Answers
9514 1404 393
Answer:
a) f(-2.5) = 62.6875; f(-1.5) = -13.0625; (-2.5, -1.5) contains a real root
b) there are 1 each of positive and negative real roots; 2 complex roots
c) -2 and 1/3 are the rational real roots
d) x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}
Step-by-step explanation:
a) f(-2.5) = 62.6875; f(-1.5) = -13.0625. The function changes sign between -1.5 and -2.5, so there is a real root in that interval.
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b) The given coefficients have one sign change, so there is one positive real root. Changing the signs of odd-degree terms makes the signs + - + - -, so there are three sign changes. There are 1 or 3 negative real roots, and possibly 2 complex roots. The constant term is non-zero, so zero is not a root. Here's your table:
positive real roots: 1
negative real roots: 1 or 3
complex roots: 2 or 0
zero roots: none
The graph is attached. It shows 2 real roots, one positive and one negative, so there are 2 complex roots. (There are 4 roots in total, so if only 2 are real, the other 2 are complex.)
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c) Possible rational roots are of the form ...
±{1, 2}/{1, 3, 9}
Listed, they are ...
±{1/9, 2/9, 1/3, 2/3, 1, 2}
The actual real roots are -2 and 1/3.
__
d) The graph shows the real roots to be -2 and 1/3. The original leading coefficient of 3 is the product of the leading coefficients of the factors. Writing the factor (x -1/3) as (3x -1) lets us reduce the leading coefficient of the quadratic term from 9 to 3. The result of dividing factors (x+2) and (3x-1) from the original function is shown in the attachment. It is a parabola with vertex (-1/3, 2/3), so the factorization is ...
f(x) = (x +2)(3x -1)(3(x +1/3)² +2/3)
The roots of the quadratic term are ...
3(x +1/3)² = -2/3
x +1/3 = ±√(-2/9)
x = (-1 ±i√2)/3
So, the entire list of roots is ...
x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}
_____
Additional comment
The roots of a quadratic are easily found by knowing its leading coefficient and its vertex. If factoring known real roots from a higher-degree polynomial results in a quadratic, then the remaining complex roots are easily found. A graphing calculator is a wonderful tool for this process.
Related Questions
57:22 5 What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4,-3)? 2 1 (-1, 1) 513 2 1 2 3 4 % Oy+3= -41%+4) Oy+3= *(** 4) Oy+3 = *(+4) Oy+ 3 = 4(x + 4) 0,-3) Mark this and return Save and Exit Next Submit
Answers
Answer:
C. y + 3 = ¼(x + 4)
Step-by-step explanation:
✔️Find the slope of the given line:
Slope = ∆y/∆x = -(4/1) = -4
The line that is perpendicular to the given line on the graph would have a slope that is the negative reciprocal of -4.
Thus, the slope of the line that is perpendicular to the line on the graph would be ¼.
m = ¼.
Since the line passes through (-4, -3), to write the equation in point-slope form, substitute a = -4, b = -3, and m = ¼ into y - b = m(x - a)
Thus:
y - (-3) = ¼(x - (-4))
y + 3 = ¼(x + 4)
Express the rate described.
James needs to work 65 hours every 3 weeks to meet the quota for his school internship.
Answers
Answer:
21.67 hours/ week
Step-by-step explanation:
Given
[tex]Hours = 65[/tex]
[tex]Weeks = 3[/tex]
Required
Determine the rate
The rate is calculated using:
[tex]Rate = \frac{Hours}{Weeks}[/tex]
Substitute values for hours and week
[tex]Rate = \frac{65}{3}[/tex]
[tex]Rate = 21.67[/tex]
This implies that the rate is 21.67 hours/ week
Hi, can someone help me understand how to do this.I tried and I got confused and I was confident my answers were right but I got them wrong.These problems have to do with Quadratic applications I believe.
Answers
The answer is c  Explanation :
Answer:
answer c
Step-by-step explanation:
Convert 6 months to years
Answers
Answer: 0.500001
Step-by-step explanation: Hope that helps!
Which graph represents an even function?
Answers
Answer: last graph
Step-by-step explanation: Graphs of functions that are ODD, are symmetric about the origin.
Graphs of function that are EVEN, are symmetric about y-axis.
We need to figure out which one of the 4 are EVEN. So we take y-axis as the mirror and see both sides, LEFT and RIGHT and see i the points are symmetric or not.
Graph 1, 2, 3 ---- not symmetric about y-axis
Graph 4 ------- Definitely every point to left side of y-axis has a corresponding mirror point to the right of y-axis. So this is an EVEN FUNCTION.
The single equivalent discount rate of the trade discount 6/4/2 is:
Answers
Answer:
3/1
Step-by-step explanation:
Given the expression 6/4/2, we are to express as a single fraction.
6/4/2
= 6÷4/2
= 6×2/4
= 12/4
= 3/1
Hence the expression as a single fraction is 3/1
Please help!! Will make brainliest
Answers
UmmmmAnswer:
Step-by-step explanation:
Greg is saving up for a new cell phone that will cost him $550: He
already has $300 saved. If he would like to buy the phone in four weeks,
how much must he save each week if he plans to have at least $550? *
Answers
the number of customers waiting inside a restaurant was 2 less than a third of those waiting inside. if three customers were waiting inside how many were outside
Answers
Answer:
15 customers were outside
Step-by-step explanation:
Represent customers inside with x and customers outside with y.
So, we have:
[tex]x = \frac{1}{3}y - 2[/tex] --- First Statement
[tex]x = 3[/tex] --- Second Statement
Required
Find y
Substitute 3 for x in [tex]x = \frac{1}{3}y - 2[/tex]
[tex]3 = \frac{1}{3}y - 2[/tex]
Add 2 to both sides
[tex]2 + 3 = \frac{1}{3}y - 2 + 2[/tex]
[tex]2 + 3 = \frac{1}{3}y[/tex]
[tex]5= \frac{1}{3}y[/tex]
Multiply both sides by 3
[tex]3 * 5= \frac{1}{3}y *3[/tex]
[tex]15 = y[/tex]
[tex]y = 15[/tex]
Hence; 15 customers were outside
Paul picked 5482 peaches. Peter
picked four times as many as Pual
picked. Sam picked twice as many as
Peter picked. How many peaches did
hey pick altogether?
Answers
Answer:
71,266 peaches
Step-by-step explanation:
paul=5482
peter=5482*4=21,928
sam=21928*2=43,856
5482+21,928+43,856=71,266
A pound of apples cost $1.35 a pound of cherries cost $3.62. How much will it cost to by 1.6 pounds of apples and 2.5 pounds of cherries?
Answers
Answer:
apples cost a total of 2.16
cherrys cost a total of 9.05
Step-by-step explanation:
1.35*1.6=2.16
3.62*2.5=9.05
How many square feet are in 15 square yards
Answers
Hope this helps! Sorry if I’m wrong.
Hello can you tell me what the answer of this How many subets dose the set a have a= ( a,b,c,d)
Answers
Answer:
16 subsets
Step-by-step explanation:
To know the number of subsets that the set have, we will have to find the power of the set.
Given the set a = ( a,b,c,d)
P(a) = 2^n where;
n is the total number of element in the set
n = 4
p(a) = 2^4
P(a) = 16
Hence the set has 16 subsets
The expression (4a + b) – 3(2a + b) is equivalent to:
Answers
Answer:
-2a - 2b
Step-by-step explanation:
Question : (4a + b)-3(2a + b)
= 4a + b - 6a - 3b
= 4a - 6a + b - 3b
= -2a + (-2b)
= -2a -2b
If you need detail solution here ;
first + multiply both 4a and b
first -3 multiply both 2a and b and then -3×2a= -6a
-3×b = -3b
and it will be 4a + b -6a -3b,then collect like terms
4a - 6a + b -3b
= -2a +(-2b) in this part + tims - = -
= -2a - 2b
If it's not helpful ask me on comment I will try to answer
If it's helpful ❤❤
THANK YOU
Is anyone able to check this for me?
Pyragtheom theory
8th grade math
Answers
Answer:
Those are both correct
Step-by-step explanation:
To solve for the triangle 12^2+10^2=c^2, and for the other question, you are correct because the hypotenuse is NEVER the shortest side.
What language your figure the thunder rose
Answers
Answer: ok buddy
Step-by-step explanation:
Answer:
?
Step-by-step explanation:
Will give brainless ⭐️!!!
A triangle is translated 4 units down and 8 units to the right
Which translation returns it to its original location?
O(x, y) - (x + 4, y - 8)
o (x, y) - (x - 8, y + 4)
O (x, y) - (x - 4, y + 8)
O(x, y) — (x + 8, y - 4)
Answers
Answer:
It's the second on, 4 units up and 8 units to the left
A sporting goods store sold 30% of the baseball bats in stock. If they had 420 bats in stock, how many did they sell?
Answers
Answer:they sold 126 bats
Step-by-step explanation:
30/100= 3/10
3/10x420=3x42=126
You are given that angle RST and angle TUR are right angles. What additional piece of info allows you to prove they are congruent
Answers
Answer:
the additional info required is - the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle.
Step-by-step explanation:
As given , RST and angle TUR are right angles.
So the triangles are right angle triangles.
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
So, the additional info required is - the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle.
Select the reason why these triangles are
similar. If they are not, select "Not similar".
8
12
5
7
6.25
10
A. AA
B. SAS
C. SSS
D. Not similar
Answers
The triangles of the dimensions are not similar by any property of similarity. Thus option D is correct.
Concept of similarity : Two triangles can be similar by AAA, SAS, SSS property .
Given,
Two triangles with different side lengths.
Here,
The two triangles are similar if they have same shape , but can be of different sizes and corresponding sides are of same proportions.
Here,
Triangles are of same shape but the corresponding sides are not in same proportions.
∴ 8/5 = 10/6.25 ≠ 12/7
Therefore the two triangles are not similar.
Know more about similar triangles,
https://brainly.com/question/29191745
#SPJ4
can someone help me??
Strategies for finding a 30 % increase....
Answers
Answer:
Identify the original value and the new value.
Input the values into the formula.
Subtract the original value from the new value, then divide the result by the original value.
Multiply the result by 100. ...
Check your answer using the percentage increase calculator.
Step-by-step explanation:
What do the factors in the factored form represent?
Answers
Answer:
the factored form tells you times at which the object's height is zero.
Step-by-step explanation:
Hope that helps
Have a good day
Answer:
The polynomial -8x2 + 54x + 140 can be factored as (x + 2)(-8x + 70).
The factor (x + 2) represents the final price per hot dog after increasing it from the starting price of $2, where x is the number of $1 increases in price.
The factor (-8x + 70) represents the average number of hot dogs sold based on the price increase. For every $1 increase in price, the number of hot dogs sold declines by 8. So, if the price increases by x dollars, the number of hot dogs sold declines by 8x. Since the number of hot dogs sold without the price increase is 70, the number of hot dogs after a price increase is -8x + 70.
Step-by-step explanation:
PLATO
Solve using substitution.
4x – 7y = -18
x = 6
Answers
Answer:
6
Step-by-step explanation:
4(6) - 7y = -18
24 - 7y = -18
-7y= -42
y= 6
Answer: y=6
Step-by-step explanation:
4(6)-7y=-18
24-7y=-18 subtract 24 on both sides
-7y=-42 **then divide -7 on both sides**
and the answer is y=6
If p= -7 and r = 1/2, what does pr - r equal
A) -4
B) -3
C) 3
D) 4
Answers
Answer:
Step-by-step explanation:
Factor the expression.
pr - r = r(p-1) = ½(-8) = -4
Answer:
-4
Step-by-step explanation:
pr = -7 × 1/2-7 × 1/2 = -3.5-3.5 - r = -3.5 - 1/2-3.5 - 1/2 = -3.5 - 0.5-3.5 - 0.5 = -4I hope this helps!
1/? x 1/2 = 1/10
PLEASE HELP
Answers
Answer:
5
Step-by-step explanation:
Answer:
Answer:5
Step-by-step explanation:
hope it helps.
-3(2x+1)+x
Please help me thx:)
Answers
You have already saved $55. You earn $9 per hour at your job. You are
saving for a bicycle that costs $199. What inequality represents the possible
numbers of hours you need to work to buy the bicycle?
Answers
Answer:
$55+$9x≥$199
You must work for at least 16 hours to be able to buy the bicycle.
Step-by-step explanation:
Let x represent the number of hours you need to work to buy the bicycle.
You already have $55.
⇒$55+ −−−−−≥ −−−−−
You also earn $9 per hour.
Algebraically, this can be written as 9x.
⇒$55+$9x≥ −−−−−
You need to earn at least $199 to buy the bicycle.
⇒$55+$9x≥$199
The ≥ sign is used because the left-hand side of the inequality must be "greater than or equal to" $199.
Let's find out how many hours you need to work to buy the bicycle.
Subtracting $55 from both sides of the inequality:
⇒$55−$55+9x≥$199−$55
⇒$9x≥$144
Dividing both sides by $9:
⇒$9x$9$=$144$9
∴x≥16
Therefore, you need to work at least 16 hours to afford the bicycle.
144 divided by 9 is 16
16 Hours is your answer
3.6(x + 2) - 6 = 3.6x + 1.2
Answers
Answer:
3.6(x + 2) - 6 = 3.6x + 1.2 can change it on him
Karen spent 39 minutes knitting 3 hats. In all, how many hats could Karen knit in 117 minutes?
Answers
Answer:
9
Step-by-step explanation:
i did the math
pls help :)
Given the function y = x + 3, what is the value of y if x is 7?
Answers
Answer:
10
Step-by-step explanation:
y=x+3; x=7
Substitute x in with 7
y=7+3Add 7 and 3
y=10