The number of roots of a polynomial is always less than or equal to the degree of the polynomial because the degree of f(x) is the sum of the degrees of the factors
Why is the number of roots less than or equal to the degree?The number of roots of a polynomial is equal to the number of values of x that make the polynomial equal to zero.
The degree of a polynomial is the highest exponent of the variable in the polynomial. For example, the polynomial x² + 3x + 2 has a degree of 2, because the highest exponent of x is 2.
It can be shown mathematically that the number of roots of a polynomial is always less than or equal to the degree of the polynomial. This is known as the Fundamental Theorem of Algebra.
Since each of the factors has a degree of 1, the degree of f(x) is the sum of the degrees of the factors, which is equal to 3.
Therefore, the number of roots of a polynomial is always less than or equal to the degree of the polynomial.
Learn more about Fundamental Theorem of Algebra on:
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4(x+2)=4x+8 need help
Answer:
True
Step-by-step explanation:
Any value of x makes the equation true
All Real numbers
(-∞)(∞)
Find the sum. Write your answer in standard form.
(7x +13) + (x3 + 4x2 – 8)
Answer:
. Simplify: (4x2 - 2x) - (-5x2 - 8x).
Solution:
(4x2 - 2x) - (-5x2 - 8x)
= 4x2 - 2x + 5x2 + 8x.
= 4x2 + 5x2 - 2x + 8x.
= 9x2 + 6x.
= 3x(3x + 2).
Answer: 3x(3x + 2) Step-by-step explanation:
Question 1
The expression (-4a3b)2 is equivalent to
16a6b2
16a5b2
8a6b2
-16a6b2
23. Three businessmen A, B and C enter into
partnership and agree to share the total
profit in the ratio of their investments. A
invested GH¢450, B invested GH¢150
and C invested GH¢600. C received a
profit of GH¢24.70, find
i) the total profit.
ii) the profits made by A and B.
Step-by-step explanation:
A invested 450
B invested 150
C invested 600
total investment was 1200
share of A is 450/1200 = .375
share of B is 150/1200 = .125
share of C is 600/1200 = .5
C received a profit of 24.70.
that would be .5 of the total profit.
if we let x = total profit, we get .5 * x = 24.70
solve for x to get x = 24.70 / .5 = 49.40
A share of total profit = .375 * 49.4 = 18.525
B share of total profit = .125 * 49.4 = 6.175
C share of total profit .5 * 49.4 = 24.7
total profit = 49.4 as we had calculated earlier.
Find the circumference of the semi circle 7cm
Given:
A semicircle with radius 7 cm.
To find:
The circumference of the given semi circle.
Solution:
We know that,
Circumference of a semi circle = Half of circumference of the circle + Diameter
[tex]=\dfrac{1}{2}(2\pi r+d[/tex]
[tex]=\pi r+2r[/tex]
Putting [tex]\pi=\dfrac{22}{7},r=7[/tex], we get
Circumference of the semi circle [tex]=\dfrac{22}{7}(7)+2(7)[/tex]
[tex]=22+14[/tex]
[tex]=36[/tex]
Therefore, the circumference of the given semi circle 36 cm.
Grade 6 Unit 4 Equations and Inequalities PC Each of three brothers was given the same amount of money by their grandfather. The total amount they received was $45. $45 How much money did each brother receive? Answer with a complete sentence.
The town of Butler received 6 more inches of snow than the town of Chicora. Let c represent the amount of snow in Chicora. Which algebraic expression represents the amount of snow in Butler?
pls help i have been stuck on this for like an hour now.
Answer:
y=c+6
Step-by-step explanation:
this is the only equation I could think that fits the situation
hope this helped!
How does the concept of trust relate to debt?
Answer:
A trust can protect your assets for the next generation. However, if you have debt, the trust will not necessarily protect assets from creditors. If you or your beneficiaries file for bankruptcy, for example, the trust could be seized for repayment of debts.
Rashaad has a bag that contains apple chews, strawberry chews, and watermelon chews. He performs an experiment. Rashaad randomly removes a chew from the bag, records the result, and returns the chew to the bag. Rashaad performs the experiment 24 times. The results are shown below:
An apple chew was selected 11 times.
A strawberry chew was selected 5 times.
A watermelon chew was selected 8 times.
Based on these results, express the probability that the next chew Rashaad removes from the bag will be watermelon chew as a fraction in simplest form.
Answer:
1/3
Step-by-step explanation:
8 divided by 24 is .33
which in fraction form is 1/3
Answer:
1/3
Step-by-step explanation:
5x + 2y = 18
-5x + 5y = 45
Answer:
the answer for this problem is (x,y)=(0,9)
Answer:
y = 9
x = 0
Step-by-step explanation:
5x + 2y = 18
-5x + 5y = 45 add two equations up
5x + 2y -5x + 5y = 18 + 45 add like terms (note that, 5x will eliminate -5x)
7y = 63 divide both sides by 7
y = 9 to find the value of x we can use this information
5x + 2y = 18 replace y with 9
5x + 2*9 = 18
5x + 18 = 18 subtract 18 from both sides
5x = 0 and x = 0
Find the mean of the data.
9, 16, 13, 14, 10, 16 , 17, 9
Thanks! Will mark brainly!
Answer:
13
Step-by-step explanation:
The mean of the data is also known as the average. To find the mean/average, add up all the data and divide it by the number of inputs recorded.
9 + 16 + 13 + 14 + 10 + 16 + 17 + 9 = 104
There are 8 terms.
104 / 8 = 13
The mean is 13.
Hope this helps!
Una comercializadora de café necesita construir una bodega con forma de cubo. La capacidad de la bodega debe ser de 216 metros cúbicos ¿cuánto debe medir la arista de la bodega?
Answer:
La arista de la bodega debe medir 6 metros.
Step-by-step explanation:
Podemos encontrar la arista de la bodega sabiendo su volumen:
[tex] V = a^{3} [/tex]
En donde:
V: es el volumen de un cubo = 216 m³
a: es la arista del cubo =?
La arista del cubo es:
[tex] a = \sqrt[3]{V} = \sqrt[3]{216 m^{3}} = 6 m [/tex]
Por lo tanto, la arista de la bodega debe medir 6 metros.
Espero que te sea de utilidad!
If m Z1 = 11x + 5 and m2 = 8x - 15, find m2.
A.) 75
B.) 115
C.) 10
D.) 65
Answer:
D) 65
Step-by-step explanation:
<1 = 11x + 5
<2 = 8x - 15
These angles are supplementary so,
11x + 5 + 8x - 15 = 180
19x - 10 = 180
19x = 190
x = 10
m<2:
8x - 15
8(10) - 15
80 - 15
65
Help please it’s due
Step-by-step explanation:
Since ABC is a triangle,
Angle A + Angle B + Angle C = 180 (Sum of angles in a triangle)
given Angle A = 3x + 1
Angle B = 4x - 17
Angle C = 5x - 20
[tex]3x + 1 + (4x - 17) + (5x - 20) = 180 \\ 3x + 4x + 5x + 1 - 17 - 20 = 180 \\ 12x - 36 = 180 \\ 12x = 180 + 36 \\ 12x = 216 \\ x = 216 \div 12 \\ = 18[/tex]
Now substitute x into all 3 angles.
A = 3(18) + 1 = 54 + 1 = 55 degrees
B = 4(18) - 17 = 72 - 17 = 55 degrees
C = 5(18) - 20 = 90 - 20 = 70 degrees
Since Angle A = Angle B but not equal to Angle C,
Triangle ABC is a isosceles triangle as 2 angles must be the same for it to be a isosceles triangle.
Answer:
it is C
Step-by-step explanation:
I need help with this question,im stuck.
Answer:
4
Step-by-step explanation:
ration of rectangle ABCD to EFGH=> 24 : 12=> 2 : 1
2 : 1 = 8 : FG
=> FG = 4
Susan estimated she would spend $250 on school clothes at the start of the school year. She actually ended up spending only $230. What was her percent of error in her calculations?
Answer:
8.70%
Step-by-step explanation:
Percentage error = (difference between estimated value and actual value / actual amount spent) x 100
difference between estimated value and actual value = estimated value - actual amount
$250 - $230 = $20
($20 / $230) x 100 = 8.6957%
answer anybody?? i can't do math like at all lol
Essentially, what we're looking at here are two alternate interior angles.
Wait. What? Alternate interior angles?
It sounds like some super fancy math jargon, but it's a fairly simple concept that I'll try my best to explain. First, let's look at lines L and M as two parallel lines, meaning that these two are lines with equal slopes, and will never intersect. See that line that goes in between the parallel lines L and M? That's called a transversal. It's basically a line that goes through two parallel lines.
Now we know that there's a transversal going through the parallel lines. So what? Well, there's a couple of special attributes to transversals. See the two angles, 7x-7 and 4x+14? As you can tell, these two angles alternate in the interior space between the transversal and the parallel lines.
Alternate interior angles are equal. There's a way to prove that they're equal, but I won't bore you with the specifics since that's not what the question's asking.
If the angles need to be equal for lines L and M to be parallel, we can make an equation that'll solve for x:
7x - 7 = 4x + 14
Subtract 4x from both sides:
7x - 4 x - 7 = 4x - 4x + 14
3x - 7 = 14
Add 7 to both sides:
3x - 7 + 7 = 14 + 7
3x = 21
Divide both sides by 3 to completely isolate x:
[tex]\frac{3x}{3}[/tex] = [tex]\frac{21}{3}[/tex]
x = 7
And that's our answer! If you need me to explain anything any further, just ask!
- breezyツ
HURRY ITS TIMED !!
Look at the table shown below:
х у
0 0
2 3
4 6
6 9
8 12
Determine the slope of the line that passes through the points.
ANSWER CHOICES
A. 1/2
B. 2/3
C. 2
D. 3/2
Answer:
D) 3/2
Step-by-step explanation:
(0 , 0 ) and (2,3)
Slope:
m=(y2-y1)/(x2-x1)
m=(3-0)/(2-0)
m= 3/2
Answer:
D. 3/2Explanation:
Slope = y/x
once the variable x > 0 the table satisfies 3/2
write a statement that correctly describes the relationship between these two sequences: 2, 4, 6, 8, 10 and 1,2,3,4,5.
Answer:
The relationship between these two sequences is it always doubles. When we look at each sequence, 1, 2, 3, 4, 5, each number is multiplied by 2 to create the other sequence.
1 x 2 = 2.
2 x 2 = 4.
3 x 2 = 6.
4 x 2 = 8.
5 x 2 = 10.
When we arrange these numbers, 2, 4, 6, 8, 10, this is the exact sequence as before. Therefore, this is the relationship.
Answer: 2, 4, 6, 8, 10, < |
|
Step-by-step explanation: | if you just arange the numbers to 1 x 2 = 2 |
2 x 2 = 4 |
2 x 3 = 6 |
and then so on and so on you would get this answerer. |
Please help will mark brainliest
So , correct option is A
I hope you can see the above image.
PLZ HELP
Determine if the sequence is arithmetic or geometric, and find the common difference or ratio.
x 1 2 3 4
f(x) 81 72 63 54
Arithmetic, common difference = 9
Arithmetic, common difference = −9
Geometric, common ratio = 9
Geometric, common ratio = −9
Answer:
The second item is the correct one , i mean arithmetic , common difference = -9 .
Step-by-step explanation:
Hope this helps u , good luck ;)
Answer:
The correct option among the others is B
Step-by-step explanation:
Za and Zb are complementary angles. Za measures 37°.
What is the measure of Zb?
Answer: 53 degrees
Step-by-step explanation:
Complementary angles add up to 90 degrees. Subtract Za from the 90. 90-37=53.
A man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52°. How far away is the man from the spot directly under the kite?
Answer:
61.57 ft
Step-by-step explanation:
Look at the picture. You need to find the base value.
so we can sue the cosine formula here.
cos x° = adjacent / hypotaneous
cos 52 ° = adj / 100
adjacent = 100 cos 52°
=61.57 ft
Answer:
the man is 61.6 ft away from the spot directly under the kite.
Step-by-step explanation:
in order to find the bottom length which is b we need to First find the height of this right angle triangle.
to find the height we need to use sin:
sin 52° = X/100
sin 52° * 100 = h
h= 78.8 ft
next we can find b which is the base of the triangle.
a^2+b^2=c^2
100^2 +b^2 = 78.8^2
100^2 -78.8^2 = b^2
b^2= 3790.56
b= √3790.56
b= 61.6 ft
therefore the man is 61.6 ft away from the spot directly under the kite.
!!!!!!!!! PLEASE HELP !!!!!!!!!!
please show work
will give brainliest to whoever shows their work correctly
Solve x² - 6x - 7 = 0
Answer:
x= 7
x=-1
Step-by-step explanation:
- Multiply the coefficient of the first term by the constant 1 -7 = -7
- Find two factors of -7 whose sum equals the coefficient of the middle term, which is -6 .
-7+ 1 = -6
-Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 1.
x^2-7x+1x-7
- Add up the first 2 terms, pulling out like factors.
x • (x-7)
Factor the common factor out of each expression.
8x-40
Answer:
The common factor of this equation is 8
Step-by-step explanation:
8/8 & 40/8
1 & 5
Answer:
Hi! The answer to your question is 8 (x-5)
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
how do i Add 5/8 = 3/7
Answer:
Add 11/56
Step-by-step explanation:
3/7 = 24/56 (×8)
5/8 = 35/56 (×7)
35/56 - 24/56 = 11/56
Alicia’s family wants to save for a four-year college education for her. After some research, they estimate that the total cost will be about $78,000. How much should her family save if she is 12 years old and plans to go to college in 6 years?
Select one:
$6,500 each month
$1,100 each month
$4,350 each month
$550 each month
Answer:
Step-by-step explanation:
$1,100
Which organisms are examples of decomposers?
A. rabbits
B. lions
C. fungi
D. trees
Answer:
C. fungi
Step-by-step explanation:
Here only Fungi is an example of decomposer.
Rabbits and lions are examples of consumers.
Trees are an example of producers.
The following list defines and provides examples of the feeding (trophic) levels that comprise food webs:
Producer: organism on the food chain that can produce its own energy and nutrients. Examples: grasses, Jackalberry tree, Acacia tree
Primary consumer/herbivore: organism that eats mainly plants. Examples: cows, impalas, warthogs, zebras
Secondary consumer/carnivore: organism that eats meat. Examples: leopard, lion
Omnivore: organism that eats a variety of organisms, including plants, animals, and fungi. Examples: humans, aardvarks
Decomposer/detritivores: organisms that break down dead plant and animal material and waste and release it as energy and nutrients in the ecosystem. Examples: bacteria, fungi, termites
Scavenger: animal that eats dead or rotting animal flesh. Examples: vultures, hyenas
Insectivore: organism that mostly eats insects. Example: Red-billed oxpecker
Answer:
C. Fungi
B. Lions
Step-by-step explanation:
C. fungi are called decomposers because they break down the dead and decaying organic matter into simpler substances such as carbon dioxide, water, simple sugars, and mineral salts and provide the nutrients back to the soil
B. A decomposer is a living thing that gets energy by breaking down dead plants and animals, lions eat other animals to get energy.
If you can buy four bulbs of elephant garlic
for $8 then how many can you buy with
$72.50?
Answer:
36 bulbs
Step-by-step explanation:
$8/4 = $2 each
72.50/2 = 36.25
Answer:
36 bulbs with $0.25 left over.
Step-by-step explanation:
4 bulbs for $8
8/4 = 2
1 bulb per $2
72.50/2 = 36.25
David made a batch of 5 liters of blue liquid everyday for 3 days how many milliliters of blue liquid did he make in all
Answer: 15000 millimeters
Step-by-step explanation:
Since David David made a batch of 5 liters of blue liquid everyday. The number of liters that'll be made for 3 days will be:
= 5 liters × 3
= 15 liters
We should note that 1000 millimeters = 1 liter. Therefore, 15 liters will be converted to millimeters which will be:
= 15 × 1000
= 15000 millimeters