000,000,000,000,000,00 dollars
Answers
Answer: buy all the crop tops
Step-by-step explanation:
Answer:
Well with that amount of money u should most definitely buy them, if you liked the of course
Step-by-step explanation:
I'm just saying
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The measure of angle D of the given Kite is: 127°
How to find the angle of the Kite?From the diagram, the figure represents a kite.
Properties of a kite are:
- Two pairs of adjacent sides are equal.
- Two diagonals intersect each other at right angles.
- The longer diagonal bisects the shorter diagonal.
- The angles opposite to the main diagonal are equal.
Thus:
The angle B = the angle D
The sum of all angles of a quadrilateral = 360
Given: ∠A = 36 and ∠C = 70
Thus:
2∠D = 360 - (36 + 70)
2∠D = 254
∠D = 127°
So, the measure of angle D = 127°
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Solve the equation for Y
3y=-6x+1
Answers
y is -2 is the answer for the question
Answer:
6x + 3y = 1
I hope this helps!
the Mexican gray wolf population in southern Arizona increased from 112 wolves to 128 in 5 years. use this information to approximate the wolf population's growth rate, as a decimal value, and create an exponential growth model for the wolf population. A) what is the yearly growth rate? round to two decimal place. B) if F is the population of the Mexican gray wolf at the time t, in years, create an exponential model for the population of the Mexican gray wolf
Answers
Answer:
59
Step-by-step explanation:
4y^2 - 15y = 4
Need help
Emergencyyyyyyyyyyy
Answers
Answer:
I don't know if this is correct but I got this. y=1/4,y2=4
The following tables each show the amount of money, in dollars, in four different bank accounts over time.
Which table best represents an exponential relationship?
A.
Years 1 2 3 4 5
Account Balance 1100.00 1350.00 1600.00 1850.00 2100.00
B.
Years 1 2 3 4 5
Account Balance 1100.00 1210.25 1320.50 1430.75 1541.00
C.
Years 1 2 3 4 5
Account Balance 1100.00 1190.00 1340.00 1550.00 1820.00
D.
Years 1 2 3 4 5
Account Balance 1100.00 1210.00 1331.00 1464.10 1610.51
Answers
Answer:
C
Step-by-step explanation:
it is not my percentage, it is not constant, it is increasing over time
Find equation of the line shown
Answers
The equation of the line is y = x + 6
How to detemrine the equatiin of the lineFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following highlights
The graph intersect the y-axis at y = 6
This means that the intercept c is 6
Also, as x changes by 1, the y values changes by 1
This mean sthat the slope is 1
So, we have
y = mx + c
This gives
y = x + 6
Hence, the equation is y = x + 6
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The linear equation on the graph can be written as:
y = (3/2)*x + 6
How to find the equation in the graph?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁), then the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we can see the points (0, 6) (so the y-intercept is b = 6) and (4, 10)
Then the slope will be:
a = (10 - 6)/(4 - 0) = 6/4 = 3/2
Then the linaer equation is:
y = (3/2)*x + 6
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2(cos^4 60 +sin^4 30) -(tan^2 60 +cot^2 45) +3*sec^2 30
Answers
The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)
Let's simplify the expression step by step:
Recall the values of trigonometric functions for common angles:
cos(60°) = 1/2
sin(30°) = 1/2
tan(60°) = √(3)
cot(45°) = 1
sec(30°) = 2
Substitute the values into the expression:
\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)
= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)
= 2(1/16 + 1/16) - (3 + 1) + 3*4
= 2(1/8) - 4 + 12
= 1/4 - 4 + 12
= -15/4 + 12
= -15/4 + 48/4
= 33/4
Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)
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In an aquarium 2/5 of the fish or surgeonfish. Of these, 3/4 are yellow tangs. what fraction of all fish in the aquarium or yellow tangs
Answers
Answer:
3/10 of the aquarium are yellow tangs.
Step-by-step explanation:
Given that in an aquarium 2/5 of the fish or surgeonfish and of these, 3/4 are yellow tangs, to determine what fraction of all fish in the aquarium are yellow tangs the following calculation must be performed:
2/5 = 0.40
0.40 x 3/4 = X
1.20 / 4 = X
0.30 = X
0.30 = 3/10
Therefore 3/10 of the aquarium are yellow tangs.
The equation that represents ⨀A is (x+1)2+(y−1)2=16. Determine whether point B(3,1) is on the circle.
Answers
Answer:
Step-by-step explanation:
center=(-1,1)
radius=√16=4
distance between (-1,1) and (3,1)=√[(3+1)²+(1-1)²]=√[16+0]=√16=4=radius
Hence point lies on the circle.
2
Select the correct answer.
Ray should consume 2,000 calories every day. He consumes 1,735 calories to get essential nutrients. What is Ray's discretionary calorie
allowance?
OA 115 calories
B. 265 calories
O c. 1,735 calories
OD. 2,000 calories
Answers
Answer:
2000-1735= discretionary amount Hencd your answer is 265Answer:
B
Step-by-step explanation:
2,000 - 1,735= 265
1,735+ 265= 2,000
Iehdjdbdjdhd PLEASE HELP
Answers
In Exercises 10–14, use the diagram to determine whether you can assume the
statement.
Answers
Answer:
it depends on what he means
Step-by-step explanation:
The friend needs to clarify the meaning of "if three lines intersect each other." If Line A intersects lines B and C, there will be two points of intersection, one at line B and one at line C.
If those lines are all in the same plane, and B and C are not parallel, so that line B intersects line C, then there will be a total of three points of intersection.
If the point of intersection of B and C is also the point where line A intersects them, then there will be only one point of intersection.
__
So, if the meaning is "if there are three non-parallel lines in the same plane, and each intersects the other two", then the Line Intersection Postulate guarantees there will be 1 or 3 points of intersection.
If the meaning is "if there are three lines not necessarily in the same plane, and one intersects the other two (but those two don't intersect each other)", then there may be 1 or 2 points of intersection (allowing that all lines may intersect at the same point).
This table shows data collected by a runner.
A three column table with 7 rows. The first column, Time in minutes, has the entries, 1, 2, 3, 4, 5, 6. The second column, Distance in miles, has the entries, 0.19, 0.38, 0.57, 0.76, 0.95, 1.14. The third column, Elevation in meters, has the entries, 12, 28, 67, 98, 124, 145.
Which statement about the scenario represented in the table is true? Assume time is the independent variable.
The distance run is a nonlinear function because it does not have a constant rate of change.
The elevation is a nonlinear function because it does not have a constant rate of change.
Both the distance run and the elevation are nonlinear functions because they do not have constant rates of change.
Both the distance run and the elevation are linear functions because they have a constant rate of change.
Answers
Answer:
a
Step-by-step explanation:
Answer:
The correct answer is B, The elevation is a nonlinear function because it does not have a constant rate of change.
Step-by-step explanation:
when the ___ calculates an increasing ___ ; the ___ may choose to decrease .
Answers
The answer that correctly fills the missing portions is option A.
The full sentence is: When the Bureau of Labor Statistics (BLS) calculates an increasing Consumer Price Index (CPI); the Federal Reserve (FED) may choose to Quantitative Easing.
Quantitative easing is a monetary policy operation in which a central bank buys government bonds or other financial assets to infuse monetary reserves into the economy in order to encourage economic activity.
The goal of QE is to level the playing field in order to make spending and investing money more enticing and accessible to people. Lower interest rates may improve the possibility that company and civilian borrowers will borrow to make purchases, promoting economic activity.
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Full Question:
When the ___ calculates an increasing ___ ; the ___ may choose to decrease______.
A) BLS, CPI. FED, QE
B) OECD, QE, BLS, CPI
C) BEA, GDP, BLS, CPI
D) BEA, CPI, OECD, GDP
Determine the total surface area of each right triangle-based prism
Answers
Answer:
small prism: 630 m²large prism: 2520 m²Step-by-step explanation:
The total surface area of the prism is the sum of the base area and the lateral area. The base area is made up of two right triangles, so will be the product of the triangle leg dimensions. The lateral area is made up of three rectangles whose width is that of the prism and whose equivalent length is the perimeter of the triangle base.
For the smaller prism, the area is ...
(20 m)(21 m) +(3 m)(20 m + 21 m + 29 m) = 420 m² +210 m² = 630 m²
The larger prism is similar, with a scale factor of 2, so its area will be 2² = 4 times that of the smaller prism:
4×630 m² = 2520 m²
__
In summary, the total surface area of each prism is ...
small prism: 630 m²large prism: 2520 m²1)
Science 5
Measurement Assignment
Name each measurement instrument below. Then, indicate which
type of measurement is performed with each one. Remember,
some instruments can be used for more than one type of
measurement!
Instrument
Name of Instrument
Measurement Type
Answers
Answer: See below
Step-by-step explanation:
The first is a beaker, it's used to measure liquid volume
The second is a ruler, it's used to measure length.
Last is a thermometer, it's used to measure temperature.
Graph the solution of the inequality 2x - (3 – x) > x + 1 on the number line.
Answers
Answer:
do multiply
Step-by-step explanation:
and take line in right side
The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2. Therefore, option D is the correct answer.
The given inequality is 2x - (3 – x) > x + 1.
What is the solution of the inequality?A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement.
Now, 2x - (3 – x) > x + 1 can be solved as follows:
2x -3+x>x+1 (Simplify the bracket)
⇒3x-3>x+1
Subtract x on both the sides of the inequality.
That is, 3x-3-x>x+1-x
⇒2x-3>1
Add 3 on both the sides of the inequality.
That is, 2x>4
Divide 2 on both the sides of the inequality.
That is, 2x÷2>4÷2
⇒ x > 2
The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2. Therefore, option D is the correct answer.
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Can someone please give me this answer
Answers
Answer:
42°
Step-by-step explanation:
According to Exterior Angle Theorem,
an exterior angle of a ∆ is equal to the sum of the opposite interior angles.
So,
h+96°=138°
h=138°-96°
h=42°
Please help me I’m giving brainliest and I need help
Answers
Answer:
c is the answer
Step-by-step explanation:
Answer:
A NUMBER
Step-by-step explanation:
The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph? Choose 1 answer: Choose 1 answer: (Choice A) � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 A � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 (Choice B) � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 B � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 (Choice C) � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 C � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 (Choice D) � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4y, equals, vertical bar, x, minus, 9, vertical bar, plus, 4 D � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4
Answers
An equation of the new graph is: A. y = ∣x - 4∣ - 9.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:
g(x) = f(x - N)
Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:
g(x) = f(x) + N
Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:
y = ∣x - 4∣ - 9
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
(SAT prep) Find the value of x in each case of the following exercises:
Answers
The value of x from the figure is 70°
How to determine the valueIt is important to note that alternate angles are equal and angles in a triangle sum up to 180°
We then have that,
x + 50 + 60 = 180 °
x + 110 = 180°
Make 'x' subject
x = 180 - 110
x = 70 °
Thus, the value of x from the figure is 70°
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Where does the normal line to the paraboloid z = x2 + y2 at the point (4, 4, 32) intersect the paraboloid a second time?.
Answers
The normal line intersects the paraboloid again at the point (-2, -2, 20).
Where does the normal line to the paraboloid intersectThe normal to the paraboloid at point (4, 4, 32) is perpendicular to the tangent plane at that point. The equation of the tangent plane is given by:
z - 32 = f_x(4,4)(x-4) + f_y(4,4)(y-4)
where f_x and f_y denote the partial derivatives of f(x,y) = x^2 + y^2 with respect to x and y, evaluated at (4,4):
f_x(4,4) = 8
f_y(4,4) = 8
Therefore, the equation of the tangent plane is:
z - 32 = 8(x-4) + 8(y-4)
Simplifying:
z = 8x + 8y - 32
The normal to the paraboloid at (4, 4, 32) is the gradient of f(x,y) = x^2 + y^2 at that point, which is:
grad f(4,4) = <8, 8>
Therefore, the equation of the normal line passing through (4, 4, 32) is:
x = 4 + 8t
y = 4 + 8t
z = 32 + 8t
We need to find where this line intersects the paraboloid z = x^2 + y^2 a second time. Substituting the equations of x and y into the equation of the paraboloid, we get:
z = (4 + 8t)^2 + (4 + 8t)^2
Simplifying:
z = 128t^2 + 64t + 32
Setting this equal to the equation of the line, we get:
32 + 8t = 128t^2 + 64t + 32
Simplifying:
128t^2 + 56t = 0
Factorizing:
t(128t + 56) = 0
Therefore, t = 0 or t = -7/16.
When t = 0, the line intersects the paraboloid at the point (4, 4, 32), which is the point of tangency.
When t = -7/16, the line intersects the paraboloid a second time. Substituting t = -7/16 into the equations of x, y, and z, we get:
x = 4 + 8(-7/16) = -2
y = 4 + 8(-7/16) = -2
z = 32 + 8(-7/16) = 20
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