Explain how you could transform a function to reflect it over the line x = y.
Answers
we will interchange the x coordinates and the y coordinates.
Explanation:
To transform a function to reflect over the line y = x, the x axis and y axis switch places.
For example, if we reflect the point (2, 3) over the line y = x
the x-coordinate and y-coordinate change places:
It becomes: (3, 2)
Since transforming a function to reflect over the line y = x is the same as transforming a function to reflect it over the line x = y.
So, (x, y) becomes (y, x)
We can conclude that, to transform a function to reflect it over the line x = y, we will interchange the x coordinates and the y coordinates.
Related Questions
the table shows how many middle school high school students prefer playing each type of instrument. how would you find the joint relative frequency of being a middle school student who prefers to play brass instruments?
Answers
The joint relative frequency of being a middle school student who prefers to play brass instruments is 0.0833 or approximately 8.33%.
To find the joint relative frequency of being a middle school student who prefers to play brass instruments, you need to look at the intersection of the "Middle School" row and the "Brass" column in the table, and then divide that value by the total number of students.
The joint relative frequency represents the proportion of students who fall into both categories (middle school and prefer brass instruments) out of the total number of students.
The joint relative frequency of being a middle school student who prefers to play brass instruments would be:
Joint relative frequency = Number of middle school students who prefer brass instruments / Total number of students
Joint relative frequency = 10 / 120 = 0.0833
So the joint relative frequency of being a middle school student who prefers to play brass instruments is 0.0833 or approximately 8.33%.
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The table shows how many middle school high school students prefer playing each type of instrument. how would you find the joint relative frequency of being a middle school student who prefers to play brass instruments?
If ∠A=8x+14
∠
A
=
8
x
+
14
and ∠B=2x+50
∠
B
=
2
x
+
50
, what is m∠B
m
∠
B
?
Answers
Answer:
yah yeet yeet yah
Step-by-step explanation:
y=−2x+2
4x+2y=4
Substitute the resulting expression in the other equation
Answers
Answer:
In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.
Step-by-step explanation:
1. What is the value of
4(x − 2)(x – 3) + 7(x − 2)(x – 5) – 6(x − 3)(x – 5)
when x = 5?
Answers
Answer:
Your Answer is in the attachment!!HOPE IT HELPS U!!!!
Suppose that P(x,y) means astronaut x will visit planet y. What is the predicate form of (1) Some planets will be visited by every astronaut. (2) Every planet will be visited by some astronaut. (3) Every astronaut will visit some planet. (4) Some astronauts will visit every planet.
Answers
(1) Some planets will be visited by every astronaut: ∃y ∀x P(x,y). (2) Every planet will be visited by some astronaut: ∀y ∃x P(x,y). (3) Every astronaut will visit some planet: ∀x ∃y P(x,y). (4) Some astronauts will visit every planet: ∃x ∀y P(x,y).
(1) Some planets will be visited by every astronaut: This statement asserts that there are certain planets that will be visited by every single astronaut. In predicate form, it can be represented as ∃y ∀x P(x,y).
The existential quantifier (∃) indicates that there exists at least one planet (y) for which the universal quantifier (∀) holds true for every astronaut (x) visiting that planet.
(2) Every planet will be visited by some astronaut: This statement states that for every planet, there will be at least one astronaut who will visit it. In predicate form, it can be represented as ∀y ∃x P(x,y).
The universal quantifier (∀) signifies that the statement applies to all planets (y), and the existential quantifier (∃) denotes that there exists at least one astronaut (x) who will visit each planet.
(3) Every astronaut will visit some planet: This statement asserts that for every astronaut, there is at least one planet that they will visit. In predicate form, it can be represented as ∀x ∃y P(x,y).
The universal quantifier (∀) indicates that the statement applies to all astronauts (x), and the existential quantifier (∃) denotes that there exists at least one planet (y) that each astronaut will visit.
(4) Some astronauts will visit every planet: This statement states that there are certain astronauts who will visit every single planet. In predicate form, it can be represented as ∃x ∀y P(x,y).
The existential quantifier (∃) signifies that there exists at least one astronaut (x) who will visit every planet (y), and the universal quantifier (∀) indicates that the statement holds true for all planets.
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The value of a company's equipment is $33,000 and decreases at a rate of 12% each year. Write an exponential decay function for the value of the equipment after t years.
Answers
Answer:
Below
Step-by-step explanation:
Value = 33000 ( .88)^t each year, t , the value is only 88% ( or in decimal: .88) of the prior year ( 12 % decrease leaves 88% )
Pls help with a and b
Answers
Part a: The value of x such that the both lines are parallel to each other is (x = 12).
Part : The value of y such that the both lines are parallel to each other is (y = 108).
What is defined as the corresponding angles?Corresponding angles are generated when two parallel lines have been intersected by a transversal. The definition of corresponding angles states that when two parallel lines intersect with a third, the angles that take up the same relative position at every intersection are said to be corresponding angles to one another.In the given figure;
Part a: For making the lines w and t parallel to each other; their corresponding angles must be equal.
Thus,
4x + 60 = 9x
Solving;
9x - 4x = 60
5x = 60
x = 12
Thus, the value of x for which both lines w and t are parallel is 12.
Part b: For making the lines u and v parallel to each other; their corresponding angles must be equal.
Thus, 9x = y
Put x = 12.
y = 9×12
y = 108.
Thus, the value of y for which both lines u and v are parallel is 108.
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Timothy makes reduced copies of a photograph that has an actual length of 8 in. Each time he presses the reduce button on the copier, the copy is reduced by 12%. What formula shows the pattern for the size of each copy of the photograph as it is reduced? What is the length of the photograph’s copy if Timothy presses the reduce button 5 times? Round to the nearest tenth.
Answers
Answer:
length of the photograph will be 4.2 in. after pressing the button 5 times.
Step-by-step explanation:
By pressing the button, every time size of the photograph gets reduced by 12%.
Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,
L = \(l(1-\frac{12}{100})^{n}\)
Where l = Actual length of the photograph
L = length of the reduced image
n = Number of times the button has been pressed
For l = 8 in. and n = 5
L = \(8(1-0.12)^{5}\)
= \(8(0.88)^{5}\)
= 4.22 in
L ≈ 4.2 in.
Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.
The length of the photograph's copy when the button is pressed the 5th times is 4.2 inches
The question is an illustration of an exponential function.
An exponential function is represented as:
\(y = ab^x\)
Where:
a represents the initial value i.e. a = 8b = 1 - r; and r represents the rate. i.e. r = 12%.So, the function becomes
\(y = 8 \times (1 - 12\%)^x\)
Express 12% as decimal
\(y = 8 \times (1 - 0.12)^x\)
This gives
\(y = 8 \times 0.88^x\)
When the button is pressed the 5th times, we have:
\(y = 8 \times 0.88^5\)
\(y = 4.2\)
Hence, the length of the photograph's copy is 4.2 inches
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Answers
Answer:
The area is 285.1 mi^2
Step-by-step explanation:
Here, we want to find the area of the larger sector
Mathematically, that would be;
theta/360 * pi * r^2
= 270/360 * 3.142 * 11^2
= 285.1 mi^2
4. Recursively defined sets ( 3 points) Give a recursive definition of the set below. The set of positive integer powers of 5 . 5. Divisibility (4 points) Prove that if a∣b and b∣a, then a=b or a=−b.
Answers
4. We start with the base case of \(5^0 = 1\) and recursively generate the next element in the set by multiplying the previous element by \(5\).
5. if a divides \(b\) and \(b\) divides \(a\), either a equals \(b\) or \(a\) equals negative \(b\).
4. The recursive definition of the set of positive integer powers of 5 can be expressed as follows:
Base case: \(5^0 = 1\) is in the set.
Recursive step: If n is in the set, then \(5^(n+1)\) is also in the set.
Using this definition, we start with the base case of \(5^0 = 1\)and recursively generate the next element in the set by multiplying the previous element by \(5\).
5. To prove that if a divides \(b\) and \(b\)divides \(a\), then a equals \(b\) or \(a\) equals negative \(b\), we can use the definition of divisibility.
Assume that \(a\) divides \(b\), denoted as \(a | b\) , and \(b\) divides \(a\), denoted as \(b | a.\)
By definition, if a divides b, there exists an integer k such that b = ak.
Similarly, if \(b\) divides \(a\), there exists an integer m such that \(a = bm.\)
Substituting the expression for\(b\) in terms of \(a\), we have \(bm = ak.\)
Dividing both sides by b (since b is nonzero), we get m = a/b.
Since \(m\) is an integer, \(a/b\) must be an integer, which means \(a\) is divisible by \(b\).
If \(a/b\) is an integer, it implies that \(b/a\)is also an integer, which means \(b\) is divisible by \(a\).
Therefore, if \(a\) divides \(b\) and \(b\) divides \(a\), it follows that \(a/b\) and \(b/a\) are both integers.
If \(a/b = m\) and \(b/a = k\), then we have \(a = bm\) and\(b = ak.\)
\(If m = k = 1, then $a = b.\)
\(If m = k = -1, then a = -b.\)
Therefore, if \(a\) divides \(b\) and \(b\) divides \(a\), either \(a\) equals \(b\) or \(a\) equals negative \(b\).
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Anne Runs from one side of a park to the other. The park is 80 meters across. She takes 16 seconds to go to the park. What is the speed of Anne?
Answers
The speed can be calculated using the formula below:
\(speed=\frac{dis\tan ce}{\text{time}}\)In this question:
Distance = 80 meters (distance of the park).
Time = 16 secons.
Substituting the values:
\(\begin{gathered} speed=\frac{80}{16} \\ speed=5\text{ m/s} \end{gathered}\)Answer: The speed of Anne is 5 m/s.
What is the sign of the third term of the expansion of (x - y)n for n = 3, 4, and 5?
Answers
Cⁿ₁ is always positive, then the second term has negative sign.
What does binomial expansion mean?
Theorem that states that any power of a binomial (a + b) can be expanded as a specific sum of products (aibj), such as (a + b)2 = a2 + 2ab + b2.
The i-th term of the binomial expansion \((x- y)^{n}\)
Ti = nCi - 1 . (x)ⁿ+¹⁺i . (-y)i - 1
For any n, when i=2,
T₂ = nC₂₋₁ . xⁿ⁺¹⁻² . (-y)²⁻¹ = -Cⁿ₁ xⁿ⁻¹ . y
Given that is consistently positive, the second term has a negative sign.
Cn1 is consistently positive, and the second term is always negative.
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Prove that the two ratios below are equivalent. 9 cents for every 4 people and 18 cents for every 8 people.
Answers
Answer:
R
Step-by-step explanation:
Let's rewrite this to the ratio of the amount of cents to the amount of people.
9 cents every 4 people -> 9:4
18 cents for every 8 people -> 18:8
Using the direct proportion : If one quantity increase/decrease an amount, the other one increase/decrease the same amount respectively.
So, we can rewrite 9:4 as 9x2/4x2 (both increase by 2 times) = 18:8
And since 18:8=18:8, these 2 ratios are equivalent.
Hi! Let me help you! :)
A ratio looks like so:a:b (the ratio of a to b)In this case, we have the following ratios:9:4 (also written as \(\displaystyle\frac{9}{4}\)18:8 (also written as \(\displaystyle\frac{18}{8}\)Now, equivalent means equal, so we need to prove that these ration are equal to each other.9:4 and 18:8To prove that the given ratios are equal, let's simplify the second ratio and write it in its simplest form.To simplify it, divide the numerator and the denominator by 2:9:49:4 and 9:4 are equal.Thus, 9:4 IS equal to 18:8Thus, the two ratios are equivalent.Hope it helps!
~Stargazing~
Water is leaking out of an inverted conical tank at a rate of 13100.0 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 8.0 m and the the diameter at the top is 3.5 m. If the water level is rising at a rate of 29.0 cm/min when the height of the water is 3.0 m, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Answers
The rate at which water is being pumped into the tank is 37490.0 cm³/min.
Given: Water is leaking out of an inverted conical tank at a rate of 13100.0 cm³/min at the same time that water is being pumped into the tank at a constant rate. The tank has a height 8.0 m, and the diameter at the top is 3.5 m. The water level is rising at a rate of 29.0 cm/min when the height of the water is 3.0 m.
The volume of the inverted cone tank = 1/3 πr²hThe diameter of the top of the conical tank = 3.5 m, therefore the radius, r = 1.75m, and the height, h = 8m. Therefore, the volume V of the tank is given by:V = 1/3 π (1.75²)(8) = 102.91 m³At time t, the height h of the water in the conical tank is 3 m, then the radius r of the surface of the water can be calculated using similar triangles.
Using the ratio of the similar triangles, we can write:r / (h - 3) = 1.75 / 8Therefore, r = 0.583 m and the volume of the water in the tank is given by:V = 1/3 π (0.583²)(3) = 0.377 m³.The water level is rising at a rate of 29.0 cm/min, therefore the volume V of the water is increasing at a rate of:dV/dt = πr² dh/dtWe know r = 0.583 m, h = 3m, and dh/dt = 29.0 cm/min, thusdV/dt = π (0.583)² (29/100) = 0.249 m³/minThe volume of water that is leaking out of the tank is 13100.0 cm³/min.
Therefore, the volume of water that is being pumped into the tank is given by:Pumping rate = Rate of increasing water volume + Rate of water leaking out of the tankPumping rate = (0.249 x 1000000) + 13100.0 = 37490.0 cm³/min. Therefore, the rate at which water is being pumped into the tank is 37490.0 cm³/min.
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Which expression represents the prime factorization of 192?
A. 2 x 2 x 2 x 2 x 12
B. 2 x 2 x 2 x 2 x 2 x 3
C. 3 x 2 x 2 x 2 x 2 x 2 x 2
D. 2 x 2 x 2 x 2 x 2 x 3 x 3
Answers
Answer:
A
Step-by-step explanation:
2x2=4 4x2=8 8x2=16 16x12=192
I need help pleaseee
Answers
Answer:
The hundred thousands place
Step-by-step explanation:
calculate vred, the speed of red light in the diamond. to four significant figures, c=2.998×108m/s.
Answers
The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.
According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.
To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.
Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.
Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.
Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.
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2 2.1 Mathematical intro show that there is another form for spherical harmonics: 1 3 3 Y₁ x iy 1/√√2 (²-1) 2πT 2π 1 3 3 z YO 2 2π π r 1 3 x iy Y₁¹ 3 2π - - 12 √ √ 2² (²+²) 2 2π
Answers
Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:
Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)
Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:
Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)
Y1,0 = 1/2 √(3/π)cosθ
Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)
Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ
Y2,0 = 1/4 √(5/π)(3cos²θ-1)
Y0,0 = 1/√(4π)
The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.
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what’s the awnser for this???
Answers
1.4 is less than 1.5
Step-by-step explanation:
Method 1 data from internet
\( \sqrt{2} = 1.414213562373095........\)
\( \sqrt{2} < 1.5\)
or Method 2
\( \sqrt{2} ....1.5 \\ \)
\( { \sqrt{2} }^{2} ..... \: \: {1.5}^{2} \\ \)
2 ..... 2.25
square root2 < 1.5
PLEASE HELP
Which of the following are true if event A and B are independent
Answers
Answer:
a) \(P(B/A) = P(B)\)
Step-by-step explanation:
Step(i):-
Given that A and B are independent events
P(A∩B) =P(A) P(B)
we will use the conditional probability
\(P(A/B) = \frac{P(AnB)}{P(B)}\)
or
\(P(B/A) = \frac{P(AnB)}{P(A)}\)
Step(ii):-
Given that A and B are independent events
P(A∩B) =P(A) P(B)
\(P(B/A) = \frac{P(AnB)}{P(A)}\)
\(P(B/A) = \frac{P(A)P(B)}{P(A)} = P(B)\)
\(P(B/A) = P(B)\)
HELP ME PLEASE WHAT IS THE ANSWER OF THE FRACTIONS
Answers
-2 1/5
at least I think so lol
People spend on average 80 euros per week for online shopping with variance of 6 euros. Assume the distribution is normal. The number of analysed people is set to 50 . Answer the following questions: a. What is the z-value of a person, who spends 74 euros for online shopping? Interpret the meaning of the obtained value. (4 points) b. What is the z-value of a person, who spends 84 euros for online shopping? Interpret the meaning of the obtained value. (4 points) c. Find the proportion of people who spend no more than 74 euros for online shopping. ( 2 points) d. Find the proportion of people who spend more than 84 euros for online shopping. ( 2 points) e. What is the proportion of people who spend between 74 and 84 euros ? (2 points) f. Interpret the meaning of the obtained result in question e. ( 3 points) g. Set the significance level to 5% and find the margin of error. (4 points) h. Interpret the meaning of the margin of error obtained in question g. (3 points) i. Construct a 95% confidence interval for the people's spending for online shopping. (4 points) j. Interpret the meaning of the obtained confidence interval.
Answers
We need to utilize the concept of the z-score and the properties of the normal distribution. Given that the distribution is normal and the population variance is known, we can calculate the z-score, proportions, margin of error, and confidence interval.
a. To calculate the z-value for a person who spends 74 euros, we use the formula: z = (x - μ) / σ where x is the value, μ is the mean, and σ is the standard deviation. z = (74 - 80) / √6 ≈ -2.45 The z-value of -2.45 indicates that the person's spending of 74 euros is approximately 2.45 standard deviations below the mean. It suggests that the person's spending is relatively low compared to the average.
b. To calculate the z-value for a person who spends 84 euros, we use the same formula:
z = (84 - 80) / √6 ≈ 1.63
The z-value of 1.63 indicates that the person's spending of 84 euros is approximately 1.63 standard deviations above the mean. It suggests that the person's spending is relatively high compared to the average.
c. To find the proportion of people who spend no more than 74 euros, we calculate the cumulative probability using the z-score:
P(X ≤ 74) = P(Z ≤ -2.45)
Using a standard normal distribution table or calculator, we find that P(Z ≤ -2.45) ≈ 0.0071
Therefore, approximately 0.71% of people spend no more than 74 euros for online shopping.
d. To find the proportion of people who spend more than 84 euros, we calculate the complementary probability:
P(X > 84) = 1 - P(X ≤ 84) = 1 - P(Z ≤ 1.63)
Using a standard normal distribution table or calculator, we find that P(Z ≤ 1.63) ≈ 0.9474
Therefore, approximately 5.26% of people spend more than 84 euros for online shopping.
e. To find the proportion of people who spend between 74 and 84 euros, we calculate the difference between cumulative probabilities:
P(74 < X < 84) = P(X ≤ 84) - P(X ≤ 74)
P(74 < X < 84) = P(Z ≤ 1.63) - P(Z ≤ -2.45)
Using a standard normal distribution table or calculator, we find that P(Z ≤ 1.63) ≈ 0.9474 and P(Z ≤ -2.45) ≈ 0.0071
P(74 < X < 84) ≈ 0.9474 - 0.0071 ≈ 0.9403
Therefore, approximately 94.03% of people spend between 74 and 84 euros for online shopping.
f. The obtained result in question e means that approximately 94.03% of people fall within the range of 74 to 84 euros for online shopping.
g. To find the margin of error at a 5% significance level, we use the formula:
Margin of Error = z * (σ / √n)
Since the sample size is not provided, we assume it to be the same as the number of analyzed people, which is 50.
Margin of Error = z * (σ / √n) = z * (
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For a two-sample t test where n1 = 16 and n2 = 12, what are the appropriate degrees of freedom?
Answers
The degrees of freedom for an independent t-test when n1 = 16 and n2 = 12 are 26.
Given,
n1 = 16
n2 = 12
Here,
An independent t-test, often known as a two-sample t-test, compares the means of two unrelated groups to see whether they are significantly different from each other. The t-test is an essential method that can help you determine whether or not a certain hypothesis is true, regardless of whether or not it is accurate.
Degree of freedom for independent t test: DF = (n1 + n2) - 2
DF = (16 + 12) - 2
DF = 26
Therefore, the degrees of freedom for an independent t-test when n1 = 16 and n2 = 12 are 26.
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At a car dealership, salespeople earn a 5% commission on the first $10,000 of every sale, plus a 3% commission on any amount over $10,000. A salesperson sold a car for $12,300. What was the total commission on the sale?
a.$369 b.$569 c.$615 d.$984
help pls!!! due tmrw!!!!
Answers
Answer:
B
Step-by-step explanation:
multiply 10000 by .05 = 500
multiply the remaining 2350 by .03 = 69
Add 500+69= 569
We-haul rents a moving truck for $20.00 and $0.45 per mile. You-haul rents the same size moving truck for $1.00 per mile but with no upfront charge.
Part A- Write two equations to represent the situation.
Part B- Represent the two equations on the graph below
Part C- What is the rate of change for each? What do they represent?
Part D- What do the y-intercepts of each line represent
Part E- Use the substitution method to help the renter determine when the two truck rentals will cost the same amount
Part F- Describe the situation when renting from We-haul would be a better deal than renting from You-haul
PLEASE HELP!!!
Answers
The two truck companies would cost the same amount at 36.36 miles.
Linear equationLinear equation is in the form:
y = mx + b
where y,x are variables, m is the rate of change and b is the initial value of y.
Let y represent the total cost of rental for each truck for x mile.
From the table, for we-haul:
y = 0.45x + 20For you-haul:
y = xFor the two trucks to cost the same:
0.45x + 20 = x
x = 36.36
The two truck companies would cost the same amount at 36.36 miles.
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Quadrilateral ABCD below is a parallelogram. Use the figure to select the best answer from the choices provided. If AD = 3x + 5, AB = 7x – 3, and BC = 8x – 10, what is the value of x? Select the best answer from the choices provided. A. 2 B. 3 C. 7 D. 8
Answers
Answer: 3
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so AD=BC.
\(3x+5=8x-10\\5=5x-1015=5x\\x=\boxed{3}\)
the base of a triangle is shrinking at a rate of 2 cm/min and the height of the triangle is increasing at a rate of 3 cm/min. find the rate (in cm2/min) at which the area of the triangle changes when the height is 38 cm and the base is 32 cm.
Answers
When the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.
The rate at which the area of a triangle changes can be found by multiplying the rate at which the base is shrinking by the rate at which the height is increasing.
Given:
Rate of shrinking of the base = -2 cm/min
Rate of increasing of the height = 3 cm/min
Height of the triangle = 38 cm
Base of the triangle = 32 cm
To find the rate at which the area of the triangle changes, we use the formula for the area of a triangle:
Area = (1/2) * base * height
Differentiating the area formula with respect to time gives us:
dA/dt = (1/2) * (db/dt) * height + (1/2) * base * (dh/dt)
Substituting the given values, we have:
dA/dt = (1/2) * (-2) * 38 + (1/2) * 32 * 3
Simplifying, we get:
dA/dt = -38 + 48
dA/dt = 10 cm²/min
Therefore, when the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.
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What are the 4 steps to solving inequalities?.
Answers
For solving the inequalities, there are more than four steps.
The step to solve given inequalities, the first step is to add the same number to both sides, the second step is to Subtract the same number from both sides and the third step is to Multiply both sides by the same positive number, and the fourth step is to Divide both sides by the same positive number, and the fifth step is to Multiply both sides by the same negative number and reverse the sign and the last step is to Divide both sides by the same negative number and reverse the sign. Out of which steps 2,3,4 and 5 are the most important steps.
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Write an equation in point-slope form of the line that passes through the point (5, 1) and has a slope of -3
Answers
Answer:
y - 1 = -3(x - 5)Step-by-step explanation:
An equation in point-slope form of the line that passes through the point (x₁,y₁) and has a slope of m:
y - y₁ = m(x - x₁)
m = -3
(5, 1) ⇒ x₁ = 5, y₁ = 1
Therefore:
y - 1 = -3(x - 5)
PLEASE HELP ME PLEASE
Answers
Answer:
45
Explaination:
If you divide 60 by 4 you get 15. That means 15 is 1/4 of the students.
60-15=45
This means that the other 45 students are girls because only 15 of the students are boys.
Final answer: 45