A line that is perpendicular to the line y = -1/3x + 7 has a slope that is the negative reciprocal of -1/3 which is 3.
We know that the line intersects the point (4,2), so we can use this point and the slope to write the equation of the line in point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.
So the equation of the line that is perpendicular to y = −1/3x + 7 and intersects the point (4,2) is:
y - 2 = 3(x - 4)
Simplifying this, we get
y = 3x - 2
To convert this to the slope-intercept form we can rewrite it as
y = 3x + b
Therefore, the equation of the line that is perpendicular to y = −1/3x + 7 and intersects the point (4,2) is y = 3x - 2
THE AREA OF A SECTOR IS A = 384 in².
A. IF THE RADIUS IS 24 IN. , WHAT IS THE MEASURE OF THE CENTRAL ANGLE, IN RADIANS?
B. IF THE CENTRAL ANGLE MEASURES RADIANS, WHAT IS THE RADIUS OF THE CIRCLE? ROUND TO THE NEAREST HUNDREDTH.
A) The measure of the central angle is [tex]\frac{4}{3} \pi[/tex] .
B) The radius of the circle is 55.43 in.
A) We know,
The area of a sector is [tex]\frac{n}{2\pi } \pi R^{2}[/tex]
where n = the degree of the central angle of the sector
R = radius of the circle
Suppose, the measure of the central angle is x.
[tex]\frac{x}{2\pi } .\pi .24^{2} = 384\pi[/tex]
⇒ [tex]\frac{x}{2\pi } = \frac{384\pi }{576\pi }[/tex]
⇒ [tex]x = \frac{384\pi }{576\pi } * 2\pi[/tex]
⇒ [tex]x = \frac{4}{3} \pi[/tex]
So, the measure of the central angle is [tex]\frac{4}{3} \pi[/tex].
B) Suppose the radius of the circle is r in.
[tex]\frac{\pi /4}{2\pi } .\pi .r^{2} =384\pi[/tex]
⇒[tex]\frac{1}{8} .\pi .r^{2} =384\pi[/tex]
⇒ [tex]r^{2} = 384\pi / \frac{1}{8} \pi[/tex]
⇒ [tex]r^{2} = 3072[/tex]
As r > 0
So, r = 55.43
Hence, The radius of the circle is 55.43 in.
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t
he points that are on the graph of the function defined by y=2x+3
.
The point that lies on the function defined by the equation is (2, 7)
How to determine the point that lies on the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 3
The point in the ordered pair that lies on the graph of the equation is the solution set
Take for instance, we set x = 2
So, we have the following representation
y = 2 * 2 + 3
Evaluate the product and the sum
This gives
y = 7
When repesented as an ordered pair, we have
(2, 7)
Hence, the point is (2, 7)
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Divide the following: MUST SHOW WORK. (30 points)
On dividing the expression [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)], the value obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The expression is given as - [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)]
Apply the fraction rule, (a/b)/(c/d) = a·d/b·c
= [(x²-9) × (x²-2x-15)]/[(x²-4x-5) × (x²+5x+4)]
= [(x²-9) × (x+3)]/[(x²-4x-5) × (x+1)]
Expand the expression -
= [(x²-9) × (x+3)]/(x³-3x²-9x-5)
= (x³+3x²-9x-27)/(x³-3x²-9x-5)
= 1 + [(6x²-22)/(x³-3x²-9x-5)]
Therefore, the expression obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].
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give three points that lie on a line with a slope of -2/5
The three points that lie on a line y = -2/5x with a slope -2/5 will be:
(0, 0)
(5, -2)
(10, -4)
How to illustrate the slope?Given slope = m = -2/5. We suppose the line passes through the origin, so b = 0
substituting m = -2/5 and b = 0 in the slope-intercept form
y = -2/5x + 0
y = -2/5x
Thus, the equation of line with the slope m = -2/5 and passes through the origin (0, 0) will be:
y = -2/5x
As the equation of line passes through (0, 0), thus the point (0, 0) lies on the line.
Putting x = 0 in the equation y = -2/5x
y = -2/5 × (0)
y = 0
Thus, (0, 0) is the point which also passes through the line
Putting x = 5 in the equation y = -2/5x
y = -2/5 × 5
y = -2
Thus, (5, -2) is the point which also passes through the line.
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a light post casts a shadow on a small boy. the boy, who is 4 feet 6 inches tall, notices that his shadow is 3 feet 4 inches long. he decided that if he measures how far he is from the light post, he can determine how tall the post is from the ground. explain how he can figure out the height of the light post. use mathematical reasoning.
The small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.
Similar triangles are triangles that have the same shape but can have different sizes. In this case, the shadow of the boy, the boy himself, and the light post form similar triangles.
Let h be the height of the light post, x be the distance between the boy and the light post, and s be the length of the shadow, we can use the following ratios -
(boy's height) / (boy's shadow) = (light post height) / (light post shadow)
i.e. (4 feet 6 inches) / (3 feet 4 inches) = (h) / (x)
Now, we can find the height of the light post by using the above equation and the given values of the boy's height and the shadow.
The small boy can measure the distance between him and the light post, and he can use this value in the above equation to determine the height of the light post. The equation is h/x = (4.5)/(3.33)
This is the ratio of the height of the light post and the distance between the boy and the light post, so h = (4.5 * x) / (3.33)
In this way, the small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.
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• The dimensions of a rectangle are 3x by 4x-9. Find x if the perimeter is 52.
Draw a picture if you need a visual
Answer:
x = 6, length of the rectangle is 18cm, and width is 21cm
Step-by-step explanation:
To solve this problem, we can use the perimeter of a rectangle formula: P = 2l + 2w.
Here, l = 3x and w = 4x - 9, so the perimeter is P = 2(3x) + 2(4x - 9) = 52.
Solving for x, we get x = 6.
Therefore, the length of the rectangle is 3x = 18 cm, and the width is 4x - 9 = 21 cm.
Quadrilateral ABCD'is a reflection of quadrilateral ABCD over the x-axis.
What is the length of A'D' ?
A. 3 units
B. 7 units
C. 4 units
D. 6 units
option D is correct- The length of quadrilateral of A’D’ is 6. When it is reflected ,the lengths don’t change.
image is attached below,
Quadrilateral
A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.
Reflection
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
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Systems of Linear Inequalities
PLEASE HELP
Th systems of Linear Inequalities are:
x>=-7,
y<6-2x/3,
y<=-1,
y>3/5x-5,
y<6+5x
How to solve the linear inequalities?Step1:
x>=-7,y<6-2x/3,y<=-1,y> 3/5x-5,y<6+5x: [x>=-7]
[y<6-2x/3]
[y<=-1]
[ y>3/5x-5]
[y<6+5x]
x>=-7
[tex]3y+2x < 6\sy < =-1\sy > \frac{3}{5}[/tex]
x-5\sy-5x<6
Separate y for 3y+2x6 as follows: y6-2x/3 3y+2x6
Step2:
shuffle twice to the right side
Divide both sides by 3 using the formula 3y/6/3-2x/3.
simplify
3y/3<6/32x/3
Simplify 3y/3 by dividing it by y.
3/3=1
simplify 6/3-2x/3: 6-2x/3
6/3-2x/3
Apply the formula a/c + b/c = a+-b/c = 6-2x/3 y 6-2x/3
Identify y for y-5x6: y6+5x y-5x6.
Y=6+5x move the right side by 5x.
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dr. green is interested in conducting a 2 x 2 x 3 within-group factorial design, with 20 participants in each cell. how many participants does she need overall?
she need 240 number of participant .
Graphing cell means to picture primary impacts and connections. The numbers in the secret elements address bunch implies in a 2 x 2 x 3 plan. The negligible means for factors An and B are likewise shown. The cell implies are plotted as line diagrams and as reference charts.
Now, According to the question:
We have Dr. Green is interested in conducting a 2 x 2 x 3 within-group factorial design.
There are 12 cells in factorial, and each cell 20 participant.
Then, number of participant = 20(12) = 240 participant.
Thus, she need 240 number of participant .
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A painter is making a mural on the side of a building. In planning this project, he first creates the same painting on a normal sized sheet of paper at a scale of 2 in. to 5 ft. If the width of the paper drawing is 4.9 inches, what will be the width of the mural (in feet) when it is finished?
The width of the mural (in feet) when it is finished is equal to 12.25 feet.
What is scale factor?In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Scale factor = 2/5
For the width of the mural (in feet), we have:
2/5 = 4.9/x
x = (5 × 4.9)/2
x = 24.5/2
x = 12.25 feet.
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researchers collect data about juuling by asking users to keep track of the number of times per day they turn their device on and the number of inhalations each time they turn the device on. what type of data are these? group of answer choices interval nominal ratio ordinal
The given data is ordinal data.
This type of data is ordinal data, as the variables are collected on an ordered scale (the number of times per day the device is turned on and the number of inhalations per activation). Although the actual numerical values may not have equal distances, they can still be ordered and compared based on the magnitude of the numbers.
Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. These statistics are presented on an ordinal scale, one of the four measurement levels that S. S. Stevens described in 1946.
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What do the measures of angles BDA and BEA and the fact that and are radii of circle A tell us about and Explain your answer
The measures of angles BDA and BEA is 90 degree and the fact that AD and AE are radii of circle A tell us about BD and BE must be a tangent to the circle.
The tangents to the circle are BD and BE.
∠BDA = 90
∠BEA = 90
Radii = AD and AE
A tangent's angle with a circle's radius is always measured as a 90-degree angle.
∠BDA = 90, and since AD is a radius, BD must be a tangent to the circle.
Similar, ∠BEA = 90 suggests that BE is a tangent to the circle and that AE is a radius.
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The complete question is:
What do the measures of angles BDA and BEA and the fact that AD and AE are radii of circle A tell us about BD and BE?
16/1 x 3/8 in simplest form
Answer: 6
Step-by-step explanation:
1. 16/1 × 3/8= 48/8
2. 48/8= 6
Find a unit vector that has the same direction as the given vector. -3i + 7j
The unit vector that has the same direction as the given vector is[tex]& (3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
The given vector(v) is -3i+7j
The unit vector is found by dividing the vector by its magnitude
Unit vector of [tex]$v=\frac{v}{\|v\|}$[/tex]
A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector.The formula of unit vector in the direction of a given vector is:
Unit Vector = Vector/Vector's magnitudeWe have to find the magnitude first
So,
[tex]& \|v\|[/tex] =[tex]\sqrt{(3)^{2}+(-7)^{2} } =\sqrt{9+49} =\sqrt{58}[/tex]
[tex]& \|v\|=\sqrt{58}[/tex]
The unit vector is:
The i, j, and k are the unit vectors in the directions of the x-axis, y-axis, and z-axis respectively in a 3-dimensional plane. i.e.,
|i| = 1|j| = 1|k| = 1[tex]$$\begin{aligned}& =(1 / \sqrt{58})(3 \mathrm{i}-7 \mathrm{j}) \\& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}\end{aligned}$$[/tex]
Therefore, the unit vector is [tex]& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
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From the observation deck of a skyscraper, Morgan measures a 67
∘ angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
Angle of depression and elevation:The angle of depression refers to the angle above the hill.The ship is 349.8 feet away from the skyscraper's base horizontally.
How far does the ship extend horizontally from the skyscraper's base?You could calculate the angle of elevation, for instance, if you were standing on the ground and were looking up at a mountain's summit.
The angle between a line of sight's horizontal axis and its downward axis is known as the angle of depression.
The ship is 349.8 feet away from the skyscraper's base horizontally.
Angle of depression and elevation:The angle of depression refers to the angle above the hill.
given the aforementioned variables
The harbor is 824 feet tall.
Depression angle is 67 degrees.
SOH CAH TOA identification claims that:
Tan = opp/adj Tan = 824 Tan = 67
d = 824.8/tan67 d = 349.8 feet
Therefore, the vertical distance from the skyscraper's base to the ship is 349.8 feet.
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Find the measures of the numbered angles.
Answer: ∠1= 75°, ∠2= 105°, ∠3=105°, ∠4=75°, ∠6=105°, ∠7= 105°, ∠8=75°
Step-by-step explanation:
∠1 is corresponding to angle 75° which make them equal.
∠2 is supplementary to ∠1 which means they add up to 180°. Since ∠1 is 75° you would subtract 75° from 180° to get 105°.
∠3 is vertical to ∠2 which makes them equal.
∠4 is vertical to ∠1 which makes them equal.
∠6 is corresponding to ∠2 which makes them equal.
∠7 is vertical to ∠6 which makes them equal.
∠8 is vertical to 75° which makes them equal.
Does someone mind helping me with this problem? Thank you!
Answer:
0.01 goes in the first box
0.10 goes in the second box
Therefore, the first equation is 0.01p + 0.10d = 1.50
===========================================================
Reason:
The last part mentions "A penny is 0.01" which means $0.01 or 1 cent. The 0.01 is the coefficient of the variable p.
1 penny = $0.01
p number of pennies = 0.01p dollars
A similar situation happens with the dimes.
Use the box method to distribute and
simplify (-5x - 2) (5x + 4). Drag and
drop the terms to the correct locations of
the table.
( − 5x − 2)(5x+4)
You must answer all questions above
in order to submit.
Create a table with the place values for the first and second factors down the left and the top and bottom, respectively.
What is the box method?
Multiplication using the box method: Create a table with the place values of the first and second factors down the left and the top and bottom, respectively. Second step: multiply the place values and add the results to the table. Step 3: Add up all of the table's rows. Step 4: Add the sums of these rows.
Placing the first word in the first box and the last term in the last box is the first step in utilizing the box technique to factor a trinomial. Multiply the first and last boxes after that. Identify the first and last boxes' products, which together make up the middle word. Put these words in the remaining spaces.
Here's how you can use the box method to distribute and simplify the expression:
( -5x - 2 ) ( 5x + 4 )
⇒-5x -2
⇒5x 4
⇒-25x^2 -10x + 20x - 8
⇒-25x^2 + 10x - 8
So the simplified expression is:
-25x^2 + 10x - 8.
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Set up a system of equations for the given information by filling in the boxes with the coefficients of the variables and the constant values, where is the amount invested in stocks, is the amount invested in bonds, and is the amount invested in CD's. If there is no visible coefficient, then enter for the coefficient. If a specific variable is not present in the equation, then enter for the coefficient. Country Day's scholarship fund receives a gift of $200000. The money is invested in stocks, bonds, and CDs. CDs pay 5% interest, bonds pay 2.9% interest, and stocks pay 10.9% interest. Country day invests $20000 more in bonds than in CDs. The total amount earned from the investments is $11165. Total amount invested: + + = Total amount earned from investements: + + = Relation of bonds and CDs: + + =
The system of equations is:
a + b + c = 2000000.109a + 0.029b + 0.05c = 11165b = c + 20000How to determine the system of equationsFrom the question, we have the following parameters that can be used in our computation:
Total amount invested = $110000
Using the fiollowing variable representations:
Amount invested in stocks = a Amount invested in bonds = bAmount invested in CD's = cWe have
a + b + c = 200000
Using the total interest earned of 7145, we have:
10.9% * a + 2.9% * b + 5% * c = 11165
So, we have
0.109a + 0.029b + 0.05%c = 11165
Country day invests $20000 more in bonds than in CDs.
So, we have
b = c + 20000
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Mary decided to look at new and used cars. Mary found a used car for $10000. Mary found that she paid 40% of the price of a new car. How much would a new car cost
Answer: i don't know sorry 99
Step-by-step explanation:
56+80
Solve the system by substitution. Check your solution. 0.5 x + 0.25 y = 36. y + 18 = 16 x. a. (36, 72) c. (49, 81) b. (9, 126) d. (21, 9) Please select the best answer from the choices provided A B C D
Answer:
Answer is in attached photo. (B)
Step-by-step explanation:
SolutionThe solution is in the attached photo , do note the question might specify the method to use to solve the equations, just like this the question:
1) Substitution Method
2) Elimination Method
The ratio of the volumes of the bags of dog food is [ Select ] which means the scale factor of the dimensions of the two bags is [ Select ] . Therefore the scale factor of the surface area of the two bags is [ Select ] .
Answer:
Step-by-step explanation:
Answer:
20, 2.7, 7.4
Step-by-step explanation:
I completed the assingment and got it 100
Identify bias based on a survey of 2718 people the national opinion research center concluded that 30% 32% of americans always make a special effort to sort and recycle glass cans plastic or papers 24% americans often make such an effort
Based on a survey of 2718 people, a research center concluded that 32% of Americans "always" make a special effort to sort and recycle glass, cans, plastic, or papers. Participation bias is there in this case.
The bias would have no effect on a reader's perception of the assertion because no group of persons is much more likely to respond to the poll than any other.
When comparisons are performed between groups of patients who differ in outcome determinants and the differences are connected to the result, participation bias emerges.
1. Participation bias is inherent in studies that involve participant enrollment.
2 Because selective participation might jeopardize study external validity, determining the magnitude of participation bias is critical for optimizing inference from these investigations.
Few community studies have looked into the impact of participation bias. Nonparticipants in one population-based study of myocardial infarction (MI) were older, had more comorbidity, and had a lower survival rate than participants.
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A local hamburger hop old a combined total of 491 hamburger and cheeeburger on Friday. There were 59 fewer cheeeburger old than hamburger. How many hamburger were old on Friday?
The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.
432 hamburgers.
We can write an equation to represent the information given.
Hamburgers + Cheeseburgers = 491
Cheeseburgers = Hamburgers - 59
Substitute the second equation into the first equation:
Hamburgers + (Hamburgers - 59) = 491
Solve for 'Hamburgers':
2Hamburgers - 59 = 491
2Hamburgers = 550
Hamburgers = 275
Since the question asks for the number of hamburgers, the answer is 275 hamburgers.
The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.
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The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810. Use the mean, median, mode, and range of the rents to answer the following question: Which measure of central tendency best described the advertised rents? Calculate the four measures of central tendency and provide two to four sentences supporting the answer. (I already calculate the four, I just need help with picking out the best one. Range: 880. Mode: 670. Mean: 898. Median: 790)
The MEAN best describes the monthly rents.
The best one is Mean : 898
Now, According to the question:
The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810.
We are required to use the mean, median and mode to explain which measure of central tendency best describes the monthly rent.
The mean, median and mode (as calculated) are the measures of central tendency for the data set given.
This measures which value is closest to the center such that it can conveniently represent every other data. Observe carefully that the least value is 670 while the highest is 1550.
Also, observe that the value which is "more central" to both extremes is the mean.
The median is closer to the lowest value and much farther from the highest value.
The mode is actually at the lowest end of the data set.
However, the mean is safely between both ends. Its farther away from the least value than the median which means its moving closer to the "center" unlike the other two measures.
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Ella has .5 of sugar. How much water should she add to make 1.5% syrup concentration
We need to find how much water Ella needs to make the different concentrations of syrups. The solution will be for 1.5%, we need 32.83 lbs of water.
How to explain the concentration?The percentage in the concentration tells us how much in the mixture is sugar.
So for example, in the 50% syrup, we have a 50% of sugar, meaning that half of it is sugar, and we have 0.5 lbs of sugar, so we need to add the same amount of water, 0.5 lbs of water.
For the 1.5% syrup, this will be:
= (0.5 - 0.5 × 0.015) / 0.015
= 32.83 lbs
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Complete question
Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case. 1.5% syrup?
earle bailey has 20 songs to choose from but can play only 7 in the next half-hour on sirius xm classic.how many different (ordered) playlists are possible
Applying combination, the number of playlist is: 75,435.
How to Apply Combination to Solve a Problem?A combination is a way of selecting a certain number of items from a larger set, without regard to the order of the items.
The number of possible playlists would be the number of ways to select 7 songs out of 20 without regard to order, which is commonly known as a combination.
The formula for combination is nCr, where n is the total number of items and r is the number of items being chosen at a time. So in this case, the number of possible playlists would be 20C7.
This can also be written as 20!/(7!*13!)
The answer is 75,435
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y=x^2+6x+8
solve by using completing the square.
what are the roots/zeros/x-intercepts of your parabola?
The roots of the parabola are given as follows:
x = -2 and x = -4.
How to obtain the roots of the quadratic function?The quadratic function for this problem is defined as follows:
y = x² + 6x + 8.
Completing the squares, the quadratic function can be factored as follows:
y = (x + 4)(x + 2).
As:
The sum of the roots is of 6.The product of the roots is of 8.Then the roots are obtained as follows:
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how many 10-element subsets of {1, 2, 3, . . . , 20} contain at least one odd element? (hint: we are selecting a subset of the previous set, so {1,2,3,4,5,6,7,8,9,10} is the same as {1,2,3,5,4,6,7,8,9,10}.)
The no. of subsets with at least one odd number is ²⁰C₁₀ - 1
We have the sample set to be {1, 2, 3, 4, ... 20}
Now we need to make subsets of 10 from these 20 elements.
Hence, the number of possible subsets of 10 elements will be
²⁰C₁₀
Now, there are 10 odd elements in the given sample set.
Hence the number of sets that contain at least 1 odd element
= Total no. of possible sets - no. of possible sets with no odd no.
Now since there are only 10 even numbers, there can be only one such set possible.
Hence no. of the subsets with at least one odd number is
²⁰C₁₀ - 1
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R
102°
o
S
What is the measure of arc RT?
102 degrees
156 degrees
204 degrees
88 degrees
Previous
E
Please help
The measure of arc RT is: C. 204 degree.
How to find the measure of arc RT?arc ORT = 102° - 90°
arc = 12°
arc ROT = 180° - 2×12°
arc ROT = 180° - 24°
arc ROT = 156°
Hence:
Measure of arc RT
arc RT= 360° - 156°
arc RT = 204°
Therefore the correct option is C.
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