A line passes through the points (-2, 9) and (1, 3).
Click “show your work” and provide work for calculating the slope and y-intercept. Then, write the equation for the line in slope-intercept form. Please write your answers on the lines provided on the whiteboard.
The slope is 4.
The y-intercept is 17.
The slope-intercept form is y = 4x +17
How to write the equation of a line in slope-intercept form?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system
The slope-intercept form of the equation of a line is y = mx+b,
where m is the slope and b is the y-intercept
The line passes through points (-2, 9) and (1, 3).
m = (y₂-y₁)/(x₂-x₁)
where (x₁, y₁) = (-2, 9)and (x₂, y₂) = (1, 3)
m = (3-(-9)) / (1-(-2)) = 12/3 = 4
Using y = mx + b with (-2, 9) to find b:
9 = 4(-2) + b
9 = -8 + b
b = 9 + 8
b = 17
Thus, the equation of the line is y = 4x + 17
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Circles centered at $A$ and $B$ each have radius 2. Point $O$ is the midpoint of $\overline{AB}$, and $OA = 2\sqrt2$. Segments $OC$ and $OD$ are tangent to the circles centered at $A$ and $B$, respectively, and $\overline{EF}$ is a common tangent. What is the area of the shaded region $ECODF$? Round your answer to the nearest tenth.
The area of the shaded region ECODF is given by 8√2 - 4 - π units and rounding it to the nearest tenth we get, 4.2 units.
From the given diagram we can deduce that -
Area(ECODF) = Area(ABFE) − Area(OAC) − Area(OBD) − Area(CAE)− Area(DBF)
OA = OB = 2√2
⟹AB = EF = 4√2
AE = BF = 2
Area(ABFE) =2 × 4√2 = 8√2
Now, AC = BD =2
OC = OD = [tex]\sqrt{(2\sqrt{2})^{2} - 2^{2}}[/tex]
=√(8−4)
= √4
= 2
Area(OAC) = Area(OBD) = 12 × 2 × 2 = 2
Triangles OAC and OBD are isosceles right triangles:
∠OAC = ∠OBD = 45°
Sectors CAO and DBF have central angles:
∠CAE = ∠DBF = 90° − 45° = 45°
Area(CAE) = Area(DBF) = 45/360 × π(2^2) = π/2
hence, the area of region ECODF is given by -
Area(ECODF) = 8√2 - 2(2) - 2(π/2)
Area(ECODF) = 8√2 - 4 - π
and rounding it to the nearest tenth we get, 4.2 units.
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The complete question is -
Circles centered at $A$ and $B$ each have radius 2. Point $O$ is the midpoint of $\overline{AB}$, and $OA = 2\sqrt2$. Segments $OC$ and $OD$ are tangent to the circles centered at $A$ and $B$, respectively, and $\overline{EF}$ is a common tangent. What is the area of the shaded region $ECODF$? Round your answer to the nearest tenth.
Graph the solution to this inequality on the number line.
x+3<-6
First select the correct ray. Then select the location of the endpoint to plot the inequality on the number line.
The solution set for the inequality given in the task content as required is; x < -9.
The graph of the inequality on the number line is such that it includes all points to the left of -9 on the number line.
What is the graph of the inequality; x + 3 < -6?It follows from the task content that the graph of the inequality x + 3 < -6 as required is to be determined.
Since the given inequality is; x + 3 < -6.
The inequality can be solved by first subtracting 3 from both sides of the inequality; subtractive proper of inequalities;
x + 3 - 3 < -6 - 3
x < -9.
On this note, the correct ray is that which points leftwards with an open ring (indicating the < sign).
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pls solveee (correct answers only and explaintion)
There are 26 children in a class, 16 brown-haired and 10 black-haired. Two students are randomly selected for a stage performance. What is the probability of two brown-haired students being selected?
A: 61.5%
B: 36.9%
C: 35.5%
D: 13.8%
The probability of selecting brown-haired children is 61.5%. The correct option is A.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of samples
Given that there are 26 children in a class, 16 are brown-haired and 10 are black-haired. Two students are randomly selected for a stage performance.
The probability will be calculated as,
Probability = 16 / 26
Probability = 0.615 x 100
Probability = 61.5%
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a taguchi loss function implies that the loss to company as the process output varies on either side of the process mean remains constant regardless of how far the output varies from this mean.T/F
The given statement "A Taguchi loss function suggests that regardless of how much the output deviates from the process mean on either side, the loss to the company remains constant" is TRUE.
What is the Taguchi loss function?The Japanese business statistician Genichi Taguchi created the Taguchi loss function, a graphical representation of loss, to describe a phenomenon that affects the value of a company's products.
It clarified the idea that quality does not suddenly decline when, for example, a machinist exceeds a strict plan tolerance, which was praised by Dr. W. Edwards Deming, the business guru of the e American quality movement in the 1980s.
Instead, the value of the "loss" grows over time as the deviation from the anticipated condition rises.
This was seen as a milestone in describing the quality and contributed to the growth of the continuous improvement movement.
According to the Taguchi loss function, as process variation drifts further and further from the mean, the loss to the organization grows.
Therefore, the given statement "A Taguchi loss function suggests that regardless of how much the output deviates from the process mean on either side, the loss to the company remains constant" is TRUE.
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POINTS!!!!!!!!!!
Answer:
Step-by-step explanation:
a) correct
b) incorrect, its actually approximately 94cm^3
c) correct
d) correct
e) incorrect, its actually around 188cm^3
i tried, i hope this works :)
a department srore is ordering the fall line of shoes. which of the following statistical measurements would they use to determine what sizes they should order the most?
The statistical measurement used by the stores to order the shoes to determine the appropriate sizes is mode.
What is mode?It is referred to as the mode value and is defined as the data's highest frequency as well as how frequently the element appears in the data set. The value that appears most frequently in a given set is the mode. Additionally, we can refer to the value or number in a data collection that occurs more frequently as the mode or modal value.
When a department store is ordering line of shoes, the store needs to collect the data and analyze the representation and organization.
Hence, mode is the correct answer.
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Use the distributive property with factoring to find the equivalent expression.
21x + 39z = (7x + z)
The equivalent expression is 14x + 38z = 0.
What is an expression?We have to note that an expression has to do with a mathematical statement. According to the distributive property, we can be able to open up the brackets over the values that we have in the question.
As such we would have;
21x + 39z = (7x + z)
Removing the brackets;
21x + 39z = 7x + z
Then we collect the like terms;
21x - 7x = z - 39z
14x = -38z
14x + 38z = 0
This is the expression that is equivalent to the one given above.
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What is the value of angle A
Answer:
130
Step-by-step explanation:
add 140 and 90
subtract 230 from 360
through: (1,1), slope =5
Answer:
y = 5x - 4
Step-by-step explanation:
For this question, use the slope-intercept formula: y=mx+b
y=mx+b ==> 1 = (5)(1) + b ==> plugin point (x=1, y=1) and m=5; m is the slope
1 = 5 + b ==> solve for b
-4 = b ==> subtract 5 on both sides
y = 5x + (-4) ==> plugin -4 for b in the equation y=mx+b
y = 5x - 4 <== simplified equation
Answer:
The line is y = 5x - 4-----------------------------------
The line has a slope of 5 and passes through the point (1, 1).
Use point-slope form:
y - y₁ = m(x - x₁)Substitute coordinates:
y - 1 = 5(x - 1)Convert the equation into slope-intercept form:
y - 1 = 5x - 5y = 5x - 5 + 1y = 5x - 4When drawing a card from a deck of 52 cards, (13 clubs, 13 hearts, 13, spades, and 13 diamonds with each kind having A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, O, k) what is the probability of drawing a Heart or a Seven?
Answer:
There are 52 cards in a deck, and 13 of them are hearts. Therefore, the probability of drawing a heart is 13/52, or approximately 0.25.
There are also four sevens in a deck (one of each suit), so the probability of drawing a seven is 4/52, or approximately 0.08.
To find the probability of drawing either a heart or a seven, we need to add the probabilities of these two events together. Therefore, the probability of drawing a heart or a seven is 0.25 + 0.08, or approximately 0.33. This can also be written as a fraction as 13/52 + 4/52, which simplifies to 17/52.
Overall, the probability of drawing a heart or a seven from a standard deck of cards is approximately 0.33, or 17/52.
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The length of the metal bar if The sides of the cuboid are 2 m, 3 m, and 4 m, is 5.4 meters approximately so, option C is correct.
What is a cuboid?A shape created by stacking numerous congruent rectangles on top of one another. The resultant shape is known as a cuboid. Take a look at the following cuboid to see how it displays its three dimensions: length, width, and height.
Given:
The sides of the cuboid are 2 m, 3 m, and 4 m,
Calculate the length of the metal bar as shown below,
The length of the metal = √(2² + 3² + 4²)
The length of the metal = √(4 + 9 + 16)
The length of the metal = √29
The length of the metal = 5.38 meter
Thus, the length of the metal bar is 5.4 meters.
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A 12 year old child has been prescribed tofranil at bedtime for enuresis a typical adult maintenance dose of tofranil is 100 mg daily the medication is available in 10 25 and 50 mg tablets what is the approximate maintenance dose that can be administered to the child based on this information
Based on this information the approximate maintenance dose that can be administered to the child to achieve 100 mg daily of the medication is as follows for:
10 mg (10 tablets)25 mg (4 tablets) 50 mg ( 2tablets)SolutionThe question states that the 12-year-old child be administered 100 mg daily the medication is available in 10, 25 and 50 mg tablets.
For the administration of 10 mg tabletsto achieve 100 mg daily dose
1 tablet = 10 mg
10 mg *10tablets = 100 mg
For the administration of 25 mg tabletsto achieve 100 mg daily dose
1 tablet = 25 mg
10 mg *4tablets = 100 mg
For the administration of50 mg tabletsto achieve 100 mg daily dose
1 tablet = 50 mg
10 mg * 2tablets = 100 mg
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Please help!! Thank you so much if you do :)
The area of the triangle ABD is 45 inches², the area of the triangle ADC is 30 inches², and the area of the triangle ABC is 75 inches².
What is triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices, known as a triangle.
Given:
The measure of sides CD = 6 inches, BD = 9 inches, AD = 10 inches,
Calculate the area of ABD and ADC as shown below,
The area of ABD = 1 / 2 × BD × AD
The area of ABD = 1 / 2 × 9 × 10
The area of ABD = 45 inches²
The area of ADC = 1 / 2 × AD × CD
The area of ADC = 1 / 2 × 6 × 10
The area of ADC = 30 inches²
The area of Δ ABC = 1 / 2 × BC × AD
The area of Δ ABC = 1 / 2 × 15 × 10
The area of Δ ABC = 75 inches²
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A city requires that smoke detectors be installed in all houses. There is concern that too many houses are still without detectors, so a costly inspection program is being considered. Let p be the proportion of all houses that have a detector. A random sample of 25 houses is selected. If the sample strongly suggests that p < 0.80 (less than 80% have detectors), as opposed to p ≥ 0.80, the program will be implemented. Let x be the number of residences among the 25 that have a detector, and consider the following decision rule: Reject the claim that
p ≥ 0.8
and implement the program if x ≤ 17. (Round your answers to three decimal places.)
The probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 17) = 0.10912
How to solve binomial probability distribution?A binomial experiment is defined as one in which the probability of success doesn't change with every run or number of trials.
The outcome of each trial of a binomial experiment is independent of one another.
Binomial distribution function is represented by the formula;
P(X = x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ
Where;
p is the true proportion.
n is sample size
x is number of successes
a) We want to find the probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 17)
We are given that the claim is that 80% of houses have smoke detectors is rejected if in a sample of 25 houses, not more than 15 houses have smoke detectors.
Thus;
Sample size; n = 25
Number of successes required = 17
Probability of success; p = 0.80
Thus;
P(X ≤ 17) = Sum of probabilities from P(X = 0) to P(X = 17)
Using online binomial probability calculator gives us;
P(X ≤ 17) = 0.10912
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Word blanks are:
Blank 1: The Pythagorean Theorem
Blank 2: √91.
Blank 3: a leg
Blank 4: The hypotenuse.
Blank 5: 10.34
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
From the diagram:
To find the length of the diagonal from point A (front/bottom/left) to point G (back/top/right):
You would first use the Pythagorean Theorem on the bottom of the box rectangle to find the diagonal AC = √91
Then use CG as a leg of the triangle ACG, with AG being the hypotenuse.
AG is approximately = 10.34
Word blanks are:
Blank 1: The Pythagorean Theorem
Blank 2: √91.
Blank 3: a leg
Blank 4: The hypotenuse.
Blank 5: 10.34
Therefore, the blank words are given above.
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he profit for a production process is equal to $2,000
minus two times the number of units produced. The
mean and variance for the number of units produced
are 500 and 900, respectively. Find the mean and variance of the profit.
Answer:I don’t know
Step-by-step explanation:
Find A given that (3, 1, -1) || (A, -4, 4)
Answer: A=-12
Step-by-step explanation:
-4/1 is -4
4/-1 is also -4
Then multiply 3 by -4 to get -12
what is equivalent to 2/1 & 4/2
Answer:
There are infinite answer for this. Here are a few.
6/3, 10/5, 0.5, 100/50, 25/50, -10/-5
Step-by-step explanation:
If 40% of a number is 56, what was the original number?
-4,-1,-6,-11,-16,Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.)?
Here we have an arithmetic sequence where we just need to add 5 to each term to get the next one.
Which is the pattern in these numbers?The actual pattern seems to be:
-4, 1, 6, 11, 16
This seems to be an arithmetic sequence, to check that, just take any pair of consecutive terms and take the difference between them.
For the first two:
1 - (-4) = 5
For the second two:
6 - 1 = 5
For the third two:
11 - 6 = 5
And so on.
So we just add 5 to the previous term to get the next one, that is the pattern.
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Ill give brainliest to the person who answer
Answer:
1/2
Step-by-step explanation:
Perpendicular slopes must be opposite reciprocals of each other (their product should equal -1), so first find the slope of the line in the graph.
Slope = rise / run = -2 / 1 = -2
If the slope of the perpendicular line is m, we know -2m=-1. Dividing both sides by -2, we get m = 0.5 = 1/2
Model Real Life You want to stack
1/4cups in minute. Your first
attempt takes 1/2minute. Your second
attempt takes 3/10minute less than your
first attempt. Do you meet your goal?
Explain.
The real life need to stack ¼ cups in a minute would not be met in the given time after being calculated.
What is the equivalent of one minute?The equivalent of one mini is 60 seconds. The given expressions would be calculated in seconds to find the portion of minutes in each phase.
The actual desire is to Stack 1/4 = 60 seconds
The first attempt = 1/4 for 1/2 ×60 seconds = 30 seconds
The second attempt = 1/4 for 3/10 × 60 secs = 18 secs less than first attempt which is= 30 -18 = 12 secs
Since in both cases 30 and 18 seconds are not up to 1 minute, you weren't able to reach your goal.
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An online music club offers individual songs for one price or entire albums
for another Kendrick pays $14.90 to download 5 individual songs and
1 album Geoffrey pays
s $21.75 to download 3 individual songs a
s and 2 albums.
S
a. How much does the music club charge to download a song?
b. How much does the music club charge to download an entire album?
Answer:
To solve for the price of a single song, we can set up the following equation:
Kendrick paid $14.90 for 5 songs + 1 album = $x for a single song
We can solve for x by dividing both sides of the equation by 5:
$14.90 / 5 = $x / 5
This simplifies to:
$x = $2.98
So the music club charges $2.98 to download a single song.
To solve for the price of an entire album, we can set up the following equation:
Geoffrey paid $21.75 for 3 songs + 2 albums = $y for an entire album
We can solve for y by subtracting the cost of the songs from both sides of the equation:
$21.75 - $2.98 * 3 = $y - $2.98 * 3
This simplifies to:
$12.79 = $y
So the music club charges $12.79 to download an entire album.
Step-by-step explanation:
Answer:
$1.15 and $9.15
Step-by-step explanation:
let s represent the cost of a song and a represent the cost of an album , then
5s + a = 14.9 → (1)
3s + 2a = 21.75 → (2)
multiplying (1) by - 2 and adding to (2) will eliminate a
- 10s - 2a = - 29.8 → (3)
add (2) and (3) term by term to eliminate a
- 7s + 0 = - 8.05
- 7s = - 8.05 ( divide both sides by - 7 )
s = 1.15
substitute s = 1.15 into either of the 2 equations and solve for a
substituting into (1)
5(1.15) + a = 14.9
5.75 + a = 14.9 ( subtract 5.75 from both sides )
a = 9.15
(a) the charge for downloading a song is $1.15
(b) the charge for downloading an album is $9.15
In a pizza eating contest, a participant can eat 3 slices of pizza in 2 minutes. If he continues to eat at this rate, then how many slices of pizza will he eat in 10 minutes? Double number lines
Answer:
Step-by-step explanation:
15
Answer: The answer is 30
Step-by-step explanation: Just do 2 times 3. 10 times
Given f (x)=-3x-2 and g (x)=-4x+4, find (f times g)(4).
f (x) = 3x - 2
g(x) = 4x + 4
fg (4) = ?
fg (x) = f (4x + 4)
3( 4x+4) - 2
12x + 12-2
fg (x) = 12x+10
fg(4) =( 12 × 4) + 10
fg(4) = 48 + 10 = 58
Q3. The diagonals AC and BD of a parallelogram ABCD intersect at O. If P is the midpoint of AD, prove that
a) PQ || A B
b) PO=1/2 CD.
Answer:
Step-by-step explanation:
a) To prove that PQ || AB, we can use the fact that in any parallelogram, the opposite sides are parallel and equal. Therefore, since AD is parallel to AB, the line PQ which connects the midpoint of AD to the opposite corner A will also be parallel to AB.
b) To prove that PO = 1/2 CD, we can use the fact that in any parallelogram, the diagonals bisect each other. Therefore, since AC and BD intersect at O, PO must be equal to 1/2 of its length. Since the length of CD is twice that of PO, it follows that PO = 1/2 CD.
Find g(x), where g(x) is the translation 6 units left of f(x) = x².
Write your answer in the form a(x - h)+k, where a, h, and k are integers.
The function g(x) can be expressed as g(x) = a(x - h) + k, where a is the coefficient of x (which is 1 for f(x) = x^2), h is the horizontal shift, and k is the vertical shift.
To translate a function 6 units left, we need to shift it horizontally by -6 units. So, h = -6.
Since the function g(x) is a translation of f(x), a and k will have the same values as in f(x). In this case, a = 1 and k = 0.
Therefore, the function g(x) that represents the translation 6 units left of f(x) is:
g(x) = a(x - h) + k
= 1(x - (-6)) + 0
= 1(x + 6) + 0
= x + 6
the answer is: g(x) = x + 6
the equation of a line is y+4=6x+13
what is the value of y at the point where the line crosses the y-axis?
y = 9
The y-axis is the vertical axis in a coordinate system, and a point on the y-axis has an x-coordinate of 0. The equation of a line is a mathematical expression that describes the relationship between the x- and y-coordinates of points on the line.
To find the value of y at the point where the line crosses the y-axis, we need to substitute x=0 into the equation of the line and solve for y. This will give us the value of y at the point where the line intersects the y-axis.
For the given equation y+4=6x+13, substituting x=0 gives us:
y + 4 = 6*0 + 13
y + 4 = 13
y = 9
Therefore, the value of y at the point where the line crosses the y-axis is 9. This means that the point where the line intersects the y-axis has coordinates (0,9).
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