An expression equivalent to (a - b)³ is a³ - 3a²b + 3ab² - b³.
What other expressions are the same as 2 5?The fractions 4/10, 6/15, 8/20, etc. are identical to 2/5. In the reduced form, equivalent fractions have the same value. Explanation: When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number.
One way to expand (a - b)³ is to use the binomial formula:
(a - b)³ = C(3,0) * a³ * (-b)^0 + C(3,1) * a² * (-b) + C(3,2) * a * (-b)² + C(3,3) * a * (-b)³
where C(n,k) denotes the number of ways there are to select k objects from a set of n objects, and "n choose k" is the binomial coefficient.
Simplifying the above expression, we get:
(a-b)³ = a³-3a²b+3ab²-b³.
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The average of 6 numbers is 15. The average decreases by 1 when the 7th
number is added. What is the value of the 7th number?
A. 7 C. 9
B. 8 D. 10
the 7th number is 8. Answer B is correct. The sum of the first 6 numbers can be found by multiplying the average by the number of numbers:
sum of first 6 numbers = 6 x 15 = 90
Let the 7th number be x. Then the sum of all 7 numbers is:
sum of all 7 numbers = sum of first 6 numbers + 7th number = 90 + x
The new average is 1 less than the original average, so:
new average = 15 - 1 = 14
This means that the sum of all 7 numbers divided by 7 is 14:
(sum of all 7 numbers)/7 = 14
Substituting the expression we found for the sum of all 7 numbers, we get:
(90 + x)/7 = 14
Multiplying both sides by 7, we get:
90 + x = 98
Subtracting 90 from both sides, we get:
x = 8
Therefore, the 7th number is 8. Answer B is correct.
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For what values of c does the quadratic equatrion x^2-2x+c=0 have two roots of the same sign
The roots have positive or same signs when c>0.
Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.
[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]
Roots of quadrant equation have Samsame sign if product of roots >0.
[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]
Roots of quadratic equation have positive sign if product of roots<0.
c>0.
Combining results, we get:-
roots have positive signs when:-
c>0.
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find the nth term of this quadratic sequence 4, 7, 12, 19, 28, . ..
Answer:
an = a1 + (n-1)d
Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:
an = 4 + (n-1)3
a5 = 4 + (5-1)3
a5 = 4 + 12
a5 = 16
Jadi, suku ke-5 dari barisan ini adalah 16.
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The graph of the step function G f(x) equals negative [X ]+3 is shown what is the domain of G(x)
The domain of a step function is all real numbers. The equation G(x) = -[x] + 3 can be expressed as G(x) = { -x for x < 0; 3 for x ≥ 0}. The domain of G(x) is all real numbers.
To explain further, a step function can be expressed as two separate equations, one for x < 0 and one for x ≥ 0. The equation for x < 0 is G(x) = -x and the equation for x ≥ 0 is G(x) = 3. The domain of G(x) is all real numbers. This means that any x value, whether it is greater than or less than 0, will be included in the domain of G(x).
How many sides has a polygon if the sum of its
interior angles is 1440⁰
Answer:
10 sides
Step-by-step explanation:
We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:
S = (n - 2) x 180 degrees
If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:
1440 = (n - 2) x 180
Dividing both sides by 180, we get:
8 = n - 2
Adding 2 to both sides, we get:
n = 10
Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.
A company is buying new computers. The company needs no more than 220 desktops and at least 50 laptops. A total of at least 200 computers must be bought. Write a system of linear inequalities to represent the constraints of this situation. Let x represent the number of desktops, and let y represent the number of laptops.
given the following limit lim(x;y)!(0;0) xy x y , show that the function f (x; y) does not have a limit as (x; y) ! (0; 0).
To show that a function does not have a limit as (x, y) approaches (0, 0), we need to examine the limit along different paths .
How can we show that a function does not have a limit as (x, y) approaches (0, 0)?
To show that the function f(x, y) does not have a limit as (x; y) ! (0; 0), we need to examine the limit lim
(x;y)!(0;0) xy x y .
Convert the given limit into a more recognizable form. The given limit is
lim(x, y) -> (0, 0) (xy / (x + y)).
Analyze the limit along different paths. Let's examine the limit along two distinct paths - the
x-axis (y = 0)
and
the y-axis (x = 0).
For the x-axis (y = 0), the limit becomes
lim(x, 0) -> (0, 0) (x * 0 / (x + 0))
= lim(x, 0) -> (0, 0) (0) = 0.
For the y-axis (x = 0), the limit becomes
lim(0, y) -> (0, 0) (0 * y / (0 + y))
= lim(0, y) -> (0, 0) (0) = 0.
Compare the results of the two paths. Both limits along the x-axis and y-axis are equal to 0. However, this is not enough to conclude that the function f(x, y) has a limit as (x; y) ! (0; 0).
Examine another path, such as the line y = x. In this case, the limit becomes
lim(x, x) -> (0, 0) (x * x / (x + x))
= lim(x, x) -> (0, 0) (x^2 / 2x)
= lim(x, x) -> (0, 0) (x / 2)
= 0 / 2 = 0.
Consider another path, like
y = -x.
For this path, the limit becomes
lim(x, -x) -> (0, 0) (x * -x / (x - x))
which is undefined, since the denominator is zero.
Since we have found a path
(y = -x)
where the limit is undefined, we can conclude that the function f(x, y) does not have a limit as (x; y) ! (0; 0).
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15x - 5y = 30. solve for y
(please help!!)
Move all terms that don't contain [tex]y[/tex] to the right side and solve.
Answer:[tex]y=6-3x[/tex]Hi I need help on this question It's teacher conferences week and I want to get this done before this week
Answer:
y = -3/8x + 3
Step-by-step explanation:
The slope intercept form is y = mx + b
Our equation is 3x + 8y = 24
3x + 8y = 24
8y = -3x + 24
y = -3/8x + 3
So, the answer is y = -3/8x + 3
Click to show the supplementary angle of each angle.
26∘
44∘
45∘
136∘
135∘
154∘
The supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
Supplementary Angles of Given AnglesSupplementary angles are pairs of angles that add up to 180 degrees. To find the supplementary angle of each given angle, we simply subtract the angle from 180 degrees.
Therefore, the supplementary angles of the given angles are:
The supplementary angle of 26 degrees is 154 degrees (180 - 26 = 154).The supplementary angle of 44 degrees is 136 degrees (180 - 44 = 136).The supplementary angle of 45 degrees is 135 degrees (180 - 45 = 135).The supplementary angle of 136 degrees is 44 degrees (180 - 136 = 44).The supplementary angle of 135 degrees is 45 degrees (180 - 135 = 45).The supplementary angle of 154 degrees is 26 degrees (180 - 154 = 26).Therefore, the supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
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What is the slope of the line described by the equation below?
y = -6x +3
O A. -6
() в. -з
O C. 6
OD. 3
SUBMIT
6. If g(x) = 7x-4, find g(8)-g (-5)
PLEASE HELP I BEG
Let f be a differentiable function defined by f(x) = 3x + 2e −3x , and let g be a differentiable function with derivative given by g′(x) = 1 x + 4. It is known that lim g(x) = [infinity].
x→[infinity]
The value of lim f(x) g(X) is:______
x→[infinity]
The value of lim f(x)g(x) as x approaches infinity is 0.
L'Hopital's rule is a mathematical tool used to evaluate limits of functions that are in an indeterminate form.
To find the limit of f(x)g(x) as x approaches infinity, we can use L'Hopital's rule since it is an indeterminate form of infinity times zero. We have:
lim x→[infinity] f(x)g(x) = lim x→[infinity] [(3x + 2e^(-3x))(1/x + 4)]
= lim x→[infinity] [(3 + 2e^(-3x)/x)/(1/x + 4)^(-1)]
Applying L'Hopital's rule to the fraction in the numerator, we get:
lim x→[infinity] [(2e^(-3x)(-3)/x^2)/(1/x + 4)^(-1)]
= lim x→[infinity] [(6e^(-3x)/x^2)/(1/x + 4)]
= lim x→[infinity] [(6e^(-3x)/(x + 4x^2))]
= 0
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which type of number property is 28
It is a composite number, its proper divisors being 1, 2, 4, 7, and 14.
The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A. (true or false)
The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.
The above statement is True.
Eigenvalue:
An eigenvalue is a special set of scalar values associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.
According to the Question:
If the geometric multiple of the eigenvalues is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.
Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is
Ax = λx.
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Over 9 days Jaison jogged ----- 10m, 6m, 6m, 7m, 5m, 7m, 5m, 8m, 9m
Find the mean distance Jaison jogged
The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.
To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 7)
From the use of the angle of elevation, the length of ladder is 47 feet.
What is the angle of elevation?The angle between the horizontal and a line of sight or an object above the horizontal, which is commonly stated in degrees or radians, is known as the angle of elevation. Determining an object's position in relation to an observer or a reference point is a common use of trigonometry and geometry.
We know that we have to use the idea of the angle of elevation in this case. We know that;
Cos 65 = 20/x
x is the length of the ladder
x =20/Cos 65
x = 20/0.4225
x = 47 feet
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What is the volume of the prism below?
Answer:30
Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.
Here is a sketch of a curve.
The equation of the curve is y = x² + ax + b
where a and b are integers.
The points (0, -7) and (7, 0) lie on the curve.
Find the coordinates of the turning point of the curve.
Finish your answer by writing, Turning point at (..., ...)
YA
O
+
[tex]{\Large \begin{array}{llll} y=x^2+ax+b \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=-7 \end{cases}\implies -7=0^2+a(0)+b\implies \boxed{-7=b} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=7\\ y=0 \end{cases}\implies 0=7^2+a7+\stackrel{b}{(-7)}\implies 0=49+7a-7 \\\\\\ 0=42+7a\implies -42=7a\implies \cfrac{-42}{7}=a\implies \boxed{-6=a} \\\\\\ ~\hfill {\Large \begin{array}{llll} y=x^2-6x-7 \end{array}}~\hfill[/tex]
now, let's get the "vertex" using the coefficients.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(1)}~~~~ ,~~~~ -7-\cfrac{ (-6)^2}{4(1)}\right) \implies \left( - \cfrac{ -6 }{ 2 }~~,~~-7 - \cfrac{ 36 }{ 4 } \right) \\\\\\ \left( 3 ~~~~ ,~~~~ -7 -9 \right)\implies {\Large \begin{array}{llll} (3~~,~-16) \end{array}}[/tex]
3) One piece of fencing is 71/8 feet long. How long will a fence be that is made up of 9 of these pieces?
Answer:
Step-by-step explanation:
71/8*9 which it 639/8 feet long
22) i) A cuboid has dimensions 60cm x 24cm x 30cm. How many small cubes with side 5cm can be placed in the given cuboid?
Answer:
345.6
Or 345 full cubes
Step-by-step explanation:
To answer this question we first need to find the volume of the cuboid!
To find volume we use the equation...
area of cross-section × heightor l × w × hFor the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...
60 × 24 × 30 = 43200We now need to the the volume of the cube which we can just do by cubing the value given
5³ = 125We now need to divide the two results together to find out how many cubes would fit...
43200 ÷ 125 = 345.6Or 345 full cubesHope this helps, have a lovely day!
a bin can hold 28 pounds. each toy car weighs 7 ounces. how many toy cars can the bin hold? (2 points) 64 toy cars 72 toy cars 88 toy cars 92 toy cars
A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.
How to determine the number of toy carsTo determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.
We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).
Here's how to solve the problem:
1 pound = 16 ounces
Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces
The weight of one toy car is 7 ounces.
Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):
448 ÷ 7 = 64
Therefore, the bin can hold 64 toy cars.
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If x = 14 units and h = 5 units, then what is the area of the triangle shown above?
Answer:
b: 70
Step-by-step explanation:
10 times 5 is 50 and 4 times 5 is 20. 50 plus 20 is 70
The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. What
is the probability of event B?
Enter a number to the nearest hundredth in the box.
The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. The probability of event B is 0.68.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probabilities of two complementary events A and B - either A occurring or B occurring - add up to 1.
Given that:
P(A) =0.65
P(A∩B) = 0.33
And event A and B are independent.
Using the probability formula:
P(B) = 1 - P(A) + P(A∩B)
⇒ P(B) = 1 - 0.65 + 0.33
⇒ P(B) = 0.68
Therefore , the probability of event B is 0.68.
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pls help find y. 4x+5y-y+3x
Answer:
7x+4y
Step-by-step explanation:
combine like terms
Answer:
4?
Step-by-step explanation:
solve for x.Figures are not necessarily drawn to scale
-1/2 (6- 8x to the power of 2)
(The 8x is to the power of 2)
Answer:
-3+[tex]4x^{2}[/tex]
Step-by-step explanation:
the sides of a triangle have lengths 15, 20, 25. find the length of the shortest altitude of the triangles.
The length of the shortest altitude of the triangles is 15 units by using Heron’s formula.
We have, The sides of a triangle have lengths of 15, 20, and 25.
To find, The length of the shortest altitude of the triangle.
Steps to solve the problem:
Let us assume that the length of the b is h.According to the property of triangles, the area of the triangle can be calculated as:Area = 1/2 * base * height
We can choose any side as the base of the triangle, let us assume that 20 is the base of the triangle, and its corresponding height is h.Area of the triangle = 1/2 * 20 * h ⇒ 10h
Using Heron’s formula, the area of the triangle can be calculated as:A = √(s(s-a)(s-b)(s-c))
Where a, b, and c are the sides of the triangle, and s is the semi-perimeter of the triangle.
According to the given problem, the sides of the triangle are 15, 20, and 25.
s = (a + b + c)/2
= (15 + 20 + 25)/2
= 30
Therefore, the area of the triangle can be calculated as:
A = √(30(30-15)(30-20)(30-25))
= √(30*15*10*5)
= 150 sq. units
Therefore, we can write the formula for the area of the triangle as:
150 = 10 h
h = 15 units
Therefore, the length of the shortest altitude of the triangle is 15 units.
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what is the answer to 1.4(x+5) +1.6x=52
Answer: x = 15
Step-by-step explanation:
Expand 1.4(x+5): 1.4x+7+1.6x = 52
Combine like terms: 3x+7 = 52
Subtract 7 from both sides: 3x = 45
Divide both sides by 3: x = 15
Answer:
The answer is x=15
Please give me Brainliest :)
1. Expand the expression
1.4x+7+1.6x=52
2. Simplify
3x+7=52
3. Separate the constants and variables
3x=52−7
4. Add or subtract numbers
3x=45
5. Divide both sides by 3
6. Simplify
x=15
A statue casts a shadow that is 16 feet long. A nearby maple tree casts a shadow that is 10 feet long. If the statue is 20 feet tall, how tall is the maple tree, to the nearest tenth of a foot?
We can solve this problem by using proportions. 20/16 = x/10 => x = 12.5 Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.
what is proportions ?
proportions are statements that two ratios or fractions are equal. A ratio is a comparison of two quantities, typically expressed as the quotient of one quantity divided by the other. For example, if we have 5 apples and 3 oranges, the ratio of apples to oranges is 5/3.
what is height ?
Height typically refers to the measurement of how tall or high something is, usually from its base to its top. In geometry, height is often used to refer to the perpendicular distance
In the given question ,
Let x be the height of the maple tree in feet. Then we have:
(height of statue) / (length of statue's shadow) = (height of maple tree) / (length of maple tree's shadow)
Substituting the given values, we get:
20/16 = x/10
on solving this equation, we can cross-multiply to get:
16x = 200 => x = 12.5
Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.
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