Use distributive law
[tex]\boxed{\sf a(b+c)=ab+ac}[/tex]
Now
[tex]\\ \sf\longmapsto 2x(x-y)+3y(x-y)[/tex]
[tex]\\ \sf\longmapsto 2x^2-2xy+3xy-3y^2[/tex]
[tex]\\ \sf\longmapsto 2x^2-3y^2-2xy+3x^2[/tex]
[tex]\\ \sf\longmapsto 2x^2-3y^2+xy[/tex]
Taking common
Answer: 2x (x-y) + 3y (x-y)
= ( x-y ) ( 2x-3y )
The following table gives a partial set of values of a polynomial function.
x –2 –1 0 1 2 3
g(x) –14 –2 0 –4 –6 2
Between which two values would a relative maximum most likely occur?
–2 and 0
–1 and 1
0 and 2
1 and 3
The values of x between which the relative maximum occurs is between the x-values; -1 and 1
The known parameters;
The table of the partial set of the polynomial values is presented as follows;
[tex]\begin{array}{rcr}\mathbf{x}&&\mathbf{g(x)}\\-2&&-14\\-1&&-2\\0&&0\\1&&-4\\2&&-6\\3&&2\end{array}[/tex]
From the table above, we have that g(x) is maximum (g(x) = 2) when x = 3
Method;
Define and find the relative maximum
The relative maximum of a function, is given by a point where the graph of the function changes direction from 'continuously' increasing values of the function before the point to 'continuously' decreasing values of the function after the point
From the table, at x = -2, -1, 0, g(x) = -14, -2, 0, and is therefore, increasing
Where, x = 0, 1, 2, we have g(x) = 0, -4, -6, therefore, g(x) is decreasing
The maximum value of g(x), in the region where g(x) changes from increasing to decreasing is g(x) = 0, which is given between the x-values of -1 and 1
Therefore, the relative maximum is most likely to occur between the values of x = -1, and x = 1, which is the option -1 and 1
Learn more about relative maximum here;
https://brainly.com/question/2321623
Gloria is designing an outdoor garden for her client and needs to find the
perimeter of the total shape. Write an expression that would represent the
total perimeter so Gloria can buy enough plants to go around the entire
shape.
Show work here: (Make sure answer is in simplified form)
Answer:
21x+4
Step-by-step explanation:
X’s: 21x
#’s: 4
So it will be 21x+4
Which expression is a polynomial
Answer:
[tex]4x^3-2x^2+5x-6+\frac{1}{x}[/tex] is a polynomial
Step-by-step explanation:
a polynomial is a set of numbers with multiple terms that are not simplify able
[tex]9x^7y^{-3} z[/tex] is not a polynomial because its actually one term, there is no addition/subtraction of different terms.
-13 is a single number, so not a polynomial
13x^-2 is also a single number, not a polynomial
What is the volume??
Answer:
245 cm³
Step-by-step explanation:
Volume of a triangle = length x width x height / 3
7 x 7 x 15 = 735
735/3 = 245
volume of a triangle =length×width height 3
7×7×15=735
735/3=24
A cook has 4 cups of raisins to make oatmeal cookies. The recipe requires 3 cup of raisins for each
batch of cookies. How many batches of cookies can the cook make?
Answer: 1⅓ batch of cookies
Step-by-step explanation:
From the question, we are given the information that a cook has 4 cups of raisins to make oatmeal cookies and that the recipe requires 3 cup of raisins for each batch of cookies.
Therefore, the number of batches of cookies that the cook can make will be the number of cups of rasins that the cook has divided by the number of reasons needed for each cookie. This will then be:
= 4/3
= 1⅓ batch of cookies
i’ve came so far and i’m almost there please help!
Answer:
what the product of 2 and 3
The terminal point of 0 is (|3/2, 1/2). What is 0 if 0 <\ 0 < 360?
A. 60
B. 30
C. 45
D. 15
which graph matches the linear equation x-3y=6
Step-by-step explanation:
x-3y=6
-3y=6-x
3y=x-6
y=x/3-2
option 4 is the answer
which of the following points lies in the solution set to the system of inequalities shown below
y = -4
y ≤ 10
———————————————
(1) (-4, 10)
(2) (-2, 7)
(3) (2, 14)
(4) (-6, 2)
thank you in advance:))
Answer:
1,2, and 4
Step-by-step explanation:
I attached a picture with the graph
y= -4 is a straight horizontal line (red line) and
y≤10 will give a horizontal line passing trough y=10 (blue line)
the solution is all points under and on the line y=10
1, 2, and 4 are part of the solution set
(the blue area is the solution of the system of equations)
Answer:
( - 2, 7 )
Step-by-step explanation:
ni
Critique Patrick thinks that when a is a negative integer and b is a positive
below and decide whether they are true or false. For statements that are true, give
integer, each of the following statements is always true. Read the statements
an example to support Patrick's claim. For statements that are false, give a
counterexample.
a. 0-b is positive.
b.
b. b-a is positive.
100
60-(-6) is negative.
80
Answer:
Step-by-step explanation:
Patrick thinks that when 'a' is a negative integer and 'b' is a positive,
Let "a = -2" and "b = 3"
a). a - b is positive.
a - b = -2 - 3
= -5 {negative]
Therefore, statement is False.
(a - b) is negative.
b). b - a is positive.
b - a = 3 - (-2)
= 3 + 2
= 5 [Positive]
Statement is True.
c). a - (-b) is negative.
a - (-b) = a + b
= -2 + 3
= 1 [Positive]
False.
But it's true when a = -5 and b = 3
a - (-b) = -5 - 3
= -8 [Negative]
Stacy spent £18 on ingredients for bread.
She made 12 loaves and sold them for £1.80 each.
Calculate her percentage profit.
For which distributions is the median the best measure of center?
Select each correct answer.
Answer:
it will be the correct answer..
because
The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.
I need help what’s the answer?
Answer:
30 words per minute
Step-by-step explanation:
Take the number of words and divide by the number of minutes
150/5 = 30
300/10 =30
450/15 = 30
600/20 = 30
30 words per minute
Answer:
janae types 30 words each minutes.
Step-by-step explanation:
if 5minutes = 150 words
[tex]1 \: minute = \frac{150words}{5minutes} [/tex]
[tex] = \: 30words[/tex]
2. Which inequality represents all solutions of -3b-52-6b - 13.
Ob26
Ob>-8/3
O b s8/3
Obs6
Answer:
b≥ - 8/3
Step-by-step explanation:
-3b-5≥-6b - 13.
Add 6b to each side
-3b+6b-5≥-6b+6b - 13
3b-5≥ - 13
Add 5 to each side
3b-5+5≥ - 13+5
3b≥ - 8
Divide by 3
3b/3≥ - 8/3
b≥ - 8/3
please help me with this
Calculate expression value : G = 2x^3 + 35x^2 + 15x + 1 with x = -17
2. If a figure is at points (2,1), (-3,4), and (0,0) and it is translated using the rule (x+2, y-1), what would the new points be?
Answer:
(4, 0)
(-1, 3)
(2, -1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Step-by-step explanation:
Step 1: Define
Identify
Point (2, 1)
Point (-3, 4)
Point (0, 0)
Rule (x + 2, y - 1)
Step 2: Translate
Substitute in points into rule.
Point (2, 1) → (2 + 2, 1 - 1) = (4, 0)
Point (-3, 4) → (-3 + 2, 4 - 1) = (-1, 3)
Point (0, 0) → (0 + 2, 0 - 1) = (2, -1)
The graph of y = the square root of x is translated so that the domain of the new function is {x | x > –6} and the range is {y | y > 0}.
Which graph represents the translated image?
Answer:
A is the correct answer
Step-by-step explanation:
Answer:
A is the correct answer
please help i will give brainliest
Solve for x. round to the nearest tenth, if necessary.
Answer:
50.7
Step-by-step explanation:
38+1.3+90 from the right angle=129.3
180-129.3=50.7
qrx + prx + pqx > pqr . Find x
Answer:
[tex]x(qr + pr + pq) > pqr \: \: \: by \: dividing \: both \: sides \: by \: (qr + pr + pq)[/tex]
we get that
Step-by-step explanation:
[tex]x > \frac{qr + pr + pq}{pqr} [/tex]
Step by step explanation of finding the value of x and y
Answer:
[tex]x=4\sqrt{2}\\y=7[/tex]
Step-by-step explanation:
In order to solve this problem, the easiest approach is to draw a line connecting the vertex between the side with a measure of (y) and (3) to the side with the length (x). This side should be parallel to the side with a length of (4).
Since the new side constructed (call this side (b)), is parallel to the side with a length of (4) and is intersected by segments that are perpendicular to the side with a length of (4), the side (b) and (4) must have the same measure. Therefore (b = 4).
The triangle formed with sides (x) and (b) is a (45 - 45 - 90) triangle. Meaning that its angles have the following measure, (45 - 45- 90). This means that its sides follow the following ratio:
angle : side opposite
[tex]45:x\\45:x\\90:x\sqrt{2}[/tex]
Apply this logic to the given situation.
[tex]x=b*\sqrt{2}\\x = 4\sqrt{2}[/tex]
The side (b) divides the side (y) into two parts. Call the part that is a side of the triangle ([tex]y_1[/tex]) the side that is a part of the rectangle is called ([tex]y_2[/tex]). As per the logic used to find the lengths of side (b), one can use similar logic to find the length of side ([tex]y_2[/tex]). The sides ([tex]y_2[/tex]) and (3) are parallel and are intersected by the sides with a measure of (4) and (b), therefore ([tex]y_2[/tex]) and (3) are cognrunet. Thus ([tex]y_2[/tex] = 3).
The base angles converse theorem states that when two angles in a triangle are congruent, the triangle is isosceles, and the sides opposite the congruent angles are also congruent. Thus, one can state the following:
[tex]y_1=b\\y_1=4[/tex]
Now add up the measurement of ([tex]y_2[/tex]) and ([tex]y_1[/tex]) to find the measure of (y):
[tex]y_2+y_1=y\\4+3=y\\7=y[/tex]
Celine goes to the book fair where paperback books are $2 and hardback books are $4.50. Celine buys three
paperback and 5 hardback books. How much change will Celine receive if she has $35?
7. Equation:
8. Solve:
Answer:
7. 35-(2*3+5*4.5)
8. 6.5
Find NM
--------------------------------
Answer:
[tex] MN= \boxed{15}[/tex]
Step-by-step explanation:
refer the attachment
therefore Let,
[tex]a = x - 3 + 16 = x + 13[/tex][tex]b = x - 3[/tex][tex]c = x + 3[/tex]according to the question
[tex] \displaystyle (x - 3 ) (x + 13) =( x + 3 {)}^{2} [/tex]
simplify square and Multiplication:
[tex] \displaystyle {x}^{2} + 10x - 39 = {x}^{2} + 6x + 9[/tex]
cancel x² from both sides:
[tex] \displaystyle 10x - 39 = 6x + 9[/tex]
cancel 6x from both sides:
[tex] \displaystyle 4x - 39 = 9[/tex]
add 39 to both sides:
[tex] \displaystyle 4x = 48[/tex]
divide both sides by 4:
[tex] \displaystyle \boxed{x = 12}[/tex]
given that,
[tex] MN= x + 3[/tex]
substitute the got value of x:
[tex] MN= 12 + 3[/tex]
simplify addition hence,
[tex] MN= \boxed{15}[/tex]
what is a = with a ~ thing on top?
how do you solve this
Answer:
x = 8
Step-by-step explanation:
The angles shown are vertical angles
Vertical angles are congruent hence 8x + 36 = 5x + 60
( Notice that we just created an equation that we can use to solve for x )
We now solve for x algebraically
8x + 36 = 5x + 60
Step 1: Subtract 5x from both sides
8x - 5x + 36 = 5x - 5x + 60
Outcome: 3x + 36 = 60
Step 2: Subtract 36 from both sides
3x + 36 - 36 = 60 - 36
Outcome: 3x = 24
Step 3: Divide both sides by 3
3x/3 = 24/3
Outcome: x = 8
Is it possible to relate cyclones to mathematics?
If yes, explain your thinking with the help of drawings (no need to use
downloaded images) What are the mathematical concepts, theorems and
shapes related to cyclones.
Answer:
Yes
Step-by-step explanation:
Statistics can perdict cyclones for example lets say that somewhere a cyclone happens almost every February then its statistically likely to happen this February too.
Classify the triangle.
obtuse
equiangular
right
acute
Answer:
acute triangle
Step-by-step explanation:
We have 3 angles that are not equal to each other
They are all smaller than 90 degrees which means they are acute angles
Answer:
Acute
Step-by-step explanation:
Acute=less than 90 degrees
Obtuse=more than 90 degrees
Right=1 side has 90 degrees
Equiangular=every side has the same degree
Therefore, it would be Acute
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $57,077 , and the variable costs will be $11.75 per book. With the other method, the one-time fixed costs will total $22,459, and the variable costs will be $21.25 per book. For how many books produced will the costs from the two methods be the same?
Answer:
for 3644 produced books the costs will be the same.
Step-by-step explanation:
x = number of books
f(x) = production method 1 costs
g(x) = production method 2 costs
f(x) = 11.75x + 57077
g(x) = 21.25x + 22459
for what number of books (x) will that be the same ?
11.75x + 57077 = 21.25x + 22459
34618 = 9.5x
x = 34618 / 9.5 = 3644
Point Q is the centroid of △ABC. QF = _____
A. 10
B. 5
C. 15
D. 9
Answer: QF = 5
Step-by-step explanation:
We know that if a triangle has a centroid, the ratio of the longer segment to shorter segment is 2:1. We can set up a proportion [tex]\frac{2}{1} = \frac{10}{x}[/tex], where x is the length of QF. By cross multiplying and dividing, you get x = 5 or QF = 5.
Answer:
5
Step-by-step explanation:
