Answer:
Take \(b = \frac{3}{10}(6,2)\) as the vector in Span(u) and \(w = \frac{4}{5}(-1,3)\) as the orthogonal vector to u
Step-by-step explanation:
Given vectors a,b we can calculate the projection of a onto b by the formula
\( \frac{a\cdot b}{b\cdot b}b\). where \(\cdot\) is the dot product of vectors.
For this example, we will take y = [1,3] and u = [6,2].
Let b be the projection of y onto u. That is
\( b= \frac{y\cdot u}{u\cdot u}u = \frac{1\cdot 6+ 3\cdot 2}{6\cdot 6+2\cdot 2}(6,2) = \frac{3}{10}(6,2)\)
Now, we want to find an orthogonal vector w such that b+w = y. From this equation, we can find w by taking w = y-b. Then
\( w = (1,3)-\frac{3}{10}(6,2) = \frac{4}{5}(-1,3)\)
We must check that w and u are orthogonal. Note that if the vectors a,b are orthogonal, then the vectors a, kb are also orthogonal for every non-zero value of k. So, to check that a,kb are orthogonal, it suffices to check that a,b are orthogonal. We know that two vectors are orthogonal if and only if their dot product is zero. In our case, take the vector (6,2) and (-1,3). Note that
\((6,2)\cdot(-1,3) = -6+2\cdot3 = 0\)
So, by the previous analysis, w and u are orthogonal.
What is a doubles fact for 7 8?
With "near doubles facts" or "doubles facts plus one," the actual magic happens. When we observe 7+8, we know that 8 is one more than 7, since we already know that 7+7=14. Thus, 15 is one greater than 14. So, 15 is the answer.
We can also consider the fact that it is one less than the doubles. We are aware that 7 + 7 = 14. I then realise that 6 is one less than 7 when I see 7 plus 6. 14 minus one equals 13, thus.
Thus, our knowledge of ten items with doubles increased to approximately 33 information with near doubles! Therefore, it's a really effective tactic!
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Find the degree measure of each angle.
(In picture)
kori spent $46.20 on 12 gallons of gasoline. What was the price per gallon
Answer:
3.85 because you have to divide 46.20 and 12
Step-by-step explanation:
A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 13 inches. The side to the right of the base is 7 and one-half inches. The small side parallel to the base is 5.18 inches. There are two sides that form a point at a right angle. The smaller is 5 inches, and the larger is 6 inches.
What is the area of the shape for the quilt block?
sixty-three and three fourths in2
one hundred twelve and one half in2
one hundred twenty-seven and one half in2
225 in2
The total area of the quilt is: 112.5 square inches
How to determine the total area of the quilt?The six-sided figure is given, and we can deduce the following parameters from the question:
The shape is made of a triangle and a rectangle
The side lengths derived from the question are:
The triangle on top:
base: 5 inches and height: 5.18 inches
The rectangle at the bottom:
Base: 16 inches with a height of 7.5 inches
So, we have the total area of the figure to be
Area of figure = 1/2 * 5 * 6 + 13 * 7.5
Area of figure = 112.5
Based on the parameters, the total area is 112.5 square inches
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What is the value of x?
X
II
m< BAE
11
m
m
E
4
B
2x 76°
U
D
a)while wages have increased, spending power has mostly remained the same since 2000
b) as wages go up, so does spending power
c) the spending power of men is less than the spending power of the overall population
d) the wages of women have increased faster than the wages of men
Based on the information, the answer is A). While wages have increased, spending power has mostly remained the same since 2000.
How to explain the informationThe fact that the cost of living has also increased, eating up much of the gains from wage growth. In addition, many Americans are now working multiple jobs, which can leave them with less time and energy to spend money on discretionary items.
According to the Bureau of Labor Statistics, the average hourly wage for all workers in the United States increased by 16.3% between 2000 and 2021. However, the Consumer Price Index (CPI), which measures the cost of a basket of goods and services, increased by 26.5% over the same period. This means that the purchasing power of the average worker has actually declined by 10.2% since 2000.
The rise of the gig economy has also contributed to the decline in spending power. Many Americans are now working multiple jobs, often in low-wage industries such as food service and retail.
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While wages have increased, spending power
a)has mostly remained the same since 2000
b) as wages go up, so does spending power
c) the spending power of men is less than the spending power of the overall population
d) the wages of women have increased faster than the wages of men
Find the average of the following numbers: 55.1, 67.9, 59.2, 64.1, 61.8, 62.7. Round
your answer to one decimal place *
Your answer
Answer:
61.8
Step-by-step explanation:
\( \frac{55.1 + 67.9 + 59.2 + 64.1 + 61.8 + 62.7}{6} \)
Mary's mom gave her $100.00 to go shopping. She spent $22.65 on a shirt and 3
$33.31 on a skirt. She had a coupon for 10% off. How much change did the cashier give back to her?
The clerk did not give Mary any change, so that is the correct response.
How does discount work?A price decrease from the normal or list amount or a proportional deduction from such a debt account, typically applied in exchange for on-time or cash payments.
The total cost of the shirt and three skirts before the coupon is:
$22.65 + 3($33.31) = $122.58
With the 10% discount, the total cost becomes:
$122.58 - 0.1($122.58) = $110.32
To find out how much change the cashier gave back to Mary, we need to subtract the total cost from the amount of money Mary's mom gave her:
$100.00 - $110.32 = -$10.32
Since the result is negative, it means Mary did not have enough money to pay for her purchases and would have to give the cashier an additional $10.32 to cover the full cost of her shopping.
Therefore, the answer is that Mary did not receive any change from the cashier.
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If anyone can do this for me step by step i will give you 30 points please help me out
Answer:
after 10 months
Step-by-step explanation:
Let x be the number of months and y be the amount they still owe.
Sin Ian borrows $1000 from his parents, then the y-intercept b= 1000 since he owes $1000 when x = 0. He pays them back $60 each month The slope is then m = -60 . Substituting in b = 1000 and m = -60 into the slope-intercept form of a line then gives y= mx + b=-60x +1000.
Sin Ken borrows $600 from his parents, then the y-intercept b = 600 since he owes $600 When x= 0. He pays them back $20 per month so the amount he owes decreases $20 each month. The slope is then m = -20 . Substituting in
b= 600 and m = -20 into the slope-intercept form then gives y = mx +b = -20x + 600.
They will owe the same amount when they have the same y-coordinate. Therefore -60x+ 1000= y= -20x+600. Solve this equation for x:
-60x+ 1000 = -20x+ 600
1000 = 40x+ 600
400 = 40x
10=x
They will then owe the same amount after 10 months.
Recall that with base-ten blocks: 1 long 10 units, 1 flat 10 longs, and 1 block 10 flats. What is the fewest number of multibase blocks that can be used to represent the corresponding numeral in the given base?
a. 20 longs in base seven
b. 10 longs in base three
a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.
In base seven, we have the following conversions:
1 long = 1 unit
1 flat = 10 units
1 block = 10 flats
To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.
So, the fewest number of multibase blocks required would be 2 flats.
Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.
In base three, we have the following conversions:
1 long = 1 unit
1 flat = 3 units
1 block = 3 flats
To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.
So, the fewest number of multibase blocks required would be 3 flats and 1 unit.
Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
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Please help me i have been struggling for two days
we have the equation
\(\log _5(x+1)-\log _2(x-2)=1\)using a graphing tool
see the attached figure
The solution is x=2.90The area of a gymnasium floor is 264 square yards. the floor is 11 yards wide. How long is the floor?
Answer:
24 yards long
Step-by-step explanation:
if A=l*w then it's 264=l*11
if you divide 264 (area) by 11 (width) then the answer is 24 which is the length
Solve for the roots: x3-2x2+3x-6
Answer:
x = 2, i\(\sqrt[]{3}\), -i \(\sqrt{3}\)
x^3 - 2x^2+ 3x - 6 = 0
Hint: Solve by grouping.
-2x+y=1 solve with steps
Answer:
x=1 and y=3
Step-by-step explanation:
-2x1=-2
-2+3=1
So this answer makes sense
Answer:
y = 2x + 1
Step-by-step explanation:
Given: -2x+y=1
Add 2x to both sides: y=1+2x
Reorder: y = 2x + 1
I am not sure exactly what you need for this point, but here is the equation in y=mx+b form aka slope-intercept form
m = slope = 2
b = y-intercept = 1
Hope this helps, have a nice day :D
A
07
06
O15
09
B
15 m
2x+3
Given that
ABCD is a parallelogram, find the x.
Given that ABCD is a paralle log ram, find the value of x.
D
C
Answer:
x = 6
Step-by-step explanation:
the opposite sides of a parallelogram are congruent , then
2x + 3 = 15 ( subtract 3 from both sides )
2x = 12 ( divide both sides by 2 )
x = 6
Which of the following sets of ordered pairs represents a function? PLEASE HELP
The set of ordered pairs that represents a function is (D) {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.
A set of ordered pairs represents a function if each unique input (x-value) is associated with only one output (y-value).
{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}
In this set, both (-2, -1) and (-2, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.
{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3,0)}
In this set, all the ordered pairs have the same x-value (-5). Since (-5, -5), (-5, -4), (-5, -3), and (-5, -2) have the same x-value but different y-values, this set does not represent a function.
{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}
In this set, (-4, -5) and (-4, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.
{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}
In this set, each unique x-value is associated with a single y-value. There are no repeated x-values. Therefore, this set represents a function.
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Factorise fully 6x+8
Answer: To factorize the expression 6x + 8 fully, we can first look for the greatest common factor (GCF) of the two terms. In this case, the GCF is 2.
Step 1: Factor out the GCF:
2(3x + 4)
Now, we have the expression 3x + 4 inside parentheses. This expression cannot be further factorized since there are no common factors other than 1.
Therefore, the fully factorized form of 6x + 8 is:
2(3x + 4)
Step-by-step explanation:)
The factored expression is:
↬ 2(3x + 4)Step-by-step explanation:
To factor the expression, look at its GCF (greatest common factor).
Clearly the GCF of both terms is 2. So what we do next is we divide both terms by 2 :
6x ÷ 2 + 8 ÷ 2The result is :
3x + 4And now the 2 goes outside the parenthesis:
2(3x + 4)Hence, the answer is 2(3x + 4).
URGENT
A group of 24 people go to the theatre. Adult tickets cost $45 each and children's tickets cost $25 each. If the group paid $860 altogether how many children were in the group?
Answer:
CHILDREN =5
SEE THE IMAGE FOR SOLUTION
Compared to last year, the population of Boom Town has increased by 25%.The population is now 6,600. What was the population last year?
The model below can be used to find the quotient of one over two divided by one over eight. What is the quotient?
Answer:
The answer is 0.25
Step-by-step explanation:
I hope this helps please rate me and like me.
Answer:
0.25 or 1/8
Step-by-step explanation:
I had your question in a quiz so i understand your troubles I hope this helps.
The change in water vapor in a cloud is modeled by a polynomial function, C(x). C(x) = x^3+ 5x^2+3x+30 Describe how to find the x-intercepts of C(x) and how to construct a rough graph of C(x) so that the meteorologist can predict when there will be no change in the water vapor.
Answer:
Suppose the equation that describes the change in water vapor in a cloud (y) with respect to temperature (x): C(x) = x³ - 4x² - 7x + 10
You find the x-intercepts of the cubic equation by finding the roots. Let y be zero:
x³ - 4x² - 7x + 10 = 0
Now, find possible factors of the constant term in the equation: 10. These could be 1, 2, 5, and 10. Suppose we choose 1. We substitute x=1. If the answer is zero, then x=1 is one of the roots.
(1)³ - 4(1)² - 7(1) + 10 = 0
Hence, x=1 or x-1 = 0 is one of the roots. We use this to manipulate the rest of the terms in the original equation, such that you can factor out (x-1). Substitute -x² - 3x² to -4x³ because they are just equal. Same is true for +3x - 10x for -7x:
x³ -x² - 3x²+3x - 10x + 10 = 0
Factor out like terms such that they have a common factor of (x-1) as much as possible.
x³ -x² = x²(x-1)
- 3x²+3x = -3x(x-1)
- 10x + 10 = -10(x-1)
The factored equation is:
x²(x-1)-3x(x-1)-10(x-1) = 0
Factor out (x-1):
(x-1)(x²-3x-10) = 0
Now, we have the quadratic equation left to be solved:x²-3x-10
Use the quadratic formula to find the roots:
x = [-b +/- √(b²-4ac)]/2a,
The a, b and c coefficients are based on the general form of the quadratic equation: ax² + bx + c. Hence, a=1, b=-3 and c=-10. Substituting the values:
x = [-(-3) +/- √((-3)²-4(1)(-10))]/2(1)
x = 5, -2
Therefore, the roots of the cubic equations are x = 1, x = 5 and x =- 2. These are the x-intercepts of the equation. At temperatures °C, 5°C and -2°C, there is no change in water vapor in a cloud. The graph is shown in the attached picture
Step-by-step explanation:
A sinusoid with amplitude 6 has a minimum value of 4. What is its maximum value?
Answer: Max Value is y = 16
========================================================
Explanation:
The amplitude is the vertical distance from the horizontal center line to either the peak or valley.
The minimum value is 4. The distance from the min value to the center is 6 units. So the center is at 4+6 = 10.
Then we go another 6 units up to arrive at the max value 10+6 = 16
Refer to the diagram below. I recommend drawing out a sine curve along with the vertical y axis number line.
Answer:
The maximum value: 16
Step-by-step explanation:
Given
Amplitude A = 6Minimum value min = 4We know that a function's amplitude A can be interpreted as the difference between the average between its maximum and minimum and its minimum.
\(A\:=\:\frac{max+min}{2}-min\)
solving for max
\(2A\:=\:max+min\:-2\:min\)
\(2A+2\:min=max+min\)
\(\:2\left(A+min\right)=max+min\)
\(max\:=2\left(A+min\right)-min\)
substituting A = 6 and min = 4
\(max\:=2\left(6+4\right)-4\)
\(max=\:2\left(10\right)-4\)
\(max\:=\:20-4\)
\(max = 16\)
Therefore, the maximum value: 16
Solve 58 - 10x ≤ 20 + 9x.
Helpppppppppppppppppp
Answer:
B is the right answer I believe
Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
Answer:
(a). y = 3x - 11 ; (b). y = \(-\frac{1}{3}\) x - 1
Step-by-step explanation:
Parallel lines have the same slopes
Slopes of perpendicular lines are opposite reciprocals.
(3, - 2)
The slope of given line is 3
(a). Equation of ║ line is
y + 2 = 3(x - 3)
y = 3x - 11
(b). Slope of perpendicular line is \(-\frac{1}{3}\)
y + 2 = \(-\frac{1}{3}\) (x - 3)
y = \(-\frac{1}{3}\) x - 1
The required equation of a line parallel to the line will be y = 3x - 7
The required equation of the perpendicular line is y = -1/3 - 7
Using the coordinate points to get the equation of the line (1, -4) and (2, -1)
The standard form of the equation is expressed as y = mx + b
m is the slope
b is the y-intercept
Get the slope:
m = y2-y1/x2-x1
m = -1+4/2-1
m = 3/1
m = 3
Get the y-intercept
-4 = 3(1) + b
b = -4-3
b = -7
The required equation of a line parallel to the line will be y = 3x - 7
For the equation of the line perpendicular, the slope of the line will be -1/3
The required equation of the perpendicular line is y = -1/3 - 7
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Simplify - 4 of u-2
Answer:
it's 30
Step-by-step explanation:
30+4_2= dakukabilat
a rising unemployment rate affect a society by:
A. discouraging busissnesses from investing
B.making it harder for citizens to find jobs
C. causing inflation rates to rise rapidly.
D.reducing the value of a country's currency
Answer: B
Step-by-step explanation:
just took the quiz
A rising unemployment rate affect a society by making it harder for citizens to find jobs.
What is Unemployment?The term unemployment refers to a situation where a person actively searches for employment but is unable to find work.
As, we know that unemployment means the shortage of jobs for the citizens.
So, rising unemployment rate in society creating trouble for the citizens to find jobs.
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Here are the shopping times (in minutes) of ten shoppers at a local grocery store.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of shopping times in that class.
(Note that we are using a class width of 5.)
The frequency which is to filled in the table is 1, 4, 2 and 4.
Given that;
All shopping time of ten shopkeeper:
25, 29, 25, 18, 24, 28, 36, 25, 33, 37
We have to complete the frequency in the table. Frequency of something is the number of times that number is coming.
Since, Shopping time is given as ,
25, 29, 25, 18, 24, 28, 36, 25, 33, 37
And, Intervals for which frequency is given is ,
18 to 22, 23 to 27, 28 to 32, 33 to 37.
Hence, WE get;
Numbers in the range 18 to 22 = 18 therefore 1
Numbers in the range 23 to 27 = 25, 25, 24, 25 therefore 4
Numbers in the range 28 to 32 = 29, 28 therefore 2
Numbers in the range 33 to 37 = 36, 33, 37, therefore 3
Hence, the frequency which is to filled are 1, 4, 2 and 4.
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Helppppp quick please!!
This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.
What are functions ?
In mathematics, a function is a rule that maps each element in a set (the domain) to a unique element in another set (the range). It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are commonly represented using function notation, where the symbol "f" is used to represent the function, and the input value is placed inside parentheses. For example, if the function takes the input "x" and returns the output "y"
According to the question:
To prove algebraically that g(x) = f(x), we need to show that the expressions for g(x) and f(x) are equivalent for all values of x. That is, we need to show that:
2x²+3x-1 = x²-3
We can start by simplifying both sides of the equation:
2x²+3x-1 - (x²-3) = 0
Simplifying the left side, we get:
2x²+3x-1 - x²+3 = x²+3x+2
Now we can simplify the right side:
x²+3x+2 = (x+1)(x+2)
Substituting this expression back into the equation, we get:
2x²+3x-1 - x²+3 = (x+1)(x+2)
Simplifying the left side again, we get:
x²+3x-4 = (x+1)(x-4)
Now we have:
(x+1)(x-4) = (x+1)(x+2)
We can cancel out the factor of (x+1) from both sides, since it is not equal to zero for any value of x:
x-4 = x+2
Subtracting x from both sides, we get:
-4 = 2
This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.
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It is expected that 30% of the criminals in our prisons are violent offenders, 65% are nonviolent, and 5% are actually innocent. A sample of 300 inmates showed that 90 were violent offenders, 200 were nonviolent, and 10 were innocent. At the .05 significance level, can we conclude that the observed frequencies are different than the expected frequencies?