Explanation:
Factoring to linear factors generally involves finding the roots of the polynomial.
The two rules that are taught in Algebra courses for finding real roots of polynomials are ...
Descartes' rule of signs: the number of positive real roots is equal to the number of coefficient sign changes when the polynomial is written in standard form.Rational root theorem: possible rational roots will have a numerator magnitude that is a divisor of the constant, and a denominator magnitude that is a divisor of the leading coefficient when the coefficients of the polynomial are rational. (Trial and error will narrow the selection.)In general, it is a difficult problem to find irrational real factors, and even more difficult to find complex factors. The methods for finding complex factors are not generally taught in beginning Algebra courses, but may be taught in some numerical analysis courses.
Formulas exist for finding the roots of quadratic, cubic, and quartic polynomials. Above 2nd degree, they tend to be difficult to use, and may produce results that are less than easy to use. (The real roots of a cubic may be expressed in terms of cube roots of a complex number, for example.)
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Personally, I find a graphing calculator to be exceptionally useful for finding real roots. A suitable calculator can find irrational roots to calculator precision, and can use that capability to find a pair of complex roots if there is only one such pair.
There are web apps that will find all roots of virtually any polynomial of interest.
_____
Additional comment
Some algebra courses teach iterative methods for finding real zeros. These can include secant methods, bisection, and Newton's method iteration. There are anomalous cases that make use of these methods somewhat difficult, but they generally can work well if an approximate root value can be found.
segment DE is a midsegment of triangle ABC. find the value of x
Answer:
x = 10
Step-by-step explanation:
The value x is 10 units.
What is midsegment?A midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments.
Given that, segment DE is a midsegment of triangle ABC.
According to the midpoint theorem, “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
Therefore, DE = 1/2 AB
5 = 1/2x
x = 5×2
x = 10
Hence, the value of x is 10 units.
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PARALLEL PERPENDICULAR OR NEITHER OR SAME LINE
Answer:
parallel, perpendicular are opposite
Answer:
PARALLEL PERPENDICULAR
Step-by-step explanation:
What's ( Round to the indicated place value
1. 6085 to the nearest hundred
2. 51,672 to the nearest ten thousand
3. 321.6396 to the nearest thousand)
Answer:
I'm not going to give the answer yet to see if you can figure it out.
Step-by-step explanation:
1. Find the place that your are rounding to. Ex: 6085
2. Then, look "nextdoor"; the number to the right of the number underlined. Ex: 6085
3. If this number is 1-4, then keep it the same. If it is 5-9, then add one to the digit to the left. Ex: 6085 becomes 6185
4. All of the digits to the right stay the same. Ones to the left become zero. Ex: 6185 becomes 6100.
I hope this helps!
write the ratio in simplest form.
12 DVDS to 10 books.
Answer:
6:5
Step-by-step explanation:
divide both numbers by using gcd/ greatest common divisor
= 12:10/ 2
=6:5
please mark me as brainliest!!! Good luck with your tests!
If Jada runs 5 laps around the track in 6 minutes how many minutes per lap is that
Answer:
1.2 minutes
Step-by-step explanation:
5 laps >> 360 ( 6×60)
1 lap >> x
cross multiplication
5x = 360
x = 360/5
x= 72 second
x = 72/60 = 1.2 minute
there is a sale of soft drinks, so four stores are competing with each other. which store offers the best buy ?
store A:12 pack for 3.00
store B: 22 packs for 5.50
store C: 18 pack for 4.75
store D: 36 pack for 8.00
( ill give brainly to whoever answer first w an explanation)
Answer:
desculpa,mais eu preciso de ponto para ajudar meu irmão
I don't know what im doing help
Answer:
81/256
Step-by-step explanation:
3/4*3/4*3/4*3/4
first multiply the numerators (3) together, which equals 81
then multiply the denominators (4) together, which equals 256
81/256 can't be simplified further
Answer:
[tex]\frac{3^4}{4^4} =\frac{81}{256}[/tex]
Reasoning:
According to exponent law:
[tex](\frac{a}{b} )^{x} =(\frac{a^x}{b^x} )[/tex]
Now apply this to your problem.
[tex](\frac{3}{4} )^{4}[/tex]
[tex](\frac{3^4}{4^4} )[/tex]
[tex](\frac{81}{256} )[/tex]
Help me please!! This is timed and I’m stuck
Let's solve
[tex]\\ \sf\longmapsto 2x^2+7x-15=0[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7\pm\sqrt{7^2-4(2)(-15)}}{2(2)}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7\pm\sqrt{169}}{4}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7\pm13}{4}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7+13}{4}\:or \:\dfrac{-7-13}{4}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{6}{4}\:or\:\dfrac{-20}{4}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{3}{2}\:or -5[/tex]
Subtract
[tex]\\ \sf\longmapsto 3/2-(-5)=3/2+5=13/2[/tex]
Option B
Answer:
Option (B.)
Step-by-step explanation:
Answer in the picture.hu
what is this question 9 + x to the power of 10
Answer:
ok im not sure but here is what i think the answer is
Step-by-step explanation:
answer 60466185
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8x + 6y = -54
Answer:
y = - 4/3x - 9
Step-by-step explanation:
Answer:
[tex]y = -\frac{4}{3}x - 9[/tex]
Step-by-step explanation:
The standard form of linear equation is: Ax + By = C, where A, B, and C are integers; A and B ≠ 0, and A is a non-negative integer.
Given the linear equation in standard form, 8x + 6y = -54, we can transform this equation into its slope-intercept form, y = mx + b.
First, subtract 8x from both sides:
8x + 6y = - 54
8x - 8x + 6y = - 8x - 54
6y = -8x - 54
Divide both sides by 6 to isolate y:
[tex]\frac{6y}{6} = \frac{-8x - 54}{6}[/tex]
[tex]y = -\frac{4}{3}x - 9[/tex] ⇒ This is the slope-intercept form where the slope, m = [tex]- \frac{4}{3}[/tex], and the y-intercept, b = -9.
X=6 and 6=K so x=
Use the transitive property of equality to finish the equation
Answer:
X=6
Step-by-step explanation:
Hope this helps.
Answer:
x = K
Step-by-step explanation:
If,
x = 6
and 6 = k
=> x = 6 = k
=> x = k
The Transitive Property of Equality states the same fact as:
"If two units are equal to each other and the second unit is equal to a third unit, then the first unit is also equal to the third unit."
I need help with this! Please asap
Answer:
1:Not
2:Not
3:Not
4:Not
5:Viable
6:Viable
7:Viable
8:Viable
9:Viable
10:Not
Step-by-step explanation:
What is the answer to (6 1/2)/2
Answer:
3.25
Reasoning:
[tex]\frac{6.5}{2}[/tex]
[tex]3.25[/tex]
The algebraic expression that represents twice the sum of some number and 3 is?
n + 2(3)
2(n + 3)
2 + n + 3
2n + 3
Answer:
2(n+3)
Step-by-step explanation:
The sum to 3 = n+3
That sum doubled (~twice) = 2(n+3)
Answer:
2(n+3)
Step-by-step explanation:
Let's look at the statement:
'twice the sum of some number and 3'
Twice means 2 multiplied by something.
What is that something? It is the sum of some number and 3.
Let's replace the some number with variable n.
So it becomes the sum of n and 3, which translates to n+3.
So you put the two parts together:
2 multiplied by (n+3), rewritten as 2(n+3).
I have to do the evens- I was out due to epilepsy and have no clue what I'm doing
Worth 50 points
Step-by-step explanation:
I'm assuming your solving for [tex]x[/tex]
Picture 2.
For this one since the two sides are equal
[tex]2x-12=12\\2x=24\\x=12[/tex]
Picture 4.
We can use the Pythagorean theorem for this one, which is [tex]a^2+b^2=\sqrt{c}[/tex]
[tex]4\cdot4=16\\3\cdot3=9\\16+9=25\\\sqrt{25}=5[/tex]
[tex]x=5[/tex]
Picture 6.
We can use the Pythagorean theorem for this one, which is [tex]a^2+b^2=\sqrt{c}[/tex]
[tex]6\cdot6=36\\9\cdot9=81\\36+81=117\\[/tex]
[tex]\sqrt{117}=approximately[/tex] [tex]10.81[/tex]
Picture 8.
[tex]EG=6[/tex]
Since half of [tex]EG[/tex] is [tex]3[/tex]
[tex]3\cdot2=6[/tex]
[tex]EG=6[/tex]
Brainliest, please :)
Nell has a piggy bank full of dimes and nickels. She empties the bank and counts the coins. She counts 30
coins in all, with a total value of $2.90. Nell says she has 14 dimes and 16 nickels.
(a) Write a system of linear equations to represent the number of coins that Nell had in her piggy bank
and the total value of the coins.
(b) Determine whether Nell could have counted the number of dimes and nickels correctly. Show all your
work to prove whether she counted the coins correctly.
[a] A dime is worth 10 cents (0.10 dollars) and a nickel is worth 5 cents (0.05 dollars). If there are 30 coins in all, we can set up a linear equation in standard form to look like this:
30 - n = d
Since the total is 2.9, we can do the following:
{ 30 - n = d
{ .05n + .10d = 2.90
And our system is in bold
(where n is nickels and d is dimes, you could also use x and y if you wish)
[b] She could have counted the number of dimes and nickles correctly, but she did not. The number of nickles is 2 with there being 28 dimes.
Now, we will solve:
.05n + .10(30 - n) = 2.90
.05n + 3 - .1n = 2.9
3 - .05n = 2.9
3 = .05n + 2.90
.05n = 0.1
n = 2
(dimes is 30 - 2 = 28)
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Pls help fast
What is the recursive rule for the sequence shown in the graph
Answer:
[tex]a_{n} =a_{n-1} -4[/tex]
explanation:
The recursive rule for the given graph will be [tex]a_{n} = a_{n-1}-4[/tex] thus, option (A) is correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
In the given graph, as n increases [tex]a_{n}[/tex] decreases.
At n = 4 , a₄ = a₃ - 4 = 5 - 4 = 1
Thus, [tex]a_{n} = a_{n-1}-4[/tex] will be the recursive rule.
Hence "The recursive rule for the given graph will be [tex]a_{n} = a_{n-1}-4[/tex]".
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HELP AGAIN PLSSSSSSS
Answer:
didn't you already do it? im confused
Step-by-step explanation:
halp me please and explain
Answer:
-2×2+1/2×(-1×3+2/3)
-3/2×(-1/3)
3/6
In \triangle HIJ,△HIJ, \overline{HI}\cong \overline{JH} HI ≅ JH and \text{m}\angle J = 13^{\circ}.m∠J=13 ∘ . Find \text{m}\angle I.m∠I.
Answer:
13
Step-by-step explanation:
two angles are congrunet
The measurement of angle I in the given triangle HIJ is 83.5°.
Given is a triangle HIJ, where HI ≅ JH, and m ∠J = 13°, we need to find m ∠I.
Since HI ≅ JH (given) and ∠J = 13° (given), then ∠HJI ≅ ∠HIJ (by the isosceles triangle property).
In an isosceles triangle, the angles opposite the congruent sides are also congruent. Therefore, ∠HJI = ∠HIJ.
Now, let's denote ∠I as x (which is what we're trying to find). Since ∠HJI = ∠HIJ, we can set up an equation:
x + 13° + x = 180° (sum of angles in a triangle)
Solving for x:
2x + 13° = 180°
2x = 180° - 13°
2x = 167°
x = 167° / 2
x = 83.5°
So, m ∠I is 83.5°.
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Complete question is given below:
In △HIJ, HI ≅ JH and m∠J = 13°. Find m ∠I.
Somebody please help
Answer:
c/ y=20x
Step-by-step explanation:
solve the equation
x/-14 = 13
x = -52
x = 17
x = 52
x = -13/4
If the supplies on shelf A are normally $7 each and the supplies on shelf B are normally $6 each, how much will you save on each package plan from part a? Buying the first package will save $ and buying the second package will save $
recent ecological survey showed that the ratio of deer to foxes was 7 to 3 in one county in Texas. If there were 210 foxes in the county, what was the number of deer in the county?
Answer:490
Step-by-step explanation:
Write three consecutive multiples of 13 in a general form.
Answer:
answer given in step by step...
Step-by-step explanation:
13x+13(x+1)+13(x+2)=312
13x+13x+13+13x+26=312
39x+39=312
39x=312-39
39x=273
x=7
first number=13x=13*7=91
second number=13(8)=104
third number=13(9)=117
What is the slope intercept equation from the graph?
Please help thank u
Answer:
the desired equation is y = (-3/2)x + 3
Step-by-step explanation:
Two points through which the graph passes are (0, 3) and (2, 0). (0, 3) is the y-intercept. Thus, the slope-intercept equation y = mx + b becomes
y=mx + 3. Borrowing the coordinates of (2, 0) and substituting them into this last result, we get
0 = m(2) + 3,
which, after having been solved for m, gives us m = -3/2
and so the desired equation is y = (-3/2)x + 3.
PERSONALLY I thought it would be 98 Bc like yk..BUT I FEEL LIKE IM WRONGsend help beggin cryin throwin up I hate geometry so much
Answer:
98
Step-by-step explanation:
It is 98! x and the 98 degree angle are corresponding angles and m is parallel to n. dw I hate geometry too.
Write the subtraction expression as an equivalent addition expression and then evaluate it.
22−37
Answer:
-15
Step-by-step explanation:
22+(-37)
What is the solution to the system of equations?
y = 2x -1
y = -x +5
x= −2 and y=3
I can't explain this very well, sorry.
4) Monica swam 4 laps in 15 minutes. At this rate, how many laps would she swim in 45 minutes?
O 8 laps
O 12 laps
O 15 laps
o 21 laps
Answer:
12 laps
Step-by-step explanation:
15÷4=3.75
45÷12=3.75
not sure whether it's true or not but at least I got the answer-
