Answer:
What is factoring?Factoring is finding what to multiply to find an expression. It is like splitting expression into a multiplication of simplified expression.
Why is it useful to try to factor out the GCF first when factoring?Greatest common factor or GCF of two numbers is the largest number that divides evenly in both numbers, GCF works the same in polynomials, which divide the expression evenly .
Explain the relationship between factoring and multiplying polynomials. Give an example to help explainFactoring take away the multiplication, to factorize a polynomial it means take apart what is multiplied. the best example is a²+b²+2ab ( multiplied)
factorize :(a+b)(a+b) take apart what is multiplied
Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6x²-25 =(x+5)(x-5)
3x²-12x-15 = 3(x²-4x-5) GCF=3
3(x-5)(x+1)
x³+2x²+3x+6 (x+2) common factor
(x+2)(x²+3)
What are the key features needed to graph a polynomial function?the key features are the vertex, axis of symmetry, x and y intercept
Explain how to find these key features to sketch a rough graph of a polynomial functionparabola : y=ax²+bx+c
ex: 3x²-12x-15
find vertex (h,k)
h=-b/2a =-(-12)/2(3)=2
k=f(h)=f(2)=3(2)²-12(2)-15
k=12-24-15=-27
vertex=(2,-27)
x intercept is when the graph =0 (y=0)
y intercept when x=0 then y= the constant c and where the graph cross the y axis
axis of symmetry is the x of the vertex: is a line about which a parabola is symmetrical and vertical when the axis of symmetric is vertical.
Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.factor a polynomial helps us understand more about equations,factoring helps us rewrite the polynomial into simpler expression.
example from real life:
A homeowner has a back yard and wants to turn it to garden beds so he can plant his vegetables, he wants to fill it with dirt he needs 240 cubic feet to fill it the length is 4 feet than the width , and the height is 4
solve:
length=W+4
height=1/3 w
V=length* width* height
240=(w+4)(w)(4)
351= 4w²+16w
4w²+16w-240=0
take 4 as common factor
4(w²+4w-60)
now factorize:
4(w-6)(w+10)=0
Sketch the graphs y=1/3x+2
Answer:
mark a dot 2 on the y axis and from there go up one right 3 until you can anymore then go back to the two and go down one left 2
Step-by-step explanation:
Possible Points: 100 One January day, the low temperature in Fargo, ND was -8 degrees. Over a period of six hours, the temperature rose 4 degrees per hour. After si hours, what was the temperature?
A 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15. Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing? (–6, –3) (–3, –1) (–3, 0) (–6, –5)
Answer:
Step-by-step explanation:
The only place that the function is increasing is [-3, -1] (learn your interval notation). At x = -3, y = -11; at x = -2, y = -6 (-6 is greater than -11); and at x = -1, y = -1 (-1 is greater than -6). The next x value, 0, returns a y value of -2. But -2 is less than -1, the value before it, so it begins deceasing again at x = 0.
Based on the values given in the table for f(x), the interval of x-values that show the function increasing is (-3, -1).
Which interval shows the function increasing?The value of f(x) was decreasing from 34 until it got to -11 where it then started to rise again. The relevant value of x here is -3.
The value then began to rise until it reached -1 where it then fell to -2. The x value here is -1.
The interval of x-values where the function is increasing is therefore (-3, -1).
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The sales tax for an item was $15.60 and it cost $390 before tax. Find the sales tax rate. Write your answer as a percentage.
Answer:
15.60 times 100 divided by 390=4%
Step-by-step explanation:
The required sales tax rate percentage is 4%.
The sales tax for an item was $15.60 and it cost $390 before tax. To find the sales tax rate. Write your answer as a percentage.
the percentage is defined as, the composition of something out of whole inbounds of 100.example 10% of 150 = 10 * 150/100
= 15
It shows that 10 percent of 150 is 15.
sales tax = $15.60
cost = $390
To get the sales tax percentage we have to find out the tax composition of tax to the cost. So,
Sale tax percent = sale tax/cost * 100
= 15.60/390 * 100
= 0.04 * 100
= 4 %
Thus, the required sales tax rate percentage is 4%.
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the area of a square is given by s2 and the perimeter is given by 4s, where s is the side length of the square if the side length of a square is 4 inches its area is ... square inches and its perimeter is ... inches
Answer:
Area = s² = 4² = 16 sq. In.
Perimeter = 4s = 4(4) = 16 in.
Who’s salary represents the median of the data in the table?
Answer:
Rajesh salary is the median
Step-by-step explanation:
Am not good in explanation
Answer:
1: Ram
Step-by-step explanation:
The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values
if we put these salaries in order we can find out what the median salary is.
32,701 , 45,600 , 52,000 , 67,250 , 71860.
The number in the centre or the middle is 52,000. That is Ram's salary.
The answer is 1. Ram
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Aug 19,7:01:38 PM
Kylie is moving and must rent a truck. There is an initial charge of $50 for the rental
plus a fee of $3 per mile driven. Make a table of values and then write an equation for
C, in terms of m, representing the total cost of renting the truck if Kylie were to
drive m miles.
Number of Miles Driven Total Cost to Rent Truck
Answer:
0 miles- $50
1 mile- $53
2 miles- $56
3 miles-$59
Step-by-step explanation:
you add $3 to the original 50 as you go each mile.
Does someone know how to solve this?
Answer:
6 quarts
Step-by-step explanation:
8 bags
--------
2 quarts
Multiply top and bottom by 3
8*3 bags
--------
2*3 quarts
24 bags
--------------
6 quarts
Answer:
6
Step-by-step explanation:
2 quarts of iced tea = 8 tea bags.
x quarts of Iced tea = 24 tea bags
=> 2/8 = x/24
=> Multiply the extremes and means
=> 8x = 48
=> 8x / 8 = 48 / 8
=> x = 6
6 quarts of iced tea can be made with 24 tea bags.
How many solutions does this system of inequalities have graphed below
Answer:
There is only one solution set.
Step-by-step explanation:
The set can contain any number of solutions or none.
This is all I know, hope it helps.
When the factors of a trinomial are (x-p) and (x+q) then the constant teen of the trinomial is
(x-p)(x-q)
y(x-q) .... let y = x-p
yx - yq ... distribute
x(y) - q(y)
x(x-p) - q(x-p) ... replace y with x-p
x^2 - px - qx + pq .... distribute
x^2 + (-p-q)x + pq
The last expression is in the form ax^2+bx+c with a = 1, b = -p-q and c = pq
The constant term is the term without any variable x attached to it (either x or x^2), so the constant term is pq
Help plz ASAP!!!!!!!!
Answer:
D
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = lbh ( l is length, b breadth and h is height )
Here l = 7, b = 2 and h = 4 , thus
V = 7 × 2 × 4 = 56 in² → D
A golf ball is hit off a tee toward the green. The height of the ball is modeled by the function h(t) = −16t2 + 96t, where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground. t = 3; It takes the ball 3 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Answer:
t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Step-by-step explanation:
To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.
h(t) = -16t² + 96t
= -16(t² - 6t)
= -16(t² - 6t + 9) - (-16) * 9
= -16(t - 3)² + 144
Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".
The time will be t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
What is Function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable the dependent variable.
To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.
h(t) = -16t² + 96t
= -16(t² - 6t)
= -16(t² - 6t + 9) - (-16) * 9
= -16(t - 3)² + 144
Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum.
We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground.
The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".
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What is 33⁄5 as an improper fractions
Answer:
6 3/5
Step-by-step explanation:
33/5 = 6 R3
Answer:
6.6
Step-by-step explanation:
33÷5=6.6
33 divided by 5equal
Find the product (4x-3y)(2x+5)
Answer:
8x²−6xy+20x−15y
Step-by-step explanation:
(4x−3y)(2x+5)
=(4x+−3y)(2x+5)
=(4x)(2x)+(4x)(5)+(−3y)(2x)+(−3y)(5)
=8x²+20x−6xy−15y
=8x²−6xy+20x−15y
The graph of y=3x^2-3x-1 is shown. Use the graph to find estimates for the solutions of i)3x^2-3x+2=2 ii) 3x^2-3x-1=x+1
Intersection point of graph of function is known as solution of the function.
Graph is attached below, in which solution is shown.
1. Here, given that [tex]3x^2-3x+2=2[/tex]
It can be written as, [tex]y=3x^2-3x+2\\\\y=2[/tex]
Intersection point of graph of above two equation will be the solution of given function,
Solutions are (1, 2) and (0, 2)
2. Given that , [tex]3x^2-3x-1=x+1[/tex]
It can be written as
[tex]y=3x^2-3x-1\\\\y=x+1[/tex]
Intersection of graph of above two equation will be the solution of given equation.
Solutions are (1.721, 2.721) and (- 0.387, 0.613)
Both graph attached below,
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How many of the positive integer factors of 15552 are perfect squares?
There are 12 factors which are perfect squares is 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
What is factors?Factors can be define splitting the value in multipliable values.
Factorization of 15552
= 1 * 4 * 4 * 4* 9 * 9 * 3
Perfect squares can be formed by above factors are
= 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
Thus, there are 12 factors which are perfect squares is 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
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. Find two polynomial expressions whose quotient, when simplified, is 1/x . Use that division problem to determine whether polynomials are closed under division.
Answer:
The two polynomials are:
(x + 1) and (x² + x)
Step-by-step explanation:
A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.
Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.
Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.
So,
Let's multiply both numerator and denominator by (x + 1) to get;
(x + 1)/(x(x + 1))
This gives; (x + 1)/(x² + x)
Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.
Two fractions equivalent to 1/3
Answer:
2/6 or 3/9
Step-by-step explanation:
1/3 x 2 = 2/6
1/3 x 3 = 3/9
Answer:
2/6 3/9
Step-by-step explanation:
to find equivalent fractions you can just multiply, or count by the denominator for example, 3 , 6 , 9 and so on and then with the numerator you count how much you went like, if you went to sixths than it was 2 because you skip counted.
A can do a piece of work in 10 days and B in 12 days.
With the help of C they can finish the work in 4 days. How
long will C take to do it alone?
a) 12 days b) 15 days c) 18 days d) 20 days
Answer:
B. 15 days
Step-by-step explanation:
A=10=1/10 of the job
B=12=1/12 of the job
A+B+C=4=1/4 of the job
A+B
=1/10 + 1/12
=10+12/120
=22/120
=11/60
(A+B+C) - (A+B)
=1/4 - 11/60
=5 - 11/60
=4/60
=1/15
It would take C alone 15 days to finish the job
f(x)=x^2 what is g(x)?
pls help me
Part C Now try this one. Write a description of the partitioned function using known function types, including transformations.
Answer:
Following are the function description to the given question:
Step-by-step explanation:
In the given-question, three functions are used, that can be defined as follows:
In function 1:
This function is also known as the modulus on the absolute value function, for example:
[tex]f(x)=| x| \left \{ {{x , \ \ \ x>0} \atop {-x, \ \ \ \x<0 }} \right.[/tex]
In the given in the above graph, that is [tex]f(x) = -x , \ \ x<0[/tex]
In function 2:
In this function, It is an algebraic function that is [tex]y=x^2[/tex]
It is also a part of the quadratic polynomial function, and its value is [tex]y=x^2 , \ \ \ x> 0[/tex]
In function 3:
In this function, it is the cubic polynomial equation that's value is [tex]y=x^3[/tex]
In the graph its value is:
[tex]y=-x^3\\\\and \\ \\\to y= f(x) \\\\ \to y=-f(x)\\[/tex]
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6
Step-by-step explanation:
We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.
n/5 ≥ 11
Multiply by 5 on both sides.
n ≥ 55
Now, let's do the second one.
-3y ≤ -18
Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)
y ≥ 6
Find the surface area and volume of cone. A = rs + r2 V = 1/3r2 h A cone's slant height (s) is 15 cm and its radius is 8 cm. Surface area (to the nearest tenth) = cm2 Volume (to the nearest tenth) = cm3
Answer:
a) 483.6cm²b) 850.1 cm³Step-by-step explanation:
Given the slant height 's' and its radius 'r' to be 15cm and 8cm respectively.
the total surface of the cone A = πrs+πr² and the volume is expressed as
V = 1/3πr²h
For the surface area of the cone;
Given parameters
radius = 8 cm and slant height s = 15 cm
Total surface area A = π(8)(15) + π(8)²
A = 90π+64π
A = 154π
If π = 3.14
A = 154(3.14)
A = 483.56cm²
A = 483.6cm²
Hence the total surface area of the cone to the nearest tenth is 483.6cm²
For the volume of the cone;
V = 1/3πr²h
Using pythagoras theorem to get the height of the cone;
l² = h²+r²
h² = l²-r²
h² = 15²-8²
h² = 225-64
h² = 161
h = √161
h = 12.69cm
V = 1/3π* (8)² * 12.69
V = 1/3π* 64 * 12.69
V = 1/3*3.14* 64 * 12.69
V = 2550.1824/3
V = 850.06 cm³
V = 850.1 cm³
Hence, the volume of the cone is 850.1 cm³ to the nearest tenth.
How can I find how many 13 are in 33?
Answer:
therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)
Step-by-step explanation:
Long division:
13 33
13*2 = 26
33 - 26 = 7
we have: 33/13 = 2 r7
we know that we can rewrite the remainder as 7/13
therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)
(48. PERSEVERE Wha
PERSEVERE What is the greatest number of planes determined using any three of
the points A, B, C, and D if no three points are collinear?
Answer: 4
Step-by-step explanation:
We know that a plane is 2 dimensional surface that extends infinitely far.
The number of points required to define a plane = 3
Here , we have 4 points A, B, C, and D.
So, the number of possible combinations of 3 points to make a plane from 4 points = [tex]C(4,3)[/tex]
[tex]=4[/tex] [ [tex]C(n,n-1)=n[/tex] ]
Hence, the greatest number of planes determined using any three of the points A, B, C, and D if no three points are collinear = 4.
The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.
how many are 4 raised to 4 ???
Answer:
256Step-by-step explanation:
The expression 4 raised to 4 can be written in mathematical term as [tex]4^4[/tex] and this means the value of 4 in four places as shown;
[tex]4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\[/tex]
Hence the expression 4 raised to 4 is equivalent to 256
Help c/8+5 = 24 a) 192 b) 3 c) 7 d) 152
Answer:
c = 152
Step-by-step explanation:
c/8+5 = 24
Subtract 5 from each side
c/8+5-5 = 24-5
c/8 = 19
Multiply each side by 8
c/8*8 = 19*8
c =152
Answer:
D. 152
Step-by-step explanation:
First, subtract 5 from both sides:
c/8 + 5 = 24
c/8 = 19
Multiply both sides by 8:
c = 152
So, the correct answer is D, 152
HELP ASAP
Points $A(-1, -2)$ and $B(3, 2)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\pi$.
Answer:
8π units²
Step-by-step explanation:
center=((-1+3)/2,(-2+2)/2)=(1,0)
[tex]radius~r=\sqrt{(3-1)^2+(2-0)^2} =\sqrt{4+4} =\sqrt{8} \\area~of~circle=\pi r^2=\pi \times (\sqrt{8} )^2=8\pi ~square~units.[/tex]
Can someone help me find the amount on year 11
Answer:
525 dollars
Step-by-step explanation:
simple interest yearly ( year 11 does not count because the question asking at the amount at the beginning of year 11)
interest=300*0.075*10= 225
the amount in the account : 300+225=525 dollars
