Answer:
3m4 + 5m3 - 5m2 + m - 3
3
Step-by-step explanation:
Step-by-step explanation:
step by step
STEP
1
:
Equation at the end of step 1
((((3•(m3))+5m2)-5m)+1)
(———————————————————————•m)-1
3
STEP
2
:
Equation at the end of step
2
:
(((3m3+5m2)-5m)+1)
(——————————————————•m)-1
3
STEP
3
:
3m3 + 5m2 - 5m + 1
Simplify ——————————————————
3
Checking for a perfect cube :
3.1 3m3 + 5m2 - 5m + 1 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 3m3 + 5m2 - 5m + 1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -5m + 1
Group 2: 5m2 + 3m3
Pull out from each group separately :
Group 1: (-5m + 1) • (1) = (5m - 1) • (-1)
Group 2: (3m + 5) • (m2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(m) = 3m3 + 5m2 - 5m + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of m for which F(m)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers m which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 3 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 8.00
-1 3 -0.33 3.11
1 1 1.00 4.00
1 3 0.33 0.00 3m - 1
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
3m3 + 5m2 - 5m + 1
can be divided with 3m - 1
Polynomial Long Division :
3.4 Polynomial Long Division
Dividing : 3m3 + 5m2 - 5m + 1
("Dividend")
By : 3m - 1 ("Divisor")
dividend 3m3 + 5m2 - 5m + 1
- divisor * m2 3m3 - m2
remainder 6m2 - 5m + 1
- divisor * 2m1 6m2 - 2m
remainder - 3m + 1
- divisor * -m0 - 3m + 1
remainder 0
Answer is 3
Diego compro un libro y tres cuadernos,pago por ellos 180 solo recuerda que el libre le costó el doble de lo que le costaron los tres cuadernos juntos
Answer: Cada cuaderno cuesta 20, y el libro 120.
Step-by-step explanation:
Vamos a definir:
L = precio de un libro
C = precio de un cuaderno.
Sabemos que Diego compro un libro y tres cuadernos por 180, entonces tenemos:
1*L + 3*C = 180
También sabemos que el libro costo el doble de lo que costaron los 3 cuadernos juntos, entonces:
L = 2*(3*C) = 6*C
Tenemos un sistema de ecuaciones:
1*L + 3*C = 180
L = 6*C
Para resolverlo, podemos reemplazar la segunda ecuación en la primera, para así obtener:
1*(6*C) + 3*C = 180
6*C + 3*C = 180
9*C = 180
C = 180/9 = 20
Cada cuaderno costo 20.
Y el precio del libro se puede obtener con la ecuación:
L = 6*C = 6*20 = 120
El libro costo 120
Which number line shows the solution set for [n]< or equal to 2
no number line is shown so this answer is improvible
Which fraction represents the product of -7/8 and -9/11 in simplest form?
Answer:
63/88
any more help just ask
Answer:
c
Step-by-step explanation:
bc it is
A stone is thrown vertically upwards with an initial velocity 20m/s. Find the maximum height it reaches and the time taken by it to reach the height.
(g= 10m/s)
who gives answer with explanation i will make him braillint
Answer:
The maximum height it reaches is 20 meters
The time taken by it to reach the height is 2 seconds
Step-by-step explanation:
The formula of the height of the stone is h = u t - [tex]\frac{1}{2}[/tex] g t², where
t is the time to reach the height hu is the initial velocityg is the acceleration of gravity∵ A stone is thrown vertically upwards with an initial velocity of 20 m/s
∴ u = 20 m/s
∵ g = 10 m/s²
→ Substitute them in the equation above
∴ h(t) = 20t - [tex]\frac{1}{2}[/tex] (10) t²
∴ h(t) = 20t - 5t²
→ Arrange the terms of the right side according to the greatest power of t
∴ h(t) = -5t² + 20t
To find the maximum height and the time of it find the vertex of the quadratic function (m, k), where m = [tex]\frac{-b}{2a}[/tex] and k is the value of h at t = m, a is the coefficient of t² and b is the coefficient of t
∵ The coefficient of t² is -5
∴ a = -5
∵ The coefficient of t is 20
∴ b = 20
→ Use them to find h
∵ m = [tex]\frac{-20}{2(-5)}[/tex] = [tex]\frac{-20}{-10}[/tex] = h
∴ m = 2
→ Substitute it in the equation above to find k
∵ h(m) = k
∵ k = -5(2)² + 20(2)
∴ k = -5(4) + 40
∴ k = -20 + 40
∴ k = 20
∴ The coordinate of the vertex of the function are (2, 20)
→ m represents the time of the maximum height and k represents
the maximum height
∴ The maximum height it reaches is 20 meters
∴ The time taken by it to reach the height is 2 seconds
whats is 10000000000000000+00+0000000++000000+0000000010000000000001010101010102010202010200100202020202020.
jk, here is a gift from me Merry Christmas :)
Answer:
aww I find this so cutee
Step-by-step explanation:
Merry Christmas :) :) ^ ^
Answer:
its past t but it never too late to celebrate christmas happy christmas past and future
Step-by-step explanation:
please help. i have 20 minutes left
Answer:
You need to insert different x values and plot the point. So let's say x=1 the answer would be 10 and for 2 it would be 17
a model for the performance of a stock is P= -2.5d^2+50d where d represents the days of trading and P is the price per share. What is the maximum price per share of stock and after how many days of trading did this price occur?
Answer:
The maximum price per share is $250 and it happens after 10 days of trading.
Step-by-step explanation:
The performance of a stock is modeled by the function:
[tex]P(d)=-2.5d^2+50d[/tex]
Where d is the number of days of trading and P is the price per share.
To find the maximum price, we use the first derivative:
[tex]P'(d)=-5d+50[/tex]
Equating to zero:
-5d+50=0
Solving for d:
-5d = -50
d = -50/(-5) = 10
d = 10
The price for d=10 is:
[tex]P(10)=-2.5*10^2+50*10[/tex]
[tex]P(10)=-2.5*100+500= 250[/tex]
The maximum price per share is $250 and it happens after 10 days of trading.
In trapiziod ABCD with bases AB and DC , diagonals intersect at point O. Find the length of diagonal BD, if BO=6 cm and A/O=3/1
Answer:
the length of the diagonal BD is 8 cm
Step-by-step explanation:
The computation of the length of diagonal BD is as follows
Here the trapezoid diagonals divides each other in an equivalent ratio
So, equation would be
AO ÷ OC = OB ÷ OD
Now put there values to the above equation
3 ÷ 1 = 6 ÷ OD
3OD = 6
Now divided it by 3 in both the sides
OD = 2
Now the BD would be
= BO + OD
= 6 + 2
= 8 cm
hence, the length of the diagonal BD is 8 cm
help me please what is i really need help
Step-by-step explanation: -6.3 x 8 = -50.4
A. Increasing
B. Constant
C. Decreasing
Answer:
A. Increasing
Step-by-step explanation:
According to the graph, we see that as the x-values increase, the y-values also increase. Therefore, the entire graph is increasing.
Tony wants to make a dog bed for his dog. He has a Golden Retriever and wants to make sure the bed is big enough so his dog can stretch out. He buys 8 yards of fabric for the bed. The fabric he chooses costs $6.99 per yard. He also needs to buy a filling for the bed. He buys 3 bags of polyester filling, which are $7.99 a bag. How much will Tony pay for the materials for the dog bed?
A. $23.97
B. $55.92
C.$38.87
D.$79.89
Answer:
D.$79.89
Step-by-step explanation:
Cost of one yard of fabric = $6.99
Length of fabric bought = 8 yards
Cost of one bag of polyester filling = $7.99
Number of bags of polyester filling bought = 3
Total cost of fabric = [tex]6.99\times 8=\$55.92[/tex]
Total cost of polyester filling = [tex]7.99\times 3=\$23.97[/tex]
Total cost of materials bought = Total cost of fabric + Total cost of polyester filling
[tex]=55.92+23.97=\$79.89[/tex]
Total cost of materials bought is [tex]\$79.89[/tex].
The population of a town called Smallville grows by 3,000 people every year. After 7 years of the town's development, the population is 31,000 people. Find the equation for this situation, letting x represent time (in years) and y represent the town's population. Show your work below:
Write the equation of a line passing through (12, 279) and perpendicular to x=19
Step-by-step explanation:
The equation of the line is y = 279.
3.2 geometry worksheet
Answer/Step-by-step explanation:
5. 21x + 4 = 22x - 2 (corresponding angles)
Collect like terms
21x - 22x = -4 - 2
-x = -6
divide both sides by -1
x = 6
6. (x + 72) + (x + 132) = 180 (linear pair)
x + 72 + x + 132 = 180
Add like terms
2x + 204 = 180
2x = 180 - 204
2x = -24
x = -12
7. 90 = 22x + 2 (vertical angles)
90 - 2 = 22x
88 = 22x
Divide both sides by 22
4 = x
x = 4
8. 12x + 10 = 13x + 3 (vertical angles)
Collect like terms
12x - 13x = -10 + 3
-x = -7
Divide both sides by -1
x = 7
9. 17x = 16x + 5 (alternate exterior angles)
17x - 16x = 5
x = 5
✔️17x
Plug in the value of x
17(5) = 85°
10. 21x - 6 = 20x (corresponding angles)
Add like terms
21x - 20x = 6
x = 6
✔️20x
20(6) = 120°
Triangle A is rotated 270° counterclockwise with the origin as the center of
rotation to create a new figure. Which triangle shows the new location?
Answer:
B
Step-by-step explanation:
The triangle which shows the new location would be Triangle B.
What is the rotation used?From the coordinates of XYZ transformed to coordinates of triangle X'Y'Z', we can see that the transformation pattern is;
(x, y) -----> (-y, x)
Consider the point be having coordinates (x,y).
Case 1: If the point is in first quadrant:
Subcase: Clockwise rotation, Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 2: If the point is in second quadrant:
Subcase: Clockwise rotation, Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
On origin, No effect as we assumed rotation is being with respect to origin.
Now, this pattern of transformation occurs when Triangle A is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure.
However, the other rotation that can be used to achieve this is a 270° counterclockwise rotation. so the correct option triangle is B.
Read more about rotation at;
brainly.com/question/4289712
#SPJ6
You randomly sample 8 graduate students from an NYU event. 5 of the 8 exhibit higher IQ’s than the median of the general population. The probability of obtaining this result by chance (if those graduate students do not differ in IQ from the general population) is
Answer:
The probability that five of the eight students exhibit an higher IQ than the median of the general population is 0.21875
Step-by-step explanation:
The given parameters are;
The number of students in the sample, n = 8
The number of the students, x, that exhibit higher IQ's than the median = 5
The probability of obtaining the given result by chance is given as follows;
P(x) = n!/((n - x)!x!) × pˣ × qⁿ⁻ˣ
The probability that a student exhibit higher IQ's than the median = 0.5 = p
Similarly, we have, the probability that a student exhibit lower IQ's than the median = 0.5 = q
Substituting the known values, gives;
P(5) = (8!/((8 - 5)!×5!)) × 0.5^(5) × 0.5^(8 - 5) = 0.21875
Therefor, the probability that 5 of the 8 students exhibit an higher IQ than the median of the general population, P(5) = 0.21875.
A television is on sale for 20% off its original price,p. Write a multiplication expression to
describe the sale price of the television.
A. 0.20p
C. 0.20p + P
D. p-0.20p
B. 0.20p-p
sale price of the television is c
15.
enuse AC
Find the
In the accompanying diagram of right triangle RST,
altitude TP is drawn to hypotenuse RS. If TP = 6
and RP is 5 less than PS, find the length of
hypotenuse RS. [Only an algebraic solution will
be accepted.]
Someone help me please
Answer:
13
Step-by-step explanation:
Let PS = x and RP = x-5
Using Pythagorean theorem on the two smaller rt triangles formed,
6^2 + x^2 = (ST)^2
6^2 + (x-5)^2 = (RT)^2
Now use Pythag on big triangle and sub in above values:
(2x-5)^2 = 6^2 + x^2 + 6^2 + (x-5)^2
Multiply out and simplify to
x^2 - 5x -36 = 0
Factor the quadratic: ((x-9)(x+4)=0 Therefore x=9 or x=-4. We may disregard the negative answer so x = 9. So PS is 9 and RP is 4.
Therefore entire hypotenuse is 4 + 9 or 13.
Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6,-9)?
A.
x= -9
B.
x= -6
C. y=-9
D. y=-4
Answer:
I’m guessing D
Step-by-step explanation:
As the perpendicular would be -4 the negative reciprocal. I just worked out the whole equation including the point it passes.
Answer:
-6
Step-by-step explanation:
I don't get this... someone explain this plum thing please...... Before a plum is dried to become a prune, it is 92% water. A pruneis just 20% water. If only water is evaporated in the drying process, how many pounds of prunes can be made with 100 pounds of plums?
Answer:
21.74 But if it tells you to round I would round to 21 lbs
Step-by-step explanation:
its basically just a ratio of 92 to 20
92/20=4.6
92-20=72% the amount that is lost
so given that the plum is 100 lbs we know that 72% is depleted
(72/92 = .78)X100= 78 lbs depleted
Lastly 100-78 =22 for the remaining weight of the prunes.
PLEASE SOMEONE DO THIS FOR ME: Determine the x - and y - intercepts of the following linear function: 4x + 8y =16
4x+8y=16
4x/4+8y/8=16÷4/8
x+y=16×8/4
x+y=16×2
x+y=32
PLEASEEEE HELP!!
Which is the graph of y = ⌊x⌋ – 2?
Answer:
the second graph
Step-by-step explanation:
helppppppppppppppppppppp
Drag the tiles to the correct boxes. Not all tiles will be used.
What are the domain and the range of function f?
By undestanding the theory behind rational functions and functional theory, we conclude that the function have:
Domain: (- ∞, - 3) ∪ (- 3, + ∞)
Range: (- ∞, 0) ∪ (0, + ∞)
How to determine the domain and the range
In this question we have a rational function and we must determine its domain and range, whose elements exist if and only if the denominator evaluated at respective point is distinct of zero. Graphically speaking, the domain of the function represents the set of x-values, whereas the range represents the set of y-values.
By a graphing tool (i.e. Desmos) we construct the rational function and derive the following conclusions:
Domain: (- ∞, - 3) ∪ (- 3, + ∞)
Range: (- ∞, 0) ∪ (0, + ∞)
By undestanding the theory behind rational functions and functional theory, we conclude that the function have:
Domain: (- ∞, - 3) ∪ (- 3, + ∞)
Range: (- ∞, 0) ∪ (0, + ∞)
To learn more on rational functions: https://brainly.com/question/27914791
#SPJ1
Answer:
Range: (negative infinity, 0) U (0, 1/9) U (1/9, infinity)
Domain: (negative infinity, -3) U (-3, 6) U (6, infinity)
Step-by-step explanation:
100% on the test
An airplane flying with the wind can cover a certain distance in 2 hours. The return trip against the wind takes 2.5 hours. Find the average airspeed and wind speed, if the one-way distance is 600 miles.
Answer:
Wind speed = 30 mph
Plane speed = 270 mph
Step-by-step explanation:
Given that :
Distance = 600 miles
Let speed of airplane = a ; speed of wind = b
Net speed ; with wind = a + b
Net speed against wind = a - b
Time taken with wind = 2 hours
Time taken against wind = 2.5 hours
Recall :
Speed = distance / time ; distance = speed * time
(a + b) * 2 = (a - b) * 2.5
2a + 2b = 600
a + b = 300 - - - (1)
a = 300 - b
2.5a - 2.5b = 600
a - b = 240 - - - (2)
300 - b - b = 240
300 - 2b = 240
-2b = - 60
b = 30
a = 300 - 30
a = 270
Wind speed = 30 mph
Plane speed = 270 mph
A cylinder has a volume of 360 cubic centimeters. Find the volume of a cone with the same height and diameter as
the cylinder.
Formula for the cylinder = V=πr2h
Formula for the cone = 1/3πr²H
Description:
So if the cone and a cylinder have the same radius and the same height then it will be greater. So plug in these formula.
Formula:
Vcone = 3Vcone
Vcylinder = 360cm³
Vcone = 1/3 360cm³ = 120cm³
Answer: 120cm³
Hope this helps.
The value of x is -14. Order these expressions from least to greatest:
x1−xx−1-1÷x
Answer:
-197
Step-by-step explanation:
x1-xx-1-1÷x
-14(1)+14(-14)-1-1÷-14
-14-196-1(-1÷-14)
-211+14
-197
Answer:
x-1, x, 1-x, -1/x
Step-by-step explanation:
What expression is equivalent to ^3 square root of 2y^3 times 7 square root of 18y
Answer:
[tex]\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]
Step-by-step explanation:
The question is poorly formatted.
Given
[tex]\sqrt[3]{2y^3} * 7\sqrt{18y}[/tex]
Required
Derive an equivalent expression
[tex]\sqrt[3]{2y^3} * 7\sqrt{18y}[/tex]
Express 18 as 9 * 2
[tex]\sqrt[3]{2y^3} * 7\sqrt{9 * 2y}[/tex]
Split the expression as follows:
[tex]\sqrt[3]{2y^3} * 7\sqrt{9} * \sqrt{2y}[/tex]
Take positive square root of 9
[tex]\sqrt[3]{2y^3} * 7*3 * \sqrt{2y}[/tex]
[tex]\sqrt[3]{2y^3} * 21 * \sqrt{2y}[/tex]
[tex]21*\sqrt[3]{2y^3} * \sqrt{2y}[/tex]
The cube root can be rewritten to give:
[tex]21*\sqrt[3]{2}*\sqrt[3]{y^3} * \sqrt{2y}[/tex]
[tex]\sqrt[3]{y^3} = y^{3*\frac{1}{3}} = y[/tex]
So, we have:
[tex]21*\sqrt[3]{2} * y * \sqrt{2y}[/tex]
Rewrite as:
[tex]21y *\sqrt[3]{2} * \sqrt{2y}[/tex]
Split [tex]\sqrt{2y[/tex]
[tex]21y *\sqrt[3]{2} * \sqrt{2} * \sqrt{y}[/tex]
Collect Like Terms
[tex]21y*\sqrt{y} *\sqrt[3]{2} * \sqrt{2}[/tex]
Represent in index form
[tex]21y*y^{\frac{1}{2}} *2^\frac{1}{3} *2^\frac{1}{2}[/tex]
Apply law of indices
[tex]21*y^{1+\frac{1}{2}} *2^{\frac{1}{3} +\frac{1}{2} }[/tex]
[tex]21*y^{\frac{2+1}{2}} *2^{\frac{2+3}{6}}[/tex]
[tex]21*y^{\frac{3}{2}} *2^{\frac{5}{6}}[/tex]
[tex]21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]
Hence:
[tex]\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})[/tex]
I need help solving
Answer:
well if you're looking for angles then
angle ADB = 30°
angle CBD = 80°
angle CDB = 120°
but they asked to classify triangle ADC ,whose measurements are 90° , 40° and 50° ...so of they're asking what type of triangle then it is a right angled triangle.
Answer:
Triangle ADC is a right triangle.
Step-by-step explanation:
Triangles Classification
An acute triangle is a triangle with three acute angles or with less than 90° each.
An obtuse triangle has one obtuse angle or more than 90°.
A right triangle has one right angle of 90°
From the figure, we can see angle D is marked as a right angle (90°), thus triangle ADC is a right triangle.
To complete the answer, triangle ADB is obtuse (has an angle of 100°), and triangle ABD is acute.
The graph of y =(x-3)^2 is shifted left 4 units and down 2 units. What is the axis of
symmetry of the transformed graph?
Answer:
x = -1
Step-by-step explanation:
The axis of symmetry of the graph [tex]y=(x-3)^2[/tex] is x=3 but,
If shift the graph 4 units to the left it would mean the new value of x would be -1 as shown here:
[tex]x=3-4\\x=-1[/tex]
-4 because it shifted 4 units to the left so the axis of symmetry of the transformed graph would be x = -1 and since it shifted 2 units down the y-coordinate of the turning point would be -2 so the turning point of the original graph is (3 , 0) and the turning point of the transformed graph is
(-1 , -2) I attached an image so you can visualize clearly