Step-by-step explanation:
This is a polynomial so we can use rational roots Theorem to solve the equation.
The rational roots simply states that the roots of a polynomial, in the form of
[tex]p{x}^{n} + ax {}^{n - 1} + bx {}^{n - 2} .....r {}^{0} [/tex]
The possible roots of the polynomial are the factors of
p/r.
We say r^0 to represent the constant and p to represent the leading coeffceint.
So the rational roots states the possible roots of a polynomial is
the factors of leading coeffceint/ the factors of the constant.
In this case, the polynomial leading coeffecient is 3 and its constant is 6 so we do the factors of 3 divided by the factors of 6.
The factors of 3, are plus or minus 1 and 3. divided by factors of 6 which are plus or minus 1,2,3,6. So our possible roots are
positive or negative (1,1/2, 1/3,1/6, 3, 3/2).
Now, we see which of the following roots will that the polynomial, P will equal zero.
It seems that -1 can work so by definition, (x+1) is the a factor of the polynomial. So now we use synetheic or long division to cancel out that factor.
So our factored version of the polynomial is
[tex](x + 1)(3x {}^{3} - 14 {x}^{2} + 13x + 6)[/tex]
Now can we continue and factor the right side of the factors.
3 also works so x-3 is a factor as well so
[tex](3 {x}^{2} - 5x - 2)(x + 1)(x - 3)[/tex]
Now factor the quadratic using factoring by grouping
[tex]3 {x}^{2} - 5x - 2 = 3 {x}^{2} - 6x + x - 2 = 3x(x - 2) + 1(x - 2) [/tex]
So our factor are
[tex](3x + 1)(x - 2)[/tex]
So in conclusion our factors are
[tex](3x + 1)(x - 2)(x + 1)(x - 3)[/tex]
And our x values are -1/3, 2, -1, and 3.
Factorize: 2ay + 10ax - 3by - 15bx
Answer:
(2a-3b)(y+5x)
Step-by-step explanation:
2ay + 10ax - 3by - 15bx
2a(y+5x)-3b(y+5x)
(2a-3b)(y+5x)
Answer:
(y+5x) (2a - (3b))
Step-by-step explanation:
2a (2ay/2a + 2 x 5ax/2a) + 3b (-3by/3b - 3 x 5bx/3b)
2a (y+5x) + 3b (-y - (5x))
(y+5x) (2a(y+5x)/y+5x + 3b (-y-5x)/y+5x)
A 17 ft ladder leans against the side of a house. The top of the ladder is 14 ft off the ground. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree.
Answer:
55.4
Step-by-step explanation:
Think of it as a right angled triangle, the length of the ladder (17ft) is the hypotenuse, the length of the ground (14ft) is the rise, we then use sin to get the angle as the angle of elevation is the angle between the ladder and the ground hence sin^-1 (14/17) and you get your angle.
Write an algebraic equation to represent the situation.
A bacon cheeseburger cost $1 more than a regular cheeseburger. If 5 cheese burgers cost the same as 3 bacon cheeseburgers, how much does a regular cheeseburger cost.
I don't know if I'm just tired or what but I do not understand how I can make an equation out of this.
3(x+1) = regular cheese burger
hi guys can y’all help me with this problem? i’m stuck :p
Plz help brainiest to the correct answer!
Answer:
1. x (multiplication)
2. / (division)
3. - (subtraction)
4. - (subtraction)
5. / (division)
Step-by-step explanation:
1. 24 x 3/4= 18
2. 24/-3/4=-32
3. 12- 15= -3
4. 12- (-15)= 12 + 15 = 27
5. -18 / -3/4= 24
#a
[tex]\\ \sf{:}\dashrightarrow 24\times \dfrac{3}{4}=18[/tex]
#b
[tex]\\ \sf{:}\dashrightarrow 24\div \dfrac{-3}{4}=-32[/tex]
#c
[tex]\\ \sf{:}\dashrightarrow 12-15=-3[/tex]
#d
[tex]\\ \sf{:}\dashrightarrow 12-(-15)=27[/tex]
#e
[tex]\\ \sf{:}\dashrightarrow -18\div \dfrac{-3}{4}=24[/tex]
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars
made. If x cars are made, then the unit cost is given by the function C(x)=0.2x2 - 92x+29,516. What is the minimum
unit cost?
Do not round your answer.
Answer:
check online for more information
A scientist counted 3,921 total eggs in
49 sea turtle nests. Each nest had about
the same number of eggs. Which is the
best estimate of the number of eggs
she counted in each eggs?
Answer:
The Answer is 80
Step-by-step explanation:
So I turned 3,921 to 4,000 then 49 to 50.
After that I divided the too 4,000÷50= 80
A system of equations is created by using the line represented by 2x+4y = 0 and the line represented by the data in
the table below.
What is the x-value of the solution to the system?
Step-by-step explanation:
the answer 0 I think that's it
Answer:
2
Step-by-step explanation:
The slope of the line represented by the table is ...
m = (y2 -y1)/(x2 -x1)
m = (-4 -8)/(3 -(-1)) = -12/4 = -3
The y-intercept of that line is ...
b = y -mx
b = 8 -(-3)(1) = 5
Then the slope-intercept equation of the line represented by the table is ...
y = mx +b
y = -3x +5
Substituting that into the equation for the given line, we have ...
2x +4(-3x+5) = 0
2x -12x +20 = 0
20 = 10x . . . . . . . . add 10x and simplify
2 = x . . . . . . . . . . divide by 2
The x-value of the solution to the system of equations is x = 2.
Can someone please help? :(
Answer:
with what?
Step-by-step explanation:
Answer:
what do you need help with :p
Step-by-step explanation:
Rani makes a special design called a rangoli for Diwali. Her design is square with
a side length of 15 in. Rani then makes a larger rangoli by tripling this side length.
How many times as large is the area of the new rangoli than the area of the
original rangoli?
Answer: 180
Step-by-step explanation:
• 15 x 4 = 60
• 60 x 3 = 180
Therefore the answer is 180.
Given: RS is the perpendicular bisector of AB
Prove: RA ≅ RB
Answer:
See answer below
Step-by-step explanation:
RS ⊥ bisector of AB Given
AS ≅ BS Definition of ⊥ bisector
∠RSB is a right angle Given
∠RSB = 90° Definition of right angle
∠RSB & ∠RSA form a linear pair Definition of linear pair
∠RSB + ∠RSA = 180 A linear pair = 180°
90° + ∠RSA = 180° Substitution
∠RSA = 90 Subtraction
∠RSB = ∠RSA Substitution
∠RSB ≅ ∠RSA If equal then congruent
RS ≅ RS Reflexive
Δ RAS ≅ ΔRBS SAS
RA ≅ RB CPCTC (corresponding parts of
congruent triangles ≅
Rewrite the equation y + 6 = -5(x + 3) into general form (ax + by + c = 0)
Work Shown:
y + 6 = -5(x + 3)
y + 6 = -5x - 15
y + 6 + 5x + 15 = 0
5x + y + 21 = 0
The equation is now in the form ax+by+c = 0 where a = 5, b = 1, c = 21.
Answer:
5x + y = -21
Step-by-step explanation:
y + 6 = -5x - 15
5x + y + 6 = -15
5x + y = -21
What is the measure of an angle of a regular polygon with nine sides?
Answer:
140 degrees
Step-by-step explanation:
To find the value of an internal angle within this polygon, we can just multiply the number of triangles by 180 ° , then divide by the number of internal angles, which is nine. Excellent! So the interior angle of a 9 -sided polygon is 140 ° .
How much money is saved by buying a baker’s dozen instead of 13 individual rolls?
Number of rolls
6
8
Baker’s dozen
Price ($)
$3.60
$4.80
$7.20
Answer:
0.60
Step-by-step explanation:
If you purchase 6 rolls, you pay $3.60
Each roll is $0.60.
If you purchase 13 individual rolls, you pay
13 x 0.6 = $7.80
But if you purchase the Baker's dozen, you pay only $7.20, so you save $0.60
7.80 - 7.20 = 0.60
Answer: 0.60
Step-by-step explanation:
If you purchase 6 rolls, you pay $3.60
Each roll is $0.60.
If you purchase 13 individual rolls, you pay
13 x 0.6 = $7.80
But if you purchase the Baker's dozen, you pay only $7.20, so you save $0.60
7.80 - 7.20 = 0.60
Help please (MATH)......................
Answer:
ft hu hu mmmmmmmmmuaaaaaaaaaaaaaah
Which list shows the numbers below in order from least to greatest? 5.78,-5.9,58%,-(23)/(4) A -5.9,-(23)/(4),5.78,58%, C -5.9,-(23)/(4),58%,5.78 B -(23)/(4),-5.9,58%,5.78, D 58%,-(23)/(4),5.78,-5.9
Answer:
D
Step-by-step explanation:
similar statement of √111
Pls help
What is the probability of drawing a king, then an ace (with replacement)?
Answer:
So there is a 2 in 13 chance to pull out either an ace or king from the deck
Step-by-step explanation:
jackie is saving money for a coat that costs $121 if she already has $61 and saves $15 each week in how many weeks can she buy the coat make a function table
Answer:
4 weeks
Step-by-step explanation:
Total cost of coat = $121
Money saved = $ 61
Will save $15 per week
So let x = number of week = $15x
Money saved + will save = Total cost of the coat
$61 + $15x = $121
-$61 = - $61
$15x = $60
x = $60 ÷ 15
x = 4
34. Find the average rate of change for x 0.5 to 35 for the following temperatures in degrees Fahrenheit
recorded beginning at noon. Also interpret the meaning of x = 3.5.
The average rate of change between the interval x = 0.5 to x = 3.5 is: 5.
x = 3.5 represents 3.5 hours after noon.
How to Find Average Rate of Change Over an IntervalGiven an interval of x = a to x = b, the average rate of change over the given interval of a function can be calculated using the formula below:
[tex]\frac{f(b) - f(a)}{b - a}[/tex]
Given table representing the function as shown in the image attached below, let's determine the average rate of change for x = 0.5 to x = 3.5.
a = 0.5
f(a) = 47 (from the table, when x = 0.5, y = 47)
b = 3.5
f(b) = 62 (from the table, when x = 3.5, y = 62)
Plug the values into [tex]\frac{f(b) - f(a)}{b - a}[/tex]
Average rate of change = [tex]\frac{62 - 47}{3.5 - 0.5} = \frac{15}{3} = 5[/tex]
Average rate of change = 5
x = 3.5 represents 3.5 hours after noon.
Learn more about average rate of change on:
https://brainly.com/question/11627203
Help with geometry question
Answer:
see explanation
Step-by-step explanation:
On each median the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint, or
the distance from the centroid to the midpoint is one third of the median
23
LF = 2 × HL = 2 × 30 = 60
HF = HL + LF = 30 + 60 = 90
24
KL = [tex]\frac{1}{3}[/tex] KE = [tex]\frac{1}{3}[/tex] × 15 = 5
LE = 2 × KL = 2 × 5 = 10
25
LJ = [tex]\frac{1}{2}[/tex] DL = [tex]\frac{1}{2}[/tex] × 24 = 12
DJ = DL + LJ = 24 + 12 = 36
simplest form of 76% as a fraction.
Answer:
19/25
Step-by-step explanation:
Percentages are always out of 100.
76/100 = 38/50 = 19/25
Answer:
19/25
Step-by-step explanation:
76% as a fraction is 76/100. The greatest common factor of 76/100 is 2, this simplifies to 38/50, then 19/25.
Find the inverse function. 1 f(x) = 1 = 2x+2 + f-1(x) = [? ]x + [
Answer:
y= 2x - 1
Step-by-step explanation:
i hope that helps
The equation 5y = 6 represents purchasing 5 tubs of yogurt for $6. Which of these equations are equivalent to the equation 5y = 6?
a
15y = 18
b
5y - 1 = 3
c
5y + 4 = 10
d
5y = 12
Answer: a 15y=18 and c 5y+4=10
Step-by-step explanation:
Plz send right answers I need this right plzzz !!!!
Answer:
its d
2.52x
3.40
____
0.00+
1.080+
7.5600
______.
8.658
Answer:
D. 8.568
Step-by-step explanation:
A quick tip is ignore the decimal points and just multiply, (which they already did for you) then add the decimal how many ever points forward the two multiples are combined.
So for 8568, since you have 2 . 52 3 . 4 you take it 3 points forward to right between the 8 and 5 for 8.568....
Also, just a word of advice, 4*4 is 16 so the answer couldn't be higher than 16, so A and C are wrong. B is actually switching the 6 and 5 so it's also wrong leaving only D
Perform the following computation with radicals. Simplify the answer.
\sqrt{3}\cdot 2\sqrt{2}
Answer:
[tex]\sqrt{3}\cdot 2\sqrt{2}= 2 \sqrt{6}[/tex]
you can't simplify it any more
Round your answer to the nearest hundredth
Answer:
9.49
Step-by-step explanation:
Using the Pythagorean Theorem, we know a²+b²=c².
So 3²+9²=(BA)²
9+81=(BA)²
90=(BA)²
From this, we know BA=√90
BA=9.486
Rounding to the nearest hundredth, this is 9.49
Please consider a brainliest! Thank you!
Can someone help me with this problem plz
Answer:
mq - 12
ql - 36
Step-by-step explanation:
I am not for sure but this is what I think it is because the m-q is smaller than the q-l
A bird flies down from a higher elevation to a lower elevation at a rate of 3 meters per second. Which equation models the bird's change in elevation, in meters, after 120 seconds?
O A. (-120)(-3) = -360
O B. 120. 3 = 360
O C. 120(-3) = 360
O D. 120(-3) = -360
No links please
Answer:
D
Step-by-step explanation:
Answer: The answer is 120(-3)= -360
Step-by-step explanation:
A. P. E. X.
Jamal finds some dimes and quarters in his change purse. How much money (in dollars) does he have if he has 9 dimes and 4 quarters? How much money (in dollars) does he have if he has xx dimes and yy quarters? Total value, 9 dimes and 4 quarters (dollars): Total value, xx dimes and yy quarters (dollars):
Answer:
$1 dollar and $0.90cents
Step-by-step explanation: