The value of h for which b in the plane spanned by a1 and a2 is 11.
A vector b is in the plane spanned by two vectors a1 and a2 if it can be written as a linear combination of a1 and a2. This means that there exist scalars x and y such that:
b = xa1 + ya2
[5, 4, h] = x[1, 4, -1] + y[-6, -20, 2]
Solving for x and y, we have:
5 = x - 6y
4 = 4x - 20y
h = -x + 2y
Using the first two equations, we can solve for x and y:
x = 5 + 6y
20y + 4 = 4x = 4(5 + 6y)
20y + 4 = 20 + 24y
4y = -16
y = -16/4 = -4
Substituting this value of y back into the first equation:
x = 5 + 6y
= 5 + 6 * -4
= 5 - 24
= -19
Finally, substituting x and y into the third equation:
h = -x + 2y
= -(-19) + 2 * (-4)
= 19 - 8
= 11
So for h = 11, the vector b is in the plane spanned by a1 and a2.
--The question is incomplete, answering to the question below--
"Let a1 = [1 4 -1], a2 = [-6 -20 2], and b = [5 4 h]. For what value(s) of h is b in the plane spanned by a1 and a2?"
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Arianna practices the piano 665 minutes in 5 weeks. If t represents the total time she practices for any number of days, d, write a proportional equation for t in terms of d that matches the context.
Answer:
The proportional relation for t in terms of d is:
t = (53 min/day)*d.
Step-by-step explanation:
Gavin buys 36 packets of raisins. Each packet of raisins costs £0.35.
Work out the total cost of all the packets that Gavin buys.
Answer: I'm not sure if it's right but I got 12.6
Step-by-step explanation: Multiplication
Pls answer pls i need for last questions of homework
The slope of the line that runs through the points (1,5) and (6,2) is -3/5.
What is the slope of the line?Slope is simply expressed as change in y over the change in x.
Slope m = rise / run
The change in y-axis is the rise and the change in x-axis is the run.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Since the line runs through the points (1,5) and (6,2).
Point 1 (1,5)
x₁ = 1y₁ = 5Point 2 (6,2)
x₂ = 6y₂ = 2Plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 2 - 5 )/( 6 - 1 )
Slope m = ( -3 )/( 5 )
Slope m = -3/5
Therefore, the slope of the line is -3/5.
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In Activity 1. 3
For the second set of values：
a. Which among the missing components can be solved using the given？
b. How will you solve the next missing component？
The Pythagorean Theorem can be used to solve for the missing sides of a triangle when given two other sides
a. The missing components that can be solved using the given values are the missing sides of the triangle (side b and side c).
b. To find the missing side, we can use the Pythagorean Theorem, which states that a^2 + b^2 = c^2, where a and b are the two sides of the triangle, and c is the hypotenuse. Therefore, we can solve for c by taking the square root of (a^2 + b^2).
The Pythagorean Theorem can be used to solve for the missing sides of a triangle when given two other sides. To do this, we take the square root of the sum of the squares of the two given sides, which gives us the length of the hypotenuse.
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El mundo cuenta con 6,974,400,000 de personas y si la población mundial aumenta en un 1. 2% anualmente ¿Cuántas personas aumentan en un año?
The population of the world after 1 year will be 6,974,400,000 + 1.2% of 6,974,400,000 = 7,058,092,800
What is percentage ?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
By dividing the value by the entire value and multiplying the result by 100, one may get the percentage. The percentage calculation formula is (value/total value)100%.
The word "percentage" means "out of 100." In mathematics, percentages are used, together with fractions and decimals, to denote parts of a whole. The total is split into 100 equal pieces to calculate percentages.
Total population of the world is 6,974,400,000
The population is incresing at a 1.2% rate annually
The population of the world after 1 year will be 6,974,400,000 + 1.2% of 6,974,400,000 = 6,974,400,000 + 836928000 = 7,058,092,800
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PLEASE HURRY AND ANSWER ASAP FOR BRAINLIEST AND POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!! PLEASE ANSWER MY OTHER QUESTIONS TOO BECAUSE I ALWAYS GIVE THE RIGHT ANSWER A BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!
The function f(x) represents the number of texts sent this week, and g(x) represents the number of texts sent last week. Given f(x) = 6x + 8 and g(x) = 2x − 9, find (f − g)(x) to find how many more texts were sent this week than last week.
(f − g)(x) = 4x − 1
(f − g)(x) = 8x − 1
(f − g)(x) = 4x + 17
(f − g)(x) = 8x + 17
Answer:
(f − g)(x) = 4x + 17
Step-by-step explanation:
find (f − g)(x) = f(x) - g(x)
f(x) = 6x + 8 and g(x) = 2x − 9
6x + 8 - (2x − 9)
multiply the -1 to 2x − 9
6x + 8 - 2x + 9
Combine like terms
4x + 17
Answer: choice C
Step-by-step explanation:
Took exam on FLVS
A baeball team play in a tadium that hold 44000 pectator. With the ticket price at $11 the average attendance ha been 19000. When the price dropped to $8, the average attendance roe to 22000. Aume that attendance i linearly related to ticket price. What ticket price would maximize revenue?
Answer:
$8 because the ticket would be affordable.
Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album of 12 songs. If you assume he takes an equal amount of time to compose each song and graph this relationship with the number of weeks on the x-axis and the number of songs on the y-axis, what is Wayne's unit rate for composing a song?
the unit rate for composing a song will be 3 weeks per song.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album of 12 songs.
He took 36 weeks to compose 12 songs.
Since,
Unit rate: Divide total weeks by total songs.
Thus,
Unit Rate = 36 / 12 = 3 weeks per song.
Therefore, the unit rate for composing a song will be 3 weeks per song.
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22 VA-Geometry IC (Year)
Determining Truth Values
Suppose statement p is true but statement q is false. Which of these compound statements are true? Check all that
apply.
О р^g
Opvq
Op-q
9-P
Op-q
q-p
If statement p is true but statement q is false, then the following compound statements are true -
Option B: p ∨ q
Option D: q → p
What is compound statement?
A compound statement is a collection of two or more statements joined together using terms like "or," "and," "if then," and "only if." Each component statement of a compound statement can be determined to be true or untrue with clarity.
If the truth value of the statement p is 'True' and truth value of statement q is 'False',
p ∧ q → False [Conjunction of both the statements will be true only when both the statements are True]
p ∨ q → True [Disjunction of two statements will be false only when both the statements are false]
(p → q) → False [p is same as q]
(q → p) → True [Implication of both the statements is false only when p is true and q is false otherwise true]
(p ↔ q) → False [Bi-conditional statements are true if and only when both the statements are true]
(q ↔ p) → False [Bi-conditional statements are true if and only when both the statements are true]
Therefore, the compound statements p ∨ q and (q → p) is true.
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what is the x-intercept of the function yx? the x-intercept is enter your response here. (enter your response as an integer or a decimal.)
The x-intercept of the function is 0.
The x-intercept of a function is the point where the graph of the function intersects the x-axis.
In other words, it is the point at which the y-value is equal to zero. For the function y = x, the x-intercept occurs when y = 0, and we can find the x-coordinate of this point by solving the equation x = 0.
Here we need to find the x-intercept, we set y equal to zero and solve for x. In this case, we have:
=> y = x
=> 0 = x
So the x-intercept of the function y = x is x = 0. This means that the graph of the function intersects the x-axis at the point (0,0).
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What is the equation of the following line? Be sure to scroll down first to see all answer options. (8,2) (0, 0)
The equation of the line is y = 4x
How to determine the equation of the lineThe general equation of a line is expressed with the formula;
y = mx + c
Where the parameters are given as;
y is a point of the line on the y -axis of the graphx is a point of the line on the x -axis of the graphm is the slope of the line in the graphc is the intercept of the iine on the y -axis of the graphFrom the information given, we have the expression;
Slope, m = y₂ - y₁/x₂ - x₁
Substitute the values into the formula
Slope, m = 0 - 8/0 - 2
Subtract the values
Slope, m = -8/-2 = 4
For the intercept
0 = 4(0) + c
c = 0
Hence, the equation is y = 4x
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solve 14A and 14B please
The slope of the graph is 1 and the y-intercept is -273.15. The slope presents the ratio between Celcius and Kelvin temperature and y-intercept shows the difference between both scales.
Based on the given graph:
(273.15, 0)
(0, -273.15)
m ?
y-intercepts?
slope:
m = y₂ - y₁
x₂ - x₁
m = -273.15 - 0
0 - 273.15
m = 1
y-intercept --> x = 0
x = 0 is when y = -273.15
The graph represents the relationship between temperature in Celcius scale and Kelvin scale.
The slope shows that both Celcius and Kelvin have equal ratio in measuring temperature. However, the y-intercepts shows that both scales have different zero points. The same temperature will be 273.15 lower in value under Kelvin scale than Celcius.
Then:
0°C = -273.15K
0K = 273.15°C
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What is the equation of the line described below written in slope-intercept form?
the line passing through point (2, 2) and perpendicular to the line whose equation is y = x
y = x + 4
y = -x + 4
y = x - 4
The slope of the line perpendicular to y = x is -1. The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. Substituting m = -1 and using the point (2, 2), we have:
y = -x + b
2 = -2 + b
b = 4
So the equation of the line passing through (2, 2) and perpendicular to y = x is:
y = -x + 4
Please Brainliest
The area of a hexagon is the space that is enclosed by all six sides of the hexagon.
True
False
It is true that The area of a hexagon is the area enclosed within its six sides. It is measured in square units such as m2, cm2, yard2,in2, etc. A hexagon is a two-dimensional closed shape that has six sides and six angles.
What is a six-sided shape's area?The area of a hexagon is calculated using the formula Area = (33 s2)/2, where s is the length of one of the regular hexagon's sides. The area of a hexagon can also be calculated using the apothem by using the formula Area of hexagon = (1/2) a P, where an is the apothem's length and P is the hexagon's perimeter.
There are six lines of symmetry in regular hexagons. The midpoints of its two opposite sides are joined by three lines, and the diagonals are joined by three more lines. This denotes the existence of "mirror symmetry" in a regular hexagon.
A regular hexagon is a regular polygon with six sides. determine the regular hexagon's side length, Apply the formula for the hexagon's surface area (33 s2)/2 to calculate the area, where s is the hexagon's side length.
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May you please help me
Answer:
33
Step-by-step explanation:
44
Kate is filling out her income tax return. Her tax for last year is $973. Her employer withheld $712 in federal taxes. What is the difference between Kate’s tax and the amount withheld by her employer?
Therefore , the solution of the given problem of unitary method comes out to be $261 is the difference between kate's tax and amount with held by employer.
What exactly is a unitary method?After establishing the size of a little slice, multiply the quantity by two to complete a task utilizing unitary technique. Simply expression, the unit technique serves to isolate a programmed thing from a certain set or sets of sets. For example, the price of 40 pens is 400 pounds ($1.01) or Rs. It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality. It can equally integrate and reciprocate (mathematics, algebra).
Here,
Given :
=> tax for last year is $973
=> employed with held is $712
the difference between Kate's tax and amount with held is:
=> 973 - 712
=> $261.
Thus , $261 is the difference between kate's tax and amount with held by employer.
Therefore , the solution of the given problem of unitary method comes out to be $261 is the difference between kate's tax and amount with held by employer.
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A survey of statistics undergraduate at prosperity university completed a survey that asked for their verbal and math sat scores. They wanted to predict the verbal score based on the math score. The value of r-squared was 12. 78%. The least squares regression equation is yhat = 383. 3 + 0. 3489x. Find r.
The coefficient of determination (r-squared) provides an indication of how well the regression model fits the data and the value of r is 0.3574
In this example, the r-squared value is 12.78%, which means that 12.78% of the variation in verbal SAT scores can be explained by the variation in math SAT scores. The least squares regression equation is yhat = 383.3 + 0.3489x, where yhat is the predicted verbal score and x is the math score.
The coefficient of correlation (r) provides a measure of the strength of the linear relationship between two variables. In this example, the coefficient of correlation (r) can be calculated from the coefficient of determination (r-squared) as follows: r = √r-squared = √12.78% = 0.3574. This indicates that there is a weak linear relationship between verbal and math SAT scores.
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how is calculus used in disasters
Answer: quantifies the economic devastation of natural and man-made disasters
Is this the answer anyone???
The amount of same profit is $19.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
It costs $20 to rent a hot dog roller and it costs $10 to rent a nacho chip warmer.
The cost of additional supplies for the hotdog is $0.02 per tray.
The additional cost for the nachos is $0.06 per container.
Team A will sell the hot dogs for $1.50 each.
Team B will sell the nachos for $1.00 each.
let x be the same amount of profit both earn.
1.48x - 20 = 0.94x - 10
1.48x - 0.94x = 10
0.54x= 10
x = 18.51
hence, the profit is $19.
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What does the expected value of a binomial distribution with n trials tell you? PICK ONE OF THE FOLLOWING.
1.the average number of successes
2. the average number of failures
3. the standard deviation of failures
By examining the expected value of a binomial distribution with n trials, (1) we may determine the typical number of successes.
What is binomial distribution?The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q=1-p).
This distribution is used in probability theory and statistics.
A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results.
For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.
The popular binomial test of statistical significance is based on the binomial distribution.
We may find out the average number of successes by looking at the expected value of a binomial distribution with n trials.
Therefore, by examining the expected value of a binomial distribution with n trials, (1) we may determine the typical number of successes.
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The one about the triangle
Answer: I split it up and got 4.
Step-by-step explanation: You will have to split it up into equal pieces.
Answer:
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees
Acceleration versus time graph for four objects are shown below. All axes have the same scale. Which object had the greatest change in velocity during the interval ?
The slope of a velocity graph represents the acceleration of the object.
Why does slope make things go faster?
Gravity is what causes the change in speed on a slope. Objects accelerate (move faster) when traveling downhill, and decelerate (move slower) when moving uphill (slow down).
They will then continue moving at the same pace on a level surface, presuming there is little friction.
= area of graph is 1/2 t₀a₀.
= area is less than 1/2 t₀a₀.
= area is more than 1/2 t₀a₀.
So in option (d) change in velocity is greatest.
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How much is 510 in meters?
510 is a quantity in the unit of feet and not in meters, so it can't be directly expressed as a quantity in meters.
How much is 510 in meters?To convert from feet to meters, you can use the following conversion factor:1 foot = 0.3048 metersFeet and meters are units of length used to measure distances and lengths.The conversion factor of 1 foot to 0.3048 meters is based on the definition of the meter as being equal to approximately 3.2808 feet.To convert from feet to meters, simply multiply the number of feet by the conversion factor of 0.3048.For example, 510 feet is equal to 510 x 0.3048 = 155.448 meters.It's important to note that this conversion factor is an approximation and may not be entirely accurate in all situations.For more precise conversions, it's best to use a conversion calculator or a reference guide that provides exact conversion factors.To learn more about meter refer:
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In ΔFGH, f= 8.8 inches, m∠F=23° and m∠G=107°. Find the length of g to the nearest 10th of an inch
The value of length g is 21.56 inches
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Therefore to find length g
f/sinF = g/sinG
8.8/sin23 = g/sin 107
8.8 × sin107 = g× sin 23
8.8 × 0.956 = g × 0.39
g = 8.8 × 0.956/0.39
g = 8.41/0.39
g = 21.56 inches
therefore the value of the length of g is 21.56 inches
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Answer:21.5
Step-by-step explanation:
solve for
secx = 1 - tanx
The required solution of the given trigonometric equation is given as x = 3π/2 + 2nπ.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
sec(x) = 1 - tan(x)
1/cosx = cosx - sinx / cosx [secx = 1 / cosx ; tanx = sinx / cosx]
cosx = 1 + sinx
1 + sinx - cosx = 0
1 + √2[sin{x - π/4}] = 0
sin{x - π/4} = -1/√2
x - π/4 = 5π/4 + 2nπ
x = 3π/2 + 2nπ
Thus, the solution of the given trigonometric equation is given as x = 3π/2 + 2nπ.
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suppose →=→×→ and is the angle between → and → where when they are drawn with their tails at the same point. it is know that is not equal to 90°. which of the following is false?
None of the following statements are false. The angle between → and → is not equal to 90°.
Given that →=→×→ and is the angle between → and → where when they are drawn with their tails at the same point, and it is known that is not equal to 90°, none of the following statements are false.
Given that → and → are two vectors drawn with their tails at the same point, and →=→×→ is the angle between them, and it is known that is not equal to 90°, none of the following statements are false:
1. The angle between → and → is not equal to 90°.
2. The angle between → and → is greater than 90°.
3. The angle between → and → is less than 90°.
4. The angle between → and → is equal to 0°.
5. The angle between → and → is not equal to 180°.
The complete question is :
Given that →=→×→ and is the angle between → and → when they are drawn with their tails at the same point, it is known that is not equal to 90°. Which of the following is false?
A. The angle between → and → is not 90°.
B. The angle between → and → is equal to 90°.
C. The angle between →=→×→ is not 90°.
D. The angle between →=→×→ is equal to 90°.
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Most kitchens have a working triangle between the sink (s), the counter (c) and the oven (o). The distance between the sink and oven is 8 feet. The distance between the sink and counter is 6 feet and the distance between the oven and counter is 7 feet. In the kitchen triangle, where is the largest angle?.
Answer:
Step-by-step explanation:
To find the largest angle in the kitchen triangle, we can use the Law of Cosines. The Law of Cosines states that in any triangle with sides a, b, and c and opposite angles A, B, and C, the following relationship holds:
c^2 = a^2 + b^2 - 2ab * cos C
In the kitchen triangle, we have the sides a = 6, b = 7, and c = 8. We can use the Law of Cosines to find the cosine of each angle and then use the inverse cosine function to find the angles themselves:
cos A = (b^2 + c^2 - a^2) / (2bc) = (7^2 + 8^2 - 6^2) / (2 * 7 * 8) = 0.41
A = cos^-1(0.41) = 61.8°
cos B = (a^2 + c^2 - b^2) / (2ac) = (6^2 + 8^2 - 7^2) / (2 * 6 * 8) = 0.95
B = cos^-1(0.95) = 18.4°
cos C = (a^2 + b^2 - c^2) / (2ab) = (6^2 + 7^2 - 8^2) / (2 * 6 * 7) = -0.15
C = cos^-1(-0.15) = 120.0°
The largest angle in the kitchen triangle is C, which measures 120.0°.
Asmine found a wooden jewelry box shaped like a right rectangular prism. What is the volume of the jewelry box?
The volume of a right rectangular prism can be calculated by multiplying the length, width, and height together. Therefore, the volume of the jewelry box will depend on the specific measurements of the box.
To calculate the volume of the wooden jewelry box, we need to know its length, width, and height. Once we have those measurements, we can multiply them together to determine the volume of the box.
For example, if the length of the box is 5 inches, the width is 3 inches, and the height is 2 inches, then the volume of the box would be 5 x 3 x 2 = 30 cubic inches.
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Given f(x) = 5 – 3x2, use a table to estimate the slope of the tangent line to f at the point P(0,5). 1. Find the slope of the secant line PQ for each point Q(x, f(c) with the x values given in the table. (Round each answer to 6 decimal places if necessary.) 2. Use the answers from the table to estimate the value of the slope of the tangent line at the point P. (Round your answer to the nearest integer.)
The value of the points in the graph is a (2,80).
According to the statement
We have to find that the points on the graph.
So, For this purpose, we know that the
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
From the given information:
f(x)=[tex]x^{3}[/tex]+6[tex]x^{2}[/tex]+17x+14; slope of the tangent line=5
Then
f(x)=[tex]x^{3}[/tex]+6[tex]x^{2}[/tex]+17x+14
Now find the drivative then
f'(x)=3x^2+12x+17
Then slope of the tangent line=5
Now,
3[tex]x^{2}[/tex]+12x+17 = 5
3[tex]x^{2}[/tex]+12x+12 = 0
[tex]x^{2}[/tex]+4x+4 = 0
Now solve the equation then
[tex]1x^{2}[/tex]+2x+2x+4 = 0
x(x+2) +2(x+2) = 0
(x+2) (x+2) = 0
Here the values of the x become -2,-2.
Then
When x = 2
f(x)=[tex]2x^{3}[/tex]+[tex]6^{2}[/tex]+17(2)+14
f(x)=8+24+34+14
f(x) = 80.
So, The value of the points in the graph is a (2,80).
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A wolf can run 110 m in 6. 3 seconds. A Tiger can run 85 m in 4. 2 seconds. Compare
their unit speeds to determine which animal is faster. Round to the nearest whole
unit.
Tiger speed? Wolf speed?
Which one is faster ?