Answer: 2x^2-y^2+5xy-2y
a. There is four terms in the simplified expression.
b. Two terms in the simplified expression are negative.
Step-by-step explanation:
Write the expression like an addition/ subtraction problem.
-3x²+2y²+5xy-2y
+5x²-3y²
_________
This makes it easier to identify what to combine for like terms.
Final answer:
The simplified expression is 2x² - y² + 5xy - 2y. There are two negative terms in the simplified expression: -y² and -2y.
Explanation:
To simplify the expression -3x² + 2y² + 5xy - 2y + 5x² - 3y², we need to combine like terms. The like terms are the ones that contain the same variables to the same power. Here’s a step-by-step explanation:
Combine -3x² and +5x² to get +2x².Combine +2y² and -3y² to get -y².The terms +5xy and -2y do not have like terms, so they remain unchanged.The simplified expression is 2x² - y² + 5xy - 2y.
Now, to answer the question about the number of negative terms: in the simplified expression, there are two negative terms, which are -y² and -2y. A term is considered negative if it has a minus sign in front of it, indicating that it is less than zero when all other variables are considered to be positive.
In the diagram shown above, ABCD is a parallelogram. The ratio of the area of triangle AGB to the area of triangle CGE is 9:25. If CG=10 and GE=15 find AG.
Answer:
The answer should be A.
Answer: The Answer is A.) AG=6
Step-by-step explanation:
A taxicab starts at (1, −2) on the grid. It goes 4 blocks south and 3 blocks east to pick up a passenger. Then it goes 6 blocks west and 5 blocks north and drops off the passenger. How many blocks is the taxicab from its starting position?
The taxicab, after all its movements, is about 3.16 blocks away from its starting position. It ends up 3 blocks west and 1 block north from where it initially started.
Explanation:The question asks us to determine the final position of a taxicab relative to its starting position after following a series of movements. The taxicab's starting position in this case is at the coordinate (1, -2).
Initially, it goes 4 blocks south (downwards in the grid, which we'll regard as negative) and 3 blocks east (to the right on the grid, which we'll regard as positive). Therefore, it moves to a point that is (+3, -4) relative to its starting position.
Next, it goes 6 blocks west (left on the grid, which is negative) and 5 blocks north (up on the grid, which is positive). So, this movement's relative position is (-6, +5).
To find out the final position of the taxicab relative to its starting position, we need to add up these movements' relative positions. The final relative position will be (+3-6, -4+5), which equals (-3, 1).
Hence, in terms of blocks, the taxicab is 3 blocks west and 1 block north of its starting position. The direct distance to the start would then be determined using the Pythagorean theorem, where the total distance is the square root of the sum of the squares of the movements in each direction (x and y coordinates). That forms the equation √((-3)² + 1²) = √10 ≈ 3.16 blocks.
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If f(x) =-x^2 +6 x-1 and g(x) =3x^2-4x-1 find ( f+g) (x)
[tex](f+g)(x)=-x^2+6x-1+3x^2-4x-1=2x^2+2x-2[/tex]
Answer: [tex](f+g)(x)=2x^2+2x-2[/tex]
Step-by-step explanation:
Given the function f(x), which is:
[tex]f(x)=-x^2 +6x-1[/tex]
And the function g(x), which is:
[tex]g(x) =3x^2-4x-1[/tex]
You can observe that [tex](f+g)(x)[/tex] indicates that you need to add the functions, then you know that:
[tex](f+g) (x)=(-x^2+6 x-1)+(3x^2-4x-1)[/tex]
Finally, to simplify it you must addthe like terms. Therefore, you get that [tex](f+g)(x)[/tex] is:
[tex](f+g)(x)=-x^2+6 x-1+3x^2-4x-1[/tex]
[tex](f+g)(x)=2x^2+2x-2[/tex]
Solve the equation.
8(4-x) = 7x + 2
Answer:
x = 2.
Step-by-step explanation:
8(4-x) = 7x + 2
32 - 8x = 7x + 2
32 - 2 = 7x + 8x
15x = 30
x =2.
If this trapezoid is moved through the translation (x+1,y-3), what will the coordinates of A be?
Please Help Me!!!
Answer:
A' = (- 5, - 1)
Step-by-step explanation:
The coordinates of point A = (- 6, 2)
Under the translation (x + 1, y - 3)
Add 1 to the x- coordinate of A and subtract 3 from the y- coordinate of A
A' = (- 6 + 1, 2 - 3) → A' = (- 5, - 1)
Based on the fact that there are 4 points which are given below, we have to move the trapezoid to the points of A will be (x+1, y-3). The coordinates of A be A(-6,2) =>A'(-5, -1)
What is a trapezoid?A trapezoid is regarded as a quadrilateral that has only one pair of opposite sides that are said to be parallel.
The points on the graph are:
A(-6,2) =>A'(-5, -1)
B(-5,4) =>B'( -4,1)
C(-2,4)=> C'(-1,1)
D( 1,2) => D'(2,-1)
It is made up of a right angles (called right trapezoid), and it can also contain a congruent sides (isosceles). Note that in the above, the only way the trapezoid can fit into the translation movement (Point A)is if it is moved to the points of (x+1, y-3) on the graph.
The coordinates of A be A(-6,2) =>A'(-5, -1).
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Fifteen years from now Ravi's age will be four times his present age what is Ravi's present age
Let x represent Ravi's current age.
Now, Ravi's age fifteen years from now is effectively Ravi's age plus fifteen, therefor we can write this as x + 15.
Four times Ravi's present age is four multiplied by his present age, therefor we can write this as 4x.
If Ravi's age fifteen years from now is equal to four times his present age, then:
x + 15 = 4x
Now all we have to do is solve for x to find Ravi's present age:
x + 15 = 4x
15 = 3x (Subtract x from both sides)
5 = x (Divide both sides by 3)
Therefor, Ravi's present age is 5 years.
If x+y = z and y−z=x which of the following must be equal to z?
(A) 0 (B) x (C) y (D) −x (E) –y
ANSWER
(C) y
EXPLANATION
We have two equations:
The first one is
[tex]x + y = z...(1)[/tex]
The second equation is
[tex]y - z = x...(2)[/tex]
Let us make z the subject of this second equation:
[tex] \implies \: -x +y = z...(3)[/tex]
We now add equation (1) and (3) to get:
[tex](-x + x) + (y + y) = z + z[/tex]
We simplify to get:
[tex]0+2y= 2z[/tex]
[tex]2y= 2z[/tex]
Divide throu by 2.
[tex] \frac{2y}{2} = \frac{2z}{2} [/tex]
[tex]y= z[/tex]
[tex] \therefore \: z = y[/tex]
The correct answer is C
PLEASE HELP
Amira is told there is a trick to finding the slope within an equation in standard form, Ax+By=C.She is told she can rewrite this equation in slope-intercept form, y=mx+b, to find the pattern. She correctly rewrites the equation 7x+9y=14 in slope-intercept form as y=−79x+149.
Which answer explains the pattern for how to find the slope using an equation in standard form?
A.In slope-intercept form, the slope is −79.These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is −BA.
B.In slope-intercept form, the slope is −79.These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is −AB.
C.In slope-intercept form, the slope is 149.. These values are C and A, but with the opposite sign, so the slope of the line from the equation in standard form is −CA.
D.=In slope-intercept form, the slope is 149. These values are C and B, but with the opposite sign, so the slope of the line from the equation in standard form is −CB.
Answer:
B.In slope-intercept form, the slope is −79.These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is −AB.
Step-by-step explanation:
A is being moved to the other side of the equation so it has to be negative and is multiplied by B since the y value has to be divided to equal the base of y not 9y but y.
Which formula can be used to determine the total number of different eight-letter arrangements that can be formed using the letters in the word "CLIMBING"?
The word "climbing" has 8 letters, so there are [tex]8![/tex] permutations of all the letters.
Nevertheless, the letters are not unique: there are 2 I's. This means that, if we start from a given word and we exchange the positions of the two I's, we'd still get the same word. So, we have to divide the number of possible permutations by [tex]2![/tex], because for any given permutation there are two identical words, given by the interchange of the I's.
So, the number of possible words is
[tex]\dfrac{8!}{2!} = \dfrac{8\times7\times6\times5\times4\times3\times2}{2}=8\times7\times6\times5\times4\times3=40320[/tex]
What is the approximate value of 0, if cos 0=8/15 ?
Answer:
The approximate value of angle theta is [tex]57.8\°[/tex]
Step-by-step explanation:
we have that
[tex]cos(\theta)=8/15[/tex]
so
using a calculator
[tex]\theta=arccos(8/15)=57.8\°[/tex]
Answer:
for plato or edmentum its option A 50 degrees
Step-by-step explanation:
10x +2y = 64
3x - 4y = -36
Use the elimination method to solve the system of equation. Choose the correct ordered pair
Answer:
x = 4, y = 12 → (4, 12)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}10x+2y=64&\text{multiply both sides by 2}\\3x-4y=-36\end{array}\right\\\underline{+\left\{\begin{array}{ccc}20x+4y=128\\3x-4y=-36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad23x=92\qquad\text{divide both sides by 2}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\10(4)+2y=64\\40+2y=64\qquad\text{subtract 40 from both sides}\\2y=24\qquad\text{divide both sides by 2}\\y=12[/tex]
Writing a quadratic equation given the roots and the leading coefficient
6,-4,1
[tex]\bf x= \begin{cases} 6\\ -4 \end{cases}\implies \begin{cases} x=6\implies &x-6=0\\ x=-4\implies &x+4=0 \end{cases} \\\\\\ (x-6)(x+4)=\stackrel{y}{0}\implies \stackrel{\mathbb{F~O~I~L}}{1x^2-2x-24}=y[/tex]
What is the third quartile, Q3, of the following distribution?
4,5, 33, 10, 12, 14, 34, 43, 21, 22, 21, 22, 44, 29, 16, 18, 20, 24, 26, 29
Answer:
The third quartile is:
[tex]Q_3=29[/tex]
Step-by-step explanation:
First organize the data from lowest to highest
4, 5, 10, 12, 14, 16, 18, 20, 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44
Notice that we have a quantity of n = 20 data
Use the following formula to calculate the third quartile [tex]Q_3[/tex]
For a set of n data organized in the form:
[tex]x_1, x_2, x_3, ..., x_n[/tex]
The third quartile is [tex]Q_3[/tex]:
[tex]Q_3=x_{\frac{3}{4}(n+1)}[/tex]
With n=20
[tex]Q_3=x_{\frac{3}{4}(20+1)}[/tex]
[tex]Q_3=x_{15.75}[/tex]
The third quartile is between [tex]x_{15}=29[/tex] and [tex]x_{16}=29[/tex]
Then
[tex]Q_3 =x_{15} + 0.75*(x_{16}- x_{15})[/tex]
[tex]Q_3 =29 + 0.75*(29- 29)\\\\Q_3 =29[/tex]
Answer:
29
Step-by-step explanation:
1. There were 36,000 people at a horse race in Lexington, Kentucky. The day's
receipts were $250,000. The only two types of seats available were clubhouse
or grandstand seats. How many people paid $12.00 for clubhouse seats and
how many people paid $5.00 for grandstand seats? Only an algebraic solution
will earn credit. State what any variables represent by writing a "let statement”.
Answer:
10000 people paid $12.00 each for clubhouse seats and26000 people paid $5.00 each for grandstand seats.Step-by-step explanation:
The question is asking for a system of equations, which make explanations easy. :)
Define the variables. Setting [tex]x[/tex] to the number of clubhouse seats sold and [tex]y[/tex] to the number of grandstand seats sold will be sufficient. The "let statement[s]" will be:
Let [tex]x[/tex] be the number of clubhouse seats sold.Let [tex]y[/tex] be the number of grandstand seats sold.The number of equations shall be no less than the number of variables for the solution to be unique. There are two variables. It will take at least two equations to find a unique solution.
Everyone at the race need a seat. The number clubhouse seats plus the number of grandstand seats shall be the same as the number people at the race. There were 36,000 people. Therefore the first equation shall be:
[tex]x + y = 36000[/tex].
Every clubhouse seat will add $12.00 to the receipt. [tex]x[/tex] clubhouse seats will add $[tex]12\;x[/tex] to the receipt. Similarly, [tex]y[/tex] grandstand seats will add $[tex]5\;y[/tex] to the receipt. The two values shall add up to $250,000.
Drop the dollar sign to get the second equation:
[tex]12\;x +5\;y =250000[/tex].
Hence the system:
[tex]\displaystyle \left\{\begin{aligned}& x + y = 36000 && \textcircled{\raisebox{-0.9pt}1}\\ & 12\;x + 5\;y = 250000 && \textcircled{\raisebox{-0.9pt}2}\end{aligned} \phantom{\small credit for the raisebox hack: tex[dot]stackexchange[dot]com/questions/7032/good-way-to-make-textcircled-numbers}[/tex].
Solve this system.
The first non-zero coefficient in equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is already one. That's the coefficient for [tex]x[/tex]. Use multiples of equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get rid of [tex]x[/tex] in other equations (equation [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] in this case.)
[tex]-12[/tex] times equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is
[tex]-12 \;x - 12\;y = -432000[/tex].
Add [tex]-12\times \textcircled{\raisebox{-0.9pt}1}[/tex] to [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] to get:
[tex]0\;x + -7\;y = -182000[/tex].
Divide both sides by -7 to get:
[tex]y = 26000[/tex].
Add -1 times this equation to equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get:
[tex]x = 10000[/tex].
That is:
[tex]\displaystyle \left\{\begin{aligned}&x = 10000\\&y = 26000\end{aligned}[/tex].
In other words,
10000 clubhouse seats were sold, and26000 grandstand seats were sold.What is the surface area of the right cylinder below?
Answer:
A≈622.04
Step-by-step explanation:
Formula: A=2πrh+2πr²
Answer: A. 622 sq. units
Step-by-step explanation:
The surface area of a cylinder is given by :-
[tex]S.A.=2\pi r(r+h)[/tex], where r is the radius , h is height of the cylinder.
Given : The height of the cylinder : h= 2 units
The radius of the cylinder : r= 9 units
Then , the surface area of a cylinder will be :-
[tex]S.A.=2(3.14159) 9(9+2)\\\\\Rightarrow\ S.A.=622.03482\approx622\text{sq. units}[/tex]
A credit union pays 5% annual interest, compounded daily, on savings deposits. Find the value after one year of $500 deposited in this account.
$525.64
$25.64
$20.40
$520.40
Step-by-step answer:
Given:
5% annual interest (APR)
compounded daily
Principal = 500
Solution:
Since it is compounded daily, we first calculate the
daily rate = 5% / 365 = 0.05/365
After one year,
future value
= 500 ( 1 + 0.05/365)^365
= 525.634 (to the tenth of a cent)
note: sometimes a year is considered to be rounded to 360 days, or 366 days for a leap year, but there is practically no difference in the results for this problem.
Final answer:
To calculate the future value of a $500 deposit with a 5% annual interest rate compounded daily for one year, we use the compound interest formula. The resulting amount is approximately $525.64.
Explanation:
To calculate the value of a $500 deposit in a credit union that pays 5% annual interest compounded daily, we will use the formula for compound interest:
A = P(1 + (r/n))^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested or borrowed for, in years.
Using the given information:
P = $500
r = 5% or 0.05 (as a decimal)
n = 365 (since the interest is compounded daily)
t = 1 year
Substituting the values into the formula:
A = 500(1 + (0.05/365))^(365*1)
After calculating, we get:
A ≈ $525.64
Therefore, the value of the $500 deposit at the end of one year with daily compounding at a 5% annual interest rate is approximately $525.64.
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
Oy-5= {(x-1)
Oy- z = 5(x-1)
O y-1 = {(x+5)
O y-1= 5(x-1)
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = [tex]\frac{1}{2}[/tex] and (a, b) = (5, 1), so
y - 1 = [tex]\frac{1}{2}[/tex](x - 5)
The equation that represents a line that passes through (5, 1) and has a slope of 1/2 is; C: y - 1 = ¹/₂(x - 5)
What is the Equation of the Line?The formula for equation of a line in point- slope form is expressed as;
y - b = m(x - a)
where;
m is the slope of line
(a, b) is a coordinate point on the line
In this question, we are given;
m = 1/2 and (a, b) = (5, 1)
Thus equation of the line is;
y - 1 = ¹/₂(x - 5)
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The temperature of an oven went from 280 to 350 what was the percent increase in temperature
Answer:
25% Increase
Step-by-step explanation:
[(350 - 280) / 280] × 100% = 0.25 × 100% = 25%
3. Sophie and Jackie each have a collection of baseball cards, Jackie has 5 more cards than
Sophie, and together they have 30 cards. By writing and solving an equation, find out how
many cards Sophie owns. Show all of your working out.
Answer:
Sophie has 12.5 cards
Step-by-step explanation:
Let
x -----> number of cards Sophie has
y -----> number of cards Jackie has
we know that
x+y=30 -----> equation A
y=x+5 -----> equation B
Solve by substitution
Substitute equation B in equation A and solve for x
x+(x+5)=30
2x=30-5
x=12.5 cards
Note I assume the problem was invented without taking into account the result, because the amount of cards should be a whole number
What are the x-intercepts of the function f(x) = 2x^2 - 3x + 20?
There are two: -4 and -5/2
Steps
0 = (2x - 5)(x + 4) | FOIL (distribution)
2x = 5 | zero product rule
x = 5/2 <<<
x = -4 <<< | zero product rule again.
Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 minutes to reach mile marker 3. When she reaches mile marker 6, she notes that 8 minutes total have passed since mile marker 0.
What is the average speed of the car in miles per minute?
mile(s) per minute
What is an equation of the line that represents n, the number of mile marker passed, as a function of t, time in minutes?
Answer:
0.75 mile(s) per minute
n-6=0.75(t-8)
hope this helps!!
Step-by-step explanation:
Answer:
0.75 miles per minute
Equation: n - 6 = 0.75(t - 8)
Step-by-step explanation:
took the test and got it right
help me please with this question
Answer:
B
Step-by-step explanation:
Ratio of sides = a : b , then
Ratio of volumes = a³ : b³
Here the ratio of volumes = 27 : 729, hence
Ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{729}[/tex] = 3 : 9
Ratio of sides = 3 : 9 = 1 : 3 ← in simplest form
Hence sides of larger cube are 3 times sides of smaller cube → B
What are the solution(s) to the quadratic equation x2 – 25 = 0?
O x = 5 and x = -5
OX=25 and x = -25
O x = 125 and x = -125
O no real solution
[tex]x^2 - 25 = 0\\x^2=25\\x=-5 \vee x=5[/tex]
Answer:
x = ± 5
Step-by-step explanation:
Given
x² - 25 = 0
There are 2 possible approaches to solving this equation
Approach 1
add 25 to both sides
x² = 25 ( take the square root of both sides )
x = ± [tex]\sqrt{25}[/tex] = ± 5
Approach 2
x² - 25 ← is a difference of squares and factors as
(x - 5)(x + 5) = 0 ← in standard form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 5 = 0 ⇒ x = 5
The previous rectangular prism had a surface area of 254 square inches. If each dimension is doubled, how does the surface area change?
The surface area doubles.
The surface area triples.
The surface area increases by 4 times.
The surface area increases by 8 times.
Answer:
The surface area increases by 4 times
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z -----> the scale factor
x ----> the surface area of the new rectangular prism
y ---> the surface area of the original rectangular prism
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=2[/tex] ----> because is doubled
[tex]y=254\ in^{2}[/tex]
substitute and solve for x
[tex]2^{2}=\frac{x}{254}[/tex]
[tex]x=(4)254=1,016\ in^{2}[/tex] ----> surface area increases by 4 times.
Answer:
The surface area increases by four times.
Step-by-step explanation:
How are they getting the numerator and denominator for the fractions for the coordinates? PLEASE HELP ASAP!!!!! 20 POINTS!!!!
Answer:
All except from point E's y-coordinate (which is -1.5 (found it through the equation y=-1.5 and trying to see if these coordinates are solutions to the above equation) All the others are integers, which you can find through aligning the point on the axis of the chosen (y or x) coordinate.
Step-by-step explanation:
Point C has -2 x-coordinate since it is on the x=-2 line
Similarly, point D has -2 y coordinate,
point E has 2 x-coordinate and -1,5 y-coordinate
and point F , since it's the two axis' common point has coordinates of (0,0).
Hope I helped! Further explanation can be given on request on your behalf.
A fish tank is in the shape of a rectangular prism with dimensions 30 in. by 12 in. by 15 in. The tank is 90% filled with water.
How much water is in the tank?
Answer:
4860 in ^3
Step-by-step explanation:
First we find the volume of the tank
V = l*w*h
V = 30*12*15
V = 5400 in ^3
It is 90% full so we multiply by 90 %
5400 * 90%
5400 * .90
4860 in ^3
Which is equivalent to sin-1(–0.4)? Round your answer to the nearest hundredth of a radian.
Answer:
-0.41 radians
Step-by-step explanation
(Credit goes to calculista)
let
A---> the angle
if sin A=-0.4
then
A=sin-1(-0.4)
using a calculator
A=-23.578°----> the angle A belong to the IV quadrant
convert to radians
if pi radians--]----> 180°
x--------> -23.578°
x=-23.578*pi/180----> x=-0.41 radians
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Answer:
C. –0.41
Step-by-step explanation:
sorry but i need your help (again) :
given the quadratic function f(x)= 3x²- 6x + 1
express the quadratic function f(x) in the form a(x+p)²+q, where a, p and q are constants. determine whether f(x) has a maximum or minimum value and state the value.
Answer:
It's minimum value
and the value is :(1 , -2)
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = 3x² - 6x + 1
To express in vertex form
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Use the method of completing the square
The coefficient of the x² must be 1, so factor out 3
f(x) = 3(x² - 2x) + 1
add/subtract ( half the coefficient of the x- term )² to x² - 2x
f(x) = 3(x² + 2(- 1)x + 1 - 1) + 1
= 3(x - 1)² - 3 + 1
= 3(x - 1)² - 2 ← in vertex form
with vertex = (1, - 2)
To determine if vertex is a max/ min
• If a > 0 then minimum
• If a < 0 then maximum
here a = 3 > 0 ⇒ minimum at (1, - 2)
The minimum value is the y- coordinate of the vertex, that is
minimum value = - 2
Origami is the Japanese art of paper folding. The diagram below represents
an unfolded paper kabuto, a samurai warrior's helmet. Which of the following
are pairs of congruent segments?
Check all that apply.
Answer:
The correct options are B, C and D.
Step-by-step explanation:
It is given that the figure is a Japanese art of paper folding. It means the figure have many lines of symmetry (i.e., AK, IO, CM and NF).
From the figure it is clear that HV is larger than GW, so segment HV and GW are not pairs of congruent segments.
Therefore option A is incorrect.
[tex]\overline{IJ}\cong \overline{LM}[/tex] (AK is line of symmetry)
[tex]\overline{AB}\cong \overline{AP}[/tex] (AK is line of symmetry)
[tex]\overline{BC}\cong \overline{PO}[/tex] (AK is line of symmetry)
Therefore the correct options are B, C and D.
From the figure it is clear that PO is smaller than ON, so segment HV and GW are not pairs of congruent segments.
Therefore option E is incorrect.
The function P(x) = 3x2 + 4x + 5,is dilated by the function I(x) = P(2x). Write the new function I(x).
Answer:
I(x) = 12x² + 8x + 5
Step-by-step explanation:
* Lets talk about the solution
- P(x) is a quadratic function represented graphically by a parabola
- The general form of the quadratic function is f(x) = ax² + bx + c,
where a is the coefficient of x² and b is the coefficient of x and c is
the y-intercept
- To find I(x) from P(x) change each x in P by 2x
∵ P(x) is dilated to I(x) by change x by 2x
∵ I(x) = P(2x)
∵ P(x) = 3x² + 4x + 5
∴ I(x) = 3(2x)² + 4(2x) + 5 ⇒ simplify
∵ (2x)² = (2)² × (x)² = 4 × x² = 4x²
∵ 4(2x) = 8x
∴ I(x) = 3(4x²) + 8x + 5
∵ 3(4x²) = 12x²
∴ I(x) = 12x² + 8x + 5