t-3.2 ≤ 7.5
"at most" means less than or equal to
Two roots of a third degree polynomial function f(x) are -4 and 4. Which statement describes the number and nature of all
roots for this function?
* f(x) has three imaginary roots.
* f(x) has three real roots.
* f(x) has two real roots and two imaginary roots.
* f(x) has three real roots and one imaginary root.
Answer:
f(x) has three real roots.
Step-by-step explanation:
f(x) has three real roots.
A third degree polynomial function with real coefficients has exactly 3 roots.
Furthermore, all complex roots come in pairs, either there is none, or there are exactly two conjugates, which are in the form e1+i(e2) and e1-i(e2) where e1 and e2 are polynomial expressions.
This also means that a third degree polynomial with real coefficients has at least one real root, or three.
Since we are given two real roots for the given polynomial, the third root cannot be complex alone, so the only possibility is that there are three real roots.
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary.
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
The polynomial function f(x) has degree 3 and two roots -4 and 4, we know that (x + 4) and (x - 4) are factors of the function.
To see why, note that when x = -4, the factor (x + 4) becomes zero, making the function zero.
Similarly, when x = 4, the factor (x - 4) becomes zero, making the function zero.
Now,
Since the function has degree 3 and two factors of degree 1, we can conclude that the third factor is also of degree 1.
This means that the function can be written in the form:
f(x) = a (x + 4) (x - 4) (x - b)
where a and b are constants.
We don't know the value of b, but we know that it is a real number (since the other two roots are real).
Thus, the three roots of the function are -4, 4, and b.
Now,
To determine whether the roots are all real or some are imaginary, we need to know the value of b.
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary (b).
Thus,
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary.
Learn more about polynomials here:
https://brainly.com/question/2284746
#SPJ7
A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is
Answer:
[tex]r =5[/tex]
Step-by-step explanation:
Given
[tex](h,k) = (-3,2)[/tex] -- center
[tex](x,y) = (1,5)[/tex] --- pass through
Required
The radius (r)
The equation of circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
So, we have:
[tex](1 - -3)^2 + (5 - 2)^2 = r^2[/tex]
[tex](4)^2 + (3)^2 = r^2[/tex]
[tex]16+9 = r^2[/tex]
[tex]25 = r^2[/tex]
Take square roots of both sides
[tex]5 = r[/tex]
[tex]r =5[/tex]
HELP PLEASE!!! HELP HELP
Answer:
f(-3) = -1/3
Step-by-step explanation:
-3 is less than -2 so we use the first function 1/x
f(-3) = 1/-3
Answer:
-1/3
Step-by-step explanation:
-3 is less than -2, so use the first one, 1/x and substitute -3 in
1/(-3)=-1/3
Me ayudan por favor ♡?
Answer:
Yes of course I would like to help u.
[tex] \frac{11}{3} \times \frac{23}{5} [/tex]
Emilia is painting a triangular picture frame. The perimeter is 30 inches. If one side is 13 inches long and another side is 5 inches long, what is the length of the other side of the picture frame?
Answer:
12 inches
Step-by-step explanation:
30-13=17
17-5= 12
Use information about the triangle's perimeter, to find the side length of C.
If the triangle frame is a right triangle, than you could use the Pythagorean Theorem and use the following formula, a^2 + b^2 = c^2, to find the measure of side c.
Have a great rest of your day, and I hope this helps!
-kiniwih426
Hey can somebody help me
Answer:
x^2/3
Step-by-step explanation:
Exponent properties!
x^4*x^9 for example,
we add the exponents because the base of the exponents is the same.
now back to the question
x^4/3 * x^2/3
we add those exponents!
6/3 or 2
so we have( x^2)^1/3
^2 and ^1/3 multiply!
we have x^2/3
if x varies directly as y,write a formula connecting x and y y.use k as a constant of variaton.
2 times the sum of a number and 9 equals 4
Answer
Step-by-step explanation:
(a) Find the standard error of the mean for each sampling situation (assuming a
normal population). (Round your answers to 2 decimal places.)
Standard
Error..
|
(a) o = 48, n = 16
(b) o = 48, n = 64
(c) 0 = 48, n = 256
Answer:
a
Step-by-step explanation:
ok
Triangle PQR has vertices P(3, 5), Q(-2, 6) and R(8, -1). Give the translation rule (x, y) → (x + 4, y – 5). What will P’ (__, __) be
=======================================================
Explanation:
The rule [tex](x,y) \to (x+4, y-5)[/tex] means we add 4 to the x coordinate and subtract 5 from the y coordinate.
The point (3,5) becomes (3+4, 5-5) = (7,0)
This shifts the point 4 units to the right and 5 units down.
A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4blue marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
Answer:
5/12 is already in simplest form
Step-by-step explanation:
12m = 5r + 3y + 4b
red is chosen = 5r / 12 = 5/12
Step-by-step explanation:
the answer is 5/12. It's quite simple
Xác suất thống kê: Người ta tổng kết các phương pháp chẩn đoán dạ dày tá tràng. Trên lâm sàng chẩn đoán đúng 60%; X-quang 70%; nội soi 80%. Kết hợp cả 3 phương pháp thì khả năng chẩn đoán đúng là bao nhiêu?
Answer:
Step-by-step explanation:
iam a gay 345366e2673
Soda is often sold in 20 ounce bottles. A pack of sugar (the kind they have at restaurants for your coffee or tea) typically contains 4 grams of sugar. If an 8 ounce bottle of cream soda has 30 grams of sugar, then drinking a 20 ounce bottle of cream soda would be equivalent to eating how many packets of sugar?
Answer:
18.75 packs of sugar
Step-by-step explanation:
20/8 = 2.5 (how many 8 ounce bottles in 20 oz)
2.5 * 30 = 75 (to find how many grams of sugar in the 20 oz bottle)
75/4 = 18.75 (how many packs of sugar it's equal to)
you can also use a ratio to solve:
8/30 = 20/x; cross multiply
600 = 8x; divide 8 on both sides
x = 75
75/4 = 18.74 (how many packs of sugar it's equal to)
i need help please if you know the answer
Answer:
The mean is 19.
Step-by-step explanation:
To find the mean, you add up all of the numbers then divide by how many numbers there are. So you would do 3+8+10+11+14+17+22+24+25+35+40, then divide it by 9 since there are 9 numbers shown, which gets you to 19.
If a 32-gram serving of pasta contains 4g of protein, how many grams of protein are in a 908-gram box of the pasta ?
Step-by-step explanation:
This is my solution you honestly just need to cross multiply
Answer:
113.5
Step-by-step explanation:
32 : 4 = 908 : X
X = (4 * 908) / 32
X = 113.5
Find the value of X and Y
Answer:
y=60 degrees ; x=120 degrees.
Step-by-step explanation:
All triangles' angles must add up to 180 degrees. An equilateral triangle has 3 equal sides and degrees. If it gives the angle of one all the other angles are the same. For x you see the parallel line below it with the line to the left going through with the same angle as the one below. The angles are the same and if it is labeled in one then it is the same in the other.
ASAP! see the picture please!!
Answer:
the second one
function A has a slope of 3
function B has a slope of 5
Use f(x) = 3x - 4 and g(x) = 5 - x2 to evaluate the expression.
(a)
(f of)(x)
(b)
(go g)(x)
Answer:
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
10 15 20
30
55
HI
Town B
5
20
30
40
55
H
0 5
10
15
20
45
50
55 60
25 30 35 40
Degrees (F)
Which statement is the most appropriate comparison of the centers?
O A. The median for town A, 30°, is less than the median for town B,
40°
B. The mean for town A, 20°, is less than the mean for town B, 30°
C. The median for town A, 20°, is less than the median for town B,
30°
O D. The median temperature for both towns is 30°.
Answer:
The answer is:
C. The median for town A, 20°, is less than the median for town B, 30°.
Step-by-step explanation:
Median is the middle (center) value.
Option (C) the median for town A, 20°, is less than the median for town B, 30°.
What is box plot?Box plot is a type of chart often used in explanatory data analysis. A graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.
For the given situation,
The diagram shows the box plot of the daily low temperatures for a sample of days in two different towns.
From the box plot, the median of town A is 20° and the median of town B is 30°.
From the data,
⇒ [tex]20 < 30[/tex]
Hence we can conclude that option (C) the median for town A, 20°, is less than the median for town B, 30°.
Learn more about box plot here
https://brainly.com/question/12591498
#SPJ2
Which is the best estimate of 2127
Answer:
20
Step-by-step explanation:
Have a nice day :)
is it 8%? i think but i just wanna make sure.
Answer:
Yeah, you're right!
Step-by-step explanation:
For 1/6 it's 17%, so just divide by two and you get 8% (rounded).
Answer:
thats right 8%
Step-by-step explanation:
numbers of samples = 6×2 = 12
6 for a cube , and 2 for a fair coin
numbers of event (5, H) is 1
so, the probability is 1/12 = 1/12 × 100%
= 8.33% => rounded => 8%
please ! solve the following equation algebraically: 2x²=50
Answer:
5,-5
Step-by-step explanation:
What is the similarity
statement for the triangle
pair?
Answer:
side-side-side
Step-by-step explanation:
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
The similarity statement for the pair of triangles is triangle XYZ similar triangle ENW by AA similarity criterionand mathematically represented as: [tex]\Delta XYZ \, \sim \, \Delta ENW\\[/tex]
Given: In the figure, the angle YXZ is equal to angle NEW and the angle XZY is equal to angle ENW are marked in the corresponding triangles.
To prove triangle XYZ similar triangle ENW by following steps:
Step 1: Consider the triangle XYZ and triangle ENW.
Compare the angle in both the triangles.
[tex]\Delta XYZ \, and\, \Delta ENW\\[/tex][tex]\angle YXZ = \angle NEW\\[/tex][tex]\angle XZY = \angle NWE[/tex]Step 2: Applying the AA similarity criterion:
The Angle-Angle AA similarity criterion states if two angles of one triangle is equal to the corresponding triangle, then two triangles are similar,
This implies triangle XYZ and triangle ENW by AA similarity criterion.
Therefore, the triangle XYZ and triangle ENW by AA similarity criterion. That is [tex]\Delta XYZ \, \sim \, \Delta ENW\\[/tex]
Learn more about AA similarity criterion here:
https://brainly.com/question/34160175
#SPJ6
Can y’all help me on question 32?!
Answer:
b. 96
Step-by-step explanation:
triangle area= b x h / 2
5 x 6 /2= 15
15 x 4 (4 triangles)= 60
square area= b x h
6x6=36
36 + 60 = 96
A rope with a length of 3.5 meters is tied from a stake in the ground to
the top of a tent. It forms a 17 degree angle with the ground. How tall
is the tent?
Answer: Approximately 1.0233 meters
Round this however you need to
====================================================
Work Shown:
Refer to the drawing below.
sin(angle) = opposite/hypotenuse
sin(17) = x/3.5
3.5*sin(17) = x
x = 3.5*sin(17)
x = 1.02330096652958
x = 1.0233
Be sure that your calculator is in degree mode.
Please answer the question below 15 points for answering!
If a card is randomly selected, what is the probability that the card is any one suit, e.g., a diamond, heart, spade, or club?
Step-by-step explanation:
there are 13 cards per 4 suits, totalling 52 cards in an entire deck
13 represents an entire 1 suit out of 52 cards
13/52 = 0.25
thus your answer is 0.25% or 1/4
A book contains the following recommend weight for kangaroos:" Give the kangaroo 120 pounds for the first 5 feet plus 5 pounds for every inch over 5 feet tall." Using this description, what height corresponds to the recommended weight of 180 pounds?
Answer:
A 180-pound kangaroo's recommended height is 6 feet.
Step-by-step explanation:
Since 120-pound kangaroo is 5 feet tall and for every inch over this height we add 5 pounds to the total weight, we can make this formula. [tex]120+x=180[/tex]. Using this we can figure out the weight difference between a 120-pound kangaroo and a 180-pound kangaroo. After solving for x we get [tex]x=60[/tex].
Now that we know the 180-pound kangaroo weighs 60 more pounds than a 120-pound kangaroo we can divide that weight difference by 5 to figure out the height difference. [tex]60/5=12[/tex]
After getting the height difference from the weight difference we can conclude that a 180-pound kangaroo's recommended height is 5 feet and 12 inches. Since 12 inches = 1 foot we can easily convert 5' 12" to 6'. This means that a 180-pound kangaroo is 6 feet tall.
A sample of 260 students enrolled at a university were asked what they intended to do after graduation. The results are shown below.
Bar Graph of Type of Employment
What percentage of students intend to go into state or local government after graduation?
Hi my name is Fabian and 69% because 69 is a man which is multi colour hair