Answer:
c = 6.
Step-by-step explanation:
x^2+cx+9 = (x + b)^2 where b is a constant
x^2 + cx + 9 = x^1 + 2bx + b^2
so 2b = c
and b^2 = 9
So b = 3
and c = 2*b = 6
To solve this problem, we will use the fact that the square of a binomial (a+b)^2 is equal to a^2 + 2ab + b^2.
Let's start by assuming that x^2 + cx + 9c is the square of a binomial (a+b)^2. Expanding (a+b)^2 using the formula above, we get:
(a+b)^2 = a^2 + 2ab + b^2
If we compare this to x^2 + cx + 9c, we see that:
a^2 = x^2 (1)
2ab = cx (2)
b^2 = 9c (3)
From (1), we get a = ±√x^2 = ±x.
Substituting a = ±x into (2), we get:
2(±x)b = cx
Simplifying this equation, we get:
b = ±(c/2)
Substituting a = ±x and b = ±(c/2) into (3), we get:
x^2 + (c/2)^2 = 9c
Multiplying both sides by 4, we get:
4x^2 + c^2 = 36c
Rearranging this equation, we get:
4x^2 - 36c + c^2 = 0
This is a quadratic equation in c. Using the quadratic formula, we get:
c = (36 ± √(36^2 - 4(4)(c^2))) / (2(4))
Simplifying this equation, we get:
c = (9 ± √(81 - c^2)) / 2
Since c is nonzero, we can ignore the solution c = 0. Therefore, we have:
c = (9 + √(81 - c^2)) / 2 or c = (9 - √(81 - c^2)) / 2
We can check that both solutions satisfy the original condition that x^2 + cx + 9c is the square of a binomial.
However, we need to ensure that the square root in each solution is real, which means that 81 - c^2 ≥ 0.
For the first solution, we have:
81 - c^2 ≥ 0
c^2 ≤ 81
|c| ≤ 9
Therefore, the first solution is valid for c such that -9 ≤ c ≤ 9.
For the second solution, we have:
81 - c^2 ≥ 0
c^2 ≤ 81
|c| ≥ 9
However, we already know that c is nonzero, so |c| > 0. Therefore, the second solution is not valid for any value of c.
Therefore, the only valid solution is:
c = (9 + √(81 - c^2)) / 2, for -9 ≤ c ≤ 9.
I hope this helps! Let me know if you have any questions.
If x^2 + cx + 9c is equal to the square of a binomial, then it can be written in the form (x + A)^2, where A is a constant. Expanding the square of the binomial, we get:
(x + A)^2 = x^2 + 2Ax + A^2
Comparing this with the given expression, x^2 + cx + 9c, we can deduce the following:
2A = c and A^2 = 9c
We are asked to find the value of c. Using the first equation (2A = c), we can substitute c in the second equation:
A^2 = 9(2A)
A^2 = 18A
Since A is nonzero, we can divide both sides by A:
A = 18
Now, using the first equation, we can find the value of c:
c = 2A
c = 2(18)
c = 36
Therefore, the value of c is 36.
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function notation. help please
Answer: i got no answer.
Step-by-step explanation:
lol sorry im just putting this for the points
The upper-left coordinates on a rectangle are (3, -3), and the upper-right coordinates are (7, -3). The rectangle has an area of 16 square units.
Draw a rectangle on the coordinate plane below.
(Khan Academy)
The coordinates of the rectangle are (3,-3), (3, -7), (7, -7) and (7, -3).
We also know that the distance between the left and right sides of the rectangle is 4 (since the x-coordinate of the right side is 7 and the x-coordinate of the left side is 3). So we have the equation:
4x = 16
Solving for x, we get x = 4. This means that the length of the top and bottom sides of the rectangle is 4 units. The height of the rectangle is 16/4 = 4 units.
Now that we know the length and height of the rectangle, we can draw it on the coordinate plane.
The left side starts at (3, -3) and ends at (3, -7). The right side starts at (7, -3) and ends at (7, -7).
The top side starts at (3, -3) and ends at (7, -3). The bottom side starts at (3, -7) and ends at (7, -7).
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Find four rational number between-1and-1/2
Answer:
For finding 4 rational numbers between two numbers we just multiply the numerator and denominator
Rational numbers -1 and -1/2 are -1/4,-1/8,-1/12,-1/16
This means the four rational numbers are -1/4,-1/8,-1/12,-1/16
Enter the letter of the graphed
function.
a.y= (x + 2)(x - 1)(x-3)
b.y = (x + 2)(x - 1)(x - 3)²
c. y = (x + 2)(x - 3)(x - 1)²
d.y= (x - 1)(x − 3)(x + 2)²
e.y = (x - 1)(x − 3)(x + 2)³
-
-
Enter
Answer: B
Step-by-step explanation:
It bounces off of x=3 take opposite sign when you put in parenthesis
(x-3)² the bounce makes it squared on outside
(x-1) goes through 1
(x+2) goes through -2
put it togehter
(x-3)²(x-1)(x+2) B
pls help with a detailed explanation!
IQ scores are normally distributed, with a mean of 100 and a standard deviation of 15. What is the minimum score required to be considered as a part of the 2%?
The minimum IQ score required to be considered as a part of the 2% is approximately 68.25, obtained by converting the score into a standard normal distribution and using the z-score for the 2nd percentile
What is percentile?A percentile is a measure used in statistics to indicate the percentage of data values that fall below a particular value in a distribution, often used to describe test scores, rankings, and other quantitative data.
What is Standard Normal Distribution?The standard normal distribution is a specific normal distribution with a mean of 0 and a standard deviation of 1, used to standardize any normal distribution to compare and analyze data from different sources.
According to the given information:
To find the minimum IQ score required to be considered as a part of the 2%, we need to use the standard normal distribution table.
First, we need to convert the given distribution with a mean of 100 and a standard deviation of 15 into a standard normal distribution with a mean of 0 and a standard deviation of 1. We can do this by using the formula:
z = (x - μ) / σ
where x is the IQ score, μ is the mean (100), and σ is the standard deviation (15).
Substituting the values, we get:
z = (x - 100) / 15
Now, we need to find the z-score corresponding to the 2nd percentile, which is the value below which 2% of the scores fall. From the standard normal distribution table, the z-score for the 2nd percentile is approximately -2.05.
Substituting this value into the formula:
-2.05 = (x - 100) / 15
Solving for x, we get:
x = -2.05 x 15 + 100
x ≈ 68.25
Therefore, the minimum IQ score required to be considered as a part of the 2% is approximately 68.25.
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the double number line shows that faye can sort 150150150 recyclable items in 333 minutes. 003333time (minutes)00150150150150items a double number line with 6 equally spaced tick marks. the line labeled time, minutes, reads from left to right: 0, two unlabeled tick marks, 3, two unlabeled tick marks. the line labeled items, reads from left to right: 0, two unlabeled tick marks, 150, two unlabeled tick marks. based on the ratio shown in the double number line, how many recyclable items can faye sort in 444 minutes?
Faye can sort 22,200 recyclable items in 444 minutes, based on the ratio shown in the double number line.
To determine how many recyclable items Faye can sort in 444 minutes, we need to use the ratio shown in the double number line. We can do this by finding the slope of the line, which is the ratio of the change in items to the change in time.
To find the slope, we start at the point (0,0) on the number line and move to the point (150,3). The change in items is 150 - 0 = 150, and the change in time is 3 - 0 = 3. Therefore, the slope is:
slope = change in items / change in time
slope = 150 / 3
slope = 50
This means that Faye can sort 50 recyclable items in one minute. To find out how many items she can sort in 444 minutes, we simply multiply the number of minutes by the rate of 50 items per minute:
items sorted = rate x time
items sorted = 50 x 444
items sorted = 22,200
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
We have a box plot.
From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.
Then, Q1 is 17 and Q3 is 21.
Now, Interquartile range
= Q3 - Q1
= 21 - 17
= 4
Thus, The IQR is the best measure of variability, and it equals 4.
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1. Given the ratio below, find the other two trig ratios for it. Show your work. Make sure to give a rationalized answer.
1) tan θ = (3-√3)/9
2. Find the other two trig ratios for it. Show your work.
2) sin θ = 8/10
Step-by-step explanation:
1) We can start by finding the adjacent and opposite sides of the right triangle using the Pythagorean theorem. Let x be the length of the adjacent side, then:
tan θ = (3-√3)/9
tan θ = opposite/adjacent
(3-√3)/9 = opposite/x
opposite = (3-√3)x/9
Using Pythagorean theorem:
(adjacent)^2 + (opposite)^2 = (hypotenuse)^2
x^2 + [(3-√3)x/9]^2 = (hypotenuse)^2
x^2 + (9-6√3+3)x^2/81 = (hypotenuse)^2
(82-54√3)x^2/81 = (hypotenuse)^2
We can simplify this expression to find the hypotenuse:
(hypotenuse)^2 = [(82-54√3)/81]x^2
hypotenuse = sqrt[(82-54√3)/81]x
Now we can find the other trig ratios:
cos θ = adjacent/hypotenuse = x/sqrt[(82-54√3)/81]x
cos θ = 1/sqrt[(82-54√3)/81]
cos θ = sqrt[(82+54√3)/81] / [(82-54√3)/81]
cos θ = sqrt(82+54√3) / (82-54√3)
sin θ = opposite/hypotenuse = (3-√3)x/9 / sqrt[(82-54√3)/81]x
sin θ = (3-√3) / sqrt(82-54√3)
2) To find the other trig ratios, we need to first find the adjacent and hypotenuse sides of the right triangle. Let x be the length of the adjacent side, then:
sin θ = opposite/hypotenuse = 8/10
opposite = (8/10)hypotenuse = 0.8hypotenuse
Using Pythagorean theorem:
(adjacent)^2 + (opposite)^2 = (hypotenuse)^2
x^2 + (0.8hypotenuse)^2 = hypotenuse^2
x^2 + 0.64h^2 = h^2
x^2 = 0.36h^2
x = 0.6h
Now we can find the other trig ratios:
cos θ = adjacent/hypotenuse = 0.6h/h = 0.6
tan θ = opposite/adjacent = (8/10)/0.6 = 4/3
cot θ = 1/tan θ = 3/4
.1428 rounded to the nearest thousandth
Rounding a number means changing its value to a number that is closer to a certain level of precision or a certain place value. When we round a number, we usually specify the level of precision or place value that we want the rounded number to have. For example, we might want to round a number to the nearest whole number, to the nearest tenth, or the nearest thousandth.
The process of rounding involves looking at the digit in the place value that we want to round to and using the digit to the right of it to determine whether to round up or down.
Rules of Rounding:
If the digit to the right of the place we are rounding to is 5 or greater, we round up. If the digit to the right of the place we are rounding to is less than 5, we round down.The place values to the right of the decimal point, or the right of one's place in number, are called decimal places. The decimal places are numbered starting from the tenth place, which is one place to the right of the decimal point. The next place to the right is the hundredth place, followed by the thousandth place, and so on.
The third place to the right of zero is the thousandth place. When rounding to the nearest thousandth we have to look at the fourth decimal place to see whether it must be rounded up or down. The fourth digit is an 8 which is greater than 5. So we must round the thousandth place up.
This gives us 0.143, rounded to the nearest thousandth.
What is the inverse of function g(x) = -x-2/x+4 ? G^-1(x)=
Answer:
Step-by-step explanation:
Malik just got hired for a new job and will make 96,000 in his first year Mallon was told that he can expect to get raises of 5,000 every night forward
The amount he will receive as his salary in the 18th year of working at this job will be $107,500
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized.
The amount of money Jamar made in his first year= $48,000
The salary rise per year = $3,500
The amount of money he will make for the extra 17 years is
= 17 × $3,500
= $59,500
he will receive as his salary in the 18th year working at this job = $48,000 + $59,500 = $107,500
Therefore the amount he will receive as his salary in the 18th year of working at this job will be $107,500
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help plssss i neeed this done
The complete answers are:
If c=√a+b² and u=√a+b² then, c must equal u.If two triangles have the same side lengths, then the triangles are congruent.ΔSTU was drawn to include a right angle at angle U.If two triangles are congruent, then the corresponding parts of the triangles are also congruent.A right triangle is defined as a triangle that has a right angle. This description fits triangle ABC, so triangle ABC is a right triangle.What are right angles and congruent angles?Right angles are angles that are equal to 90 degrees.
A triangle that includes a right angle is known as a right-angled triangle.
Congruent angles are angles that are equal in size or measure. For example, the right angles in two or more right-angled triangles are congruent.
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Quest
Which describes the correct pairing of DNA bases?
OA. A with G, and C with T
OB. A with A, and G with G
O C. A with T, and C with G
OD. A with C, and T with G
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The correct pairing of DNA bases is: A with T, and C with G. The Option C is correct.
What is the correct pairing of DNA bases?The correct pairing of DNA bases is established by the rules of base pairing in DNA structure which is known as Chargaff's rules.
According to the rule, the adenine (A) pairs with thymine (T) and cytosine (C) pairs with guanine (G); these pairing are based on the complementary nature of the DNA bases where adenine forms two hydrogen bonds with thymine, and cytosine forms three hydrogen bonds with guanine.
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Part A
Solve 83x + 1 = 16. Round to the nearest thousandth, if necessary.
x =
Part B
Find the key features of f(x) = 83x + 1.
y-intercept:
asymptote: y =
The solution to the equation 83x + 1 = 16, rounded to the nearest thousandth, is x = 0.181, the key features of the function f(x) = 83x + 1 are; y-intercept; (0, 1), and Asymptote; None.
To solve 83x + 1 = 16, we need to isolate x on one side of the equation. We can do this by subtracting 1 from both sides and then dividing by 83;
83x + 1 - 1 = 16 - 1
83x = 15
x = 15/83
Rounded to the nearest thousandth, x is approximately 0.181.
Therefore, the solution to the equation 83x + 1 = 16, rounded to the nearest thousandth, is x = 0.181.
The function f(x) = 83x + 1 is a linear function in the form y = mx + b, where m is the slope and b is the y-intercept. Therefore;
The y-intercept is (0, 1), since b = 1.
The function does not have an asymptote, since it is a linear function and it does not approach any particular value as x increases or decreases.
So the key features of the function f(x) = 83x + 1 are;
y-intercept; (0, 1)
Asymptote; None.
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Right triangle ABC is graphed in the xy coordinate plane with vertices at (0,0) , (5, 0) and (5, 12) If is the angle in the triangle at the origin, what is the cos(pi + theta)?
Answer:
Step-by-step explanation:
ince right triangle ABC is graphed in the xy-coordinate plane with vertices at (0,0), (5,0) and (5,12), we can use the coordinates of the vertices to find the lengths of the sides of the triangle.
The length of side AB is 5 units, the length of side BC is 12 units, and the length of side AC is given by the Pythagorean theorem:
AC^2 = AB^2 + BC^2
AC^2 = 5^2 + 12^2
AC^2 = 169
AC = 13
Therefore, right triangle ABC is a 5-12-13 triangle.
The angle at the origin is opposite to the side of length 12, so it is the angle opposite to the side BC. We can find this angle using the inverse tangent function:
tan(theta) = opposite / adjacent
tan(theta) = 12 / 5
theta = tan^-1(12/5) ≈ 68.2°
Since cos(pi + theta) = -cos(theta), we have:
cos(pi + theta) = -cos(theta) = -cos(tan^-1(12/5))
Using the identity cos(arctan(x)) = 1 / sqrt(1 + x^2), we can simplify this expression:
cos(tan^-1(12/5)) = 1 / sqrt(1 + (12/5)^2) = 5 / 13
Therefore, cos(pi + theta) = -cos(theta) = -cos(tan^-1(12/5)) = -5/13.
Ethan rolls a number cube with sides numbered 1 through 6. If he rolls the number cube 150 times, how many times would he expect to roll a 5 or a 6?
Answer:
Do 1:6 150x =6x5
Step-by-step explanation:
it wouuld be 2/6*150=50
y = –3x – 8 y 4x – 3y + 15 = 0
Answer:
-8xy^4 -3x -3y+ 15
The solution to the system of equations is (-3, 1).
The system of equation is given as:
y = –3x – 8 ....(i)
4x – 3y + 15 = 0 ....(i)
Substitute the value of equation (i) into (ii):
4x – 3(–3x – 8) + 15 = 0
4x + 9x + 24 + 15 = 0
13x = - 24 - 15
13x = -39
Divided by 13 both sides of the equation,
x = -3
Substitute the value of x = -3 into equation (i),
y = –3(-3) – 8
y = 9 - 8
y = 1
Thus, the solution to the system of equations is (-3, 1).
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The complete question is as follows:
Find the solution to the system of equations:
y = –3x – 8 ....(i)
4x – 3y + 15 = 0 ....(i)
A rectangular park is 75 yards wide and 110 yards long.give the length and width of another rectangular park that has the same perimeter but a larger area.
Answer: Thus, the width of the second park is 92.5 yards, and its length is also 92.5 yards.
Step-by-step explanation: The perimeter of the first rectangular park is:
P = 2L + 2W
P = 2(110 yds) + 2(75 yds)
P = 220 yds + 150 yds
P = 370 yds
Since the second rectangular park has the same perimeter as the first, its perimeter is also 370 yards. Let's call its width "x" and its length "y".
Then, we have:
2x + 2y = 370
Simplifying this equation, we get:
x + y = 185
The area of the second park is:
A = xy
To find the dimensions of the second park with the largest area, we need to maximize this expression subject to the constraint x + y = 185.
One way to do this is to use the method of Lagrange multipliers. However, in this case, we can use a simpler approach based on the fact that the area of a rectangle is maximized when its sides are equal. Therefore, we can set x = y = 185/2 = 92.5.
Let the vector
�
v have an initial point at
(
7
,
−
6
)
(7,−6) and a terminal point at
(
6
,
−
3
)
(6,−3). Determine the components of vector
�. V
The components of the vector with initial point (7,−6) and a terminal point at (6,−3) are:
(6, -6) to (3, -6)(7, -6) to (6, -6)How to find the components of the vectorThe components of a vector are the vectors that makes up the resultant as described in the problem to have starting point (7,−6) and terminal point (6,−3).
This can be gotten by plotting these points and getting the coordinates of the points that makes the initial point and the terminal point the hypotenuse of the triangle
From the graph, the coordinates are:
component 1: (6, -6) to (3, -6)
component 2: (7, -6) to (6, -6)
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Help me please stuck on this question
The number of time spent in each class is 1 1/15 ( optionA)
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
The total number of hours spend in the class is calculated as;
7 3/5 -(1/2+7/10)
38/5 - (1/2 +7/10)
38/5 - (5+7)/10
38/5 - 12/10
=( 76-12)/10
= 64/10 hours
therefore since he attended six classes,
the number of time spent In class is calculated as ;
64/10÷6
= 64/10 × 1/6
= 64/60
= 16/15
= 1 1/15 hours
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Cindy makes scented candles to give as holiday gifts to 8 friends. She melts 6 bags of wax chips. Each bag contains 20 ounces of wax chips. After melting the wax, she pours it equally into 8 candle jars. How many ounces of wax does Cindy use for each candle?
15 ounces of wax Cindy use for each candle.
To find out how many ounces of wax Cindy uses for each candle, we need to divide the total amount of melted wax by the number of candles.
First, let's find the total amount of melted wax:
6 bags * 20 ounces/bag = 120 ounces
Cindy melted 120 ounces of wax in total.
Now, let's divide the total amount of melted wax by the number of candles to find out how many ounces of wax Cindy used for each candle:
120 ounces / 8 candles = 15 ounces/candle
Therefore, Cindy used 15 ounces of wax for each candle.
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Determine which equations represent a proportional relationship. Select all that apply.
A - y=-x
B -y=9x² +3
C- y=0.5x
D- y=x+7
Lucas has 2.67 quarts of motor oil left in his garage to use for an oil change. The vehicle’s engine requires 5 quarts. How much more oil does he need?
A 1.67 quarts
B 2.33 quarts
C 5.67 quarts
D 10.67 quarts
at the forrester manufacturing company, one repair technician has been assigned the responsibility of maintaining four machines. for each machine, the probability distribution of the running time before a breakdown is exponential, with a mean of 8 hours. the repair time also has an exponential distribution, with a mean of 4 hours. (a) find the probability distribution of the number of machines not running, and the mean of this distribution. (b) what is the expected fraction of time that the repair technician will be busy?
(a) The probability distribution of the number of machines not running, and the mean of this distribution is 0.899.
(b)The expected fraction of time that the repair technician will be busy is 88.9% of the time.
(a) Let X be the number of machines not running. At that point, X can take on values 0, 1, 2, 3, or 4. We will discover the likelihood conveyance of X as takes after:
P(X = 0) = P(all machines are running) = [tex]e^(-84)^4[/tex]/4! = 0.302
P(X = 1) = P(one machine isn't running) = (4)([tex]e^(-84)^3[/tex]/3!) = 0.393
P(X = 2) = P(two machines are not running) = (6)([tex]e^(-84)^2[/tex]/2!) = 0.236
P(X = 3) = P(three machines are not running) = (4)([tex]e^(-84)^1[/tex]/1!) = 0.067
P(X = 4) = P(all machines are not running) = [tex]e^(-8*4)^0[/tex]/0! = 0.002
The cruel(mean) of this dispersion is E(X) = (0)(0.302) + (1)(0.393) + (2)(0.236) + (3)(0.067) + (4)(0.002) = 0.899.
(b) Let Y be the division of time that the repair specialist is active. At that point, Y can be communicated as
Y = T/(T + R),
where T is the full time that machines are not running
and R is the entire time that went through on repairs.
We know that
T has an Erlang dispersion with parameters
n = 4 and λ = 1/8 (since the running time of each machine has exponential dissemination with cruel 8 hours).
Subsequently, the anticipated esteem of T is E(T) = n/λ = 32 hours.
Additionally, R has an exponential dispersion with cruel 4 hours,
so E(R) = 4 hours. In this way, we have:
E(Y) = E(T/(T + R))
= E(T)/E(T + R)
= 32/(32 + 4)
= 0.889.
In this manner, ready to anticipate the repair professional to be active around 88.9% of the time.
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what line passes through (3,-1) and is perpendicular to x+4y=10
The equation of a line passing through (3, -1) and is perpendicular to x+4y=10 is y = 4x - 13.
Given that a line is passing through (3, -1) and is perpendicular to x+4y=10,
We need to find the equation of the line,
The slope-intercept of a line is, y = mx+c, where m is the slope.
Converting the given line into its slope-intercept form =
x + 4y = 10
4y = -x + 10
y = -x/4 + 5/2
Therefore, the slope is -1/4.
We know that the slopes of two perpendicular lines are negative reciprocal of each other.
So, the slope of the asked line is 4.
Therefore, the equation in form of c is =
y = 4x+c
To find c put x = 3, y = -1 in the equation above,
-1 = 4(3) + c
-1 = 12 + c
c = -13
Now, the equation is y = 4x - 13.
Hence the equation of a line passing through (3, -1) and is perpendicular to x+4y=10 is y = 4x - 13.
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one population proportion test: which of the following situations involves testing a claim about a single population proportion? a recent study estimated that 20% of all college students in the united states smoke. the head of health services at goodheart university suspects that the proportion of smokers may be lower there. a certain prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of a certain chemical. the manufacturer takes a sample to check whether the mean concentration is the required 245 ppm or not. according to the college board, which administers the sat exam, the average score for females is lower than for males among graduating seniors in 2011. an educational researcher wants to test whether this is also true in her school district. a statistics student at tacoma community colleges wants to determine whether there is a difference in
The situation involving testing a claim about a single population proportion is: "The head of health services at Goodheart University suspects that the proportion of smokers may be lower there."
In this situation, the researcher is interested in testing a claim about the proportion of smokers in a single population, namely the population of college students at Goodheart University. The researcher suspects that the proportion of smokers at Goodheart University may be lower than the estimated proportion of 20% for all college students in the United States.
To test this claim, the researcher would conduct a hypothesis test for a single population proportion, where the null hypothesis would be that the proportion of smokers at Goodheart University is equal to 20%, and the alternative hypothesis would be that the proportion is less than 20%.
Based on the sample data, the researcher would then either reject or fail to reject the null hypothesis, and make conclusions about whether there is evidence to support the claim that the proportion of smokers at Goodheart University is lower than the national average.
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Om= -4/13
Solve the system of equations.
y=1-2x
4x + 2y = 0
Ono solution
O (1,0)
O infinitely many solutions
O (0,0)
Question 13 of 20
Answer: No solution.
Step-by-step explanation:
To solve, we will substitute the first equation into the second equation for the value of y.
Given:
y = 1 - 2x
4x + 2y = 0
Substitute:
4x + 2(1 - 2x) = 0
Distribute:
4x + 2 - 4x = 0
Subtract 2 from both sides of the equation:
4x - 4x = -2
0 = -2
We see that the variables cancel out each other, and now we have nothing to solve or continue moving forward within our solution. This means that there are no solutions to this system of equations.
This means that the lines are parallel. We can also see this when we graph the system, see attached. This becomes more clear when we change both of the equations into slope-intercept form. 4x + 2y = 0 becomes y = -2x, which has the same slope as the first equation (again, parallel lines). If they also had the same y-intercept there would be infinitely many solutions, however, they do not.
help me asap pls and thank you
The probability of drawing 1 red marble and 1 blue marble from the given boxes is 2/7.
The probability of drawing 1 red marble and 1 blue marble from the given boxes can be calculated using the concept of probability and sample space. The probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. The sample space can be defined as the set of all possible outcomes.
Given, a box contains 4 white marbles and 3 red marbles. A second box has 3 white marbles and 6 blue marbles. If one marble is drawn from each box, the probability that 1 red marble and 1 blue marble will be drawn can be calculated as follows:
The total number of possible outcomes is given by the product of the number of marbles in each box:
Total number of possible outcomes = 7 × 9 = 63
The number of favorable outcomes can be calculated by considering all possible cases where one red marble is drawn from the first box and one blue marble is drawn from the second box.
The number of ways to draw one red marble from the first box = 3
The number of ways to draw one blue marble from the second box = 6
Therefore, the number of favorable outcomes = 3 × 6 = 18
Hence, the probability of drawing 1 red marble and 1 blue marble can be given as follows:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 18/63
The probability of drawing 1 red marble and 1 blue marble from the given boxes is 2/7.
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complete question:
a box contains 4 white marbles and 3 red marbles. a second box has 3 white marbles and 6 blue marbles. if one marble is drawn from each box, what is the probability that 1 red marble and 1 blue marblle will be drawn
2. Similar triangles are
are
8
10
-5: Find the value of x.
shown.
shown. Solve for the variable.
x5
Based on the corresponding sides, the calculated value of x in the similar triangles is x = 7.5
Finding the value of x in the similar trianglesFrom the question, we have the following parameters that can be used in our computation:
The similar triangles
As a general rule, the corresponding sides of similar triangles are in proportions
Using the ratio of corresponding sides, we have
x : 10 = 6 : 8
Express as fraction
This gives
x/10 = 6/8
Multiply both sides by 10
x = 60/8
Divide
x = 7.5
Hence, the value of x in the similar triangles is x = 7.5
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