The Span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
Linear Span of vectors can be represented as
let [tex]x_{1} and x_{2}[/tex] be two non collinear vectors its span be written as [tex]x=a_{1} x_{1} +a_{2} x_{2}[/tex] where [tex]a_{1}, a_{2}[/tex] are arbitrary scalars.
Subspace of vectors : a subset A of a vector space V is called a subspace of V if A is itself a vector space under scalar multiplication and addition defined on V.
The Span of two vectors is a vector space containing two vectors. Hence the span is also a vector space . It is sufficient to notice that any two independent vectors from subspace can be the basis.
Zero vector is the linear combination of these basis vector.
hence it is not possible to have a span of two non collinear vectors that does not contain origin .
Therefore, The span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
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If a - b = b = c = 2, what is the value of: (a − b)² + (b − c)²/(a - c)² ihx-ezjm-mww
Answer:
Step-by-step explanation:
If a - b = b = c = 2, what is the value of: (a − b)² + (b − c)²/(a - c)² ihx-ezjm-mww
Help please!! I would appreciate it:)
[tex]2A +B = -2 \cdot (2z +8 -2z-4) = -2 \cdot 4 = -8[/tex]
angie, a student in an advanced statistics course, was given an algebra test and she scored 80%. is this an accurate predictor of how well students in the algebra class will perform on the test? (2 points) yes, because angie is representative of the population in the algebra class yes, because angie scored high on the test so it must be easy no, because angie is not representative of the population in the algebra class no, because angie scored too high on the test
No, this is not an accurate predictor because angie is not representative of the population in the algebra test.
Here,
Angie, a student in an advanced statistics course, was given an algebra test and she scored 80%.
We have to find is this an accurate predictor.
What is Accurate predictor?
Accurate predictor describes whether the predicted values match the actual values of the target field within the incertitude due to statistical fluctuations and noise in the input data values.
Here,
Angie is the student of an advanced statistics course but she gives the algebra test and scored 80%.
We know that the advanced statistics is the higher level of math so it is not an accurate predictor.
Because, An accurate predictor should be applied when the person is 100% confirmed to the related thing. So in the given situation, the student is not 100% confirm.
Hence, this is not an accurate predictor because Angie is not representative of the population in the algebra test.
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The length of a rectangle is 3ft longer than its width. If the perimeter of the rectangle is 66ft , find its length and width.
in a reaction time study involving 12 participants, the number of participants whose average time is between 400 and 600 milliseconds
Using the concepts of continuous and discrete variables it is found that the reaction time of students would be a continuous variable.
What is the missing information?This problem is incomplete, but researching it on a search engine, it asks to classify the variable reaction time of students as discrete or continuous.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, …A reaction time of 500.5 milliseconds is a valid reaction time, hence a decimal value is accepted, meaning that the reaction time of students would be a continuous variable.
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Help pleaseeeeeeeeeeeee
The equation that can be used to find x, which is the width of the walkway will be (16 + 2x)(12 + 2x) = 396.
How to illustrate the information?It should be noted that an expression is used to show the relationship that's exists between the variables.
The equation that can be used to find x, which is the width of the walkway will be:
= (16 + x + x) (12 + x + x) = 396
= (16 + 2x)(12 + 2x) = 396
In conclusion, the correct option is C.
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what is the soluton to the equation e^3x=12
Answer:
[tex]x=\frac{ln(12)}{3}[/tex]
Step-by-step explanation:
We can solve this equation by taking the natural log of both sides.
This gives us the equation: [tex]ln(e^{3x})=ln(12)[/tex]
And the definition of natural log is basically, "what do I have to raise e to, to get this result"
The result is just e^3x, so I have to raise e to what? Well that's just 3x, you could also use log properties to bring the exponent in front and realize ln(e) = 1
So this gives us: [tex]3x=ln(12)[/tex]
Now divide both sides by 3: [tex]x=\frac{ln(12)}{3}[/tex]
Solve for the value of e.
(8e-6)°
(7e+6)°
Answer:
e = 12======================
The two given angles form a linear pair.
Sum of the two angles is 180°, set equation and solve for e:
8e - 6 + 7e + 6 = 18015e = 180e = 180/15e = 12New York State energy consumption (2008)
Transportation sector 28%
Residential sector 30%
Commercial sector 32%
Industrial sector 10%
The total energy consumption in New York State in 2008 was about 4,000 trillion btu. About how many trillion btu was consumed by the residential sector?
The energy consumes by the residential sector in 2008 was 1200 trillion btu. This is a problem from percentage.
Here, the energy consumption in different sector in New York State (2008) is
Transportation sector 28%
Residential sector 30%
Commercial sector 32%
Industrial sector 10%
So, the total energy consumption is = 28% + 30% + 32% + 10% =100%.
Therefore, the power consume by Residential sector is 4000x30% = 1200 trillion btu.
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless number; it has no unit of measurement.
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Write the equation of the line in fully simplified slope-intercept form.
-12-11-10-9-8
4-3-2
12
2H298NON-
10
-10
1 2 3 4 5 6 7 8 9 10 11 12 1
Answer:
y = -4x -4
Step-by-step explanation:
we need to get two points to calculate the gradient
points chosen are (-2,3) and (-3,7)
Gradient = change in y coordinates/ change in X coordinates
G = (7-3)/(-3- -2)
= 4/-1
= -4
to write the equation in slope -intercept form we need one known point (-2,3) and one unknown point (X,y) and the gradient.
G = ∆y/∆x
-4 = (y - 3)/ (X - -2)
-4 = (y-3)/ (X+2)
we now cross multiply
-4(X + 2) = y - 3
-4x -8 = y-3
-4x -8+4 = y
y = -4x -4
How many cubes are in the box? What fraction of the entire box do the 7 cubes represent? Explain you answer. 10*10*10
Answer:
7/10 %
Step-by-step explanation:
Hey guys i need help with numbers 3-7
Answer:
I don't know what u wanted me to solve for but here you go
Step-by-step explanation:
You purchase tickets to a rock concert for you and 5 friends. You paid a total of $483.30. Write an equation and solve to find out how much each concert ticket cost. You must have your equation, the work to solve the equation and your answer in sentence form.
Answer:
to figure out the total for each person what you need to do is divide 483.30 by 5
483.30 / 5= 96.66
Step-by-step explanation:
the median player salary for the new york yankees was $1.5 million in 2007 and $1.7 million in 2013. write a linear equation giving the median salary y in terms of the year x. (let y be in millions of dollars and let x
(a) The linear equation giving the median salary "y" in terms of the year "x" is y = 0.034x + 1.266.
(b) The median player salary in the year 2048 will be approximately $2.9.
We are given the years to be 2007 and 2013, so the corresponding "x" values are 7 and 13 respectively.x1 is 7 and x2 is 13.We are given the median player salaries to be $1.5 million and $1.7 million, so the corresponding "y" values are 1.5 and 1.7.y1 is 1.5 and y2 is 1.7.In the form of corresponding points, we can write (7, 1.5) and (13, 1.7).(a) To form a linear equation, we use the equation of a line.(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)y - 1.5 = [(1.7 - 1.5)/(13 - 7)]*(x - 7)y - 1.5 = (0.2/6)*(x-7)y = (0.2/6)*(x-7) + 1.5y = 0.034x - 0.234 + 1.5y = 0.034x + 1.266(b) For the year 2048, the "x" value is 48.y = 0.034(48) + 1.266y = 1.632 + 1.266y = 2.898Thus, the median player salary in the year 2048 will be approximately $2.9.To learn more about linear equations, visit :
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2 2/7:(0.6x)=4/21:0.25
Answer:
x = 5
Step-by-step explanation:
Given:
[tex]2 \frac{2}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]
Convert the mixed number into an improper fraction by multiplying the whole number with the denominator of the fraction, adding it to the numerator of the fraction, and placing it all over the denominator of the fraction:
[tex]\implies 2\frac{2}{7}=\dfrac{2 \times 7+2}{7}=\dfrac{16}{7}[/tex]
Therefore:
[tex]\implies \dfrac{16}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]
[tex]\implies \dfrac{\frac{16}{7}}{0.6x}=\dfrac{\frac{4}{21}}{0.25}[/tex]
Cross multiply:
[tex]\implies \dfrac{16}{7} \times 0.25 = \dfrac{4}{21} \times 0.6x[/tex]
[tex]\implies \dfrac{16\times 0.25}{7} = \dfrac{4\times 0.6x}{21}[/tex]
[tex]\implies \dfrac{4}{7} = \dfrac{2.4x}{21}[/tex]
Cross multiply again:
[tex]\implies 4 \times 21=2.4x \times 7[/tex]
[tex]\implies 84=16.8x[/tex]
Divide both sides by 16.8:
[tex]\implies \dfrac{84}{16.8}=\dfrac{16.8x}{16.8}[/tex]
[tex]\implies 5=x[/tex]
[tex]\implies x=5[/tex]
Answer:
The value of x is 5.
Step-by-step explanation:
Let's solve for the value of x,
→ 2 2/7 : (0.6x) = 4/21 : 0.25
→ 16/7 : (0.6x) = 4/21 : 0.25
→ (16/7) × 0.25 = (4/21) × 0.6x
→ 4/7 = (2.4x)/21
→ 2.4x × 7 = 4 × 21
→ 16.8x = 84
→ x = 84/16.8
→ [ x = 5 ]
Hence, the value of x is 5.
pls helpppp thank uuuuu
1, 3, and 5 are true
is 9817 completely divisible by 3
Answer:
No
Step-by-step explanation:
To know if a number is completely divisible by 3, you can add up its digits. If its digits equal a number divisible by 3, then the number itself is divisible by 3.
9817
9 + 8 + 1 + 7
= 25
2 + 5
= 7
Since 25 isn't divisible by 3, 9817 isn't completely divisible by 3 either.
Have a lovely rest of your day! :)
Select the correct answer.
Which expression is equivalent to 4x²√5x4 3√5x8, if x=0?
OA. 12x¹0 √5
OB. 60x8
OC.
35x18
O D. 7x¹⁰ √5
The expression 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] is equivalent to 60 [tex]x^{8}[/tex] if x≠ 0 which is option B
We have to simplify the given equation 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] in order to find its equivalent
Which can be simplified using the basics of square and square roots
Square and square root gets cancelled for example [tex]\sqrt{x^{2} }[/tex] = x and powers get added when same bases are multiplied for example x² × x³ = [tex]x^{2+3}[/tex] =[tex]x^{5}[/tex]
Also √25 can be written as 5
At x = 0 the whole expression can be written as zero
4x² ×√[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex]
12x²×[tex]x^{2} \sqrt{5}[/tex] ×[tex]x^{4} \sqrt{5}[/tex]
12[tex]x^{8}[/tex] ×√25
60 [tex]x^{8}[/tex]
Hence, The expression 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] is equivalent to 60 [tex]x^{8}[/tex] if x≠ 0 which is option B
The correct question is Select the correct answer.
Which expression is equivalent to 4x²√5x4 3√5x8, if x≠0?
OA. 12x¹0 √5
OB. 60x8
OC.35x18
O D. 7x¹⁰ √5
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can u please use an explanation, i need it for my answer please.
======================================================
Work Shown:
[tex]a^2 + b^2 = c^2 \ \ \text{ ... pythagorean theorem}\\\\12^2 + 9^2 = c^2\\\\144 + 81 = c^2\\\\225 = c^2\\\\c^2 = 225\\\\c = \sqrt{225}\\\\c = 15\\\\[/tex]
If k equals 42 in [tex]x^{2}[/tex] + [tex]y^{2} + z^{2}[/tex] = k, what is x?
The value of x is ±√(42 - y² - z²).
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.
Given:
x² + y² + z²=k
As, it is given that k = 42.
So, x² + y² + z²=k
x² + y² + z²= 42
x² = 42 - y² - z²
x=±√(42 - y² - z²)
Hence, the value of x is ±√(42 - y² - z²).
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george’s average bowling score is 180; he bowls in a league where the average for all bowlers is 150 and the standard deviation is 20. bill’s average bowling score is 190; he bowls in a league where the average is 160 and the standard deviation is 15. who ranks higher in his own league, george or bill?
A truck can be rented from Company A for $40 a day plus $0.30 per mile. Company B charges $20 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
The number of miles in a day at which the rental costs for Company A and Company B are the same is 200 miles per day
Let the truck is driven X miles per day
Charges of company A will be = 90+0.4X
Charges of company B will be =30+0.7X
Let us find out value of X when charges of both companies are same
which means that 90+0.4 X= 30+0.7X
90-30 = 0.7X-0.4X
60 = 0.3X
60/0.3 = X
X= 200
The charges of both companies will be same if truck is driven 200 miles per day
Company A will have better deal if truck is driven more than 200 miles per day ( because per mile rate of company A is less than company B)
A mile is defined as 1760 yards, or around 1.6 kilometers, in length. They traversed the desert for 600 km by car. She's only a half-mile away. singular noun. A large distance is indicated by the word "miles," particularly in the phrase "miles distant."
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at $2\!:\!48$ what is the degree measure of the smaller angle formed by the hour and minute hands of a $12$-hour clock?
Angle between hour and minute hand= 204°
a figure which is formed by two rays or lines that shares a common endpoint is known as Angle.
The hour hand has covered 2 h and 48 min from position 12 o'clock (reference position). And in case of minute hand 22 min from reference. Required angle is angle covered by minute hand minus the angle covered by hour hand (clearly minute hand has covered greater angle in comparison with hour hand).
For calculating angle covered by minute hand:
In 60 min the min hand covers 360°
60 min = 360°
1 min = 6° ; 48 min = 288°
For calculating angle covered by hour hand:
12 h ( of hour hand) = 360°
1 h = 30°
For [2 + (48/60)] h, the angle covered= [2 + (48/60)]*30° = 84°
Angle between hour and minute hand = (288–84)° = 204°
It is the acute angle between hour and minute hand. For finding reflex angle subtract the obtained acute angle from 360°. So the reflex angle will be 299°.
Angle between hour and minute hand= 204°
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Find an equation for the line that passes through the points (4, - 4) and (-6, 2).
Answer:
y = -0.6x - 1.6.
-2x+3y >=1 -5x+6y<=1
Answer:
x = 1 and y = 1
Step-by-step explanation:
Find the area of ABC with vertices A(4, -3) B(9,-3) , and C(10, −11)
The area of triangle ABC with vertices is 22 square units
How to find the area of ABC with vertices?The vertices are given as:
A(4, -3) B(9,-3) , and C(10, −11)
The area of the triangle is calculated using
Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|
This gives
Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|
Evaluate the sum of products
Area = 0.5 * |44|
Remove the absolute bracket
Area = 0.5 * 44
Evaluate
Area = 22
Hence, the area of ABC with vertices is 22 square units
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mr. lopez is spreading pebbles around a water garden. he spreads 2 cubic yards of pebbles in 3 4 hour. at this rate, how many cubic yards of pebbles can he spread in one hour? cubic yards in one hour answer
Mr. Lopez spread the stones at a pace of 0.059 cubic yards per hour.
What is rate of change?
A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
"Per unit of time" is a frequent sort of rate, and examples include speed, heart rate, and flux. Exchange rates, literacy rates, and electric field ratios are examples of ratios with a non-time denominator (in volts per meter).
The word "per" is used to denote the division of the units of the two measurements that make up a rate when discussing its units (for example a heart rate is expressed "beats per minute"). A rate that is defined using two numbers of the same units will provide a dimensionless quantity that can be stated as a percentage (for instance, the global literacy rate in 1998 was 80%), fraction, or multiple. Examples of these rates include tax rates and literacy rates.
2/34 = 0.0588 equals to 0.059 ( approximately).
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you note that the recipe calls for two cups of butter and three eggs (plus the other ingredients) to make six dozen cookies. you call a friend and have him bring you some eggs.
The number of cookies prepared from 1.33 cups of butter are 48.
What is ratio and proportions?A ratio in mathematics signifies how many one number appears to contain another. For instance, when there are eight oranges as well as six lemons in a fruit bowl the orange-to-lemon ratio is eight to six, or 8:6, which really is similar to the proportion 4:3.
Now, as per the given question.
In this item, we have been asked to calculate the total number of cookies that may be made by having;
Let 'x' be the cookies made by 1.33 cups of butter.
When, six dozen cookies with 2 cups of the butter = 72 cookies with 2 cups of the butter.
We will use the ratio & proportion formula to solve this problem:
a/b = c/d
Let us now enter the values:
72 cookies/ 2 cups of butter = x / 1.33 cups of butter
Cross multiplying the equations;
72 cookies × 1.33 cups of butter = x × 2 cups of butter
Thus,
x = (72 cookies × 1.33 cups of butter)/2 cups of butter
x = 48
Thus, 48 cookies will be made in proportion to 1.33 cup butter.
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The complete question is-
You are making cookies and are missing a key ingredient eggs. You have most of the other ingredients needed to make the cookies, except you have only 1.33 cups of butter and no eggs. You note that the recipe calls for two cups of butter and three eggs (plus the other ingredients) to make six dozen cookies. You call a friend and have him bring you some eggs. If you use all the butter (and get enough eggs), what number of cookies will you make?
8. A doctor allows 15 minutes for routine office visits and 45 minutes for full physicals. The doctor cannot do
more than 10 physicals per day. She schedules at least 8 routine visits per day but not more than 12 routine
visits. The doctor has 9 available hours for appointments each day. A routine visit costs $60 and a full physical
costs $70. How many routine office visits and full physicals should the doctor schedule to maximize her
income for the day? What is the maximum income?
The maximum income the doctor can get in a day is $1280
Time required for routine office visits = 15 minutes
Time required for physical visits = 45 minutes
Maximum physical visits possible in a day = 10
Maximum routine visits possible in a day = 12
Available hours for appointment = 9 hours or 540 minutes
Cost of routine appointment = $60
Cost of physical appointment = $70
In order to maximize income, she should do maximum possible routine visits as it gives more return in less time and the remaining time can be used to do physical visits, therefore:
No. of routine visits the doctor should do = 12
Time consumed in 12 visits = 12*15 = 180 minutes
Time remaining = 360 minutes
No. of physical visits she should do = 8
Time consumed in 8 physical visits = 8*45 = 360 minutes
Total income the doctor will generate in a day = 12*60 + 8*70
= 720 + 560 = $1280
Hence, the maximum income of the doctor will be $1280
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What’s a word problem that you can model by the quotient of 2 1/2 divided by 3/4
The quotient is 10/3 .
Sharing something equally is one way to view division.
Whatever we all equally share in this problem must be a part, not a whole. What are some examples of things we typically consider to be parts? We do, however, discuss food in casually.
3/4 of a pan of brownies or 2 1/2slices of pizza could be included. Additionally, we weigh some goods in division of a pound, notably bulk foods and sweets.
There are some materials that we purchase in division of a whole, such as lengths of fabric, rope, or ribbon that are sold in units of a yard. Any of those objects could be divided into equal portions as part of your word puzzle. Here are two illustrations:
At the supermarket, Dayana and her 3/4 friends purchased a candy bag weighing 2 1/2 lb. How much candy will each individual receive if they decide to divide it equally?
(2 1/2)/(3/4)= (5/2)/(3/4)= (5[tex]\times[/tex]4)/(3[tex]\times[/tex]2)=20/6=10/3
The quotient is 10/3 .
This means that after Dayana cuts each piece of board, its length will be 10/3 yards.
Therefore, the quotient is 10/3.
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