The binomial expansion of the [tex](x-4)^5[/tex] is [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
According to the statement
we have given that a equation and we have to expand it by use of the binomial theorem.
So, For this purpose we know that the
A binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form.
And the general formula is
[tex](x+y)^n= ^nC_0x^ny^0+^nC_1x^(n-1)y^1+^nC_2x^(n-2)y^2+...+^nC_nx^0y^n[/tex]
And we have to solve it with the given equation (x-4)^5.
Then
[tex](x-4)^5=x^5+20x^4+(20)/(2)x^3(4^2)+(60)/(6)x^2(4)^3+(120)/(24)x^1(4)^4+(120)/(120)x^0(4)^5[/tex]
Now after solving the equation become
[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
So, The after expanding the given statement with the binomial theorem the result output is
[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
So, The binomial expansion of the [tex](x-4)^5[/tex] is [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
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To graph the inequality t>3, you would put an open circle on 3 and shade to the left
Answer:
It is an open circle and you would shade to the right on a number line.
Step-by-step explanation:
The circle is open because you are not including 3. Put numbers in for t and you will see that the numbers greater than 3 are all on the right side of the number line.
Part 1:
A. Express the new length of the long side of the note card, once the two corners are removed.
B. Express the new width of the short side of the note card, once the two corners are removed.
Part 2:
Write a function A(x) that defines the area of the bottom of the box, once the corners are removed and the sides are folded up.
Part 3:
A. Suppose you want the bottom of your box to cover a total area of 16 in2. Set up an equation in standard form that will help you find the size (x) of the corner you need to cut in order for your box to have this area.
B. Solve this equation and take note of any extraneous solutions. Explain why the answer is extraneous, and clearly state the correct answer
The size of the corner you need to cut in order for your box to have this area is 0.5 inches
Part 1: A. Express the new length of the long side of the note card, once the two corners are removed.The base length is given as:
Length = 7
When the edges are removed, the new length becomes
New length = 7 - x - x
Evaluate
New length = 7 - 2x
Part 1: B. Express the new width of the short side of the note card, once the two corners are removed.The base width is given as:
Width = 4
When the edges are removed, the new length becomes
New width = 4 - x - x
Evaluate
New width = 4 - 2x
Part 2: Write a function A(x) that defines the area of the bottom of the box, once the corners are removed and the sides are folded up.The area of the bottom of the box is calculated as:
Area = New length * New width
This gives
Area = (7 - 2x) * (4 - 2x)
Rewrite as:
A(x) = (7 - 2x) * (4 - 2x)
Part 3: Set up an equation in standard form that will help you find the size (x)The area is given as:
Area = 16
So, we have:
(7 - 2x) * (4 - 2x) = 16
Expand
28 - 14x - 8x + 4x^2 = 16
Rewrite as
4x^2 - 14x - 8x + 28 - 16 = 0
Evaluate the like terms
4x^2 - 22x + 12= 0
Part 3: Solve this equation and take note of any extraneous solutionsWe have:
4x^2 - 22x + 12= 0
Expand the equation
4x^2 - 24x - 2x + 12 = 0
Factorize the equation
4x(x - 6) - 2(x - 6) = 0
Factor out x - 6
(4x - 2)(x - 6) = 0
Solve for x
x = 0.5 or x = 6
The value of x = 6 is too big for the dimensions of the box.
So, x = 6 is an extraneous solution for the equation
Hence, the size of the corner you need to cut in order for your box to have this area is 0.5 inches
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Which of the following inequalities matches the graph?
-8 -0
O x>4
O x<4
O y> 4
O y<4
1
Answer:
it matches with equation c
find x and y
plssss help
90 + 6x = 180
-90
6x = 90
÷6
x = 15
5y + 4y + 90 + (6x15) =360
9y + 90 + 90 = 360
9y + 180 = 360
- 180
9y = 180
÷9
y = 20
Hope this helps!
please help asap
thank you very much
Answer:
x=30 , y=165 & z=10happy to help { bts army girl }Answer:
Step-by-step explanation:
Comment
You must solve x and then y in that order. The reason for that is there are 2 x values and they can be equated to each other. The you can go after the y value, since they are supplement with the value you get from the first operation.
Equations
x + 45 = 2x+ 8
<3 + y + 30 = 180
Solution
<1 and <3 are equal Two vertically opposite angles are always =.
x + 45 = 2x + 8 Subtract x from both sides
x-x + 45 = 2x - x + 8 Combine
45 = x + 8 Subtract 8 from both sides
45 - 8 = x + 8 - 8 Combine
37 = x
<1 + <2 = 180 These two angles sit on the same straight line and have a side in common
x + 45 + y + 30 = 180 Substitute for x
37 + 45 + y + 30 = 180 Combine
112 + y = 180 Subtract 112 from both sides
112-112 + y = 180 - 112 Combine
y = 68
The function f(X) =7^x + 1 is transformed to function g through a horizontal compression by a factor of 1/3
The equation of the function g(x) is g(x) = 7^(3x) + 1
How to determine the function g(x)The function f(x) is given as:
f(x) = 7^x 1
When compressed horizontally by a factor of 1/3.
We have:
g(x) = f(3x)
This implies that:
g(x) = 7^(3x) + 1
Hence, the equation of the function g(x) is g(x) = 7^(3x) + 1
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Match each function with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3x + 5.
Answer: -5=x
Step-by-step explanation:
kmbtvonpvnp4tnv
Which of the following equations is an example of inverse variation between
the variables x and y?
Answer:
we need a whole example not just the variables.
Step-by-step explanation:
where are the two variables is part A? Tiya earns $7 an hour mowing her neighbor's lawn.
Part A: Create two variables and determine which is dependent and which is independent for this situation. (4 points)
The two variables are; earnings, y and hours, x in which case, the former is the dependent variable while the latter is the independent variable.
Which is the dependent and which is the independent variable?It follows from the task content that Tiya earns $7 an hour mowing her neighbor's lawn.
On this note, it follows that the amount of money earned by Tiya is a dependent variable which solely depends on the number of hours spent on the job, which is the independent variable.
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will give brainliest
ax² + bx + c = 0
discriminant = b² - 4ac
----> x² + 7x + 12
---> Discriminant of this equation = 7² - 12.1.4 = 49 - 48 = 1 (Positive discriminant)
x = (-7 + 1)/(2.1) = -6/2 = -3
or
x = (-7 - 1)/(2.1) = -8/2 = -4
Therefore, this equation has two real solutions and has a positive discriminant.
The correct answer is B
if sinA=4/5 solve sin2A, cos2A and tan2A
Step-by-step explanation:
1) if m(∠A)∈[0;90°), then
[tex]cos(A)=\sqrt{1-sin^2A} =\frac{3}{5};[/tex]
[tex]sin2A=2sinAcosA=2*\frac{3}{5} *\frac{4}{5}=\frac{24}{25};[/tex]
[tex]cos2A=cos^2A-sin^2A=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25};[/tex]
[tex]tan2A=\frac{sin2A}{cos2A}=-\frac{\frac{24}{25}}{\frac{7}{25}}=-\frac{24}{7}.[/tex]
2) if m∠A∈[90°;180°), then
cos(A)=-0.6;
sin2A=-0.96;
cos2A=-0.28;
tan2A=-24/7.
The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than an unknown number of inches.
Suppose the area of this rectangle is less than 12 square inches. Which of the following numbers could be the value of the unknown number? Select all that apply.
Answer:
6,4
Step-by-step explanation:
I'm not sure if 4 is correct but 6 definitely is. I hope this helps
Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.
Using the simple interest formula, it is found that the APR for the loan is of 4.472%.
What is the simple interest formula and when it is used?Simple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.The parameters for this problem are:
A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.
We solve the equation for r to find the APR.
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]3067.08 = 3000(1 + 0.5r)[/tex]
[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]
1 + 0.5r = 1.02236
r = (1.02236 - 1)/0.5
r = 0.04472.
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1. Determine the measure of angle B.
B
30
A
64
51
Answer: 51.4°
Step-by-step explanation:
Use law of cosines:
(because you are trying to find angle B, you need to use Cos B)
Cos B = c² + a²-b²/ 2ca
Then, plug in your numbers:
Cos B = 30²+64²-51²/ 2(30)(64)
Simplify:
Cos B = 0.6237
Next, to get rid of Cos B, so that we have just B, you need to do the Arccosine or 0.6237:
B = arccosine (0.6237)
Which gets you: 51.4°
The measure of angle B is 51.41 degrees after applying the cos law of the triangle.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have given a triangle in the figure:
To find the measure of the angle B
We can apply cos law:
c² = a² + b² - 2ab cosB
The a, b, and c represents the side lengths of the triangle and the measures are:
a = 30
b = 64
c = 51
51² = 30² + 64² - 2(30)(64) cosB
3840CosB = 4996 - 2601
3840CosB = 2395
CosB = 2395/3840
CosB = 0.623
B = Cos⁻¹(0.623)
B = 51.41 degrees
Thus, the measure of angle B is 51.41 degrees after applying the cos law of the triangle.
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What is the domain of the rational function f of x is equal to the quantity x squared minus x minus 12 end quantity over the quantity x cubed minus 4 times x squared minus 4 times x plus 16 end quantity question mark
{x ∈ ℝ| x ≠ –2, 2, 4}
{x ∈ ℝ| x ≠ –2, 2}
{x ∈ ℝ| x ≠ –3, 4}
{x ∈ ℝ| x ≠ –3, –2, 2, 4}
The domain of the rational function is:
{x ∈ ℝ| x ≠ –2, 2}
What is the domain of the rational function?
Here we have the rational function:
[tex]f(x) = \frac{x^2 - x - 12}{x^3 - 4x^2 - 4x + 16}[/tex]
We want to get the domain of that function. First, we can rewrite the numerator and denominator as:
[tex]x^2 -x - 12 = (x + 3)*(x - 4)[/tex]
[tex]x^3 - 4x^2 - 4x + 16 = (x - 4)*(x + 2)*(x - 2)[/tex]
Then we can rewrite the rational function as:
[tex]f(x) = \frac{(x + 3)*(x - 4)}{(x - 4)*(x + 2)*(x - 2)}[/tex]
This can be simplified to:
[tex]f(x) = \frac{(x + 3)}{(x + 2)*(x - 2)}[/tex]
Now, the domain will be the set of all real numbers, minus the values of x that generate problems.
In this case, the values:
x = -2 and x = 2 make the denominator to be zero, and we can't divide by zero, so we conclue that the domain is:
{x ∈ ℝ| x ≠ –2, 2}
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Find the area. This is a trapezoid, with bases that measure 5 feet and 10 feet, and a height of 4 feet.
Answer:
A = 30 ft²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases , then
A = [tex]\frac{1}{2}[/tex] × 4 × (5 + 10) = 2 × 15 = 30 ft²
Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).
the expression simplified is:
[tex]12x^3 - 25x^2 + 9[/tex]
How to simplify the given expression?
Here we have the expression:
[tex](4x - 3)*(3x^2 - 4x - 3)[/tex]
We just need to distribute the product, we will get:
[tex](4x - 3)*(3x^2 - 4x - 3)\\\\(4x)*(3x^2 - 4x - 3) - 3*(3x^2 - 4x - 3)\\\\12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9[/tex]
Now we just need to group terms with the same exponent of x:
[tex]12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9\\\\12x^3 + (-16 - 9)x^2 + (-12 + 12)x + 9\\\\12x^3 - 25x^2 + 9[/tex]
That is the expression simplified
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Suppose f′(6)=5 and g′(6)=7.
Find h′(6) where h(x)=4f(x)+5g(x)+1.
The value of the derivative of functions h'(6) as requested in the task content is; 55.
What is the value of h'(6)?Since it follows from the task content that the function h(x)=4f(x)+5g(x)+1.
Hence, the derivative of h(x) can be evaluated as;
h'(x)=4f'(x)+5g'(x)
On this note, by substitution, it follows that;
h'(6)=4(5)+5(7)
h'(6) = 55.
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In science class, the average score on a lab report is 87 points, with all students scoring within 1.8 points of the average. If x represents a student's score, write an equation that represents the
minimum and maximum scores.
The equations which represents the minimum and maximum scores of the students is; x = 87 ± 1.8.
Which equations represents the minimum and maximum possible scores of each student?According to the task content, the
Average score of the students in the science class is; 87 points
All students are within 1.8 points of the average,
it therefore follows from the task content that the
minimum score is;
= 87 -1.8
= 85.2
maximum score is;
= 87+1.8
= 88.8 points.
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Answer:
Step-by-step explanation:
A. |x − 87| = 1.8
-hope this helps.
23 gram put into milligrams
Answer:
Step-by-step explanation: 23000 milligrams
Write the positive or negative number that best
represents the given information.
12 ft above sea level
Answer:
12
Step-by-step explanation:
Usually, above sea level is represented by a positive number and below sea level by a negative number.
12 ft above sea level = 12
Choose the algebraic description that maps the image ΔABC onto ΔA′B′C′.
The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)
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solve this pleas i need urgent answer
Answer:
f(n)={n/2 = if n is even= n={2/2
{3n+1 {3(2)+1 =7
Step-by-step explanation:
if n is even u can put any even no in that place and u can get odd no or even no.(i think)
Find the slope of the line passing through the points (-4, -9) and (5, -9).
The slope of the line passing through the points (-4, -9) and (5, -9) is 0
How to determine the slope?The points are (-4, -9) and (5, -9).
The slope is calculated using:
Slope = (y2 - y1)/(x2 - x1)
So, we have:
Slope = (-9 + 9)/(5 + 4)
Evaluate
Slope = 0
Hence, the slope of the line passing through the points (-4, -9) and (5, -9) is 0
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A company determines that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200), where x is the price of each lamp. At which of the following prices will the company’s revenue be $10,000?
The price that will maximize company’s revenue of $10,000 is $50.
How to calculate the price?From the information, the company determines 50that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200),
Therefore, this will be:
R(x) = -20x² + 1200x
10000 = -20x² + 1200x
-20x² + 1200x - 10000 = 0
x² - 60x + 500
x² - 50x - 10x + 500
x(x - 50) - 10(x - 50)
(x - 50)(x - 10)
Therefore, x - 50 = 0
x = 0 + 50 = 50
The price is 50.
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what is the ration between 28000 and 14?
The ratio between 28,000 and 14 is 2000 : 1
How to determine the ratio?The numbers are given as:
28,000 and 14
Express as ratio
Ratio = 28000 : 14
Divide each number by 14
Ratio = 2000 : 1
Hence, the ratio between 28,000 and 14 is 2000 : 1
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What is the value of x
83
58
50
70.5
Answer:
58
Step-by-step explanation:
[tex]x = \frac{141 - 25}{2} = 58[/tex]
A model house has a scale of 1 in : 2 ft. if the real house is 26 ft wide then how wide is the model house.
Answer: 13 in.
Step-by-step explanation:
All you need to do is divide 26 by 2 in this case.
Which of the following is the largest Y value from the solution set of the giving system round your answer to the nearest hundredth
The largest y-value from the solution set of the nonlinear system is 3.78. (Correct choice: C)
What is the solution of a non-linear system
In this question we have a system of non-linear equation formed by a radical equation and a quadratic equation, which can be solved both analytically and graphically. By equalizing the two formulas we have the following equation:
√(2 · x + 4) = x² - 5 · x + 3
√(2 · x + 4) + 13 / 4 = x² - 2 · (5 / 2) · x + 25 / 4
√(2 · x + 4) + 13 / 4 = (x - 5 / 2) ²
√(2 · x + 4) = (x - 5 / 2) ² - 13 / 4
Then, we square both sides to eliminate the radical sign:
2 · x + 4 = (x - 5 / 2)⁴ - (13 / 2) · (x - 5 / 2)² + 169 / 16
2 · x + 4 = x⁴ + 4 · x³ · (- 5 / 2) + 6 · x² · (- 5 / 2)² + 4 · x · (- 5 / 2)³ + (- 5 / 2)⁴ - (13 / 2) · [x² + 2 · (- 5 / 2) · x + ( - 5 / 2)²] + 169 / 16
2 · x + 4 = x⁴ - 10 · x³ + (75 / 2) · x² - (125 / 2) · x + 625 /16 - (13 / 2) · x² + (65 / 2) · x - 325 / 8 + 169 / 16
2 · x + 4 = x⁴ - 10 · x³ + 31 · x² - 30 · x + 9
x⁴ - 10 · x³ + 31 · x² - 32 · x + 5 = 0
The real roots of this polynomial are:
x₁ ≈ 5.152, x₂ ≈ 2.862, x₃ ≈ 1.797, x₄ ≈ 0.189
Now we evaluate f(x) at each root:
y₁ ≈ 3.782, y₂ ≈ 3.118, y₃ ≈ 2.756, y₄ ≈ 2.092
The largest y-value from the solution set of the nonlinear system is 3.78. (Correct choice: C)
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Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?Answer the questions to show how to write and simplify expressions that represent the problem.
2. Use the distributive property to expand 0.05(50 + 40). (2 points)
Answer:
$4.50
Step-by-step explanation:
We can use the distributive property to solve this problem. 0.05(50+40) is the total sales tax. 0.05 being the percentage and 50 and 40 being the things we need to distribute 0.05 to. This becomes 2.5+2. This is 4.5.
Answer:
$0.45
Step-by-step explanation:
0.05(50 + 40) = 50 x 0.05 + 40 x 0.05 = 0.25 + 0.20 = 0.45