9514 1404 393
Answer:
p(x) = (x+6)(x-3)(x-5)p(x) = (x-2)(x+2)(x^2 +36)p(x) = x^3 -7x^2 -x +7p(x) = x^4 -5x^2 -36Step-by-step explanation:
Each root r gives rise to a binomial factor (x-r). Each complex root also has a conjugate root, so roots ±ri give rise to a binomial factor (x^2 +r^2).
__
1. p(x) = (x -(-6))(x -3)(x -5)
p(x) = (x+6)(x-3)(x-5)
__
2. p(x) = (x -2)(x -(-2))(x^2 +6^2)
p(x) = (x -2)(x +2)(x^2 +36)
__
If you want standard form, you can start with factored form, then multiply it out.
3. p(x) = (x -1)(x +1)(x -7) = (x^2 -1)(x -7) = (x^2 -1)x +(x^2 -1)(-7)
p(x) = x^3 -7x^2 -x +7
__
4. p(x) = (x -3)(x +3)(x^2 +2^2) = (x^2 -9)(x^2 +4)
p(x) = x^4 -5x^2 -36
it costs 13$ for admission to amusement park, plus 1.50$ for each ride.if you have a total of 35.50 to spend, what is the greatest number of rides you can go on
Answer:
Thus, the greatest number of rides I can go on is 15 rides
Step-by-step explanation:
I have $35.50 to spend for admission plus rides in the amusement park.
Admission costs $13. That leaves me with
$35.50 - $13 = $22.50
to spend on rides.
Considering each ride costs $1.50, we can find the maximum number of rides by dividing the remaining money by the cost per ride as follows:
$22.50 / $1.50 = 15
Thus, the greatest number of rides I can go on is 15 rides
These reverse processes are both part of
Answer:
you forgot the picture
Step-by-step explanation:
Please put a picture
A donor gives $100,000 to a university, and specifies that it is to be used to give annual scholarships for the next 20 years. If the university can earn 4% interest, how much can they give in scholarships each year?
9514 1404 393
Answer:
$7,358
Step-by-step explanation:
Assuming the interest is compounded annually, the amortization formula is useful here.
A = Pr/(1 -(1+r)^-t)
A is the annual scholarship, P is the principal invested at rate r for t years.
A = $100,000(0.04)/(1 -1.04^-20) = $7,358.18
The university could give $7,358 in scholarships each year.
22. Find the slope and Y intercept of the line 3x+4y-9=0
hi there! here's my answer for you...
Answer:
slope:
m = -3/4
y-intercept:
y = −3x/4 + 9/4
hope this helped. have a good one!
Let sets A and B be defined as follows.
A is the set of integers greater than - 7 and less than - 3
B={c, h, j, k, v, y}
(a) Find the cardinalities of A and B.
n(A) = ? n(B)= ?
(b) Select true or false.
True
False
-6E A
-14 EA
k E B
Q E B
The E is the signal used not the actual letter E
Answer:
n(A) = 3
n(B) = 6
-6 ∈ A => True
-14 ∈ A => False
k ∈ B=> True
Q∈B = >False
Step-by-step explanation:
Given
A is the set of integers greater than - 7 and less than - 3
B={c, h, j, k, v, y}
For set A:
The integers greater than -7 will be -6,-5 ....
As the set has integers less than -3, the set will be:
[tex]A = \{-6,-5,-4\}[/tex]
Cardinalities:
Cardinality is the number of elements in the set.
So,
[tex]n(A) = 3\\n(B) = 6[/tex]
Now for the statements:
-6 ∈ A True as -6 is a member of set A
-14 ∈ A False as -14 is not a member of A
k ∈ B True
Q∈B False
Hence,
n(A) = 3
n(B) = 6
-6 ∈ A => True
-14 ∈ A => False
k ∈ B=> True
Q∈B = >False
S= √3+2√3+3√3+...10√3
write S as a√3
Answer:
S = 55√3Step-by-step explanation:
S=
√3+2√3+3√3+...10√3 =√3( 1 + 2 + 3+...+ 10) =√3(1/2)(10)(10 + 1) =√3(55) =55√3S = 55√3
Answer:
s=✓3(1+2+3+...10)
s=✓3[10/2×(10+1)]
here, applying sum of 1st n natural number is n/2×(n+1)
so, s=✓3×5×11
hence, s=55✓3.
Liam had a container of oatmeal that contained 5 and one-half cups of oatmeal. Liam ate StartFraction 4 over 9 EndFraction cup of oatmeal every morning before school for a week. Which is the best estimate of the number of cups of oatmeal that Liam had left in the container at the end of the five-day week?
2 and one-half
3
3 and one-half
5
Answer:
3
Step-by-step explanation:
Danny bought 8 rolls of paper towels. He has 204.8 meters of paper towels in all. How many meters of paper towels are on each roll? A) 21.52 B) 25.12 C) 25.60 D) 26.52
Answer:C) 25.60
Step-by-step explanation:204.8÷8=25.60
Answer:
:C) 25.60
Step-by-step explanation:
Consider the limaçon with equation r = 3 + 4cos(θ). How does the quotient of a and b relate to the existence of an inner loop?
A polar graph that is a limacon has a formula similar to [tex]r=a+bcos\theta[/tex]
Option B is correct.
A limacon has a formula similar to [tex]r=a+bcos\theta[/tex]
Case 1 . If a < b or [tex]\frac{b}{a}>1[/tex]
Then the curve is limacon with an inner loop.
Case 2. If a>b or [tex]\frac{b}{a}<1[/tex]
Then the limacon does not have an inner loop.
Here, given that, [tex]r=3+4cos\theta[/tex]
It is observed that, a < b or [tex]\frac{b}{a}>1[/tex]
Therefore, the curve is limacon with an inner loop.
Hence, option B is correct.
Learn more:
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equation of the line with slope 1/2 that passes through the point
(-6, 1).
O 1
y = 2x - 4
v
О
1
y=2x-
-5
W
o
y = 2x + 5
-x
О 1
y = 2*+4
Step-by-step explanation:
let eqn be y = 1/2x + b
sub (-6, 1):
1 = 1/2(-6) + b
b = 4
therefore, eqn is y = 1/2x + 4
Topic: coordinate geometry
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
If 1 inch represents 10 miles on a map then how many inches will represent 120 miles ?
Answer:
12 inches
Step-by-step explanation:
We can write this as a proportion:
inches/miles = inches/miles
1/10 = x/120
Solving for x, we get 12 inches.
Katie played 5 consecutive games of soccer without being taken off the field. Then, after a single game on the sidelines, she played another 7 consecutive games. What is the percent of increase in the number of consecutive games she played?
Answer the question in the picture please!!
Answer:
Step-by-step explanation:
take the 142 degree angle and subtract it from 180 to find value of angle n, you will get 38. then you add 38 and 90 together to get 128. Since all angles of a triangle add up to 180. You subtract 128 from 180 to get 52.
Angle M = 52
Angle L = 90
Angle N = 38
Angle LNM = 180
Juan got grades of 68 and 73 on his first two math tests. What grade must he get on the third test if all were weighted equally and he wants to raise his grade to a 75 average?
Answer: 84
Step-by-step explanation: Multiply 75 by 3. That is 225, and is the value the three numbers must add up to. 73+68=141. 225-141 is 84.
simplify (3x+2) (y-2) - (7y+3) (y-3)
Answer:
3 x y − 7 y 2 − 6 x + 20 y + 5
Step-by-step explanation:
helpppppppppppppppppppp plsssss
Answer:
b
Step-by-step explanation:
The temperature drops from 7°F to -17°F. By how much did the temperature decrease?
Answer:
24 degrees
Step-by-step explanation:
If you use 0 as kind of a benchmark it is really useful, frist you subtract 7, because it is our positive number., then you subtract 17 from 0, making -17.
7+17=24
Sara invested $1,500 in a bond at a simple at a simple interest rate of 3%
Answer: N/A
Step-by-step explanation:
We need more info
A new truck costing $60,000 with a residual value of $6,000
A jogger is running home. His distance from home, as a function of time, is modeled by y=-7x +8.
Which statement best describes the function?
A. The function is nonlinear.
B. Not enough information is given.
C. The function is linear at some points and nonlinear at other points.
D. The function is linear.
Answer: the function is a liner
Step-by-step explanation: trust
15 POINTS
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will make the same shade of green paint?
A. 10 : 45
B. 30 : 54
C. 6 : 10
D. 27 : 15
explanation if you know how to explain
Answer:
The answer is B
Step-by-step explanation:
The problem is asking for the same ratio as 5:9
Multiply both sides by 6 to get 30:54
Not quite sure about the answer but it seems simple. Please answer!
Answer:
Its A
Step-by-step explanation:
-4x+6y=-7
-13x-2y=-4
Elimination or substitution
Answer:
substitution
Step-by-step explanation:
Does anyone know the solution to this question
Answer:
Graph A
Step-by-step explanation:
3x+y=5
y=-3x+5
4x-y=2
-y=-4x+2
4=2x-2
Which relation is a function?
write an equation for the line that passes through (4,10) and is perpendicular to the line 6x-3y=5
Answer:
[tex]y = - \frac{ 5}{3} x + ( - \frac{5}{3} )[/tex]
Step-by-step explanation:
-3y=5-6x
y=5-6x÷(-3)
y=(-5/3)+2x
y=2x-(5/3)
At y-intercept x is 0 and y is -(5/3)
Gradient m=10-(-5/3)÷(4-0)
=35/12
y=mx+c
10=(35/12)4+c
c=-(5/3)
Answer:
y = [tex]-\frac{1}{2}[/tex]x + 12
Step-by-step explanation:
Given expressions:
Coordinates = (4,10)
Equation of the line; 6x - 3y = 5
Unknown:
Equation of the line perpendicular = ?
Solution:
A line perpendicular to the given one will have a negative inverse slope.
Equation of any given line is expressed as:
y = mx + c
y and x are the coordinates
m is the slope
c is the intercept
Now; re-write 6x-3y = 5 in the form y= mx + c and find the slope;
6x - 3y = 5
-3y = 5- 6x
y = [tex]-\frac{5}{3}[/tex] + 2x
The slope of a perpendicular line will be [tex]-\frac{1}{2}[/tex]
Also, let us find the y-intercept, c;
y = mx + c
10 = [tex]-\frac{1}{2}[/tex] x 4 + c
10 = -2 + c
c = 12
The equation of the new line is ;
y = [tex]-\frac{1}{2}[/tex]x + 12
What is the sales tax rate if a $7,594 purchase will have $569.55 of sales tax added to it?
Answer:
0.075
Step-by-step explanation:
a leaky faucet is losing water and it is filling a 5 gallon bucket every 12 hours. At the rate, how many gallons of water will the faucet leak 48 hours
Answer:
20 gallons
Step-by-step explanation:
First start off by dividing 48 by 12 to see how many times 12 goes into 48.
48 / 12 = 4
now that you know that 12 goes into 48 4 times, multiply 4 by 5 to see how many gallons the leaky faucet will fill in 48 hours.
4 x 5 = 20
therefore the answer is 20 gallons
I hope this helps ^^
Consider the feasible region in the xy-plane defined by the following linear inequalities.
x≥0
y ≥0
x ≤ 10
x +y≥ 5
x + 2y ≤ 18
Part 2 Exercises:
1. Find the coordinates of the vertices of the feasible region. Clearly show how each vertex is determined and which lines form the vertex.
2. What is the maximum and the minimum value of the function Q = 60x+78y on the feasible region?
Answer:
1. (0,5), (0,9), (10,4), (10,0), (5,0)
2. [tex]Q_{max}=912[/tex]
[tex]Q_{min}=300[/tex]
Step-by-step explanation:
1.
In order to determine the coordinates of the vertices of the feasible region, we must first graph each of the inequalities. The feasible region is the region where all the inequalities cross each other. In this case it's the region shaded on the attached picture.
The first point is the intercept between the equations x=0 and x+y=5 so in order to find this first coordinate we need to substitute x=0 and solve for y.
0+y=5
y=5
(0,5)
The next point is the intercept between the equations x=0 and x+2y=18, so again, we substitute x for zero and solve for y:
0+2y=18
[tex]y=\frac{18}{2}[/tex]
y=9
(0,9)
The next coordinate is the intercept between the lines x=10 and x+2y=18, so we substitute x for 10 and solve for y:
10+2y=18
2y=18-10
2y=8
[tex]y=\frac{8}{2}[/tex]
y=4, so the oint is
(10,4)
The next point is the intercept between the lines x=10 and y=0, so the point is:
(10,0)
The final point is the intercept between the equations: y=0 and x+y=5. We substitute y for zero and solve for x:
x+0=5
x=5
so the point is:
(5,0).
2. In order to determine the maximum and minimum value of the function Q=60x+78y on the feasible region, we must evaluate it for each of the points found on part 1.
(0,5)
Q=60(0)+78(5)
Q=390
(0,9)
Q=60(0)+78(9)
Q=702
(10,4)
Q=60(10)+78(4)
Q=912
(10,0)
Q=60(10)+78(0)
Q=600
(5,0)
Q=60(5)+78(0)
Q=300
So now we compare the answers and pick the minimum and maximum results.
We get that:
[tex]Q_{max}=912[/tex]
when x=10 and y=4
and
[tex]Q_{min}=300[/tex]
When x=5 and y=0
The feasible region is the possible set of a constraint
The vertices are: [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]The maximum and the minimum values are 702 and 300, respectively.(a) The coordinates of the vertices at the feasible region
The constraints are given as:
[tex]\mathbf{x \ge 0}[/tex]
[tex]\mathbf{y \ge 0}[/tex]
[tex]\mathbf{x \le 0}[/tex]
[tex]\mathbf{x + y\ge 5}[/tex]
[tex]\mathbf{x + 2y\ge 18}[/tex]
See attachment for the graph of the constraints
From the graph, the vertices are:
[tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]
(b) The minimum and the maximum values of objective function Q
The objective function is:
[tex]\mathbf{Q=60x +78y}[/tex]
Substitute [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex] in Q
[tex]\mathbf{Q=60(0) +78(5) = 390}[/tex]
[tex]\mathbf{Q=60(0) +78(9) = 702}[/tex]
[tex]\mathbf{Q=60(5) +78(0) = 300}[/tex]
Hence, the maximum and the minimum values are 702 and 300, respectively.
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