To prove the given statement we can take into account the matrix produced by the tuples (1,2,0), (1,0,1) and (1,0,1). The three vectors are linearly independent if the matrix's where determinant is nonzero.
det ( -1 2 0
-1 0 1
1 0 1 ) = 4
Now that P2 has a dimension of 3, those three vectors serve as the foundation for P2 by definition.
Therefore, the polynomial forms the basis of P.
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.
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Complete the ratio 4:16 = 1:?
Answer:
1:4
Step-by-step explanation:
4:16 = 1:?
4/4 = 1
16/4 = 4
= 1:4
50 minus 2.5 x greater-than-or-equal-to 20. Negative 2.5 x greater-than-or-equal-to negative 30. x greater-than-or-equal-to 12.
Negative 2.5 x greater-than-or-equal-to negative 30 is the equivalent expression of 50 minus 2.5 x greater than or equal to 20
How to find an equivalent expression?Equivalent expressions can be defined as expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will give you the same value when you simplify
Given: 50 minus 2.5 x greater than or equal to 20
50 - 2.5x ≥ 20
Subtract 50 from both sides:
-2.5x ≥ 20-50
-2.5x ≥ -30
Therefore, the equivalent expression is "negative 2.5 x greater-than-or-equal-to negative 30"
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Identify the terms coefficients and constant 6m + 8+4+3m
Answer:
Below
Step-by-step explanation:
6m + 8+4+3m <==== 6 and 3 are coefficients 8 and 4 are constants
9m + 12 <===== 9 is a coefficient 12 is a constant
Answer:
The coefficients are 6 and 3
The constants are 8 and 4
Step-by-step explanation:
coefficients are the numbers before the letters.
Constants do not have letters.
4 2/3 - 3 3/8 + 4 3/5
Answer:
18.475?
Step-by-step explanation:
Five consecutive numbers add up to a total of 35. What is the highest of these numbers
A. 6
B. 7
C. 8
D. 9
E. 10
Answer:
9
Step-by-step explanation:
5,6,7,8,9
The following are rules for repeating patterns. For which rule will the 12th shape be a circle?
A.
triangle, circle, square
B.
circle, square
C.
rectangle, circle
D.
circle, circle, triangle
Answer:
A Square
B Square
C Circle
D Triangle
A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?
If BD bisects AC and AC bisects BD, is AABE^ ACDE? Explain.
Yes; the triangles are congruent by SSS.
Yes; the triangles are congruent by ASA.
Yes; the triangles are congruent by SAS
NO; the triangles are not congruent.
Yes; the triangles are congruent by SAS.
What is triangle ?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.
AC and BD bisects one another
AE = CE --- Side
and
BE = DE --- Side
When both lines bisect one another, they form a pair of vertical angles and
When we apply the theorem of vertical angles to this, we have that:
∠AEB = ∠CED --- Angle
At this point, we have established:
Two sides of ABE and CDE are congruent and One angle in each of ABE and CDE are also congruent
Hence, the triangles are congruent by SAS.
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A bag contains five white balls and three black balls. Your goal is to draw two white balls.
(a) You simultaneously draw two balls at random. What is the probability that they are both white?
(b) You simultaneously draw two balls at random. Once you have drawn two balls, you put back any black balls, and redraw so that you again have two drawn balls. What is the probability that you now have two white balls? (Include the probability that you chose two white balls on the first draw.)
The probability is the first and the second case will be 0.625 and 0.3683, respectively.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A pack contains five white balls and three torpedoes. You want to draw two white balls.
Total events = 5 + 3
Total events = 8
You all the while drawing two balls aimlessly. Then the probability that they are both white is given as,
P = 5 / 8
P = 0.625
You all the while drawing two balls aimlessly. Whenever you have drawn two balls, you set back any debases, and redraw with the goal that you again have two drawn balls. Then the probability is given as,
P = [(3/8) x (5/8)] + [(3/8) x (5/8) x (4/7)]
P = (15 / 64) + (60 / 448)
P = 0.3683
The probability is the first and the second case will be 0.625 and 0.3683, respectively.
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If you make $31.65 in 8 hours, how much in total?
Answer:
$253.20
Step-by-step explanation:
Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) squareroot of (9 + 49^x2) dx
The indefinite integral of given integral ∫√(9+49x^2)dx is ∫√(9+49x^2)dx = [tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex].
In the given question we have to find the indefinite integral.
The given integral is
∫√(9+49x^2)dx
Now finding the indefinite integral using the C for the constant of integration.
An integral is regarded to be indefinite if it has no lower or upper bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C.
We can write it as:
[tex]\int\sqrt{(9+49x^2)}dx = \int\sqrt{[(3)^2+(7x)^2]}dx[/tex]
Taking common 7^2
[tex]\int\sqrt{(9+49x^2)}dx = 7\int\sqrt{[(3/7)^2+(x)^2]}dx[/tex]
Using the formula
[tex]\int\sqrt{(a^2+x^2)}dx = \frac{1}{2}\times\sqrt{a^2+x^2} + \frac{1}{2}\cdot a^2In|x+\sqrt{a^2+x^2}|+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{(3/7)^2+x^2}+\frac{1}{2}\cdot(\frac{3}{7})^2In|x+\sqrt{(3/7)^2+x^2}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{9/49+x^2}+1/2\cdot(9/49)In|x+\sqrt{(9/49)+x^2}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+1/2\cdot(9/49)In|x+\frac{\sqrt{9+49x^2}}{7}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+(9/98)In|\frac{7x+\sqrt{9+49x^2}}{7}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex]
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14. A zip wire is shown as the dashed line AC in the diagram.
The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.
CD=2.6 BD=12
The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5⁰.
Work out the least possible height of the post $A B$ Give your answer correct to 3 significant figures.
The least possible height of AB is 3.650 m.
What is a word problem?
A word problem is described as a few phrases outlining a "real-life" situation where a problem needs to be solved using mathematics.
For everything from counting pennies to calculating a tip, we can employ the three primary sorts of word problems: part-part whole, separate and join, and multiply and divide.
Given, CD=2.6 m, BD=12 m
From the figure,
or, tan x = [tex]\frac{AB - 2.6}{12}[/tex]
or, tan 5 [tex]\leq \frac{AB - 2.6}{12}[/tex]
When AB be least, then
[tex]\frac{AB - 2.6}{12}[/tex] = tan 5
or, AB = (12*tan 5) + 2.6
or, AB = 3.650 m
Hence, the least possible height of the AB is 3.650 m.
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The length and width of two sides of a rectangle are consecutive odd integers. The area of the rectangle is 143 square units.
Find the dimensions of the rectangle.
The width of the rectangle is blank and length is blank
The dimensions of the rectangle are 70.5 by 72.5 units.
What is a dimension?
A length measurement that only goes one way. Dimensions include things like width, depth, and height. One dimension is that of a line, two dimensions are found in a square, three dimensions are found in a cube, and one dimension is that of something's height, length, or width. For instance, the room is 26 feet by 15 feet in size.
Solution Explained:
Given,
Area = 143 unit^2
A/Q,
Let length be x and width be x + 2.
So, Area = l X w
143 = x + x + 2
143 = 2x + 2
x = (143 - 2)/2
x = 70.5
So width = x + 2 = 70.5 + 2 = 72.5
So, the dimensions are 70.5 by 72.5
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Write the following as an inequality.
−8 is less than or equal to w, and 3 is greater than or equal to w
Use w only once in your inequality.
Answer:
Step-by-step explanation:
If -8 is less than or equal to w, and 3 is greater than or equal to w, then we can combine these two inequalities into a single inequality by combining the left and right sides:
-8 ≤ w ≤ 3
This inequality can be read as "w is greater than or equal to -8 and less than or equal to 3." It represents all values of w that are greater than or equal to -8 and less than or equal to 3, including -8 and 3.
I hope this helps! Let me know if you have any questions.
a plumber cuts 2 3/4 feet from pipe. The pipe is now 13 1/4 feet long. Write and solve an equation of to determine the original length if the pipe
2=3/4,13=1/4,2-3/4=0,13-1/4=0,2-3/4=0*13,13-1/4=0*2
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?
The required value of the production at which the company attained the same profit is 4 thousand skin care items.
Given that,
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t³ + 8t² + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million.
Here,
Plotting the graph of the polynomial equation,
P(t) = –2t³ + 8t² + 2t,
From the graph at x = 4,
The polynomial gives the same value as it gave at x = 1,
Thus, the required value of the production at which the company attained the same profit is 4 thousand skin care items.
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Please help me. This is my last question and I have no more points left.
The coordinate plane below shows the location of rectangle TUVW.
rectangle TUVW is to be dilated by a factor of 3, with the center of dilation at the point (1,0). drag and drop the the correct answers into each box.
Step-by-step explanation:
i just answered this question. how often did you post it ?
help please very easy proportional relationship due hurry please than u!
1) h=1/5 k
(10/2 = 1/5, 20/4 = 1/5... etc)
2) k=5/4 h
(5/4 = 5/4, 10/8=5/4... etc)
3) h=5/1 k
(25/5 = 5/1, 30/6 = 5/1 ... etc)
Hope this helps!
:]
Kaitlin the trainer has two solo workout plans that she offers her clients: plan A and plan B each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 8 who did plan b on Saturday there were 5 clients who did plan A and 2 who did plan b Kaitlin trained her friday clients for a total of 7 hours and her Saturday clients for a total of 6 hours how long does each of the workout plans last
Write an equation in slope-intercept form of the line that passes through (-2,-7) and (-1,6)
please help in this grade 7 percentage question im desperate
Answer:
See below
Step-by-step explanation:
320 x .1 = 32
320 + 32 = 352
352 x .5 = 176
352 + 176 = 528
320 x .65 = 208
320 + 208 = 528
Each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair what is the probability that Tess will choose a red ribbon on both Monday and Tuesday
The probability of choosing red ribbon on both Monday and Tuesday is 1/4.
What is the probability?
The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
Given that each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair.
That means probability of choosing between blue or red is 1/2 in one morning.
Now the probability of choosing red ribbon on both Monday and Tuesday,
1/2 × 1/2
= 1/4
Therefore, the probability of choosing red ribbon on both Monday and Tuesday is 1/4.
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which model can be used to find 4/5 divided by 1/10
Apply the fraction rule model can be used to find 4/5 divided by 1/10.
What is fraction rule?
For fractions to be added or subtracted, their denominators must match (the bottom value). the same denominators are used for addition and subtraction. It only requires adding or subtracting the numerators if the denominators are already equal.
[tex]$\frac{\frac{4}{5}}{\frac{1}{10}}$[/tex]
Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]
[tex]$=\frac{4 \cdot 10}{5 \cdot 1}$[/tex]
Cancel [tex]$\frac{4 \cdot 10}{5 \cdot 1}: 8$[/tex]
=8
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6x + 3y = 3 3x - y = 4
Answer:
x = 1
y = -1
Step-by-step explanation:
Given equations:6x + 3y = 3 -------------(1)
3x - y = 4 ----------------(2)
Multiply Eq. (2) by 2
2(3x - y) = 4 × 2
6x - 2y = 8 -------------(3)
Subtract Eq. (3) from Eq. (1)
6x + 3y - (6x - 2y) = 3 - 8
6x + 3y - 6x + 2y = -5
3y + 2y = -5
5y = -5
Divide 5 to both sides
y = -5/5
y = -1Put y = -1 in Eq. (1)
6x + 3(-1) = 3
6x - 3 = 3
Add 3 to both sides
6x = 3 + 3
6x = 6
Divide 6 to both sides
x = 1[tex]\rule[225]{225}{2}[/tex]
a) Work out the minimum number of dogs that could have a mass of more than 24kg}
b) Work out the maximum number of dogs that could have a mass of more than 24kg
The minimum number of dogs 24kg is 6 and the maximum number of dogs is 18
Maximum and Minimum:The highest amount or value or number that may be obtained or reached or can be counted is the Maximum value
The least amount or value or number that may be admitted or reached or can be counted is the Minimum value
Here we have a table
Which represents the masses of various dogs
Mass (x) kg frequency
0 ≤ x < 10 2
10 ≤ x < 20 7
20 ≤ x < 30 12
30 ≤ x < 40 6
Here the mass of dogs is represented in class intervals
a) The minimum number of dogs with a mass of more than 24kg.
From the given table,
24 kg will lie in class intervals 20 ≤ x < 30, and 30 ≤ x < 40
In class interval 20 ≤ x < 30, there is a possibility that the mass of dag will be less than 24 kg since it started from 20 kg and is up to 30 kg
In class interval 30 ≤ x < 40, there is no possibility that the mass will be less than 24 kg since it started from 30 kg and is up to 40 kg
So The minimum number of dogs that have a mass of more than 24kg the frequency of class interval 30 ≤ x < 40
Therefore,
The minimum number of dogs with a mass of more than 24kg is 6
b) The maximum number of dogs that have a mass of more than 24kg.
To get the maximum number of dogs we need to take the class interval of 20 ≤ x < 30 as in this the mass could be more than 24 kg.
And in class 30 ≤ x < 40 the mass will be more than 24 kg.
Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18
Therefore,
The maximum number of dogs with a mass of than 24kg is 18
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write an expression that is equivalent to 2/3 (4x + 9)
Hello,
I hope you and your family are doing well!
To write an expression that is equivalent to 2/3 (4x + 9), you can simply distribute the 2/3 over the parentheses:
2/3 (4x + 9) = (2/3 * 4x) + (2/3 * 9)
This simplifies to:
2/3 (4x + 9) = (8/3)x + (18/3)
Therefore, an expression that is equivalent to 2/3 (4x + 9) is (8/3)x + (18/3).
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Happy Holidays & New Year!
Answer: 2 2/3x + 6
Step-by-step explanation: 1 of 3 ways to find how to make the equivalent is to use the distributive property. So, that means we need to multiply or distribute 2/3 to both 4x and 9. So, 2/3 x 4 is roughly 2 2/3. Also, 2/3 x 9 = 6. So, I combined the like terms to get 2 2/3x + 6 as my equivalent expression. I hope this helps.
Writing Equations of lines
Write the equation of each line with the given information
through: (-3, 4) and (-5, -1)
Answer:
y = 5/2x + 11.5
Step-by-step explanation:
(-3, 4) (-5, -1)
m = -1-4/ -5+3
m = -5 / -2
m = 5/2
y = 5/2x + b
-1 = 5/2(-5) + b
-1 = -12.5 + b
b = 11.5
y = 5/2x + 11.5
Answer:
y-y1=y2-y1/x2-x1(x-x1)
y-4= (-1-4/-5+3) (x+3)
y-4= -5/-2(x+3)
y=5/2x+15/2+4
y=5/2x+15+8/2
y=5/2x+23/2
1.6y+y-4/15y+1 1/6y=2 1/3 pls help
The simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.
What is the domain of the function?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
We have,
1.6y+y-4/15y+7/6y=21/3
Move all terms to the left:
1.6y+y-4/15y+7/6y-(21/3)=0
Domain of the equation: 15y!=0
y!=0/15
y!=0
y∈R
Domain of the equation: 6y!=0
y!=0/6
y!=0
y∈R
Add all the numbers together, and all the variables
1.6y+y-4/15y+7/6y-7=0
Add all the numbers together, and all the variables
2.6y-4/15y+7/6y-7=0
calculate fractions
2.6y+(-24y)/90y²+105y/90y²-7=0
multiply all the terms by the denominator
(2.6y) * 90y² + (-24y) + 105y - 7 * 90y² = 0
Add all the numbers together, and all the variables
(2.6y) * 90y² + (-24y) + 105y - 7 * 90y² = 0
Add all the numbers together, and all the variables
105y+(+2.6y)*90y² + (-24y) - 7*90y² = 0
multiply elements
-630y+105y+(+2.6y)*90y² + (-24y) = 0
get rid of parentheses
-630y² + 105y + (+2.6y)*90y² - 24y = 0
Add all the numbers together, and all the variables
-630y² + 81y + (+2.6y) * 90y² = 0
Hence, the simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.
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HELPME Mike has $25.00 to rent paddleboards for himself and a friend for 3 hours. Each paddleboard rental costs $3.75 per hour.
PLEASE HELPPP!!!
The admission fee at the museum is 8.50 for children and 12.50 for adults on a certain day, a total of 240 people entered the museum and 2400$ was collected.
Use the variable c to represent children and the variable a to represent the adult
Answer:
Below
Step-by-step explanation:
a + c = 240 re-arrange to c = 240-a
revenue from child tix = 8.50 ( 240-a)
revenue from adult tix = 12.50 a summed, the revenues = 2400
8.5(240-a) + 12.5 a = 2400
2040 - 8.5 a + 12.5 a = 2400
4.5 a = 360
a = 80 tix then c = 240 - a = 160 tix