Answers
The measurement of KL is given as follows:
KL = 5.86.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Considering the similar triangles in this problem, the proportional relationship for the side lengths is given as follows:
8.7/KL = 7.8/LJ = 12.18/8.2
Hence the length KL is obtained as follows:
8.7/KL = 12.18/8.2
12.18KL = 8.2 x 8.7
KL = 8.2 x 8.7/12.18
KL = 5.86.
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Related Questions
Surface area of triangular prism
Answers
SA = (perimeter of triangle base) x (height of the prism) + (2 x area of triangle base)
So, if you know the perimeter and height of the triangular base, as well as the area of the base, you can calculate the surface area of the prism by substituting these values into the formula.
For example, if the base has a perimeter of 20 cm and height of 8 cm, and the area of the base is 24 cm², then the surface area of the triangular prism would be:
SA = (20 cm) x (8 cm) + (2 x 24 cm²)
SA = 160 cm² + 48 cm²
SA = 208 cm²
Therefore, the surface area of the triangular prism in this example is 208 cm².
P is a point on the terminal side of 0 in standard position. Find the exact value of the six trigonometric functions for 0 where P (-5, 5)
Answers
We can use the coordinates of point P (-5, 5) to find the values of the trigonometric functions for the angle formed between the positive x-axis and the line passing through the origin and point P.
First, we can find the distance from the origin to point P using the Pythagorean theorem:
r = sqrt((-5)^2 + 5^2) = sqrt(50)
Next, we can use the fact that the sine of an angle is equal to the y-coordinate of a point on the unit circle and the cosine of an angle is equal to the x-coordinate of a point on the unit circle. Since the radius of the unit circle is 1, we need to divide the x and y coordinates of point P by sqrt(50) to get the values for sine and cosine:
sin(θ) = y/r = 5/sqrt(50) = (5/10)sqrt(2) = (1/2)sqrt(2)
cos(θ) = x/r = -5/sqrt(50) = -(5/10)sqrt(2) = -(1/2)sqrt(2)
Next, we can use the fact that the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle:
tan(θ) = sin(θ)/cos(θ) = (1/2)sqrt(2)/(-(1/2)sqrt(2)) = -1
Similarly, we can use the reciprocal identities to find the values of the other three trigonometric functions:
csc(θ) = 1/sin(θ) = sqrt(2)
sec(θ) = 1/cos(θ) = -sqrt(2)
cot(θ) = 1/tan(θ) = -1
Therefore, the exact values of the six trigonometric functions for the angle formed by the line passing through the origin and point P (-5, 5) are:
sin(θ) = (1/2)sqrt(2)
cos(θ) = -(1/2)sqrt(2)
tan(θ) = -1
csc(θ) = sqrt(2)
sec(θ) = -sqrt(2)
cot(θ) = -1
IG:whis.sama_ent
what is the difference between the square of the sum and the square of a difference?
Answers
Answer:
The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared.
Step-by-step explanation:
Thus, this resulting binomial is called a difference of squares.
Answer:
Step-by-step explanation:
Square of the sum
square means you are multiplying something twice and looks like:
ex. [tex]x*x=x^{2}[/tex]
sum is the addition of numbers
so square of the sum looks like:
(a+b)²
Square of the difference
difference means subtraction of numbers
so square of the difference looks like:
(b-a)²
Answer:
The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared.
Step-by-step explanation:
Thus, this resulting binomial is called a difference of squares.
Answer:
Step-by-step explanation:
Square of the sum
square means you are multiplying something twice and looks like:
ex. [tex]x*x=x^{2}[/tex]
sum is the addition of numbers
so square of the sum looks like:
(a+b)²
Square of the difference
difference means subtraction of numbers
so square of the difference looks like:
(b-a)²
Tres amigos van de compras, Juan gasta el doble que Alicia y Ana gasta el triple de Alicia. Si entre los tres han gastado L.
720.00, ¿Cuánto ha gastado cada uno?
Answers
the three friends spent L.120.00, L.240.00, and L.360.00, respectively.
How to solve the problem?
Let's denote the amount that Alicia spends as "x". According to the problem statement, we know that Juan spends twice as much as Alicia, which means he spends 2x. Similarly, we know that Ana spends three times as much as Alicia, which means she spends 3x.
We also know that the three friends together have spent L.720.00. So, we can set up an equation to represent this:
x + 2x + 3x = 720
Simplifying this equation, we get:
6x = 720
Dividing both sides by 6, we get:
x = 120
So, Alicia spent L.120.00, Juan spent twice as much as Alicia, which is L.240.00, and Ana spent three times as much as Alicia, which is L.360.00.
Therefore, the three friends spent L.120.00, L.240.00, and L.360.00, respectively.
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Please answer, this as quick as possible, it’s very important for me, I’ll give brainliest if it’s correct, and try not to use chatgpt or you’ll get reported
Answers
Answer:
Your calculator should be in radian mode.
a)
[tex]f(x) = 56 \sin( \frac{2t\pi}{12} + \frac{\pi}{2} ) + 4[/tex]
b)
[tex]f(x) = 56 \cos( \frac{2t\pi}{12} - \frac{\pi}{2} ) + 4[/tex]
c)
The height of the wheel's central axle is 32 meters.
f(x) = 56sin((2(x + 4)π/12) - (π/2)) + 4
The venue for an outdoor summer concert was divided into 35 sections. The event planner randomly chose 8 sections and counted the number of ice chests in the section, as shown below.
45, 57, 30, 62, 57, 45, 30, 57
Assuming that the sample was representative of the entire venue, what was the mean number of ice chests in a section?
A.
48.5
B.
51
C.
47.875
D.
44.125
please answer
Answers
(45 + 57 + 30 + 62 + 57 + 45 + 30 + 57) / 8 = 383 / 8 = 47.875
Therefore, the mean number of ice chests in a section is 47.875, which is answer choice C.
Answer:
C is correct
Step-by-step explanation:
A bag contains 5 blue marbles, 7 white marbles, and 4 yellow marbles. If two different marbles are drawn from the bag, what is the probability of drawing first a blue marble and then a yellow marble?
Answers
Answer: The probability of drawing a blue marble and then a yellow marble is 1/12 or 0.0833.
Step-by-step explanation:
There are 16 marbles in the bag. To calculate the probability of drawing a blue marble and then a yellow marble, we can use the formula:
P(blue and yellow) = P(blue) x P(yellow|blue)
The probability of drawing a blue marble on the first draw is 5/16. After one blue marble has been drawn, there are 15 marbles left in the bag, so the probability of drawing a yellow marble on the second draw, given that the first marble was blue, is 4/15.
P(blue and yellow) = (5/16) x (4/15) = 1/12 or 0.0833
Tyrone factored the polynomial completely. What is the value of B?
12x4+30x3+4x2+10x
Ax(Bx2+1)(2x+5)
2
3
5
6
Answers
Answer:
the value of B is 3
Step-by-step explanation:
We can start by factoring out the greatest common factor of the polynomial, which is 2x:
2x(6x3 + 15x2 + 2x + 5)
Now, we can factor the expression inside the parentheses by grouping:
2x[(6x3 + 2x) + (15x2 + 5)]
2x[2x(3x + 1) + 5(3x + 1)]
2x(2x + 5)(3x + 1)
Comparing this expression to the given expression:
Ax(Bx2+1)(2x+5)
We see that A = 2, B = 3, and the factor (2x + 5) is the same in both expressions. Therefore, the value of B is 3.
Find the partial fraction decomposition of x^3-x/x^4+2x^2+1
Answers
the partial fraction decomposition of x^3-x/x^4+2x^2+1 is (x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1)
How to find the partial fraction decompositionTo find the partial fraction decomposition of x^3-x/x^4+2x^2+1, we first factor the denominator:
x^4 + 2x^2 + 1 = (x^2 + 1)^2
So we can write:
(x^3 - x)/(x^4 + 2x^2 + 1) = A/(x^2 + 1) + B/(x^2 + 1)^2
Multiplying both sides by the denominator, we get:
x^3 - x = A(x^2 + 1) + B
Now we can solve for A and B by choosing appropriate values for x. Let's choose x = 0 first:
0 - 0 = A(0^2 + 1) + B
B = 0
Now let's choose x = 1:
1 - 1 = A(1^2 + 1) + 0
A = -1/4
So the partial fraction decomposition of x^3-x/x^4+2x^2+1 is:
(x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1) + 0/(x^2 + 1)^2
or
(x^3 - x)/(x^4 + 2x^2 + 1) = -1/4/(x^2 + 1)
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What is the surface area of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
1 mm
1 mm
square millimeters
Answers
Answer:
13.56 mm²
Step-by-step explanation:
surface area = 2 circle area + the side
circle = π r² = 3.14
2 of them = 6.28
side = circumference * 1 = 2πr *1 = 6.28
total 6.28*2 = 13.56 mm²
Several years ago, the average earnings for male workers between the ages of 25 and 34 with a high school diploma was $31,680. Comparing this value in
constant dollars to the average earnings 21 yr later showed that the average earnings have decreased to $27,900. Find the average rate of change in dollars
year for this time period.
[ Hint: Use the ordered pairs (0, 31,680) and (21, 27,900).]
Answers
Answer:
For 25- to 34-year-olds who worked full time, year round, higher educational attainment was associated with higher median earnings.
Step-by-step explanation:
This pattern was consistent for each year from 2010 through 2020. For example, in 2020, the median earnings of those with a master’s or higher degree were $69,700, some 17 percent higher than the earnings of those with a bachelor’s degree ($59,600). In the same year, the median earnings of those with a bachelor’s degree were 63 percent higher than the earnings of those who completed high school ($36,600).
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select five peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.) Compute the probability that exactly three of the five M&M’s are green. Compute the probability that three or four of the five M&M’s are green. Compute the probability that at most three of the five M&M’s are green. Compute the probability that at least three of the five M&M’s are green. If you repeatedly select random samples of five peanut M&M’s, on average how many do you expect to be green? (Round your answer to two decimal places.) green M&M’s With what standard deviation? (Round your answer to two decimal places.) green M&M’s
Answers
The standard deviation of the number of green M&M's in a sample of 5 is 0.91
What is standard deviation?Standard deviation is a measure of the amount of variation or dispersion of a set of data values. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.
According to given information:To solve this problem, we can use the binomial probability formula:
[tex]P(X=k) = C(n,k) * p^k * (1-p)^{(n-k)[/tex]
where:
X is the number of green M&M's in the sample
k is the number of green M&M's we are interested in (3 or 4 or at most 3 or at least 3)
n is the sample size (5)
p is the probability of getting a green M&M in one trial
We can use the given percentages to calculate the probability of getting a green M&M:
p = 0.15
Now we can calculate the probabilities for the different scenarios:
Probability that exactly three of the five M&M's are green:
[tex]P(X=3) = C(5,3) * 0.15^3 * 0.85^2 = 0.0883[/tex]
Probability that three or four of the five M&M's are green:
[tex]P(X=3\ or\ X=4) = P(X=3) + P(X=4) = C(5,3) * 0.15^3 * 0.85^2 + C(5,4) * 0.15^4 * 0.85^1 = 0.1527[/tex]
Probability that at most three of the five M&M's are green:
P(X≤3) = [tex]P(X=0) + P(X=1) + P(X=2) + P(X=3) = C(5,0) * 0.15^0 * 0.85^5 + C(5,1) * 0.15^1 * 0.85^4 + C(5,2) * 0.15^2 * 0.85^3 + C(5,3) * 0.15^3 * 0.85^2 = 0.9053[/tex]
Probability that at least three of the five M&M's are green:
P(X≥3) [tex]= P(X=3) + P(X=4) + P(X=5) = C(5,3) * 0.15^3 * 0.85^2 + C(5,4) * 0.15^4 * 0.85^1 + C(5,5) * 0.15^5 * 0.85^0 = 0.2413[/tex]
To find the expected number of green M&M's in a sample of size 5, we can use the formula:
E(X) = n * p
where E(X) is the expected value of X.
E(X) = 5 * 0.15 = 0.75
Therefore, on average we expect 0.75 green M&M's in a sample of 5.
To find the standard deviation, we can use the formula:
SD(X) = sqrt(n * p * (1-p))
SD(X) = sqrt(5 * 0.15 * 0.85) = 0.9138 (rounded to two decimal places)
Therefore, the standard deviation of the number of green M&M's in a sample of 5 is 0.91
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What is the measure of angle A in this triangle?
Enter your answer in the box.
Answers
Answer:
m∠A = 50°
Step-by-step explanation:
The ∑ of all interior angles of any given triangle is 180°. Set all angle measurements equal to 180:
[tex](x + 30) + (2x - 10) + 70 = 180[/tex]
First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:
[tex](x + 2x) + (30 - 10 + 70) = 180\\(3x) + (90) = 180[/tex]
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 90 from both sides of the equation:
[tex]3x + 90 = 180\\3x + 90 (-90) = 180 (-90)\\3x = 180 - 90\\3x = 90[/tex]
Next, divide 3 from both sides of the equation:
[tex]3x = 90\\\frac{(3x)}{3} = \frac{(90)}{3}\\ x = \frac{90}{3}\\ x = 30[/tex]
Plug in 30 for x in the given angle measurement of A and simplify:
[tex]m\angle{A} = 2x - 10\\m\angle{A} = 2(30) - 10\\m\angle{A} = (60) - 10\\m\angle{A} = 50[/tex]
50° is your answer for m∠A.
~
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Answer:
m∠A = 50°
Step-by-step explanation:
The ∑ of all interior angles of any given triangle is 180°. Set all angle measurements equal to 180:
[tex](x + 30) + (2x - 10) + 70 = 180[/tex]
First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:
[tex](x + 2x) + (30 - 10 + 70) = 180\\(3x) + (90) = 180[/tex]
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 90 from both sides of the equation:
[tex]3x + 90 = 180\\3x + 90 (-90) = 180 (-90)\\3x = 180 - 90\\3x = 90[/tex]
Next, divide 3 from both sides of the equation:
[tex]3x = 90\\\frac{(3x)}{3} = \frac{(90)}{3}\\ x = \frac{90}{3}\\ x = 30[/tex]
Plug in 30 for x in the given angle measurement of A and simplify:
[tex]m\angle{A} = 2x - 10\\m\angle{A} = 2(30) - 10\\m\angle{A} = (60) - 10\\m\angle{A} = 50[/tex]
50° is your answer for m∠A.
~
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What is the domain of the function in the graph?
graph on the h-g axis, between the points (6, 80) and (11, 40)
A. 6≤g≤11
B. 40≤g≤80
C. 40≤h≤80
D. 6≤h≤11
Answers
Answer:
D
Step-by-step explanation:
The domain of a function refers to the set of all possible input values (independent variable) for which the function is defined. In this case, the graph has points (6,80) and (11,40), which means that the function is defined for the values of g (the independent variable) between 6 and 11. Therefore, the domain of the function is:
D. 6≤g≤11
The domain of the function in the given graph is 6≤h≤11, as it includes all possible values of h between and including 6 and 11 on the horizontal (h) axis. So the correct option is D.
The domain of a function refers to the set of all possible input values for the function. In the given graph, which is plotted on the h-g axis and includes points (6, 80) and (11, 40), we are interested in determining the valid range for the independent variable, h.
The lowest h-value on the graph is 6, corresponding to the point (6, 80), and the highest h-value is 11, corresponding to the point (11, 40). These are the boundaries that define the domain of the function. Any value of h that falls within this range is a valid input for the function, and any value outside this range is not represented on the graph.
Therefore, the domain of the function is 6≤h≤11, as it includes all values of h between and including 6 and 11. This range encompasses all possible inputs for this function as depicted in the graph.
In summary, the domain represents the valid input values, and in this case, it is limited to the interval from 6 to 11 on the h-axis.
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If a case of 24 water bottles is $8 per case, how much are you paying for each bottle?
Answers
if 123=2, then what is 354=
Answers
if 1 2 3 = 2
then 3 5 4 = 5
hope it helps:)
Which of the following do not belong to the group of numbers
Answers
The number that does not belong to the set of numbers is given as follows:
B. Three
What are even and odd numbers?Numbers are classified as even or odd depending on whether they are divisible by 2 or not, as follows:
Even numbers are divisible by 2, that is, their last digit is either 0, 2, 4, 6 or 8.Odd numbers are not divisible by 2, that is, their last digit is either 1, 3, 5, 7 or 9.For this problem, we have that the number five does not belong to the set of even numbers, as the numbers two, four and six do.
Missing Information?The options are:
A.Two
B.Three
C.Four
D.Six
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Can you help with this please?
Answers
The p-value associated with the test statistic of z = 2.566 is 0.0045, accurate to four decimal places.
Based on the given information, we can conduct a one-tailed right-sided test using a normal distribution calculator to find the p-value associated with the test statistic of z = 2.566.
What is a one-tailed right-sided test?In hypothesis testing, a one-tailed right-sided test is a statistical test where the alternative hypothesis (H1) is specified to detect a change typically towards larger values.
Using a normal distribution calculator, we can find the cumulative distribution function (CDF) of the standard normal distribution at z = 2.566.
The CDF gives us the probability that a randomly selected value from a standard normal distribution is less than or equal to a given value.
Using a normal distribution calculator:
CDF at z = 2.566 = 0.9955 (rounded to four decimal places)
Since we are conducting a one-tailed right-sided test, we are interested in the probability of getting a value greater than the test statistic. Therefore, the p-value for the given test statistic is:
p-value = 1 - CDF at z = 2.566 = 1 - 0.9955 = 0.0045 (rounded to four decimal places)
Thus, the p-value associated with the test statistic of z = 2.566 is 0.0045, accurate to four decimal places.
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what 95% confidence interval for a standard normal distribution
Answers
A 95% confidence interval for the standard normal distribution is typically given by (-1.96, 1.96) . mean that correspond to the upper and lower bounds of the interval
what is mean ?
In statistics, the standard deviation is a measure of the amount of variation or dispersion in a set of data. It is the square root of the variance and is denoted by the symbol σ (sigma). The standard deviation is expressed in the same units
In the Given question :
A 95% confidence interval for the standard normal distribution is typically given by (-1.96, 1.96)
This means that we are 95% confident that the true value of a normally distributed variable falls within this range. The values of -1.96 and 1.96 represent the number of standard deviations from the mean that correspond to the upper and lower bounds of the interval, respectively. This interval is often used in statistical inference to estimate the population mean or proportion based on a sample.
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what 95% confidence interval for a standard normal distribution then what is the number of standard deviations from the mean that correspond to the upper and lower bounds of the interval ?
the table below shows different make of cars own by teacher in a certain school. work out the angles and percentage then illustrate the information using a pie chart.
Toyota -- 12
Nissan --- 8
Datsun --- 8
Volvo --- 2
Peugeot -- 10
Answers
The angles and percentages have been calculated as shown below.
A pie chart for the information about the different make of cars is shown below.
How to determine the angles and percentage?For the total number of car makes, we have the following:
Total make of cars = 12 + 8 + 8 + 2 + 10
Total make of cars = 40.
Next, we would determine the angles and percentage as follows;
Toyota
12/40 × 360 = 108°
12/40 × 100 = 30%.
Nissan
8/40 × 360 = 72°
8/40 × 100 = 20%.
Datsun
8/40 × 360 = 72°
8/40 × 100 = 20%.
Volvo
2/40 × 360 = 18°
2/40 × 100 = 5%.
Peugeot
10/40 × 360 = 90°
10/40 × 100 = 25%.
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Two mountain peaks are known to be 17 kilometers apart. A person located at a vista point such that a right angle is spanned when he looks from one peak to the other
is told that the distances from the vista point to each peak differ by 7 kilometers. How far is the vista point from each mountain peak?
Answers
The person is looking at each peak on a leg of a right triangle. The hypotenuse is the distance between the mountains.
How far is the vista point from each mountain peak?The distance is determined by
x^2+(x+5)^2=25^2
x^2+x^2+10x+25=625
2x^2+10x-600=0
x^2+5x-300=0
(x+20)(x-15)=0
only positive root is x=15
x+5=20
The vista point is 15 miles from one mountain peak and 20 miles from the other.
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Juan wants to see the Grand Cayon, so he is taking a vacation in Arizona. He drove south from his house for 280 miles. Then, He drove east 64 miles.
a. Draw a diagram illustrating Juans Trip
b. How many total miles did Juan travel?
c. If a road was built directly from Juans home to the grand canyon, how long would it be? Round to the nearest mile.
d. Approximately how much shorter would Juans trip be if he was able to take the direct route?
Answers
Juan traveled approximately 288.24 miles.
The direct road would be approximately 288 miles long.
Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.
We have,
a.
Here is a diagram illustrating Juan's trip:
Grand Canyon
|
|
|
Juan's | x
house --------->
y
b.
To find the total distance Juan traveled, we can use the Pythagorean theorem:
distance² = x² + y²
Juan drove 280 miles south (y direction) and 64 miles east (x direction), so we have:
distance² = 280² + 64²
distance² = 78,976 + 4,096
distance² = 83,072
Taking the square root of both sides, we get:
distance ≈ 288.24 miles
c.
To find the length of the direct road, we can use the Pythagorean theorem again:
distance² = x² + y²
The direct road forms a right triangle with legs of 280 miles and 64 miles, so we have:
distance² = 280² + 64²
distance² = 78,976 + 4,096
distance² = 83,072
Taking the square root of both sides, we get:
distance ≈ 288.24 miles
d.
To find how much shorter Juan's trip would be if he took the direct route, we can subtract the distance he traveled from the direct road distance:
288 - 288.24 ≈ -0.24
Thus,
Juan traveled approximately 288.24 miles.
The direct road would be approximately 288 miles long.
Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.
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express the function graphed on the axis below as a piecewise function
Answers
The function graphed on the axis above should be expressed as a piecewise function as follows;
f(x) = x + 1 {x < -5}
= 5x - 10 {x > 1}
How to determine the piecewise function?In order to determine the piecewise function, we would determine an equation that represent each of line shown on the graph. Therefore, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-7 + 4)/(-8 + 5)
Slope (m) = -3/-3
Slope (m) = 1.
At data point (-5, -4) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 4 = 1(x + 5)
y = x + 1
1, -5 2 0
For the second line, we have:
Slope (m) = (0 + 5)/(2 - 1)
Slope (m) = 5/1
Slope (m) = 5.
At data point (2, 0) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 5(x - 2)
y = 5x - 10
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graph of the function h(x)=(x^2-3x-4)/x-4
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Plotting the graph of the function h(x) = [tex](x^2 - 3x - 4) / (x - 4)[/tex], we get y- intercept = 1, vertical asymptotes at x=4 and horizontal asymptotes at y=1.
What does graph of any function represents?The connection between a function's input values (usually written as x) and output values (often indicated as y) is represented by the function's graph. It gives insights on the function's characteristics, including its domain, range, intercepts, asymptotes, and general form, as well as a visual representation of how the function acts.
Steps to plot the graph of the give function h(x) =[tex](x^2 - 3x - 4) / (x - 4)[/tex]:
Put the numerator [tex](x^2 - 3x - 4)[/tex] equal to zero and solve for x to discover the x-intercepts, if any, to determine the x-intercepts.Finding the y-intercept To get the y-intercept, set x = 0 in the function and solve for y, which gives y- intercept=1.To locate any vertical asymptotes, set the denominator (x - 4) equal to zero and solve for x, which gives x=4.Find horizontal asymptotes: To find the horizontal asymptote, compare the degrees of the numerator and denominator (s). There is no horizontal asymptote if the degree of the numerator is higher than the degree of the denominator. The horizontal asymptote lies at y = ratio of the leading coefficients if the degree of the numerator and denominator are equal. The horizontal asymptote is at y = 0 if the degree of the numerator is smaller than the degree of the denominator, for given problem it is at y=1.Draw the graph of the function h(x), highlighting the x-intercepts, y-intercept, vertical asymptotes, and horizontal asymptotes using the knowledge gained from the aforementioned phases (s). Take attention to how the function behaves as x gets closer to positive or negative infinity.Name the graph, including the x- and y-axes, x- and y-intercepts, vertical and horizontal asymptotes, and any other interesting points.Learn more about Graphs here:
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Can someone help me with this question? thank you ^^
Solve the inequality.
4g ≤ 10
(Middle school)
Answers
The value of the inequality is g≤2.5
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
The given inequality is 4g≤10
To solve the inequality, divided bo sides of the inequality by the coefficient of g which is 4
This gives the value
4g/g≤10/4
⇒ that g = 2.5
Therefore the value of the inequality is g≤2.5
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suppose a scatterplot is created from the points in the following table. when x=7, what is the second coordinate in a scatterplot of the linearized data? round your answer to the tenths place. im so lost honestly.
Answers
Okay, let's break this down step-by-step:
From the table, we know the x-values are 1, 3, 5, 7, and 9.
And the y-values are 4, 6, 8, ?, 12.
So at x=7, there is a missing y-value that we need to determine.
To find this, we need to look at the linear relationship between the points. Some clues:
1) There are 5 points total.
2) The x-values increase by 2 each time.
3) The y-values also seem to be increasing by 2 each time.
So the linear relationship is: y = mx + b (where m is the slope and b is the y-intercept)
In this case, the slope is 2 (because y increases by 2 for every increase of 1 in x).
And the y-intercept is 4 (because when x = 1, y = 4).
So the equation is: y = 2x + 4
Plugging in x = 7:
y = 2(7) + 4
y = 14 + 4
y = 18
Therefore, when x = 7, the second coordinate in the scatterplot is 18.
Rounded to the tenths place: 1.8
Does this help explain the steps? Let me know if you have any other questions!
The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. Which equation correctly models the ball’s height as a function of time?
Answers
The maximum height at the moment is 191.0625 ft.
What is the projectile's height?
Let's find out the projectile's maximum height now that we know what it is. The highest vertical location along the object's flight is considered to be its maximum height. The range of the bullet is defined as its horizontal displacement.
Here, we have
Given: The equation for a projectile's height versus time is h(t)=-16t²+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second.
The equation for a projectile's height versus time is
h(t) = -16t²+Vt+h
h = 2
V = 110
Substitute these values into the function
h(t) = -16t²+110t+2
Take the first derivative
h'(t) = -32t + 110
Equate the derivative with zero h'(t) = 0
0 = -32t + 110
110 = 32t
t = 110/32
t = 3.4375
Find the maximum height at the moment
t = 3.4375 (s)
h(3.4375) = -16(3.4375)² + 110(3.4375) + 2
h(3.4375) = -189.0625 + 378.125 + 2
h(3.4375) = 191.0625 ft
Hence, the maximum height at the moment is 191.0625 ft.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
The table is completed as below
Interested in NOT Interested in Total
Athletics Athletics
Interested in
Academic Clubs 26 58 84
Not Interested in
Academic Clubs 118 38 156
Total 144 96 240
How to fill the tableTo fill in the table, we start with the total number of students, which is 240.
We know that 35% of students are interested in athletics, so we can find the number of students interested in athletics as:
0.35 x 240 = 84
Similarly, we know that 3/5 of students are interested in academic clubs, so we can find the number of students interested in academic clubs as:
(3/5) x 240 = 144
We also know that 26 students are interested in both athletics and academic clubs, so we can fill in that cell as 26.
To fill in the remaining cells, we can use the fact that the row and column totals must add up correctly. For example, in the "Interested in athletics" row, we know that there are a total of 84 students interested in athletics. We also know that 26 of these students are interested in both athletics and academic clubs. Therefore, the number of students interested in athletics but not academic clubs is:
84 - 26 = 58
We can use similar reasoning to fill in the remaining cells. For example, in the "Not interested in athletics" column, we know that there are a total of 214 students who are not interested in athletics. We also know that 144 students are interested in academic clubs. Therefore, the number of students who are not interested in athletics but are interested in academic clubs is:
144 - 26 = 118
Let x represent "not interested in academics club" and "not interested in athletic". Using the total in the horizontal (bottom row) we have:
144 + 58 + x = 240
x = 240 - 202
x = 38
Hence 58 + 38 = 96 and 118 + 38 = 156
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A bag contains 3 gold marbles, 8 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
Answers
To calculate the expected value of playing this game, we need to multiply the probability of winning each amount by the corresponding payout and then sum them up.
Let's start by calculating the probability of selecting each type of marble:
Probability of selecting a gold marble: 3/34
Probability of selecting a silver marble: 8/34
Probability of selecting a black marble: 23/34
Now, let's calculate the expected value of playing the game:
E(x) = (3/34) * $3 + (8/34) * $2 + (23/34) * (-$1)
E(x) = $0.26
So the expected value of playing this game is $0.26. This means that over many plays of the game, we would expect to win an average of $0.26 per play. However, it's important to remember that this is just an average, and in any individual play of the game, you could win more or less than this amount.
y=9/5X+6. find the equation of the line that is parallel to this line and passes through the point (-5,-2)
Answers
Answer:
9/5x+7
Step-by-step explanation:
You can keep the slope the same, because it is parallel, but the y-intercept must change to plus seven in order to go through (-5, -2)