What is the factored form of 6n4 – 24n3 + 18n? 6 n (n Superscript 4 Baseline + 4 n cubed + 3n) 6 n (n Superscript 4 Baseline minus 4 n cubed + 3 n) 6 n (n cubed minus 4 n squared + 3) 6 n (n cubed + 4 n squared + 3)
Answer:
6n(n³ - 4n² + 3)
Step-by-step explanation:
Given
6\(n^{4}\) - 24n³ + 18n ← factor out 6n from each term
= 6n(n³ - 4n² + 3) ← which may be factored further if required
6n(n³ - 4n² + 3) is the factored form.
What is expression?Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given that,
⇒6n⁴ - 24n³ + 18n
factor out 6n from each term
⇒6n(n³ - 4n² + 3)
There are two factors 6n and (n³ - 4n² + 3) of given expression.
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a) The quadratic x² - 4x-21 can be written in the form (x + a)² + b
Find the values of a and b.
quadratic formula
Please help, When do you need to approximate an irrational number with a rational value? Explain your understanding and give an example.
9514 1404 393
Answer:
in any numerical computation; numerical values can only be rational numbers
Step-by-step explanation:
Any time a number is written down as a numerical value, it is a rational number. The numerical values we give to π or e or any root, logarithm, trig function, and polynomial solution are, of necessity, rational approximations to the true value. An "exact" value for an irrational number cannot be written down, so it must be approximated any time its numerical value is needed.
Raina got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 8 cents per yard. If after that purchase there was $21.25 left on the card, how many yards of ribbon did Raina buy?
Raina bought 46 yards of ribbon with her prepaid debit card.
To find out how many yards of ribbon Raina bought, we'll need to use the given information about the price of ribbon and the remaining balance on her prepaid debit card.
1. First, we need to determine how much money Raina spent on the ribbon. Since her card had $25 initially and there was $21.25 left on it after her purchase, we can subtract the remaining balance from the initial amount:
$25 - $21.25 = $3.75
Raina spent $3.75 on the ribbon.
2. Next, we'll use the price per yard to figure out how many yards she bought. We know that the ribbon cost 8 cents per yard, so we can divide the total cost by the price per yard to find out the number of yards purchased:
$3.75 ÷ $0.08 = 46.875 yards
Since Raina can't buy a fraction of a yard, we'll round this number down to the nearest whole yard:
46.875 yards ≈ 46 yards
Raina bought 46 yards of ribbon with her prepaid debit card.
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An online retailer charges $30 for 12 cans of tennis balls. Which statement is correct ? Mark all that apply.
A.) The cost of 150 cans of tennis balls is $350.
B.) The cost of 100 cans of tennis balls is $250.
C.) The cost of 120 cans of tennis balls is $300.
D.) The cost of 180 cans of tennis balls is $500.
E.) The cost of 200 cans of tennis balls is $550.
F.) The cost of 250 cans of tennis balls is $625.
10 points !!
Answer:
The cost of 100 cans of tennis balls is $250
The cost of 120 cans of tennis balls is $300.
The cost of 250 cans of tennis balls is $625
Step-by-step explanation:
0/12 = 2.5 per can
100*2.5 = 250
120*2.5 = 300
250*2.5= 625
my mom gave me 5 dollar and I had 6 dollar and my dad gave me 8 dollar how much money I have?/
find the first term 43, 39, 35, 31, 27,
Answer:
23
Step-by-step explanation:
the difference between each number in the sequence is 4. Taking 4 away from 27 gives you 23
Hope this helps!
evaluate -6-(-5) x (-9)
Solve the system by graphing.
2x+y = -2
3x-y = -8
Use the graphing tool to graph the system.
Click to
enlarge
graph
Answer:
Step-by-step explanation:
x= -2
y=2
HELP ME PLEASE PLEADE !
Answer:
Step-by-step explanation:
4) a // b
∠11 ≅ ∠3. so, they are corresponding angles.
a // b
5) c) alternate exterior angles
a suspension bridge with weight uniformly distributed along its length has twin towers that extend meters above the road surface and are meters apart. the cables are parabolic in shape and are suspended from the tops of the towers. the cables touch the road surface at the center of the bridge. find the height of the cables at a point meters from the center.
The height of the cable is 0.15 meters and 1.35 meters at a point 200 meters and -200.
The given details are: Height of twin towers above road surface = h = 160 meters. Distance between twin towers = d = 800 meters. At the center of the bridge, the cables touch the road surface so the maximum height of the cable will be h. Using the formula for the parabolic cable we get: h(x) = a(x - d/2)(x + d/2). Let's find the value of "a" using the maximum height of the cable at the center of the bridge .i.e., h = a(0 - d/2)(0 + d/2) => h = a(d/2)^2 => a = (4h/d^2)Therefore, h(x) = (4h/d^2)(x - d/2)(x + d/2)We need to find the height of the cables at a point x meters from the center. Therefore, we need to find the value of h(x) when x = ±200 meters from the center of the bridge. h(x) = (4h/d^2)(x - d/2)(x + d/2) => h(x) = (4 × 160)/(800 × 800) (x - 800/2)(x + 800/2)When x = -200,h(-200) = (4 × 160)/(800 × 800) (-200 - 800/2)(-200 + 800/2)= (4 × 160)/(800 × 800) (-1200)(200)h(-200) = 0.15 meters. When x = 200,h(200) = (4 × 160)/(800 × 800) (200 - 800/2)(200 + 800/2)= (4 × 160)/(800 × 800) (-400)(1200)h(200) = 1.35 meters. Hence, the height of the cable is 0.15 meters and 1.35 meters at a point 200 meters and -200 meters from the center of the bridge respectively.
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given the following: p(a) =0.3 p(b) = 0.2 p(a and b) = 0.4 which of the following is true?
Group of answer choices a. A and B are independent and disjoint.
b. A and B are independent. c. A and B are disjoint. d. A and B are neither disjoint nor independent.
By applying independent and disjoint events theory, it can be concluded that A and B are neither disjoint nor independent (option D).
In probability, based on the occurrences, there are two types of events: independent and disjoint events.
If events are unrelated, they are considered independent events. Thus P(A and B) = P(A) * P(B)If events are mutually exclusive, which means they never occur at the same time, they are considered disjoint events. Thus the sum of the probabilities of each occurring, P(A and B) = 0. While P(A or B) = P(A) + P(B)Now we observe the data given:
p(a) = 0.3
p(b) = 0.2
p(a and b) = 0.4.
First, we check the independence. Here p(a and b) = 0.4. Whereas, if a and b are independent events, then:
p(a and b) = p(a) * p(b)
= 0.3 * 0.2
= 0.06
Since the value is different, we can conclude that events A and B are not independent.
Second, we check whether these events are disjoint events. Since the value of p(a and b) is not 0, these events are disjoint events.
Therefore, we can conclude that a and b are neither disjoint nor independent (option D)
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Graph the following equation
Y = 2x - 3
Y = -3x + 2
Show a graph plz
Answer:
Step-by-step explanation:
Here, we want to graph the given equations
1. y = 2x - 3
The general form of the equation of a straight line is;
y = mx + b
m is the slope and b is the y-intercept
To plot the line, we need the x intercept and the y-intercept
At the x-intercept, the value of y is zero
at the y-intercept . the value of x is zero
From the equation, we have the y-intercept as -3
To get the x-intercept, set y = 0
0 = 2x - 3
2x = 3
x = 3/2
x = 1.5
so to graph the line, we have to join the points ;
(0,-3) and (1.5,0)
b) y = -3x + 2
The y-intercept is 2
To get the x intercept, set y = 0
0 = -3x + 2
3x = 2
x = 2/3
so, we have to join the points (2/3,0) and (0,2)
We have the lines plotted as an attachment
pesky children keep playing in Maya's yard. She wants to put a fence around her yard to keep those rebel rousers out. Her front lawn is 50 ft wide and 20 ft deep. She only wants to fence two sides and front, since the 4th side is her house. How many feet deep of fencing does she need?
Answer:
90
Step-by-step explanation:
50+20+20=90
pls vote me brainliest i need the points.
Which of the following is the correct null hypothesis for an independent-measures t test?
a. M1 - M2 = 0
b. M1 - M2 ǂ 0
c. µ1 - µ2 = 0
d. µ1 - µ2 ǂ 0
Option a,The correct null hypothesis for an independent-measures t test is option a, which states M1 - M2 = 0.
An independent-measures t test is a statistical test used to compare the means of two independent groups. In this test, the null hypothesis represents the assumption that there is no significant difference between the means of the two groups. The null hypothesis is usually expressed in terms of the difference between the means of the two groups, denoted by M1 and M2.
In summary, the correct null hypothesis for an independent-measures t test is option a, which states M1 - M2 = 0. This null hypothesis assumes that there is no significant difference between the means of the two groups and any observed difference is due to chance. Option b assumes a significant difference between the means, while options c and d use population means instead of sample means. It is important to correctly specify the null hypothesis in a statistical test to ensure that the conclusions drawn from the analysis are valid.
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If I read 9 pages in 18 minutes how many pages will I read in 10 minutes
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has already picked 1
1
2
bushels, and she picks at a rate of
5
8
bushel per hour. The scenario is represented as
5
8
h + 1
1
2
= 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels of strawberries?
2 and StartFraction 3 Over 16 EndFraction hours
2 and StartFraction 3 Over 16 EndFraction hours
5 and three-fifths hours
10 and two-fifths hours
Answer:
We can start by isolating the variable "h".
5 8 h + 1 1 2 = 5
Subtracting 11/2 from both sides:
5 8 h = 5 - 1 1 2
Simplifying:
5 8 h = 8 1 2
Dividing both sides by 5/8:
h = 8 1 2 ÷ 5 8
Converting the mixed number to an improper fraction:
h = (8 x 8 + 1) ÷ 5 8
h = 65/8
Now, we can convert this fraction to a mixed number:
h = 8 1/8
Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:
5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8
Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).
Step-by-step explanation:
- The highest common factor of two numbers is 175.
The lowest common multiple of these two numbers
is 12 600.
Both numbers are greater than their highest
common factor.
Find the two numbers.
Answer:
1400, 1575
Step-by-step explanation:
Two number: 175x , 175y (x and y no more common factor)
LCM: 175xy = 12600
xy = 72
72: (1,72) (2,36) (3,24) (4,18) (6,12) (8,9) only (8,9) fit no common factor
Two number: 8*175 = 1400 9*175 = 1575
1 out of 3 students wants pancakes and the rest want waffles. What is the ratio of the number of students who want pancakes to the number of students who want waffles?
Write your answer as two numbers separated by a colon (for example, 2:3).
Answer:
Step-by-step explanation:
2:27
A car drives 215 km east and then 45 km north. What is the magnitude of the car's displacement? Round your answer to the nearest whole number. km
Answer:
220 km
Step-by-step explanation:
Since the direction north is perpendicular to the direction east, the driver has covered the two legs of a right triangle. The hypotenuse is his displacement for the combination of the two segments.
D = √(215² + 45²)
= √(46,225 + 2,025)
= √48,250 = 219.6588... km
Nearest whole number: 220 km
Answer:
220
Step-by-step explanation:
edge
lily pours 5 liters of water into glasses each glasses each glass holds 225 milliliters calculate how many glasses lily can fill competely
Step-by-step explanation:
the answer is how many times does 0.225 l fit wholly into 5 l :
5 / 0.225 = 22.22222222...
so, she can fill 22 glasses fully.
22 × 0.225 = 4.95 l
so, she has at the end (after filling the 22nd glass) 0.050 l (= 50 ml) left.
Write the quadratic equation in standard form.
Then solve using the quadratic formula.
1+ 4x + 3x2 = 0
HELPP
Answer:
x = − 1 3 − 1
Step-by-step explanation:
Solve the equation for x by finding a , b , and c of the quadratic then applying the quadratic formula. x = − 1 3 − 1
3 Factorise 5y - 6py
Step-by-step explanation:
5y-6py
y(5-6p)
Answer
hope it helps
Answer:
5y - 6py
y(5-6p)
is the answer
4. A plane's average speed between two cities is 200 m/s. If the trip takes 2.5 hours, how far does the plane fly?
Step-by-step explanation:
Average speed (S) = 200 m/s
Time taken (t) = 2 .5 hours = 2.5 *60*60 = 9000 sec
Now distance travelled (d) = ?
We know
The distance travelled by a body per unit time is
speed so
S = d / t
200 = d / 9000
d = 9000 * 200
d = 1800000 meters.
The plane flies 1800000 meters.
Can someone help really fast with this question
The answer that describes the polygon RSTU is as follows:
QuadrilateralTrapezoidHow to find a quadrilateral?A quadrilateral is a polygon with 4 sides. Therefore, let's use the properties to find the name of the shape RSTU as follows:
The polygon has 4 sides therefore, it is a quadrilateral.
The quadrilateral has opposite side parallel to each other. The opposite sides are RS and TU.
A trapezoid is a quadrilateral with only one pair of opposite side parallel to each other.
Therefore, the shapes that defines the polygon are as follows:
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If 60 ounces cost $13.00, how much does one ounce
cost?
Answer:
.27
Step-by-step explanation:
Find the slope of the line that passes through the points \left(10,8\right)(10,8) and \left(4,12\right)(4,12).
Write your answer as a simplified fraction.
3y + 2x = 44 is the equation of the line through (10, 8) and (4, 12).
What is the Equation of line?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
Given, two coordinates of a line \(\left(10,8\right) and \left(4,12\right)\)
The slope of the line formula is:
\(m = \frac{y₂ - y₁}{ x₂ - x₁}\)
Let's substitute our numbers.
\(m = -\frac{8 -12}{4-10}\) = -4/6
The GCF of these two numbers is 2
So, our slope = -2/3
The general equation of a line is y = mx +c
Therefore the equation of the line is y = -2/3x + c
Since, this line passes through ( 10, 8 )
Hence, it must satisfy these coordinates
8 = -2/3 * 10 + c
44/3 = c
Thus the equation of the line is y = -2/3x +44/3
the equation of the line is 3y + 2x = 44.
Therefore, The equation of the line that passes through (10, 8) and (4, 12) is 3y + 2x = 44.
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Cho số phức z , w thỏa mãn |z-3-i | = 1 và | w-1 | = |w+i |. Giá trị nhỏ nhất của P = | w+1 - 3i | + | w -z | bằng?
Find the area of the shaded polygons.
Answer:
9 sq.un.
Step-by-step explanation:
The polygon it is surrounded by an imaginary square of 4 X 4 units per side
To their area we subtract the areas of the imaginary triangles in white.
Results the area of the shaded polygon:
\(A=4^{2} -\frac{(2)(3)}{2} -2(\frac{(1)(3)}{2} )-\frac{(1)(2)}{2} =16-3-3-1=16-7=9sq.un.\)
Hope this helps
Answer:
9 sq. un
Step-by-step explanation:
5. For each scenario, fill in numbers in the blanks to create a scenario that
can be solved using a system of equations. Make sure the scenario that you
provide has ONE solution. Then, answer the questions that follow.
Scenario 1
There are
some are cows. There are
total animals in the barn. Some of the animals are chickens and
legs in all.
a. What is the system of equations that represents the scenario you created?
B. Prove your solution is correct.
The scenario in this problem is described as follows:
There are 50 total animals in the barn, and there are 160 legs in total.
The system of equations that describes this situation is given as follows:
x + y = 50.4x + 2y = 160.What is the system of equations that describes this scenario?The variables that describe the system of equations are given as follows;
Variable x: number of cows in the barn.Variable y: number of chickens in the barn.There are 50 total animals in the barn, hence:
x + y = 50.
There are 160 legs in total. Considering that each cow has four legs, while each chicken has two legs, we have that:
4x + 2y = 160.
The system of equations is composed by these two equations and can be solved using any method to identify the amounts of each animal.
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