The norm or magnitude of 2v is 11.66. To find the norm, we first need to calculate 2v, which is 10i-6j. Then, we use the formula ||2v|| = [tex]\sqrt{ (100i^2 + 36j^2)[/tex] to find the magnitude of vector 2v, which simplifies to √136 or 11.66 when rounded to two decimal places.
To take care of this issue, we first need to comprehend what the vectors I and j address. In two-layered Cartesian space, I and j are unit vectors along the x-hub and y-hub, separately. That is, I = (1, 0) and j = (0, 1).
Presently, we can communicate the vector v as 5i-3j, and that implies that it has a greatness of √[tex](5^2 + (- 3)^2)[/tex] = √34.
Then, we really want to track down the standard or size of 2v, which is two times the vector v. That is,
2v = 2(5i-3j)
= 10i-6j
To track down the extent of 2v, we can utilize the equation ||2v|| = √( [tex](10i)^2 + (- 6j)^2[/tex] ).
Figuring out the two terms and disentangling, we get
||2v|| = √([tex]100i^2 + 36j^2[/tex])
Since [tex]i^2[/tex] = 1 and[tex]j^2[/tex] = 1, this streamlines to
||2v|| = √(100+36)
= √136
= 11.66 (adjusted to two decimal spots)
Hence, the standard or extent of 2v is 11.66.
To sum up, we began with the vector v = 5i-3j and viewed its greatness as √34. Then, at that point, we multiplied this vector to get 2v = 10i-6j and utilized the equation ||2v|| = √[tex]( (10i)^2 + (- 6j)^2 )[/tex] to find its size, which ended up being 11.66.
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The complete question is:
Let v = 3i-2j and w = 5i+j. Find 2v-w. None of the given answers o 11i-5j oi-5j o i-3; 0 7i+4j
Mason would receive $10,000 every year for five years. The rate of interest is 10%. What would be the present value of the amount that would be received by Mason at the end of five years?
The present value of the payments that Mason would receive over five years is $37,901.
How to Calculate the Present Value of Amount?To find the present value of the payments that Mason would receive over five years, we can use the present value formula for an annuity:
PV = PMT x [1 - (1 + r)^(-n)] / r
Where we have:
PV = present value of the payments
PMT = amount of each payment ($10,000 in this case)
r = interest rate per period (10% or 0.10 in this case)
n = total number of periods (5 in this case)
Plug in the values:
PV = $10,000 x [1 - (1 + 0.10)^(-5)] / 0.10
PV = $10,000 x [1 - 0.6209] / 0.10
PV = $10,000 x 3.7901
PV = $37,901
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Graph this point on the coordinate plane.
(−412, −2)
The given coordinate point lies in third quadrant which shown in the graph below.
The given coordinate point is [tex](-4\frac{1}{2}, -2)[/tex].
A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
In the given coordinate point both x-coordinate and y-coordinate are negative.
Hence, the given coordinate point lies in third quadrant which shown in the graph below.
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Five friends A, B. C. D and E play different musical instruments. No two friends play the same number of musical instruments. Flute is the only instrument common between C and E. B and C are the only violin players and when D joins them, all three of them play Congo. Only three friends play Guitar. The Cymbal was the only common instrument among all three-A, B and E considered together. Congo is played by most number of friends. More than 2 people play the flute.
Violin is the instrument played by least number of friends.
Given: We are given that there are five friends A, B, C, D and E. Any two friends do not play the same number of musical instruments. The only instrument that is common between C and E is Flute. B and C are the only players of violin in the whole group and when D joins them, all three of play Congo. There are only three players of Guitar. The Cymbal is the only common instrument among A, B and E. Congo is the most played instrument. Flute is played by more than 2 people.
To Find: We have to find which instrument is played by the least number of friends.
So, we are given that Violin is played by only 2 friends.
We are given that Flute is played by more than 2 people.
Guitar is played by 3 people.
Cymbal is played by at least 3 people i.e., A, B and E
Congo is played by the greatest number of people.
We can see that every instrument other than Violin is played by more than 2 people whereas Violin is played by only 2 people.
Therefore Violin is the least played instrument.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
The given inequality is -3(2x - 5) < 5(2 - x).
The inequality -3(2x - 5) < 5(2 - x) can be solved as follows
-6x+15<10-5x
Add 5x on both the sides of an inequality, we get
-6x+15+5x<10-5x+5x
-x+15<10
Subtract 10 on both the sides of an inequality, we get
-x<-5
Multiply -1 on both the sides of an inequality, we get
x>5
Therefore, an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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what is the value of x if 12= 3/x
The value of the variable x is 1/4
How to determine the valueIt is important to note that algebraic expressions are described as expressions that are made up of terms, variables, constants, factors and coefficients.
Algebraic expressions are also described as expressions that are composed of mathematical or arithmetic operations.
These operations are listed thus;
AdditionMultiplicationDivisionSubtractionBracketParenthesesWe have that;
12= 3/x
cross multiply the values
12x = 3
Make 'x' subject
x = 1/4
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Which is greater 62% or 9/20
To compare 62% and 9/20, we can convert 62% to a fraction with a denominator of 20:
62% = 62/100 = 31/50
Now we can compare 31/50 and 9/20:
31/50 = 0.62
9/20 = 0.45
Since 0.62 is greater than 0.45, we can conclude that 62% is greater than 9/20.
Identify the reflection of the figure with vertices C(-2,4), D (1,5), and E(1, 2) across the x-axis.
The coordinates of the reflected figures are C'(-2,-4), D'(1,-5), and E'(1, -2)
Identifying the reflection of the figure with verticesGiven that we have the figure of the vertices CDE
With the coordinates C(-2,4), D (1,5), and E(1, 2)
The transformation is given as
Reflection over the x-axis
The rule of this transformation is
(x, y) = (x, -y)
So, we have
Image = C'(-2,-4), D'(1,-5), and E'(1, -2)
Recall that
the rule of this transformation is (x, y) = (x, -y)
This means that the x-coordinate remains unchanged while the y-coordinate is negated as a result of this reflection.
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Please help quickly I’m not completely sure on this one
The two inequalities have all the solutions larger than 4 in common.
Which solutions are common for both inequalities?To check this, we just need to solve both inequalities:
The first one is:
-2(c - 4) ≤ -4
-2c + 4 ≤ -4
4 + 4 ≤ 2c
8/2 ≤ c
4 ≤ c
The second one gives:
(1/2)d - 6 > -4
Solving it for d:
(1/2)d > -4 + 6
d > 2*2
d > 4
Then the solutions are:
c ≥ 4
d > 4
The inequalities have almost all the solutions in common, except for c = 4 which is a solution for the first one but not for the second one.
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Quadrilateral H' is the image of quadrilateral H after a sequence of transformations. If quadrilateral H' is congruent to
quadrilateral H, which transformations could have been used?
A. a dilation by a scale factor of 2 followed by a reflection
B. a rotation followed by a dilation by a scale factor of 1/2
C. a reflection, a translation of 1 unit left, and then a dilation by a scale factor of 3
D. a translation of 6 units down, a rotation, and then a reflection
The transformations that could be used are: D. a translation of 6 units down, a rotation, and then a reflection.
How to Determine the Series of Transformation?If two shapes are congruent to each other, it means they have the same shape and size. The only series of transformation that can be used to produce an image that is congruent to a preimage of a shape is either a translation, rotation, or a reflection. This therefore implies that any transformation that involves a dilation will not produce congruent images of a shape but would rather produce similar images.
Therefore, option A, B, and C, which involves dilation cannot produce quadrilateral H' that is congruent to quadrilateral H.
The series of transformation that can produce that is: D. a translation of 6 units down, a rotation, and then a reflection.
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NEED THE ANSWERS TO ALGEBRA 1B RADICAL EXPRESSIONS UNIT 4 LESSON 8 TEST
1. simplify the radical expression
√20
A. 2√10
B. 5√2
C. 2√5
D. 2
In the attachments are some of the questions.
The simplified expressions are;
1) 2√5
2) 6x√2
3) 5xk^2√6x
4) 5√1029y^2
What is a radical expression?Any mathematical expression that uses the square, cube, or higher-order roots of a number or variable is referred to as a radical expression. Variables, coefficients, and operators like addition, subtraction, multiplication, and division can also be included.
Mathematical operations like factoring, reducing the denominator, and employing exponent rules can be used to simplify or alter radical equations.
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Which expression is equivalent to 83,120 in expanded form using powers of 10?
A (8×10) + (3 ×104) + (1x10³) + (2x10²)
B (8*10*)+(3×10³) + (1x10³) + (2x10²)
C (8×10¹)+(3×10³) + (1×10²) + (2×10¹)
D (8×10) +(3×10¹) + (1×10¹) + (2×10¹)
Answer:
The correct answer is B.
83,120 can be written as:
(8 × 10^4) + (3 × 10^3) + (1 × 10^3) + (2 × 10^2)
This is equivalent to option B.
if your restaurant serves 50 bowls of french onion soup daily and each serving has 8 ounces of onions per portion?
To calculate the total amount of onions needed per day, you can multiply the number of servings by the amount of onions per serving.
50 bowls x 8 ounces of onions per bowl = 400 ounces of onions per day.
Therefore, your restaurant will need 400 ounces of onions per day to serve 50 bowls of French onion soup daily
P is the weighted average of point C and D. Find the coordinates of P under the given conditions
Coordinates of P = [tex][(3 * xB + xC + 4 * xD) / 8, (3 * yB + yC + 4 * yD) / 8][/tex]
Coordinates of P = [tex][(4 * xC + 2 * xD + 3 * xE) / 9, (4 * yC + 2 * yD + 3 * yE) / 9][/tex]
Leave the directions of point B alone (x1, y1) and the directions of point D be (x2, y2). Then, at that point, the directions of P are:
[tex][(3x1 + x2)/4, (3y1 + y2)/4][/tex]
Let the directions of point A be (x1, y1) and the directions of point E be (x2, y2). Then, at that point, the directions of P are:
[tex][(x1 + 2x2)/3, (y1 + 2y2)/3][/tex]
Leave the directions of point B alone (x1, y1), the directions of point C be (x2, y2), and the directions of point D be (x3, y3). Then, at that point, the directions of P are:
[tex][(3x1 + x2 + 4x3)/8, (3y1 + y2 + 4y3)/8][/tex]
Leave the directions of point C alone (x1, y1), the directions of point D be (x2, y2), and the directions of point E be (x3, y3). Then, at that point, the directions of P are:
[tex][(4x1 + 2x2 + 3x3)/9, (4y1 + 2y2 + 3y3)/9][/tex]
These recipes can be inferred utilizing the weighted typical equation:
[tex][(w1x1 + w2x2 + ... + wnxn)/(w1 + w2 + ... + wn), (w1y1 + w2y2 + ... + wnyn)/(w1 + w2 + ... + wn)][/tex]
where wi is the heaviness of point I and (xi, yi) are the directions of point I. Subbing the given loads and facilitates into the equations for every issue gives the directions of P for each situation.
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The complete question is:
Find the coordinates of P that represent the weighted average of each set of points based on the given conditions. 12. Point B weighs three times as much as point D. 13. Point E weighs twice as much as point A. 14. Point B has a weight of 3 , point C has a weight of 1 , and point D has a weight of 4. 15. Point C has a weight of 4 , point D has a weight of 2 , and point E has a weight of 3.
81 − x = 9
(a) Find the exact solution of the exponential equation in terms of logarithms.
(b) Use a calculator to find an approximation to the solution rounded to six decimal places.
a) The exact solution of the exponential equation [tex]8^{1-x}=9[/tex] in terms of logarithms is: [tex]x=1-(\frac{2}{3}\times \frac{ln(3)}{ln(2)} )[/tex]
b) An approximation to the solution rounded to six decimal places = 0.056642
Consider the exponential equation [tex]8^{1-x}=9[/tex]
Taking ln (log to the base e) on both the sides of above exponential equation,
ln([tex]8^{1-x}[/tex]) = ln (9)
We solve this equation for x.
We know that the rule of logarithm that [tex]log(a^m)=m\times log(a)[/tex]
Using this rule we get,
(1 - x) ln(8) = ln(3²) ............(3² = 9)
(1 - x) × ln(2³) = 2 × ln(3)
(1 - x) × 3 × ln(2) = 2 × ln(3)
1 - x = (2/3) × (ln(3) / ln(2))
x = 1 - [(2/3) (ln(3) / ln(2))]
x = 1 - [(2/3) × 1.584963]
x = 1 - 1.056642
x = 0.056642
This is the required value of x.
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PLEASE HELP!
Town A is 7 feet below sea level and Town B is 692 feet above sea level. What is the difference in elevation between Town A and Town B?
A. 685 feet
B. 692 feet
C. 695 feet
D. 699 feet
Answer:
D. 699 ft
Step-by-step explanation:
Think of a vertical number line with sea level being 0. Town A is +692 ft and Town B is -7 ft.
Difference in elevation = 692 - (-7) = 699
6. If Jeremy has a batting average
of 0.5014
and Alex has a batting average of 0.50098
who has the better average?
Which projection method is preferred in the United States?
The ________ projection method is preferred in the United States. In this type of projection, the object lies below the horizontal plane and behind the vertical plane.
Answer:
Third Angle Projection method
Step-by-step explanation:
The Third Angle projection method is preferred in the United States. In this type of projection, the object lies below the horizontal plane and behind the vertical plane
How do you solve this? |3x+8|=x
The solutions are S={2,4}
Explanation:
Let's rewrite the equation
|3x−8|−x=0
|3x−8|=3x−8, if 3x−8≥0
and
|3x−8|=−(3x−8)=−3x+8, if 3x−8<0
Let f(x)=|3x−8|−x=0
Let's build a variation table
aaaaxaaaaaaaa−∞aaaaaaaa0aaaaaaaaaa83aaaaaaa+∞
aaaaxaaaaaaaaaaaaa−aaaa#color(white)(aaaaa)+#aaaaaaaa+
aaaa|3x−8|aaaaaa−3x+8a#color(white)(aaa)-3x+8#aaaaa3x−8
aaaaf(x)aaaaaaaaaaax=2a#color(white)(aaaaa)x=2#aaaaaax=4
The solutions are S={2,4}
graph{|3x-8|-x [-7.9, 7.904, -3.95, 3.95]}
is it possible to convert between pounds and inches or between inches and cups?
No. It is not possible to directly convert between pounds and inches or inches and cups.
Conversion between unitsIt is not possible to directly convert between pounds and inches or between inches and cups because they are measuring different things.
Pounds are a unit of weight or mass, while inches are a unit of length or distance. Cups are a unit of volume, which is also different from weight or length.
Thus, all other things being equal it is not possible to directly convert between these units.
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Please help with this questions !!!!!!!!
Based on the information about the angles, the value of x is 10.
How to calculate the value of xFrom the information, n - 2 = 43
Solving for n, we get:
n = 45
The polygon has 45 sides.
sum of interior angles = (n - 2) * 180 degrees
sum of interior angles = (45 - 2) * 180 degrees
sum of interior angles = 7560 degrees
Since the polygon is regular, all of its angles have the same measure, which we are told is (17x+2)°. Let's use this to find x:
sum of interior angles = number of angles * measure of one angle
7560 = 45 * (17x+2)
7560 = 765x + 90
7470 = 765x
x = 10
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Write an equation to represent the fraction models below
Suppose you roll an eight-sided die numbered 1 through 8 on its faces. What is the probability that you roll a 3 or a 7?
Express your answer as a simplified fraction.
The probability that you roll a 3 or a 7 is 1/4.
We have, eight-sided die numbered 1 through 8 on its faces.
Now, the probability to roll 3
= 1/8
and, probability of rolling 7
= 1/8
So, the probability that you roll a 3 or a 7
= 1/8 + 1/8
= 2/8
= 1/4
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The owner of an apple orchard has learned from previous experience that, on average, 5% of the harvested apples have blemishes. The owner randomly selects 10 apples from this year’s harvest. What is the probability that 2 of the apples have blemishes?
The probability that 2 of the apples have blemishes will be 0.0746.
Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as,
[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]
The probability is calculated as,
P(X = 2) = ¹⁰C₂ * (0.05)² * (0.95)⁸
P(X = 2) = 0.0746
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Priya hiked 1 2/3 miles. Diego hiked 1/2 mile. How much farther did Priya hike than Diego?
By taking the difference between the distances, we see that Priya hiked (1 + 1/6) miles more than Diego.
How much farther did Priya hike than Diego?To find this, we just need to take the difference betwee the two distances given.
We know that Priya hiked 1 2/3 miles and Diego hiked 1/2 mile, then the difference is:
D = (1 + 2/3) mi - (1/2) mi
D = (1 + 2/3 - 1/2) mi
D = (1 + 4/6 - 3/6) mi
D = (1 + 1/6) mi
We can see that Priya hiked (1 + 1/6) miles more than Diego.
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The distance farther Priya hike than Diego is 1 1 / 6 miles.
How to find distance travelled?Priya hiked 1 2/3 miles. Diego hiked 1/2 mile. Therefore, let's find how much farther Priya hiked than Diego.
Hence,
Distance hiked by Priya = 1 2 / 3 = 5 / 3 miles
Distance hiked by Diego = 1 / 2 miles
Therefore,
Amount of distance farther Priya hiked than Diego = 5 / 3 - 1 / 2
Amount of distance farther Priya hiked than Diego = 10 - 3 / 6
Amount of distance farther Priya hiked than Diego= 7 / 6 miles
Amount of distance farther Priya hiked than Diego = 1 1 / 6 miles
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If the slope function y=-3.5x+12.8 is changed to 1.5, which of the following best describes the graph of the new function?
The graph of the new function will be a line that is steeper than the original line and slopes upward from left to right.
Since, A slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
The slope of the function y = -3.5x + 12.8 is -3.5. If the slope is changed to 1.5, the graph of the new function will be steeper than the original function.
When the slope of a linear function is positive, the line slopes upward from left to right. When the slope is negative, the line slopes downward from left to right. The greater the absolute value of the slope, the steeper the line.
Since the new slope is positive and greater than 1, the graph of the new function will be a line that is steeper than the original line and slopes upward from left to right.
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Solve for x.
Really easy!! I need quick help tho
algebra/geometry
Answer:
x = -13/7
Step-by-step explanation:
We can solve either by cross-multiplying or by multiplying both sides by the least common denominator, which is the product of the denominators: (5x + 7)(x - 1) in this case.
Both ways will give us the same answer, although cross-multiplying seems much simpler:
[tex]4(x-1)=5(5x+7)\\4x-4=25x+35\\4x=25x+39\\-21x=39\\x=-39/21=-13/7[/tex]
We can check our answer by plugging in -13/7 for x into the equation and see if we get the same answer on both sides:
[tex]4/(5(-13/7)+7))=5/(-13/7-1)\\4/(-65/7+7)=5/(-20/7)\\4/(-16/7)=-7/4\\-7/4=-7/4[/tex]
I need some assistance with this?
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{25}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{24} \end{cases} \\\\\\ x=\sqrt{ 25^2 - 24^2}\implies x=\sqrt{ 625 - 576 } \implies x=\sqrt{ 49 }\implies x=7[/tex]
- Which part of the diagram shows the quantity x? What about 4? What about 17?
Answer:
Which part of the diagram shows the quantity x? What about 4? What about 17?
b. You must add the boxes together to show that it is 17.
How does the diagram show that x+4 has the same value as 17?
c. The value of the x+4 and 17 is the same because according to the diagram the quantity of x+4 is showing 17, so they have the same value.
Remy drew a rectangle that is 9 inches long and has an area of 45 in.² what is the width of Remy’s rectangle right and solve a division equation to show your thinking
Answer:
The division equation used to find the width is: 45 divided by 9 equals 5.
Step-by-step explanation:
The formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width. We know that the length of Remy’s rectangle is 9 inches and the area is 45 square inches. We can use this information to solve for the width: 45 = 9w To solve for w, we can divide both sides of the equation by 9: 45/9 = w 5 = w Therefore, the width of Remy’s rectangle is 5 inches. The division equation used to find the width is: 45 divided by 9 equals 5.
Hope this helps.
Question 3. Instructions are below for each part
Since then, it has spread to other rivers, colonized them, clogged the water intake pipes, and competed with local species for food. Zebra mussels are the method for removing a lot of plankton from the water column.
Here, we have,
The Caspian Sea in Asia is where zebra mussels, or Driessen polymorph, are found naturally.
They arrived in the Great Lakes region in the late 1980s via ballast water from a transatlantic ship.
The Great Lakes, Mississippi, Tennessee, Hudson, and Ohio river basins were all overrun by these mussels within ten years.
The lake's brilliant blue hue is a result of Tahoe's clean air and water.
There is more to this phenomenon than just the fact that Lake Tahoe's surface reflects the sky, which contributes to its blue color.
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complete question:
As you respond to Part A, Part B, and Part C, follow the directions below.
Address all of the instructions in each prompt.
Use evidence from the information provided and your own knowledge of science to support your responses.
Part A
Describe one way scientists near Lake Tahoe can detect if the lake has been impacted by zebra mussels.
