Show that the equation x^4/2021 − 2021x^2 − x − 3 = 0 has at least two real roots.
The roots of an equation are simply the x-intercepts of the equation.
See below for the proof that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] has at least two real roots
The equation is given as: [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex]
There are several ways to show that an equation has real roots, one of these ways is by using graphs.
See attachment for the graph of [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex]
Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)
From the attached graph, we can see that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] crosses the x-axis at approximately -2000 and 2000 between the domain -2500 and 2500
This means that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] has at least two real roots
Read more about roots of an equation at:
https://brainly.com/question/12912962
The width of a rectangleis 5 meters less than its length and the perimeter is 30 meters whats the length and width
Answer:
can anyone help me in computer pls
Solve for x:
(x + 4) (x - 3) = 0
A. x = -4 and x = 3
B. x= -1 and x = 12
C. x= 1 and x = -12
D. X= 4 and x = -3
Answer:
answer is A x = -4 and x = 3
Step-by-step explanation:
-4 , 3
switch the signs
Answer:
The answer is "A."
Step-by-step explanation:
x+4=0. x-3=0
x=0-4. x=0+3
x= -4. x= 3
x = -4 and x = 3
I NEED HELP ASAP PLS!!!!!!
Answer:
the first one is not equivalent, the second one is equivalent.
Step-by-step explanation:
What is the difference in length between the shortest worm (3/4) and the longest worm (1 1/2)
Answer: 3/4 difference
Step-by-step explanation:
Turn 1 1/2 improper = 3/2
Multiply it by 2 (to make the denominator the same)
Do 6/4 minus 3/4 to get 3/4 as your answer.
Hope that helps! :))
1. A bird that was perched atop a 15 foot tree dives down six feet to a branch
below. How far above the ground is the bird's new location?
Due Today Please help Fast
Which expression shows 20+24 with 4 as a factor of each term?
(2.5) + (2.6)
2 + (5.6)
(2.10) + (2.12)
2 + (10.12)
(2 · 10) + (2 · 12)
Step-by-step explanation:
20 + 24
= (2 · 10) + (2 · 12)
proof :
20 + 24 = 44
(2 · 10) + (2 · 12)
= 2(10 + 12)
= 2(22)
= 44
The distance from Ellen's home to her school is 4 miles. If she has already traveled 2 miles, how far does she have to go?
Answer:
6 miles
Step-by-step explanation:
PLEASE HELP! I don’t understand this problem
HELPPPPP AGAIN!!! THIS IS DIFFICULT
What can you divide a2b5 by to get a quotient of 1?
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Answer:
a^2b^5
Step-by-step explanation:
Anything divided by itself is 1.
That is, anything multiplied by its reciprocal is 1. This value (the reciprocal of the expression) is called the "multiplicative inverse." Its value is that the product of an expression and its multiplicative inverse is 1, the multiplicative identity element. (Anything times 1 is itself.)
So, to get 1 as a product, multiply by 1/(a^2b^5), which is to say, divide by a^2b^5 to get 1 as a quotient.
A store sells one pound of strawberries for $2
a: How many pounds of strawberries can you buy with only $1? Show your answer with correct units.
b: How many pounds of strawberries can you buy with $11? Show your answer with work
Answer:
a) 1/2 pound
b) 5.5 pounds
Step-by-step explanation:
a) Realize $1 buys half of what $2 buys, or half a pound.
b) 11/2 = x/1
11 = 2x = 5.5
A certain medication is available only in 400 μg tablets. If the patient needs to take 2.4 mg per day, how many tablets must she take? Help me please. SIMPLIFY YOUR ANSWER. Expert only.
Answer: 6 tablets.
Step-by-step explanation:-Given:
• A certain medication is available only in 400 μg tablets.
So, in milligrams :- 0.4 mg
• It is also given that the patient needs to take 2.4 mg per day.
Solution:
So, in order to know how many tablets she should take, please do as following:-
[tex] \frac{2.4}{0.4} [/tex]
[tex] = > \: 6[/tex]
Hence, she must take 6 tablets per day.
✍️ By Benjemin ☺️
At the begining of last year, there were 368 students at the elementary school.By the beginning of this year,72 of those students had moved.About how many students started the school this year?
Answer:
296
Step-by-step explanation:
368-72
Find the value of X for the figure given the perimeter 74+ 7m. Length is 5m + 8 and width is 3m +2
How do you find the answer for this Solve for Y -y= -33
Answer:
the equation is
Y-y = -33
-33y
sumi bought 3 tickets that cost $7 each. She paid with a $50 bill. How much change should she receive?
Answer:
$29
Step-by-step explanation:
what steps were taken to solve the equation? solve the equation.
Answer:
x = 19/3
Step-by-step explanation:
Step 1 = x - 4 = 7/3
Step 2 = x = 7/3 + 4
[(4*3)+7]/3 = 19/3
To complete a job, a plumber needs 10 sections of pipe that are 24.125 inches in length. How much pipe is needed?
Answer:
241.25
Step-by-step explanation:
24.125 x 10= 241.25
Answer:
That would be a total of 241 and a quarter inches of pipe which is equal to 20.10417 feet of pipe.
Step-by-step explanation:
24.125x10=241.25/12=20.104166666
Because there are 12 inches in a foot.
If a ray QT bisects ZRQS , what would be the measure of one of the resulting angles
Measure=?
Answer:
PQS is a straight line, so:
(3x - 5) + (x + 1) = 180
4x - 4 = 180
4x = 184
x = 46 degrees
Step-by-step explanation:
(v^3+14v^2+46v+11) / (v+9) long division polynomials
Answer:
v²+5v+1 + 2/(v+9)
Step-by-step explanation:
(v^3+14v^2+46v+11) / (v+9) = v²+5v+1 R: 2
attached is synthetic division instead of long division for easier display
Amy is training for a half marathon. in practice, she runs 2 miles in 15 minutes. If she continues at the same rate, how many miles will she run in 1 hour?
A. 4
B. 8
C. 16
D. 30
Step-by-step explanation:
B. 8
she will run for 8 miles,
stepfind Amy's speed
convert the minutes into hours by dividing by 60
[tex] \frac{2}{15 \times \frac{1}{60} } \\ = 8 \: miles \: per \: hour[/tex]
find the number of miles ran by multiplying the speed by the time, ie
[tex]8 \times 1 = 8 \\ \: therefore \: the \: answer \: is \: \: 8 \: miles[/tex]
Which of the following are remote interior angles of <6? Check all that apply.
Choices
A. 5
B. 1
C. 6
D. 4
E. 3
F. 2
Answer:
Well you see Is this GCSE
What is the value of h in this graph ?
F(x)= |x - h|
Answer:
[tex]h=4[/tex]
Step-by-step explanation:
We know that the vertex(lowest point) of [tex]|x-h|[/tex] is [tex](h, 0)[/tex].
By inspection, we can see that the vertex of the graph is [tex](4, 0)[/tex].
So, the lowest point of [tex]F(x)=|x-h|[/tex] is [tex](4, 0)[/tex], which means [tex]\boxed{h=4}[/tex]
Answer:
Step-by-step explanation:
0=|x-h|
x=h,
but y=0 when x=4
so h=4
Solve for x
simple geometry
Step-by-step explanation:
[tex]2x - 10 + 4x + 16 = 180 \\ \\ 4x - 2x + 16 + 10 = 180 \\ \\ 2x = 180 - 26 \\ \\ 2x = 154 \\ \\ x = \frac{154}{2} \\ \\ x = 77[/tex]
Answer:
From the above attachment we can conclude that,
[tex](2x - 10)° + (4x + 16)° = 180° \\ 2x - 10 + 4x + 16 = 180 \\ 2x + 4x - 10 + 16 = 180 \\ 6x + 6 = 180 \\ 6x = 180 - 6 \\ 6x = 174 \\x = \frac{174}{6} \\ \boxed{x = 29}[/tex]
Therefore, the value of x is 29
x = 29 is the right answer.tìm các đường tiệm cận của hàm số sau y=1/x+7
Answer:
i dont speak...that language can u translate to english?
Step-by-step explanation:
5x - 3y - 25 = 0 as well as the values of p, w, and draw the graph
Please help some one and if you could explain please
Answer:
t = 1 second
Step-by-step explanation:
initial height = 16
penny to hit the ground = 0
0 = -16t^2 + 16
-16 = -16t^2 ÷
-16 ÷ -16 = -16t^2 ÷ -16
1 = t^2
√1 = √t^2
1 = t
a medical terminology course has 150 total students. On the first exam 96 students passed. what is the percentage of students that did not pass the first terminology exam?
64% percent of students have not passed the first terminology exam.
96/150 = 16/25
16/25 = 64%
Pls help me I really need this today. If you need the snack price is here!
Dried Fruit $4.25 per pound
Mixed Nuts $6.75 per pound
Trail Mix $3.50 per pound
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Answer:
Yes, Yolanda bought enough
Step-by-step explanation:
a. Read and understand the question, including what is given and what is asked for. Here, we have ...
Given: mixed nuts $6.75 per pound, $21.60 spent on mixed nuts; dried fruit $4.25 per pound, $11.90 spent on dried fruit.
Find: is the total weight of purchased mixed nuts and dried fruit at least 6 pounds?
__
b. Select appropriate relations to create a path from what is given to what is asked for. Here, we have ...
weight = cost/(cost per pound)
total weight = weight of mixed nuts + weight of dried fruit
__
c. Use the relations with the given information to come to a conclusion that will answer the question.
weight of mixed nuts = $21.60/($6.75/lb) = 3.2 lb
weight of dried fruit = $11.90/($4.25/lb) = 2.8 lb
total weight = (3.2 lb) +(2.8 lb) = 6.0 lb
Yolanda wanted to buy a total of 6 pounds for the party, and she bought 6 pounds. Yolanda bought enough for the party.