Answers
On solving the provided question we can say that As a result, the matrix following provides a foundation for V': { [1, 1, 0] }
what is matrix ?A matrix is a collection of numbers that are organised in rows and columns. Learns about matrix elements and dimensions and introduces them for the first time. A matrix is a rectangular grid of numbers in rows and columns. Matrix A, for example, has two rows and three columns. Its name is derived from its single row and 1 n row matrix order. For example, A = [1 2 4 5] is a row matrix of order 1 by 4. Another example of a row matrix is P = [-4 -21 -17] of order 1-by-cubic.
To identify a basis for the R3 subspace V' spanned by the vector v = [1, 1, 0], we must first determine a set of linearly independent vectors that span V'.
One option is to row-reduce the augmented matrix [v|0] using the Gaussian elimination method, where 0 is the zero vector in R3.
[1 1 0 | 0]
[1 1 0 | 0]
[0 0 0 | 0]
This demonstrates that the vector v = [1, 1, 0] spans an R3 one-dimensional subspace, implying that any nonzero scalar multiple of v is also in V'.
As a result, a basis for V' is the set v, which consists solely of the vector v itself.
As a result, the following provides a foundation for V':
{ [1, 1, 0] }
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Related Questions
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The three true statements are
A) The radius of the circle is 3 unitsB) The center of the circle lies on the x-axisE) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.EXPLANATION :To see why A) is true, we can rearrange the equation to get it in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Completing the square, we have x² - 2x + y² - 8 = 0, which can be rewritten as (x - 1)² - 1 + y² - 8 = 0. Rearranging again, we get (x - 1)² + y² = 9, which is the equation of a circle with center (1, 0) and radius 3.To see why B) is true, note that the x-coordinate of the center of the circle is given by x = 1, so it lies on the x-axis.To see why E) is true, note that the equation x² + y² = 9 is the equation of a circle with center (0, 0) and radius 3. We can rewrite the equation of the given circle as (x - 1)² + y² = 9, which is the equation of a circle with the same radius and a center shifted to (1, 0).Step-by-step explanation:
Standard form for a circle is ( x -h)^2 + ( y-k)^2 = r^2
h, k is the center r is the radius
x^2 -2x + y^2 = 8 arrange into standard form ( complete the square for 'x')
(x-1)^2 + y^2 = 8+1
(x-1)^2 + y^2 = 9 shows center is at 1, 0
radius = 3
So
The radius of the circle is 3 units.
The center of the circle lies on the x-axis (1,0 is on the x axis)
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Which expressions are equivalent to the one below? Check all that apply. 21^x/3^x
Answers
The only equivalent expression is option (a) [tex]7^x[/tex].
What is expression ?
An expression in mathematics is a group of symbols that represent a statistical correlation or quantity, such as integers, variables, and operators. It may contain exponents, logarithms, and trigonometric functions in addition to mathematical operations like addition, multiplication, multiplication, and division. It may also contain constants, variables, and functions. Expressions can be used in a variety of subjects, including mathematics, calculus, geometry, and statistics, to represent mathematical models, resolve equations, and carry out calculations.
To find equivalent expressions for[tex]21^x/3^x[/tex], we can try to simplify the expression using exponent rules.
21 can be factored as 7*3, so we can write:
[tex]21^x/3^x = (7 × 3)^x/3^x = 7^x × 3^x/3^x = 7^x[/tex]
Therefore, we can see that option (a) 7^x is equivalent to the given expression.
To check the other options:
b) [tex](7/3)^x[/tex] = [tex](7^x)/(3^x)[/tex] which is not equivalent to the given expression.
c) [tex]3^(2x+1)[/tex] can be written as [tex]3^(2x)[/tex] × [tex]3^1[/tex] = [tex](3^2)^x[/tex] × 3 = [tex]9^x[/tex] × 3 which is not equivalent to the given expression.
d) [tex]7^(x-1)[/tex] can be written as [tex]7^x/7[/tex] which is not equivalent to the given expression.
e) [tex](3/7)^x[/tex] is not equivalent to the given expression.
Therefore, the only equivalent expression is option (a) [tex]7^x[/tex].
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The complete question is:
Which expressions are equivalent to [tex]21^x/3^x[/tex]? Check all that apply.
a) [tex]7^x[/tex]
b) [tex](7/3)^x[/tex]
c) [tex]3^(2x+1)[/tex]
d) [tex]7^(x-1)[/tex]
e) [tex](3/7)^x[/tex]
-(x+5)³ + 2 = 1
im supposed to be solving cubic equations but im stuck plez help
Answers
Answer: X= -4
Step-by-step explanation:
PLEASE HELP!! A cylinder has a volume of 128 cubic centimeters and a height of 6 centimeters. What is the volume of a similar cylinder with a height of 9 centimeters?
Answers
The volume of cylinder is 191 cubic centimeters.
What is volume?
The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.
Here cylinder with height 6 cm ,
Volume = 128 cubic centimeters.
Now using volume of cylinder formula then,
=> Volume V =
=> 128 = 3.14**6
=> = = 6.79406
=> r = 2.6 cm.
Now volume of cylinder with height 9 cm is ,
=> Volume V = 3.14**9 = 191 cubic centimeters.
Hence the volume of cylinder is 191 cubic centimeters.
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Dave buys a basketball for 15$ plus 8% tax, James buys a football for 20$ plus a 8% tax, enter the difference in the dave and James paid including tax.
Answers
Answer: $5.40
Step-by-step explanation:
First, let's calculate the tax for each purchase and then find the total amount paid by Dave and James.
For Dave:
Basketball cost = $15
Tax = 8% of $15 = 0.08 * 15 = $1.20
Total amount paid by Dave = Cost + Tax = $15 + $1.20 = $16.20
For James:
Football cost = $20
Tax = 8% of $20 = 0.08 * 20 = $1.60
Total amount paid by James = Cost + Tax = $20 + $1.60 = $21.60
Now, let's find the difference between the amounts paid by Dave and James.
Difference = Amount paid by James - Amount paid by Dave = $21.60 - $16.20 = $5.40
So, the difference in the amounts paid by Dave and James, including tax, is $5.40.
In X8, Erin had the following capital gains (losses) from the sale of her investments: $2,600 LTCG, $24,400 STCG, ($9,600) LTCL, and ($15,600) STCL. What is the amount and nature of Erin's capital gains and losses?
Answers
Erin's capital gains are the sum of her long-term capital gains (LTCG) and short-term capital gains (STCG), which is $2,600 + $24,400 = $27,000.
Erin's capital losses are the sum of her long-term capital losses (LTCL) and short-term capital losses (STCL), which is ($9,600) + ($15,600) = ($25,200).
Since Erin's capital gains exceed her capital losses, she has a net capital gain of $27,000 - $25,200 = $1,800.
The nature of Erin's capital gains and losses are as follows:
LTCG: long-term capital gain, meaning the asset was held for more than one year before it was sold.STCG: short-term capital gain, meaning the asset was held for one year or less before it was sold.LTCL: long-term capital loss, meaning the asset was held for more than one year before it was sold.STCL: short-term capital loss, meaning the asset was held for one year or less before it was sold.PLEASEE HELPP I gotta do my missing assignments tn!! (And pls explain)
Answers
Answer:
29°
Step-by-step explanation:
In the first triangle,
46 + 30 + x = 180 (Angle sum property)
76 + x = 180
x = 180 - 76
x = 104
In the second triangle,
47 + 104 + y = 180
151 + y = 180
y = 29
Thus, the required angle is 29°.
Pls like and mark as brainliest!
Answer:
the answer is 29 degrees
Step-by-step explanation:
look at the picture below
Can someone pls help me solve this!! Will give brainliest!!
if I said that angle 1 in the diagram below was 122 degrees, how can the angle relationships be used to determine the rest of the angle measures. Include how you can use these angle relationships to prove that lines are parallel.
(add any theorems you would use)
Answers
Hello!
1= 122
2= 58
3= 58
4= 122
5= 122
6= 58
7= 58
8= 122
To find angle 2, you subtract 122 from 180 because angles 1 and 2 are supplementary angles. You can find angle 3 by using the vertical angles theorem. This means that angle 2 and 3 are congruent to each other. You can use the same for angle 4, meaning 1 and 4 are also congruent. You can use the alternate interior angles theorem to prove that 3 and 6 are congruent and then use the vertical angles theorem to prove that 6 and 7 are congruent. You can find angles 5 and 8 by proving that 5 is congruent to 4 using the alternate interior angles theorem and then once again using the vertical angles theorem to prove that angle 5 is congruent to angle 8. Let me know if this is too hard to understand, I will happily simplify it.
Find the expression for both A: (x+4) (2x - 1)
Answers
Answer:
2x^2+8x-4
Step-by-step explanation:
Fwam is going to invest in an account paying an interest rate of 5.9% compounded
daily. How much would Fwam need to invest, to the nearest hundred dollars, for the
value of the account to reach $91,000 in 12 years?
Answers
In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.
what is interest ?In exchange for using borrowed funds or assets, a borrower must pay the lender interest. It is charged for a certain duration of time, typically until the loan is fully returned, and is typically stated as a percentage of the amount borrowed. This fee is known as the interest rate. For instance, if a bank lends you $1,000 at a 5% annual interest rate, after a year of borrowing the money you would still owe the bank $50 more in interest. The creditworthiness of the borrower, the risk of the loan, and current market conditions are frequently used to establish the interest rate.
given
We know that Fwam expects the account to be worth $91,000 in 12 years and that the interest rate is 5.9% compounded daily in this situation.
We must convert the interest rate and the time period to the proper units before we can use the formula.
We begin by converting the 5.9% yearly interest rate to a daily rate:
daily rate is equal to (1 + 0.059/365)(365/365)-(1-1) = 0.00015999.
4,380 days in 12 years, or 365 days per year.
We can now enter the values into the formula to find P:
$91,000 = P × 2.3226
P = $39,165.95
In order for the account value to reach $91,000 in 12 years, Fwam would therefore need to invest $39,165.95, to the closest hundred dollars, assuming the interest rate is 5.9% compounded daily.
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Simplify the expression.
three tenths squared minus 17 plus the quantity negative 7 divided by the absolute value of 4.3 minus 7.8 end quantity times 2.67
−11.57
−11.60
−21.74
−22.25
I picked b please tell me why i am wrong
Answers
Answer:
D. -22.25
Step-by-step explanation:
First, we need to simplify the expression inside the parentheses
|-3.5| = 3.5
Next, we can simplify the expression inside the parentheses:
-7 ÷ |-3.5| = -2
Now we can simplify the entire expression:
3/10^2 - 17 + (-2) x 2.67 = 0.09 - 17 - 5.34 = -22.25
Which of these statements describe properties of parallelograms? Check all
that apply.
A. Consecutive angles are supplementary.
B. Opposite sides are parallel.
• C. Opposite angles are congruent.
D. Opposite angles are parallel.
E. Opposite sides are congruent.
• F. Diagonals perpendicularly bisect each other.
Answers
Answer:
The correct answers for this question are:
A. Diagonals bisect each other.
C. Opposite angles are congruent.
D. Opposite sides are parallel.
E. Consecutive angles are supplementary. Those are the statements that describe properties of parallelograms. They are also belong to the family of quadrilateral.
Step-by-step explanation:
Alexa claims she can use counting
by 8 to find the fifth multiple of. Is Alexa correct? Explain.
Answers
Answer:
Yes, Alexa is correct.
Step-by-step explanation:
Counting by 8 means adding 8 repeatedly. The first multiple of 8 is 8 (1 x 8), the second multiple is 16 (2 x 8), the third multiple is 24 (3 x 8), the fourth multiple is 32 (4 x 8), and the fifth multiple is 40 (5 x 8). So, by counting by 8 five times, Alexa can find the fifth multiple of 8 which is 40.
Paul hits a baseball straight up in the air. The baseball is hit with an initial velocity of 70 ft/s when it is 3.5 ft off the ground. What quadratic function mods the height h of the ball after t seconds in flight?
Answers
The quadratic function that models the height h of the ball after t seconds in flight is h(t) = -16t² + 70t + 3.5
Describe Quadratic Function?A quadratic function is a type of function in algebra that involves a variable raised to the power of 2, or squared. The general form of a quadratic function is:
f(x) = ax² + bx + c
where f(x) represents the output of the function for a given input x, a, b, and c are constants that determine the shape and position of the function, and x is the input variable.
The graph of a quadratic function is a parabola, which is a curved shape that opens upwards if the coefficient a is positive, and downwards if the coefficient a is negative. The vertex of the parabola is the point at which the function reaches its minimum or maximum value, depending on the direction of the opening of the parabola. The x-coordinate of the vertex is given by:
x = -b/2a
The height h of the ball after t seconds in flight can be modeled by the quadratic function:
h(t) = -16t² + vt + s
where v is the initial velocity of the ball, s is the initial height of the ball, and -16 is the acceleration due to gravity in feet per second squared.
In this case, we know that the ball is hit with an initial velocity of 70 ft/s and is 3.5 ft off the ground, so we can substitute these values into the equation:
h(t) = -16t² + 70t + 3.5
Therefore, the quadratic function that models the height h of the ball after t seconds in flight is:
h(t) = -16t² + 70t + 3.5
Note that this function is only valid until the ball reaches its maximum height and starts falling back down to the ground.
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please solve this fast
Answers
Answer:
34
Step-by-step explanation:
5+5+2=12
12+6+3=21
21+8+5=34
Answer:45
Step-by-step explanation:
5+5(8)=45
A TV cable company has 2400 subscribers who are each paying $16 per month. It can get 120 more subscribers for each $0.50 decrease in the monthly fee. What rate will yield maximum revenue, and what will this revenue be?
Answers
If TV cable company has 2400 subscribers who are each paying $16 per month, charging $52 per month will yield a maximum revenue of $98,304.
To find the rate that will yield the maximum revenue, we can use the formula:
r = -b / 2a
where r is the rate, a is the coefficient of the quadratic term, and b is the coefficient of the linear term in the revenue equation.
The revenue equation is:
R = (2400 + 120x)(16 - 0.5x)
Expanding and simplifying, we get:
R = -0.5x^2 + 52x + 38400
So, a = -0.5 and b = 52. Plugging these values into the formula, we get:
r = -52 / 2(-0.5) = 52
This means that the company should charge $52 per month to maximize revenue. To find the maximum revenue, we can plug this value into the revenue equation:
R = (2400 + 120(52))(16 - 0.5(52)) = $98,304
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Write an equation or proportion. Define the variable/s.
Solve and label the answer/s. Three consecutive odd integers
are such that twice the smallest number is 45 less than the sum
of the middle number and twice the largest number. What are
the numbers
Answers
The lowest odd integer is [tex]35[/tex] followed by the next two odd integers in a row,[tex]37[/tex] and [tex]39[/tex] Thus, these are three consecutive odd integers.
What are integers?Numbers that can be positive, negative, or zero but are not fractions are said to be integers. All mathematical operations, such as addition, subtraction, multiplication, and division, can be performed on integers. There are integer occurrences of [tex]1, 2, 5, 8, -9[/tex], and so on. [tex]Z[/tex] represents a number.
The variable for the lowest odd integer should be defined first. Assume that [tex]x[/tex] is the lowest odd number.
Since there is always a [tex]2[/tex] difference between two successive odd integers, the following two would be [tex]x+2[/tex] and [tex]x + 4[/tex]
The problem statement states that twice the smallest number [tex](2x)[/tex] is [tex]45[/tex]less than the total of twice the largest number [tex]2(x+4)[/tex] and twice the middle number [tex](x+2).[/tex]
[tex]2x = (x+2) + 2 (x+4) ) - 45[/tex]
When we simplify and find x, we obtain:
[tex]2x = x + 2 + 4x + 8 - 45[/tex]
[tex]2x = 3x - 35[/tex]
[tex]x = 35[/tex]
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A multiple-choice test question has six possible choices.
a) If you randomly select one of the choices, what is the probability that you select the correct choice?
b) If you randomly select one of the choices, what is the probability that you select an incorrect choice?
c) If you can eliminate three of the six choices and randomly select one of the remaining choices, what is th
probability that you select the correct choice?
d) If you can eliminate three of the six choices and randomly select one of the remaining choices, what is the
probability that you select an incorrect choice?
a) P(correct) =
b) P(incorrect)
113
(Type an integer or a simplified fraction.)
6
-
(Type an integer or a simplified fraction.)
5
Answers
The probabilities that select an incorrect choice are
a) P(correct) = 1/6 b) P(incorrect) = 5/6 c) P(correct) = 1/3 d) P(incorrect) = 2/3.
What is probability?
Probability is a measure of the likelihood or chance that a particular event will occur. It is a way of quantifying uncertainty, and is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain.
What are events in probability?
In probability, an event refers to an outcome or a set of outcomes of a random experiment or a process. A random experiment is an experiment or a process that has multiple possible outcomes, and the outcome of the experiment is uncertain or unpredictable.
According to given information:a) The probability of selecting the correct choice from six possible choices is 1 out of 6, or 1/6, since there is only one correct answer among the six options.
b) The probability of selecting an incorrect choice from six possible choices is 5 out of 6, or 5/6, since there are five incorrect answers among the six options.
c) If three choices can be eliminated, then there are only three options left, with one correct answer among them. Therefore, the probability of selecting the correct choice from the remaining options is 1 out of 3, or 1/3.
d) Similarly, if three choices can be eliminated, then there are three options left, with two incorrect answers among them. Therefore, the probability of selecting an incorrect choice from the remaining options is 2 out of 3, or 2/3.
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why am i wasting my time in school?
Answers
Answer:
Because you are spending your time doing other things
Step-by-step explanation:
most of the time people waste time in school because they are busy doing other things and they probably don't think school is important.
a way to stop wasting time in school is to pay attention more in class and start developing a desire to learn.
:) i hope this helps lol
Answer:
For more opportunities to go to college, graduating college gets you a degree, the better degree the better job opportunities, the better job opportunities the more money earned. Your in school for money, the best end goal.
127.6÷10 to the power of 5
im not sure if that is how you type it
Answers
Answer:
338262.124
Step-by-step explanation:
127.6/10 = 12.76 (depending on how many zero is how much you'll move the decimal to the left)
12.76^5 = 338262.124 because it's 12.76x12.76x12.76x12.76x12.76
(Need help please and thank you!) :)
Answers
Step-by-step explanation:
In order to find the f(x) or y value, you have to replace x with the given one in the table:
x = -1,
[tex]y = \sqrt[3]{ - 1 - 7} = \sqrt[3]{ - 8} = - 2[/tex]
.
x = 6,
[tex]y = \sqrt[3]{ 6 - 7} = \sqrt[3]{ - 1} = - 1[/tex]
.
x = 7,
[tex]y = \sqrt[3]{7 - 7} = \sqrt[3]{0} = 0 [/tex]
.
x = 8,
[tex]y = \sqrt[3]{8 - 7} = \sqrt[3]{1} = 1 [/tex]
.
x = 15,
[tex]y = \sqrt[3]{15 - 7} = \sqrt[3]{8} = 2[/tex]
Also, the correct graph is in the 2nd photo, where the root is (7; 0)
A dividend of 24 cent per share is paid on OIL search shares with a market value of $3.25 and a face value of $1.60. The percentage yield is
Answers
Answer:
7.38%
Step-by-step explanation:
Which inequality is equivalent to
4x - 2y ≤ 8?
A. y ≤ 2r-4
B. y ≥ 2r-4
C. y ≤-2r-4
D. y ≥-2r-4
Answers
Answer:
B: y ≥ 2r-4.
Step-by-step explanation:
To solve for y, we need to isolate y on one side of the inequality. First, we can simplify the left side of the inequality by dividing both sides by 2:
2x - y ≤ 4
Then, we can subtract 2x from both sides to get:
-y ≤ -2x + 4
Finally, we need to isolate y by multiplying both sides by -1 and flipping the direction of the inequality:
y ≥ 2x - 4
Now we can see that the equivalent inequality is option B: y ≥ 2r-4.
what is the answer to 4n – 3?
Answers
Step-by-step explanation:
4n - 3 = 0
4n = 0 + 3
4n = 3
[tex]n \: = \frac{3}{4} [/tex]
A phone company offers two monthly plans. Plan A costs $23 plus an additional $0.12 for each minute of calls. Plan B costs $14 plus an additional $0.16 for each minute of calls.
Answers
Calculate the surface area of this right triangular prism.
Answers
Total surface area of right triangular prism is 750cm²
Define the term right triangular prism?A right triangular prism is a three-dimensional geometric shape with three rectangular faces connecting the edges of its two parallel, congruent triangular bases.
Area of the two opposite side triangles (A₁) = 2 × ( [tex]\frac{1}{2}[/tex] × 12 × 5)
Area of the two opposite side triangles (A₁) = 60 cm²
Area of upper, lower and side rectangles (A₂) = (5×23) + (12×23) + (13×23)
Area of upper, lower and side rectangles (A₂) = 115 + 276 + 299
Area of upper, lower and side rectangles (A₂) = 690 cm²
Total surface area of right triangular prism = A₁ + A₂
Total surface area of right triangular prism = 60 + 690
Total surface area of right triangular prism = 750 cm²
Therefore, the total area of the right triangular prism is 750cm²
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A rainwater system is structured as shown. The radii are the same for both rain barrels. The shorter rain barrel has a height equal to its radius. The taller rain barrel has a height twice its radius. The total surface area for both barrels with no top is about 40,212 square centimeters.
Photograph of a rainwater system with two rain barrels placed next to each other. One barrel is higher than the other one, and water flows from higher barrel to lower barrel.
How is the surface area calculated and what is the radius?
Each rain barrel is modeled by a
.
The radius of the rain barrels is approximately
centimeters.
Answers
The radius οf the rain barrels is apprοximately 40.03 cm.
What is square rοοt?A value knοwn as the square rοοt οf a number is οne that, when multiplied by itself, yields the οriginal number. An alternative tο square rοοting a number is tο use it. Therefοre, the cοncepts οf squares and square rοοts are cοnnected. The οriginal number is equal tο the square rοοt οf any integer, which is equivalent tο a number.
The tοtal surface area is given as 40,212 square centimeters. Therefοre, we can write the equatiοn:
[tex]2\pi r^2 +\pir^2 + 4\pi r^2 + \pi r^2 = 40212[/tex]
Simplifying this equatiοn, we get:
[tex]8\pi r^2 = 40212[/tex]
Dividing bοth sides by 8π, we get:
[tex]r^2 = 1602.62[/tex]
Taking the square rοοt οf bοth sides, we get:
r ≈ 40.03 cm
Therefοre, the radius οf the rain barrels is apprοximately 40.03 cm.
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Help with math problems
Answers
The expansion of the multiplication is [tex]-16+12\sqrt{3}[/tex] and [tex]5-13\sqrt{5}[/tex]
What is irrational numbers?Irrational numbers are real numbers that cannot be represented as simple fractions. If N is irrational, it is not equal to p/q, where p and q are integers and q is not equal to zero. [tex]\sqrt{2}, \sqrt{3}[/tex] are two examples.
distributive law
This property states that multiplying the total of two or more addends by a number produces the same result as multiplying each addend separately by the number and then putting the products together.
That is A(B+C)=AB+AC
According to the given information:
[tex](-2\sqrt{3} +2)(\sqrt{3}-5) = -2\sqrt{3}*\sqrt{3} + 10\sqrt{3} +2\sqrt{3} -10[/tex]
=[tex]-6+12\sqrt{3}-10[/tex]
= [tex]-16+12\sqrt{3}[/tex]
[tex](-2-3\sqrt{5})(5-\sqrt{5}) = -10+2\sqrt{5}-15\sqrt{5}+3*5[/tex]
= [tex]-10-13\sqrt{5}+15[/tex]
=[tex]5-13\sqrt{5}[/tex]
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I need help please
(In picture)
Answers
The two forms of the expression
[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]
when simplified are
[tex] = {x}^{ - 5} [/tex]
x exponents negative 5 and
[tex]\frac{1}{ {x}^{5} } [/tex]
numerator 1 over denominator x exponents 5.
What are the two forms of simplified expression?Given:
[tex] \frac{ {x}^{5} }{ {x}^{10} } [/tex]
When we have the same base but different powers in indices division, one of the bases is chosen and the powers are subtracted.
[tex] = {x}^{5 - 10} [/tex]
[tex] = {x}^{ - 5} [/tex]
[tex] = \frac{1}{ {x}^{5} } [/tex]
Therefore, the simplified expressions are x exponents negative 5 and numerator 1 over denominator x exponents 5.
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Alg 2 writing equations in vertex form
Answers
The vertex is (4,1), and the parabola opens b since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.
What is parabola?A parabola is a symmetrical U-shaped curve that can be formed by intersecting a cone with a plane parallel to one of its sides. It is a type of quadratic function, which can be expressed in the form of y = ax^2 + bx + c, where "a" is the coefficient of the squared term, "b" is the coefficient of the linear term, and "c" is the constant term.
f(x) = x²+8x-3
To complete the square, we need to add and subtract the square of half the coefficient of x:
f(x) = (x²+8x+16) - 19 --> (x+4)² - 19
So, the equation in vertex form is: f(x) = (x+4)² - 19.
The vertex is (-4,-19), and the parabola opens upwards since the coefficient of the squared term is positive. The axis of symmetry is x=-4, and the domain is all real numbers. The range is [-19, ∞), since the minimum value is -19.
f(x)=-2x² + 16x-31
To complete the square, we need to factor out the leading coefficient of -2, and then add and subtract the square of half the coefficient of x:
f(x) = -2(x² - 8x + 16) - 31 + 32 --> -2(x-4)² + 1
So, the equation in vertex form is: f(x) = -2(x-4)² + 1.
The vertex is (4,1), and the parabola opens downwards since the coefficient of the squared term is negative. The axis of symmetry is x=4, and the domain is all real numbers. The range is (-∞, 1], since the maximum value is 1.
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