Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x+y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (2x - y)⁴
By using binomial expansion theorem, we get
(2x - 3)⁷ = 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187
(2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.
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Solve m² = 0.04.
m=?
Answer:
M=0.00671
Step-by-step explanation:
[tex] \sqrt{m} = 0.04[/tex]
[tex] \sqrt{m {}^{2} } = \sqrt{0.04} [/tex]
[tex]m = 0.0067082039[/tex]
would suggest rounding off
ppppppllllllssss hhhhheeeeellllppppp
Answer: 10^-5 = 1/10^5
Step-by-step explanation: Every time you see a negative exponent, it would be 1/10^ (exponent number)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{10^{-5}}\\\\\mathsf{= \dfrac{1}{10\times10\times10\times10\times10}}\\\\\mathsf{= \dfrac{1}{100\times100\times10}}\\\\\mathsf{= \dfrac{1}{10,000\times10}}\\\\\mathsf{= \dfrac{1}{100,000}}\\\\\mathsf{= \dfrac{1}{10^5}}[/tex]
[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{\dfrac{1}{10^5}}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The slope of the car is ________
Answer:
y = 60x
slope: 6 0 probably
Step-by-step explanation:
Dunnno
Answer:
y = 60x
slope: 6 0
The ages of Lily, Oscar, Hana and Albie add
up to 80 years.
The ratio of Lily's age to Oscar's age to Hana's
age to Albie's age is 7:3:6:4.
How many years old is Hana?
Answer:
Hana is 16
Step-by-step explanation:
Total is 80. Ratio is 7:3:6:4. Ratio adds to 20. 80÷20=4. Hana is last in Ratio which is 4. 4×4= 16.
Solve. √6-3 x -2=0
Value of x = 2/3.
✓(6 - 3x) - 2 = 0
Adding 2 to both sides of the equation
✓(6 - 3x) - 2 + 2 = 0 + 2
✓(6 - 3x) - 2 = 2
Now, tor remove the square root from the Left Hand Side of the equation, square both the sides of the equation.
(✓(6 - 3x))² = 2²
6 - 3x = 4
3x = 6 - 4
3x = 2
x = 2/3
Thus, the value of x is 2/3.
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can you please answer the question in the screenshot will give brainlest
Answer:
The elevator is two floors below the ground level. The integer to represent this is -2.
Step-by-step explanation:
If Ade has 19 mangoes then he shares it in ratio 2:3 to Ana and Mide respectively, and after sharing it remained one with Ade. What is the addition of Ana and Mide's share.
Answer:
19=
2:3=
Step-by-step explanation:
Im not good at explaining things
Eight more than twice a number is four times the difference between 5 and the number
Answer:
Step-by-step explanation:
8 more= +8
twice a number = 2x
difference between the number and 5=
2x+8=4x(5-x)
2x+8=9x-x
2x+8=8x
8=8x-2x
8=6x
x=6/8
x=3/4
6(6) ÷ (2 · 9) in order of operation
#10: A Caterer’s total cost for a party includes a fixed cost, in addition the caterer also charges a certain amount for. Each guest
$300 to serve 25 guests
$420 to serve 40 guests
Find the fixed cost and the cost per guest
if f(1)=8and f(N)=f(n+1)+4 then find the value of f(6)
The function definition is an arithmetic sequence and the value of the function f(6) is -12
How to determine the value of the function f(6)?The function definition is given as
f(1) = 8
f(n) = f(n + 1) + 4
Rewrite the above function as
f(n + 1) = f(n) - 4
Set n = 1
So, we have
f(1 + 1) = f(1) - 4
This gives
f(2) = f(1) - 4
So, we have
f(2) = 8 - 4
Evaluate
f(2) = 4
Set n = 2
So, we have
f(2 + 1) = f(2) - 4
This gives
f(3) = f(2) - 4
So, we have
f(3) = 4 - 4
Evaluate
f(3) = 0
Set n = 3
So, we have
f(3 + 1) = f(3) - 4
This gives
f(4) = f(3) - 4
So, we have
f(4) = 0 - 4
Evaluate
f(4) = -4
Set n = 4
So, we have
f(4 + 1) = f(4) - 4
This gives
f(5) = f(4) - 4
So, we have
f(5) = -4 - 4
Evaluate
f(5) = -8
Set n = 5
So, we have
f(5 + 1) = f(5) - 4
This gives
f(6) = f(5) - 4
So, we have
f(6) = -8 - 4
Evaluate
f(6) = -12
Hence, the value of the function f(6) is -12
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2) Currently: 37, 30, 24, 30, 37, 30, 55, 16
Mean
Median
Mode
Range
Answer: mean: 32.375 median: 30 mode: 30 range: 39
Step-by-step explanation:
Angle A and angle B are supplementary and ∠A ≅ ∠C. If m∠A = (16x − 7)° and m∠B = (21x + 2)°, what is m∠C in degrees?
m∠C =?
Two angles have sum as 180° called supplementary angle so the measure of angle C m∠C will be 68.68°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
Given that,
Angle A and angle B are supplementary
Since the supplementary angle has a sum of 180 degrees.
So,
m∠A + m∠B = 180°
16x - 7 + 21x + 2 = 180
16x + 21x + 7 - 2 = 180
37x + 5 = 180
37x = 175
x = 4.78
So,
m∠A = 16(4.78) - 7 = 68.68°
Since m∠C = m∠A
So,
m∠C = 68.68°
Hence"The measure of angle C m∠C will be 68.68° ".
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can anyone solve it with full language?
Write each equation in logarithmic form.
8²=64
We get the equation in logarithmic form as log₈ 64 = 2
A “logarithmic equation” is an equation which involves the “logarithm” of any expression which is containing a variable.
Now, we have been given an equation:
8² = 64
We need to write it in the logarithm form.
We know that, it will be written as:
log₈ 64 = 2
Since the power goes after the equal sign, so 2 is placed after the equal sign.
The actual value is taken after log, so 64 is placed there and the base number is taken as the base for the log, so 8 is taken as the base for the log.
Therefore, we get the equation in logarithmic form as log₈ 64 = 2
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Step 1: choose the lowest common denominator
find the sum: - and
2
3 04
5 6 8 10 12
the expression written in equivalent form with a
common denominator is
-
0 000
the sum is
0
-
Answer:
Step-by-step explanation:
LCD = 24Equivalent Fractions with the LCD1 1/2=36/243/8=9/245/6=20/243=72/24
What is the area model of 37 times 9
Answer:
333
Step-by-step explanation:
How do you answer 532÷4 using long division?
If we divide five hundred and thirty two by four using long division method, we obtain one hundred and thirty three.
What is long division?The term long division implies dividing repeatedly until we are able to arrive at the final result. In this case, we are asked to carry out the division of 532÷4 using long division.
First we have to divide the digits one after the other. This process is a bit iterative and takes a little time for us to do in the process of the long division.
Now; when we divide five by 4 we obtain one remainder one we then add the one that remains to thirty two and we have one hundred and thirty two.
Then we divide one hundred and thirty two by four, we can see that there are thirty three fours in one hundred and thirty two. The final result of our long division now becomes one hundred and thirty three.
Thus, if we divide five hundred and thirty two by four using long division method, we obtain one hundred and thirty three.
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Round 12.45172 to 1 decimal place
Answer:
12.5
Step-by-step explanation:
To round to one decimal place you have to round the number to its "tenths". When you are rounding, any number which is 5 or above is rounded to the tenth above or in this situation 6 making it 12.5. But any number below 5 is going to be rounded to the tenth below so if the number was 12.44172 then the answer would 12.4. GL and mb if i messed up.
What positive value of b makes 9 x²-b x+4 a perfect square trinomial?
A perfect square trinomial is of the form a^2+2ab+b^2. Equate the given expression to the general form. Find the roots for a^2 and b^2 to get the value of a and b. Equate the unknown b term to 2ab to obtain the solution.
9x^2-bx+4
9x^2-bx+4 = a^2+2ab+b^2
a^2 = √9x^2; a = ±3x
b^2 = 4 ; b = ±2
bx = 2ac
-bx = 2(3x.-2)
-bx = -12x ; b= 12
The value of b is 12.
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5.1 Write down the: 5.1.1 Coordinates of D E(1 ;3) B (2)
This figure begins with the sentence, “We substitute x equals 3 and y equals 2 into both equations.” The first equation reads 3 times x minus 7equals 7. Then, 3 times 3 minus 2 equals 7. Then 7 = 7 is true. The second equation reads x minus 2y equals 4. The n times 2 minus 2 times 2 = 4. Then negative 2 = 4 is false.
The ordered pair (3, 2) made one equation true, but it made the other equation false. Since it is not a solution to both equations, it is not a solution to this system.
Exercise 5.1.1
Determine whether the ordered pair is a solution to the system: {x−y=−12x−y=−5
(−2,−1)
(−4,−3)
Answer
Exercise 5.1.2
Determine whether the ordered pair is a solution to the system: {3x+y=0x+2y=−5
(1,−3)
(0,0)
Answer
Exercise 5.1.3
Determine whether the ordered pair is a solution to the system: {x−3y=−8−3x−y=4
(2,−2)
(−2,2)
Answer
Solve a System of Linear Equations by Graphing
In this chapter we will use three methods to solve a system of linear equations. The first method we’ll use is graphing. The graph of a linear equation is a line. Each point on the line is a solution to the equation. For a system of two equations, we will graph two lines. Then we can see all the points that are solutions to each equation. And, by finding what the lines have in common, we’ll find the solution to the system.
Most linear equations in one variable have one solution, but we saw that some equations, called contradictions, have no solutions and for other equations, called identities, all numbers are solutions. Similarly, when we solve a system of two linear equations represented by a graph of two lines in the same plane, there are three possible cases, as shown in Figure 5.1.1 :
This figure shows three x y-coordinate planes. The first plane shows two lines which intersect at one point. Under the graph it says, “The lines intersect. Intersecting lines have one point in common. There is one solution to this system.” The second x y-coordinate plane shows two parallel lines. Under the graph it says, “The lines are parallel. Parallel lines have no points in common. There is no solution to this system.” The third x y-coordinate plane shows one line. Under the graph it says, “Both equations give the same line. Because we have just one line, there are infinitely many solutions.”
Figure 5.1.1
For the first example of solving a system of linear equations in this section and in the next two sections, we will solve the same system of two linear equations. But we’ll use a different method in each section. After seeing the third method, you’ll decide which method was the most convenient way to solve this system.
Exercise 5.1.4 : How to Solve a System of Linear Equations by Graphing
Solve the system by graphing: {2x+y=7x−2y=6
Answer
Exercise 5.1.5
Solve each system by graphing: {x−3y=−3x+y=5
Answer
Exercise 5.1.6
Solve each system by graphing: {−x+y=13x+2y=12
Answer
The steps to use to solve a system of linear equations by graphing are shown below.
TO SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.
Graph the first equation.
Graph the second equation on the same rectangular coordinate system.
Determine whether the lines intersect, are parallel, or are the same line.
Identify the solution to the system.
If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.
If the lines are parallel, the system has no solution.
If the lines are the same, the system has an infinite number of solutions.
Exercise 5.1.7
Solve the system by graphing: {y=2x+1y=4x−1
Answer
Exercise 5.1.8
Solve the system by graphing: {y=2x+2y=−x−4
Answer
Exercise 5.1.9
Solve the system by graphing: {y=3x+3y=−x+7
Answer
Both equations in Exercise 5.1.7 were given in slope–intercept form. This made it easy for us to quickly graph the lines. In the next example, we’ll first re-write the equations into slope–intercept form.
Exercise 5.1.10
Solve the system by graphing: {3x+y=−12x+y=0
Answer
Exercise 5.1.11
Solve each system by graphing: {−x+y=12x+y=10
Answer
Exercise 5.1.12
Solve each system by graphing: {2x+y=6x+y=1
Answer
Usually when equations are given in standard form, the most convenient way to graph them is by using the intercepts. We’ll do this in Exercise 5.1.13 .
Exercise 5.1.13
Sopt form.y=12x−3m=12,b=−3{y=12x−3x−2y=4 If we solve the second equation for y, we get x−2y=4x−2y=−x+4y=12x−2m=12,b=−2
The two lines have the same slope but different y-intercepts. They are parallel lines.
Figure 5.1.3 shows how to determine the number of solutions of a linear system by looking at the slopes and intercepts.
What is 9.14 divided by 0.04
[Mathematical Problem]
[tex]9.14[/tex] ÷ [tex]0.04[/tex]
Solution:
[tex]228.5[/tex]
Hope this helps! Thanks and good luck!
Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
g(x)-f(x)
The domain of the function [tex]g(x) - f(x)[/tex] for [tex]f(x)=2 x+5[/tex]and [tex]g(x)=x^2-3 x+2[/tex] is [tex]g(x) - f(x)[/tex] = [tex]x^2-4x-2[/tex]. The domain will be all real numbers for x, ( ∞,-∞)
What is the domain of the function [tex]g(x) - f(x)[/tex] ?The domain will be all real numbers for x, ( ∞,-∞)
As there are no values that can be substituted for x that can possibly make the function undefined.
Therefore,
[tex]g(x)=x^2-3 x+2 .[/tex]
[tex]f(x)=2 x+5[/tex]
[tex]g(x) - f(x)[/tex] = ([tex]x^2-3 x+2[/tex]) - ([tex]2 x+5[/tex])
[tex]g(x) - f(x)[/tex] = [tex]x^2 - 4x-2[/tex]
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4. A pizza company is interested in the average number of pizzas eaten each year by
people. They send out 30 volunteers to conduct research by collecting random
samples of 25 people each and determine the number of pizzas that the people in
the group ate in the previous year. After looking at the sample means, the company
estimates that the mean number of pizzas eaten is 6.4 with a margin of error of 1.3.
Based on these values, what interval is likely to contain the true mean number of
pizzas eaten in the previous year by the population?
Based on these values, the interval that likely to contains the true mean number of pizzas eaten in the previous year by the population is :5.1-7.7
What does a margin of error mean?
The margin of error of 1.3 means that the interval that contains the true mean of the people sampled is the mean plus or minus the margin of error, in other words, the mean of 6.4 could either be greater by 1.3 or less by 1.3
interval containing the true mean number=mean± marginal of error
upper limit of the mean interval=6.4+1.3
upper limit of the mean interval=7.7
lower limit of the mean interval=6.4-1.3
lower limit of the mean interval=5.1
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Write 5=log₂x₊₁(a+b) in exponential form.
The exponential form of the function 5 = log₂ₓ₊₁(a₊b) is (2x ₊ 1)⁵ = (a₊b).
Given the function is:5 = log₂ₓ₊₁ (a₊b)
we are asked to determine the exponential form of the above function.
The exponential form is an easier way to represent repeated multiplication involving exponents and bases.
It is easy to quickly convert an exponentially written expression into a logarithm using the following formula.
here we have the form loge b =a5 = log₂ₓ₊₁(a₊b)
then, e = 2 , a = 5 and
b = (a₊b)5 = log₂ₓ₊₁(a₊b)
therefore, exponential form is:
(2x ₊ 1)⁵ = (a₊b).
hence we get the required exponential form as (2x ₊ 1)⁵ = (a₊b).
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Use a half-angle identity to find the exact value of sin 90°
Answer:
1
Step-by-step explanation:
[tex]\sin \frac{180^{\circ}}{2}=\sqrt{\frac{1-\cos 180^{\circ}}{2}} \\ \\ \sin 90^{\circ}=\sqrt{\frac{2}{2}} \\ \\ =1[/tex]
A rectangular pool is 6 meters wide and 14 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
The swimmer will swim 15.23 cm.
What is Pythagoras Theorem?According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, the Pythagoras equation can be used to any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.
Given:
Perpendicular = 14 m
Base = 6 m
Using Pythagoras theorem
H²= P² + B²
H² = 14² + 6²
H² = 196 +36
H² = 232
H= 15.23 cm
Hence, the swimmer will swim 15.23 cm.
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simplify 14/21 = ?/? please help
Answer:
2/3
Step-by-step explanation:
Let's simplify the value,
→ 14/21
→ (14 ÷ 7)/(21 ÷ 7)
→ 2/3
Thus, the value is 2/3.
|x|<6 graph the inequality
Answer:
This is the graph on a number line.
Hope it helps.
After a major storm, your math class volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard.
b. How many students should there be to clear debris from an average-sized yard in at most 25 minutes?
9 students should there be to clear debris from an average-sized yard in at most 25 minutes.
What do we mean by time?Time is the seemingly irreversible succession of existence and events that occur from the past, through the present, and into the future. It is a component quantity of various measurements used to sequence events, compare the duration or intervals between events, and quantify rates of change of quantities in material reality or conscious experience. Along with three spatial dimensions, time is frequently referred to as a fourth dimension.So,
According to the given table:
t = k/nt = 2525 = 225/n ⇒ n · 25 = 225/n · n25n/25 = 225/25 = 9 studentsTherefore, 9 students should there be to clear debris from an average-sized yard in at most 25 minutes.
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