In elementary algebra, the binomial expansion defines the algebraic expansion of powers of a binomial. The binomial equation be 27x² - 300 exists 3(3x + 10)(3x - 10).
What is meant by binomial equation?In elementary algebra, the binomial theorem (or binomial expansion) defines the algebraic expansion of powers of a binomial. According to the theorem, it exists possible to extend the polynomial [tex]$(x+y)^n$[/tex] into a sum involving terms of the form [tex]$a x^b y^c$[/tex], where the exponents b and c exists nonnegative integers with b + c = n, and the coefficient a of each term exists a specific positive integer depending on n and b.
Let the binomial equation be 27x² - 300
Factor out common term 3:
[tex]$\quad 3\left(9 x^2-100\right)$[/tex] [tex]$=3\left(9 x^2-100\right)$[/tex]
simplifying the above equation, we get
Factor [tex]$9 x^2-100: (3 x+10)(3 x-10)$[/tex]
= 3(3x + 10)(3x - 10)
If 3(3x - b)(3x + b) then we get
= 3(3x + 10)(3x - 10)
b = 10
The value of b = 10.
Therefore, the correct answer is option a. 10.
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What is the prime factorization of 21?Enter your answer as a product of prime numbers, like 2 X 3, or asa single prime number. like 17.
Answer:
The prime factorization of 21 is;
[tex]21=3\times7[/tex]Explanation:
We want to find the prime factorization of 21;
The number 21 is a product of 3 and 7;
[tex]21=3\times7[/tex]since 3 and 7 are both prime number, then the prime factorization of 21 is;
[tex]21=3\times7[/tex]Calculate the volume for each right rectangular prism 5 3/4 in high 8 1/2 in long 2 1/4width
5 3/4 = 5.75
8 1/2 = 8.50
2 1/4 = 2.25
Volume = width × height × length
? = (5.75)(8.50)(2.25)
volume = 109.96875
in fraction form = 109 31/32
Repost, can someone help?
Answer:
x=65
y=32
Step-by-step explanation:
2x+x-15=180
combine like terms
3x-15=180
add 15 to both sides
3x=195
divide both sides by 3
x=65
now y's
4y+y+20=180
combine like terms
5y+20=180
subtract 20 from both sides
5y=160
divide both sides by 5
y=32
Answer:
x = 65
y = 32
Step-by-step explanation:
2x + (x - 15) = 180
2x + x - 15
3x - 15 = 180
+15 +15
-------------------
3x = 195
÷3 ÷3
----------------
x = 65
4y + (y + 20) = 180
4y + y + 20 =180
5y + 20 = 180
-20 -20
---------------------
5y = 160
÷5 ÷5
---------------
y = 32
2x + (x - 15) + 4y + (y + 20) = 360
2(65) + (65 - 15) + 4(32) + (32 + 20) = 360
130 + 50 + 128 + 52 = 360
180 + 180 = 360
360 = 360
I hope this helps!
3. A clothing store is having a sale with all clothes being 10% - 30% off the original retail price.
(CAREFUL)
What would be the possible prices for a shirt with an original price of $60?
Answer: between $42 and $54 including both endpoints.
In symbolic form we can say [tex]42 \le p \le 54[/tex] where p is the final price after the discount is applied.
===============================================
Explanation:
10% off means you save 10% but pay the remaining 90%
Then convert 90% to decimal form to get 0.90
If the original price is $60, then the final price is 0.90*60 = 54 dollars.
In other words,
10% of 60 = 0.10*60 = 6 dollars saved
60-6 = 54 is the final price
---------------------
If the discount is 30% then you pay the remaining 70%
0.70*60 = 42
Or you can think of it like this
30% of 60 = 0.30*60 = 18 dollars saved
60-18 = 42 dollars is the final price
---------------------
Let's summarize with this chart:
[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{Discount} & \text{Amount Saved} & \text{Final Price}\\\cline{1-3}10\% & \$6 & \$54\\\cline{1-3}30\% & \$18 & \$42\\\cline{1-3}\end{array}[/tex]
Therefore, the final price after the discount is between $42 and $54 including both endpoints.
Side note: The jump from 10% to 30% is "times 3"; so is the jump from $6 to $18 in the "amount saved" column of the table.
WILL GIVE BRAINLIST TO BEST ANSWER PLUS EXTRA POINTS
5. The cost of a ride in a taxi is $5.00 for the first half-mile plus a constant amount per half mile after that. The sequence below shows the pattern of numbers that appear on the driver's screen.
5.00, 5.75, 6.50, …
Part A: Write an Explicit Function that can be used to determine f(x), the cost in dollars, for a ride in the taxi of, x, half miles.
Part B: What is the cost, in dollars, for an 55-mile ride in the taxi? Provide mathematical justification for your answer.
The explicit function of the relation is Tn = 4.25 + 0.75n and the cost of a 55 miles ride is $45.5
How to determine the explicit function?The sequence of the relation is given as
5.00, 5.75, 6.50, …
In the above sequence, we can see that
The sequence have a common difference of 0.75
This means that the sequence is an arithmetic function
An arithmetic function is represented as
T(n) = a + (n - 1)d
Where
a = First term = 5.00d = common difference = 0.75n = Number of termsTn = Current termSubstitute the known values in the above equation
Tn = 5 + 0.75(n - 1)
Expand
Tn = 5 - 0.75 + 0.75n
Evaluate
Tn = 4.25 + 0.75n
The cost of a 55-mile rideThis means that
n = 55
Subsitute n = 55 in the equation Tn = 4.25 + 0.75n
So, we have
T55 = 4.25 + 0.75 * 55
Evaluate the product
T55 = 4.25 + 41.25
Evaluate the sum
T55 = 45.5
Hence, a 55-mile ride will cost $45.5
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Graphing transformations of sine and cosine functions: Sketch function below given the domain x e [-360, 360] <-- both are in degrees
By following the steps below, we can plot the graph of →
y = 5 cos(2x + π/3) - 1
What are trigonometric functions?The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given is the following function -
y = 5 cos(2x + π/3) - 1
We have -
y = 5 cos(2x + π/3) - 1
We can sketch the function as follows -
Let y = cos(x)
The first step is Amplitude magnification -y = 5 cos(x)
The second step can be understand in an easy way as if we multiply [x] by 2, the frequency of the cosine wave increases i.e. the distance between consecutive crests decreases.y = 5 cos(2x)
Third step include shifting of graph along the [x] axis. This can be done by adding a phase value as -y = 5 cos(2x + π/3). This will shift the graph along the negative
[x] - axis by π/3.
Finally, we will shift the graph by 1 unit towards the negative [y] - axis.Therefore, by following the steps above, we can plot the graph of →
y = 5 cos(2x + π/3) - 1
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kara is sorting buttons by length for a craft project. the line plot shows the length of each button. if kara lines up all the 3/4-inch button, what would be the total length?
When Kara is sorting buttons by length for a craft project and the line plot shows the length of each button. If Kara lines up all the 3/4 inches buttons, then the total length is [tex]2\frac{1}{4}[/tex] inches
The length of the button = 3/4 inches
Number of 3/4 inch buttons = 3 buttons
Then the total length = Number of 3/4 inch buttons × The length of the button
Substitute the values in the equation
The total length = 3×(3/4)
= 9/4 inches
Convert the simple fraction to the mixed fraction
9/4 inches = [tex]2\frac{1}{4}[/tex] inches
Hence, when Kara is sorting buttons by length for a craft project and the line plot shows the length of each button. If Kara lines up all the 3/4 inches buttons, then the total length is [tex]2\frac{1}{4}[/tex] inches.
The complete question is
Kara is sorting buttons by length for a craft project. the line plot shows the length of each button. if Kara lines up all the 3/4-inch button, what would be the total length?
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Which expression values 4? A) (4+5)×3^2-9÷3^2 B) 4+5×(3^2-9)÷3^2 C) 4+5×3^2-(9÷3^2) D) 4+5×3^2-9÷3^2 pls help me
Answer:
B)4+5×(3^2-9)÷3^2 C)
Step-by-step explanation:
The nth term of a sequence is given by 2n² + 1.
Write down the first three terms of this sequence.
Answer:
3, 9, 19
Step-by-step explanation:
substitute n = 1, 2, 3 into the nth term formula
n = 1 : 2(1)² + 1 = 2(1) + 1 = 2 + 1 = 3
n = 2 : 2(2)² + 1 = 2(4) + 1 = 8 + 1 = 9
n = 3 : 2(3)² + 1 = 2(9) + 1 = 18 + 1 = 19
the first 3 terms are 3, 9, 19
Faith Franklin sells furniture and earns 9% commission on her total sales. Last month she had $33,500 in
sales. How much did she earn?
Answer:
$3015
Step-by-step explanation:
Answer:
$3015
Step-by-step explanation:
Comment
She earned 9% of 33500
To replace th4 % sign, you always divide the number given by 100.
So 9% as a decimal is 9/100 = 0.09. Notice where the 100 goes. It is right underneath the 9. So you are dividing by 100.
So she earned
0.9 * 33500 = $3015
can someone please help with this geometry
Answer:
∠ABD = 19.5°
∠ABE = 160.5°
Step-by-step explanation:
Given angle ABC = 39° and its bisector BD, you want the measures of angle ABD and ABE, its supplement.
Angle bisectorAn angle bisector divides an angle into two equal parts, each with half the measure of the whole.
∠ABD = 1/2∠ABC
∠ABD = 1/2(39°)
∠ABD = 19.5°
Linear pairThe angles of a linear pair are supplementary: they total 180°. Angles ABD and ABE form a linear pair.
∠ABE = 180° -∠ABD
∠ABE = 180° -19.5°
∠ABE = 160.5°
Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)
First, draw a diagram to visualize the situation:
As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.
Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ =\sqrt{(8--5)^2+(-3-4)^2} \\ \\ =\sqrt{(13)^2+(-7)^2} \\ \\ =\sqrt{169+49} \\ \\ =\sqrt{218} \\ \\ \approx14.7648... \end{gathered}[/tex]Therefore, the distance between the points (-5,4) and (8,-3) is: √218.
Compute the diameter of a circle with a circumference of 34 feet
Step-by-step explanation:
we need to remember the formula for the circumference of a circle :
2×pi×r
or
2×r × pi
what is 2×r ? the double radius ? 2 times the radius is the diameter.
so, we know
diameter × pi = 34 ft
diameter = 34/pi = 10.82253613... ft
Macy made an initial deposit of $250 into a bank account. assuming no interest, the function f(x)=80x+250 represents the total amount of money she will have in the account after x months. evaluate and interpret the function for f(9).
Answer:A
Step-by-step explanation:
A 5 kg bag of grass seed covers about 650 m². How many bags should Tshering buy to seed a 60 m-by-80 m football field?
Given: 5 kg bag of grass seed covers 650 m2
To find:
Bags to seed 60m-80m field
Solution:
Area of football field- 60x80=4800m²
Bags required-
Since 650 m² is covered by 5kg
So, 4800m² will be covered by-
=4800/650x5
= 36.9 bags
Therefore, 40 bags are required to seed a 60m-by-80m football field.
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Solve for x
2x^2=5x+3
Answer:
Step-by-step explanation:
ur mom
Answer each part. If necessary, round your answers to the nearest hundredth.(a) Hans bought 11 pounds of rice for $5.How many dollars did he pay per pound of rice?I dollars per pound(b) It takes 16 pounds of seed to completely plant a 3-acre field.How many pounds of seed are needed per acre?pounds per acre
(a) Hans bought 11 pounds of rice for $5.
How many dollars did he pay per pound of rice?
the unit price is given by the total price divided by the total weight, therefore:
[tex]p=\frac{5}{11}=0.45454=0.45[/tex]He payed $0.45 per pound of rice
(b) It takes 16 pounds of seed to completely plant a 3-acre field.
How many pounds of seed are needed per acre?
the pounds of seed per unit area is given by the total pounds used to plant the total acres
[tex]s=\frac{16}{3}=5\frac{1}{3}=5.33[/tex]so, the answer is 5.33 pounds per acre
72% of what weight is 50oz
Answer:
See below
Step-by-step explanation:
72 % is .72 in decimal
.72 x = 50 oz Divide both sides by .72
X = 50 / .72 = 69.44 oz ( or 69 4/9 oz )
patrons of the grande dunes hotel in the bahamas spend time waiting for an elevator. the wait time follows a uniform distribution between 0 and 3.5 minutes. (round your answers to 2 decimal places.)
It takes 1.75 minutes to an average customer to wait
The waiting times standard deviation is 1.01
The percentage of a customer wait under a minute is 28.57%
42.86% customers wait more than two minutes
What is Uniform distribution?Uniform distribution: n probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds.
Display the 1.00 area under the curve.
The rectangle has a length of 3.5 - 0 = 3.5.
The rectangle's height is 1/3.5.
To determine the area, multiply:
3.5 * 1/3.5 = 1
How long does the average customer have to wait for an elevator?
EV stands for average between high and low.
= (0+3.5)/2
= 1.75
What is the waiting time's standard deviation?
Standard deviation is equal to sqrt(b-a2/12).
= sqrt((3.5-0)^2/12)
= 1.01
What percentage of customers wait under a minute?
It is x/(b-a) = 1/ for less than (3.5-0)
1/3.5
= 28.57%
How many customers wait more than two minutes?
It is 1 - x for greater than (b-a)
(3.5-2)/3.5
= 1.5/3.5
= 42.86%
It takes 1.75 minutes to an average customer to wait
The waiting times standard deviation is 1.01
The percentage of a customer wait under a minute is 28.57%
42.86% customers wait more than two minutes
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Savannah is creating a stained glass windowpane that will be 5 inches by 5 inches. To make
the rectangular windowpane, Savannah fuses together two triangles of colored glass. What is
the perimeter of one triangle?
The dimensions of the windowpane = 5 inches x 5 inches
This means the windowpane is square in shape.
Now, for the triangle,
Sides of the triangle = 5 inches each
Diagonal of the Square = Hypotenuse of the Triangle
The diagonal of a square is given by = [tex]\sqrt{2}[/tex] x side of the square = 5[tex]\sqrt{2}[/tex] inches
So, the perimeter of the one triangle = 5 + 5 + 5[tex]\sqrt{2}[/tex] = 10 + 5[tex]\sqrt{2}[/tex]
= 5(2+[tex]\sqrt{2}[/tex]) Inches
= 5(2+1.414)
= 17.07 inches (Approx.)
What is Perimeter?A perimeter is a closed path that embraces, encircles, or delimits a two-dimensional shape or a one-dimensional length. A circle's or an ellipse's circumference is its furthest boundary.There are various useful situations where knowing the perimeter is useful. The length of fence needed to completely enclose a yard or garden is known as the calculated perimeter. A wheel's or circle's perimeter indicates how far it will travel in a single rotation. In a similar way, the circumference of a spool is connected to the length of string looped around it; if the string were exactly the same length, the two would be equal.In addition to being the basic shapes, polygons are essential for figuring out perimeters since many shapes' perimeters are determined by estimating them with series of polygons that tend to them. Archimedes, who calculated a circle's approximate perimeter by enclosing it in regular polygons, is the first mathematician documented to have applied this line of thought.To learn more about Perimeter, refer to:
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A used boat dealership buys a boat for $2800 and then sells it for $3800 what is the percent increase
Percent increase by 35.71%
What is Profit and Loss ?
Profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year.
Given,
cost price of a boat is = $2800
selling price of a boat is = $3800
There is profit since C.P is less than S.P.
so, Profit = S.P - C.P
= $3800 - $2800
= $1000
Now, find profit percent i.e, Profit% = (Profit / C.P) * 100
=> Profit % = (1000 / 2800)*100
= 35.71%
Therefore, Percent increase by 35.71%
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Determine the quotient of 5/6 and 2/3
Answer:
5/4
Step-by-step explanation:
There is a rule that dividing by a fraction is the same as multiplying by the reciprocal.
So:
[tex]\frac{5/6}{2/3} = \frac56 \cdot \frac32 = \frac{15}{12} = \frac54[/tex]
Write each mixed number as an improper fraction 5 whole number and 1 3 fraction form. Can you show me how you did the problem.
Answer:
16/3.
Step-by-step explanation:
5 1/3
First multiply 5 by 3.
This gives 15.
Now add the numerator of the fraction (1) to 15
- to give 16.
The improper fraction is 16/3.
please help I really need and answer!
All three triangles are congruent as, △ABC ≅ △ACD ≅ △CBD under AA condition
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.So, in the given image filling the blanks as follows:
(A) ∠ACB = ∠CDA = ∠CDB = 90° (Definition of right triangles)
(B) Triangle angle sum theorem:
∠CAD = ∠CBD = 90°∠CAD = ∠CBA = 90°∠CAD = ∠CAB = 90°It is enough to prove that:
△ABC ≅ △ACD ≅ △CBD under AA condition.(C) C.P.C.T (Corresponding parts of congurent triangles)
∠CBD = ∠CAD∠CAD = ∠CBD(D) △ABC ≅ △ACD ≅ △CBD under AA condition.
Therefore, all three triangles are congruent as, △ABC ≅ △ACD ≅ △CBD under AA condition
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4 = -(x + 3) implemented as a real life problem
having a half braincell moment again
attachment below
Using similarity of triangles, the length of side GH is given as follows:
GH = 18.
Similar trianglesSimilar triangles have congruent angle measures, thus the measures of the side lengths are proportional.
In this problem, triangles CAD and HGD are similar, and the equivalent sides are given as follows:
AC = GH. (the measures are AC = 12 and GH = x).CD = HD. (the measures are CD = 30 and HD = 45).Hence the following proportional relationship is established:
x/12 = 45/30
Applying cross multiplication, we can solve for x, which is the length of side GH, as follows:
30x = 45 x 12 (simplifying by 30)
x = 1.5 x 12 (multiply 1.5 and 12).
x = 18. (which is the length of side GH).
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A car takes 49.7 seconds to travel 1 mile. How long does it take the car to travel 3.8 miles? First round to the nearest whole number to find the estimated answer. Then find the exact answer
Answer: 188.6 seconds which is rounded to 189 seconds or 3 minutes and 9 seconds
Step-by-step explanation:
Since we see that a time is given for 1 mile, to find the other distance we multiply the time for 1 mile (49.7 seconds) by the distance required (3.8 miles)
It can be also written like this:
1 mile -------> 49.7 seconds
3.8 miles-------> 49.7 seconds x 3.8 miles = 188.6 seconds rounded to 189 seconds. If asked for minutes, it can be written as 3 minutes and 9 seconds
Hope this helps!
pls help need to turn this in
Answer: y - 3 = -2(x + 2)
A bowl contains blueberries and strawberries. There are a total of 16 berries in the bowl. The ratio of blueberries to strawberries is 3 : 1. How many of each berry are in the bowl?
Answer:
12 Blueberries and 4 Strawberries
Step-by-step explanation:
12+4 = 16 and 12:4 = 3:1
URGENT PLEASE
Zachary purchased a computer for $1600 on a payment plan. five months after he purchased the computer, his balance was $900. eight months after he purchased the computer, his balance was $480. What is an equation that models the balance y after x months
If Zachary purchased a computer for $1600 on a payment plan. five months after he purchased the computer, his balance was $900. eight months after his balance was $480. The equation that models the balance y after x months is: y = -140x + 1600.
EquationMonth Balance
0 1600
5 900
8 480
Slopes:
(1600 - 900) / 5 = 700 / 5 = 140
(1600 - 480) / 8 = 1120 / 8 = 140
(900 - 480 ) / - 3 = - 140
Hence,
y = -140x + 1600
Therefore the equation is y = -140x + 1600.
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