By empirical rule, 99.7% of the students have a grade point average which is between 1.38 and 3.84.
Suppose that the grade point average of undergraduate students at one university has a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41.
Here, μ = 2.61 , σ = 0.41
Using the empirical rule :
The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.
2.61 − 0.41 = 2.2
2.61 + 0.41 = 3.02
The range of numbers is 2.2 to 3.02
The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.
2.61 − 2(0.41) = 1.79
2.61 + 2(0.41) = 3.43
The range of numbers is 1.79 to 3.43
Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.
2.61 − 3(0.41) = 1.38
2.61+3(0.41) = 3.84
The range of numbers is 1.38 to 3.84.
Hence, 99.7% of the students have a grade point average which is between 1.38 and 3.84.
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Question 5
BLUEPRINTS Ezra is redrawing the blueprint shown of a stage he is planning to build for his band. By what percentage should he multiply the
dimensions of the stage so that the dimensions of the image are the size of the original blueprint? What will be the perimeter of the updated
blueprint?
10 units
LF
4 units
8 units
%; The perimeter of the updated blueprint will be
10 units
2 units
units.
The perimeter of the updated blueprint would be = 62units.
How to calculate the perimeter of the blueprint?The percentage that she can use to multiply the dimensions of the stage so that the dimensions of the image is half the size of the original blueprint would be = 50%.
To calculate the perimeter of the blueprint is to add the sides of the whole blue print that was given. That is;
= 10+4+2+4+2+4+10+2+2+8+2+2
= 62 units.
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There are cups in a gallon.
The equation gives the number of cups in terms of the number of gallons.
Write an equation for this situation that gives the number of gallons in terms of the number of cups.
Answer:
16c
Step-by-step explanation:
Answer:
g = 16c
Step-by-step explanation:
Let's use g (the number of gallons) and c (the number of cups).
Since there are 16 cups in one gallon, the equation can be represented by:
one gallon = 16 cups →
g = 16c.
We use the coefficient to represent the quantity of cups needed to make one gallon.
Change the denominator of the fraction
7/y-b to b-y
Answer:
[tex]\frac{- 7}{b - y}[/tex]
Step-by-step explanation:
Algebraic manipulation (i.e. a process involving rearranging or rewriting variables and, multiplication or division, to achieve an algebraic expression in a desired form) will be applied:
The expression in the denominator (y - b) will be algebraically manipulated by being multiplied by negative one:
[tex](y - b)[/tex]×[tex](-1)[/tex]
The parenthesis will be expanded by applying the Distributive Law. The derived variables will be rearranged to achieve the desired form of the algebraic expression:
[tex][(-1)(y)] - [(-1)(b)][/tex] = [tex]-y - (-b)[/tex]
= [tex]-y + b[/tex]
= [tex]b - y[/tex] (Desired form achieved)
∴The multiple factor of negative one will also need to be multiplied with the numerator of the fraction for balance. This is because the negative one (that is being multiplied with the denominator) was NOT present originally:
[tex](-1)[/tex]×[tex](7)[/tex] = [tex]-7[/tex]
∴The desired form of the fraction is:
[tex]\frac{-7}{b - y}[/tex]
The fraction 7/(y - b) after changing the denominator (b - y) becomes - 7/(b - y).
Fraction is a comparison between two mathematical quantities or numbers in general.
The number which is being compared is called Numerator and the with whom it is compared is called Denominator.
In mathematical words, if a fraction is look like A/B where A and B are two numbers then A is called Numerator and B is called Denominator.
Here given the fraction is, 7/(y - b)
So here numerator = 7 and denominator = y - b
We have to change the denominator that is (y - b) with (b - y).
Rearranging the fraction we get,
7/(y - b) = 7/[- (b - y)] = - 7/(b - y).
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Express 486 as a product of its prime factors, leaving your answer in index notation.
The product of 486 as a product of it's prime factor is 2¹×3⁵
What are prime factors?A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.
Expressing a number as a product of it's prime factors simply means that we are going to use only prime numbers as factors.
for example expressing 12 as a product of it's factor means 2²× 3 i.e 4 × 3 will give 12
Similar expressing 486 as a product of it's prime factors;
486/2 = 243
243/3 = 81
81/3 = 27
27/3 = 9
9/3 = 3
3/3 = 1
therefore 486 = 2¹× 3⁵
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Julissa wants to join her local gym. A gym membership is $27 a month with a one–time initiation fee of $117. Which equation represents the amount of money, y, she will spend on her gym membership for x months?
y=117x+27
y=27x+117
x=117y+27
x=27y+117
The equation to represent the amount of money, y, Julissa will spend on her gym membership for x months is y=117x+27, which means that for each month Julissa has a membership, she will pay $117 for the initiation fee plus $27 for the monthly fee.
If Julissa has a gym membership for 3 months:
y = 117x + 27
y = 117(3) + 27
y = 360 + 27
y = 387
The equation y=117x+27 is used to represent the amount of money, y, that Julissa will spend on her gym membership for x months. This equation states that for each month of membership, Julissa will pay $117 for the initiation fee plus $27 for the monthly fee. This can be calculated for any number of months by substituting the value of x into the equation. For example, if Julissa has a gym membership for 3 months, y = 117x + 27 can be rearranged as y = 117(3) + 27, which equals y = 360 + 27. This is a total of 387 dollars, which is the amount Julissa will spend for 3 months of gym membership.
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The table shows the cost of renting a moving truck frm u-move-it based on the number of hours the truck is rented. c _+_t
65 49 16 40.5
The required equation models the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented is C = 49 + 16(t - 1). Option A is correct.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
To determine the equation model for the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented we need to put values on (specific one ordered pair in the given equation) to determine the correct equaiton model,
So, for hours of rented is 1.
For A,
C = 49 + 16(1 - 1) = 49 [satisfy the eqation]
Similarly,
For b
C = 16t = 16 [not satisfied]
For C,
C = 49 + 16t = 65 [not satisfied]
For D,
C = 49 + 16(t + 1) = 81 [not satisfied]
Thus, the required equation models the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented is C = 49 + 16(t - 1) . Option A is correct.
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s this true or false? fraction numerator n squared plus 2 n space plus 5 over denominator n end fraction space element of space capital omega (n squared )true
The given expression is a fraction in the form of[tex](n^2 + 2n + 5)/n[/tex], which is an element of the set Omega ([tex]n^2[/tex]). This expression is true.
The given expression is a fraction in the form[tex](n^2 + 2n + 5)/n[/tex], which belongs to the set Omega[tex](n^2).[/tex] This statement is valid, as the fraction is simply a simplified form of a polynomial, which is an element of the Omega set. The numerator of the fraction is [tex]n^2 + 2n + 5[/tex], which is a quadratic equation in n. The denominator is n, which is a linear equation in n. As the numerator and denominator are both polynomials of n, the fraction is an element of the Omega set. Therefore, the statement is true.
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The equation 7(2W + 3) = 14W + 20 has no solutions. Change one term in the original equation to create a new equation with infinitely many solutions.
The equation with infinitely many solutions is given as follows:
7(2W + 3) = 14W + 21.
How to obtain the equation with infinitely many solutions?
The system of equations for this problem is defined as follows:
7(2W + 3) = 14W + 20.
Applying the distributive property to the left side, we will have that:
14W + 21 = 14W + 20.
The two lines have the same slope but different intercepts, hence the system contains zero solutions.
To contain an infinite number of solutions, they must have the same slope and the same intercept, then the equation is given as follows:
7(2W + 3) = 14W + 21.
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Step-by-step explanation:
=
[tex]7(2w + 3) = 14w \\ 14w + 21 = 14w \\ 14w - 14w = - 21 \\ 0 = - 21 \\ = - 21[/tex]
For what value of x is △ABC ~ △DEF?
Answer:
x=12
Step-by-step explanation:
Since b would equal E
We can make an equation.
x^2 -5x = 84
So that can be solved down to
x^2 -5x -84= 0
(x-12)(x+7)=0
x=12
x=-7
Now we see which one equals 84.
(12)^2 -5(12)=84
-7^2-5(-7)=14
therefore 12 is the correct answer and -7 does not work.
Wanda did 145 random math problems from each math book in her library. Each math book
in the library has an equal number of problems.
Is this sample of the math problems in the library likely to be representative?
Answer:
According to Kepler's third law, what is the orbital period of this asteroid in terms of Earth years? A certain asteroid is approximately 50 AU from the Sun.
Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.
The least squares regression equation is:
Expected Profit = 1.45 • Customers – 28.83.
Use the drop-down menus to complete the statements below about what this linear model tells you about Ivan's daily profit.
Ivan would expect to make $43.67 in profit if he had 50 customers.
How much profit would Ivan expect to makeFrom the question, we have the following parameters that can be used in our computation:
Expected Profit = 1.45 • Customers – 28.83.
If Ivan had 50 customers, using the least squares regression equation, the expected profit would be:
Expected Profit = 1.45 * 50 - 28.83
So, we have
Expected Profit = 72.5 - 28.83
Evaluate the difference
Expected Profit = 43.67
Hence, the expected profit is $43.67
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Complete question
Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.
The least squares regression equation is:
Expected Profit = 1.45 * Customers - 28.83.
How much profit would Ivan expect to make if he had 50 customers?
Please Help WILL MARK BRANLIEST
Answer:
n = 7
Step-by-step explanation:
You have a geometric sequence with first term 625 and common ratio 1/5, and you want to know the number of the term whose value is 1/25.
Geometric sequenceThe general term of a geometric sequence is ...
tn = t1·r^(n-1)
Using the given values, we can solve for n:
1/25 = 625·(1/5)^(n-1)
1/(5^2·5^4) = 1/5^(n-1) . . . . . . divide by 625; write as powers of 5
Comparing exponents of 5, we have ...
6 = n -1
7 = n
The value of n for which tn = 1/25 is 7.
__
Additional comment
The attachment shows the first 7 terms of the sequence.
<96141404393>
Which one of the following points lies on the line 3x=2x-1
The point (-1, 2) lies on the line 3x = 2x - 1.
The equation 3x = 2x - 1 can be simplified by subtracting 2x from both sides to get x = -1.
So the line passes through the point (-1, y) for any value of y.
To check which of the following points lie on the line, we can substitute the x and y coordinates of each point into the equation and see if it is true.
a) (0, -1)
3(0) = 2(0) - 1
0 = -1
This point does not lie on the line.
b) (-1, 2)
3(-1) = 2(-1) - 1
-3 = -3
This point does lie on the line.
c) (1, -4)
3(1) = 2(1) - 1
3 = 1
This point does not lie on the line.
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Find the dot product of the position vectors whose terminal points are (25, 16) and (8,5). 120 65 280 903
Answer:
280
Step-by-step explanation:
Give me a moment, I am still gathering my explanation
Find the simplified product:^3sqrt2x^5 x ^3sqrt64x^9
The simplified product of the ^3sqrt2x^5 x ^3sqrt64x^9 is [tex]24\sqrt{2} x^{17}[/tex]
Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
For finding the simplified product we will first remove the squareroot possible and simplify the value in a simplest way as possible. In the given question, first we will simplifying [tex]\sqrt{64}[/tex] and after simplifying it we will then apply [tex]a^{n} . a^{m} = a^{n+m}[/tex], and lastly we will multiply the two numbers i.e., 3 and 8.
[tex]3\sqrt{2}x^5x^3\sqrt{64}x^9[/tex]
[tex]3\sqrt{2}x^5x^3\sqrt{8^{2} }x^9[/tex]
[tex]3.8\sqrt{2}x^{5+3+9}[/tex]
[tex]3.8\sqrt{2}x^{17}[/tex]
[tex]24\sqrt{2}x^{17}[/tex]
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Cleopatra and her brother, Ptolemy, each have cylindrical water clocks (so they drain uniformly), but their clocks have different heights and diameters. Cleopatra’s clock drains from full down to empty in 4 hours and Ptolemy’s does so in 5 hours. After two hours of draining, the water height in both clocks is the same. What fraction of the height of Cleopatra’s clock is the height of Ptolemy’s? After each has been draining for three hours, what fraction of the water height of Ptolemy’s clock is equal to the water height of Cleopatra’s?
The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5
What is the volume of a cylinder?A cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved lateral surface. The volume of a cylinder is the amount of space contained within the cylinder. It can be calculated using the formula:
Volume of cylinder = πr^2h
Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively. Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:
Volume of Cleopatra's clock =[tex]\mathrm{ \pi r_c^2h_c}[/tex]
Volume of Ptolemy's clock = [tex]\mathrm{\pi r_p^2h_p}[/tex]
Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock. We are given that after 2 hours of draining, both clocks have the same water height. Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:
(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)
[tex]\pi r_c^2h_c / 4 = \pi r_p^2h_p / 5[/tex]
[tex]h_c / h_p = (r_p / r_c)^2 \times (5 / 4)[/tex]
We are not given the values of the radii, but we can see that the ratio of heights depends only on the ratio of the radii squared. Therefore, we don't need to know the actual sizes of the clocks, only the ratio of their radii. Let's call this ratio x:
[tex]x^2 = (h_c / h_p) \times(4 / 5)[/tex]
After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:
[tex]\pi r_c^2(h_c - 2h_c/4) = \pi r_p^2(h_p - 2h_p/5)[/tex]
[tex]\pi r_c^2h_c/2 =\pi r_p^2h_p/5*3[/tex]
[tex]r_c^2h_c/2 = r_p^2h_p/15[/tex]
Now, we can solve for the ratio of water heights after each clock has been draining for three hours:
Water height in Cleopatra's clock after 3 hours = [tex]\mathrm{h_c - (3/4)h_c = (1/4)h_c}[/tex]
Water height in Ptolemy's clock after 3 hours = [tex]\mathrm{ h_p - (3/5)h_p = (2/5)h_p}[/tex]
([tex]h_p[/tex] / (2/5)[tex]h_p[/tex] ) = ((1/4)[tex]h_c / h_c[/tex])
([tex]h_p[/tex] / (2/5)) = 1/4
[tex]h_p[/tex] = 2/5 * 1/4
[tex]h_p[/tex] = 1/10
Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:
[tex]h_p / h_c[/tex]= 1/10 / (1/4) = 2/5
And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:
[tex]h_c / (2/5)h_p[/tex] = (1/4) / (2/5)(1/10) = (1/4) / (1/20) = 5/4
Hence,
The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5
The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.
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Compare the experimental and theoretical probabilities of each outcome.
Getting two tails
Getting two heads
Getting one heads and one tails
The theoretical probability of getting two tails is 1/4 = 0.25 = 25%. The experimental probability of getting two tails will change for every experiment.
The theoretical probability of getting two heads is 1/4 = 0.25 = 25%.
The theoretical probability of getting one head and one tail is 2/4 = 0.50 = 50%.
What is experimental probability?
The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Given that two coins flip together. The outcomes of a coin is {H,T}.
The outcomes after flipping of two coins are
{HH, HT, TH, TT}
The total number of outcomes is 4.
The number of outcomes to get two tails is 1.
The probability of getting two tails is 1/4 = 0.25 = 25%.
The number of outcomes to get two heads is 1.
The probability of getting two heads is 1/4 = 0.25 = 25%.
The number of outcomes to get one head and one tail is 2
The probability of getting one head and one tail is 2/4 = 0.50 = 50%.
The theoretical probabilities will change for every experiment.
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Please help me by finding the degree measure of angle x
We can say in this triangle by Pythagorean theorem A2 = B2 + C2 => AC = sqrt115 after answering the provided question.
What exactly is a triangle?Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.
Pythagorean theorem applies here, in this triangle
[tex]A^2 = B^2 + C^2[/tex]
[tex]AC = \sqrt{14^2 - 9^2}[/tex]
[tex]AC = \sqrt{196 - 81}[/tex]
[tex]AC = \sqrt{115}[/tex]
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3, -24, 192, ... Find the 19th term:
Answer:
Step-by-step explanation:
a
n
=ar
n−1
a
3
=ar
2
=24...(1)
a
6
=ar
5
=192...(2)
dividing (2) by (1) we get
ar
2
ar
5
=
24
192
r
3
=8⇒r=2
From (1)
ar
2
=24
a=
2
2
24
=6
∴a
10
=(6)(2)
10−1
=3072
Find the volume of the triangular prism as pictured below with a = 10 cm, b =
cm, and h = 10 cm.
The volume of the triangular prism is 433.013cm^3.
What is the formula for finding the volume of a triangular prism?Triangular prism formulas
volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length. area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.
We are given that;
Base area of prism = 10cm
Breadth of prism= 10cm
Height of prism = 10cm
Now,
To find the volume of triangular prism
Volume = base area × length of the prism
=10x43.3013cm
=433.013
Therefore, the volume of prism will be 433.013cm^3
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if you assume all outcomes are equally likely, what is the probability of getting either two odd numbers or two even numbers?
The probability of getting two odd numbers or two even numbers is 50%, since there are an equal number of odd and even numbers.
There are 6 possible outcomes when rolling two dice:
(1,1), (1,2), (2,1), (2,2), (1,3), (3,1).
The probability of getting two odd numbers is
2/6, or 1/3.
The probability of getting two even numbers is also
2/6, or 1/3.
Therefore, the probability of getting either two odd numbers or two even numbers is 2/3.
The probability of getting two odd numbers or two even numbers is 50%. This is because there are an equal number of odd and even numbers, so each outcome is equally likely. This means that the probability of getting two odd numbers or two even numbers is the same as the probability of getting one odd number and one even number. In both cases, the probability is 50%, since each outcome is equally likely. Therefore, the probability of getting two odd numbers or two even numbers is 50% as there are an equal number of odd and even numbers. This is because all possible outcomes are equally likely, and there are an equal number of odd and even numbers, so the probability of getting either two odd numbers or two even numbers is the same.
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For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games. For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games. For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games
[tex]m=15-0.75g[/tex] is the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games.
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. While the definition of an equation in English is any well-formed formula consisting of two expressions related by an equals sign, the definition of an equation and its cognates in other languages may have subtly different meanings. For instance, an équation is defined as having one or more variables in French.
According to the question,
Total money = $15
The games at the arcade cost $0. 75.
Let total amount of money be 'm' and arcade games played by him be 'g'.
Now,
Equation to represent the remaining money,
[tex]m=15-0.75g[/tex]
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The triangles are similar.
What is the value of x?
See the attachment for the problem to be answered.
Answer:
16
Step-by-step explanation:
20/5 = 12/3 = x/4
x/4 = 4
x = (4)(4) = 16
Answer:16
Step-by-step explanation:multiply 4 by 4
A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is h(t) = 36t^2 - 64.
t= 3.56 seconds
t= 1.78 seconds
t= 1.33 seconds
t= 8 seconds
the assumption being that h(t) is the height of the rock in "t" seconds, so by the time the rock hits the ground h(t) = 0, namely it has reached 0 height because, well, is on the ground :)
[tex]h(t)=36t^2 - 64\implies 0=36t^2 - 64\implies 64=36t^2\implies \cfrac{64}{36}=t^2 \\\\\\ \sqrt{\cfrac{64}{36}}=t\implies \sqrt{\cfrac{16}{9}}=t\implies \cfrac{4}{3}=t\implies 1.\overline{33}=t[/tex]
You are given the dollar value of a product in 2015 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 15 represent 2015. )
2015 Value Rate $260,000 $5600 decrease per year
The linear equation that gives the dollar value V of the product in terms of the year t is V = - $5600t + $344,000.
V(t) is a function of t that expresses the value in the year 2000+t.
We know that the decrease is $5600 per year.
So,
V(t) = -$5600t + c
where c is the constant.
V(15) = -$5600 (15) + c = $260,000 [t = 15]
Hence, we can say that -
c = $260,000 + $5600 (15)
c= $260,000 + $84,000
c= $344,000
Now we got the value of c. We can write the equation as follows -
V = - $5600t + $344,000
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6. 56% of
_ is 3.92 *
Answer:
60
Step-by-step explanation:
3.92 = (6.56/100) * _
To solve for _, we can multiply both sides by 100:
100 * 3.92 = (6.56/100) * _
100 * 3.92 = 6.56 * _
_ = (100 * 3.92) / 6.56
Therefore, _ = 60.
Answer: 60
Step-by-step explanation:
Differentiate: y = 2 + ln(3-2x)
Can any one help with me please
Answer:
85
Step-by-step explanation:
The vertical line that y is on adds up to 180 so if we take 180 - the number we already know (95) we get 85
The vertices of △JKL are J(−3, −2), K(1, 4), and L(4, 2). Find the vertices of the image of △JKL under the dilation centered at the origin with scale factor 5.
The coordinate pairs of vertices D₅ (△JKL) of are J'(-15,-10), K'(5,20) and L'(20,10).
What does a math definition of a coordinate plane mean?
A surface with two dimensions known as the coordinate plane is created by two number lines. The x-axis is a single number line that runs horizontally. The y-axis is the name given to the vertical number line that is the other number line.
A place known as the origin is where the two axes collide. To graph points, lines, and other things, we can utilize the coordinate plane.
We know that, D₅ (△JKL) means triangle JKL dilated by scale factor 5 with origin as center of dilation.
If a figure is dilated by factor k and origin is the center of dilation, then
( x, y ) ⇒ ( kx , ky )
From the given problem, the rule of dilation is
( x , y ) ⇒ ( 5x , 5y )
Now
J( -3 , -2 ) ⇒ J'( 5(-3), 5(-2)) = J'( -15 , -10 )
K( 1,4 ) ⇒ K'(5(1) , 5(4)) = K'( 5,20 )
L( 4,2 ) ⇒ L'(5(4), 5(2)) = L'( 20,10 )
Therefore, the coordinate pairs of vertices D₅ (△JKL) of are J'(-15,-10), K'(5,20) and L'(20,10).
Learn more about a coordinate plane
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A ladder leans against the side of a house. The angle of elevation of the ladder is 68° when the bottom of the ladder is 7 ft from the
is the top of the ladder from the ground? Round your answer to the nearest tenth.
Check
68°
O
X
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T
Answer:
17.3 feet
Step-by-step explanation:
We can use the tangent function to evaluate the height of the building.
The definition of the tangent function is
[tex]\tan x=\frac{O}{A}[/tex]
Where
[tex]A[/tex] is the side adjacent to the angle
[tex]O[/tex] is the side opposite to the angle
In this example we are given values of the adjacent side and the angle.
Knowing that we can evaluate the side opposite to the angle.
Numerical Evaluation
We are given
[tex]x=68\\A=7[/tex]
Substituting these values into the equation for the tangent function yields[tex]\tan 68=\frac{O}{7}[/tex]
Lets solve for [tex]O[/tex].
Multiply both sides by [tex]7[/tex].
[tex]O=7*\tan 68[/tex]
Evaluate [tex]\tan 68[/tex].
[tex]O=7*2.47508685[/tex]
[tex]O=17.325608[/tex]
Rounding to the nearest tenth gives us
[tex]O=17.3[/tex]
Learn more about the trig functions here
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