Without a diagram or additional information, it is impossible to determine the value of the x-coordinate of point A.
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Compute the number of 12 letter combination of the 26 letters in alphabet.
key answer:
9,675,700
To compute the number of 12 letter combinations of the 26 letters in the alphabet, we can use the formula for combinations, which is:
nCr = n! / r!(n-r)!
where n is the total number of items (26 letters in this case), r is the number of items to choose (12 letters in this case), and ! means factorial (the product of all positive integers up to that number).
Using this formula, we can plug in the numbers:
26C12 = 26! / 12!(26-12)!
= (26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15) / (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
= 9,675,700
Therefore, there are 9,675,700 possible 12 letter combinations of the 26 letters in the alphabet.
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3−(−1)+(−1)−33, minus, left parenthesis, minus, 1, right parenthesis, plus, left parenthesis, minus, 1, right parenthesis, minus, 3
The calculated value of the expression 3 - (-1) + (-1) - 3 using a calculator is 0
Finding the value of the expression 3 - (-1) + (-1) - 3From the question, we have the following parameters that can be used in our computation:
The expression 3 - (-1) + (-1) - 3
We can add the numbers using a calculator
So, we have the following representation
Value = 3 - (-1) + (-1) - 3
Using the above as a guide, we have the following:
Value = 0
This means that the value of the expression 3 - (-1) + (-1) - 3 using a calculator is 0
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Casho signed up for a streaming music service that costs $7 per month. The service allows Casho to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1. 50 per song. How much total money would Casho have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded ss songs?
To find out how much Casho would have to pay in a month in which she downloaded 30 songs, we need to consider both the monthly subscription cost and the cost per song for offline listening.
Step 1: Determine the cost of the monthly subscription, which is $7.
Step 2: Calculate the cost of downloading 30 songs for offline listening. To do this, multiply the cost per song ($1.50) by the number of songs (30).
1.50 * 30 = $45
Step 3: Add the monthly subscription cost ($7) to the cost of downloading 30 songs ($45).
7 + 45 = $52
So, Casho would have to pay $52 a month in which she downloaded 30 songs.
Now, let's find out how much Casho would have to pay if she downloaded ss songs.
Step 1: The cost of the monthly subscription remains the same at $7.
Step 2: Calculate the cost of downloading ss songs for offline listening. Multiply the cost per song ($1.50) by the number of songs (ss).
1.50 * ss = 1.50ss
Step 3: Add the monthly subscription cost ($7) to the cost of downloading ss songs (1.50ss).
7 + 1.50ss = 7 + 1.50ss
The total amount Casho would have to pay if she downloaded ss songs is 7 + 1.50ss.
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7. Membership at the local Sky Zone costs $189 per year and an hour costs $15 each.
Write an expression (make sure it looks like an expression, not an equation) to
represent the total cost of going to Sky Zone for the year. Evaluate the expression
(make it an equation) if you jump for 19 hours in a year. Write a "therefore"
statement. (4 marks)
189*365=68985
68985/15= $4599
Step-by-step explanation:
or $5000 if you round up
I need help on this question, and please explain how you did it.
The expression for AB in terms of x and √3 is:
AB = x√3.
What is an expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
In a right triangle ABC, if sin B = 0.5, then we know that:
sin B = opposite / hypotenuse
So, we can write:
0.5 = AB / CB
We also know that:
CB² = AB² + AC²
Substituting the value of AC, we get:
CB² = AB² + (3x)²
CB² = AB² + 9x²
Now, we can substitute the value of CB² from the first equation:
(AB / 0.5)² = AB² + 9x²
4AB² = AB² + 9x²
3AB² = 9x²
AB² = 3x²
The expression for AB in terms of x and √3 is:
AB = x√3
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(1 point) Calculate T..T,, and n(u, v) for the parametrized surface at the given point. Then find the equation of the tangent plane to the surface at that point. (u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v) = . The tangent plane: = 92
Given points:
(u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v)
the equation of the tangent plane at the point (u, v) = (24, 9) is:-8x + z = -183T
Process of finding equation:
To start, let's find T..T,, which represents the magnitude of the tangent vector at the given point:
T..T, = ||n(u, v)|| = ||n(24, -31, 72)|| = ||<48, -62, 144>|| = sqrt(48^2 + (-62)^2 + 144^2) = sqrt(11668) ≈ 108.03
Next, let's find the normal vector n(u, v) at the given point:
n(u, v) =
where f_u and f_v are the partial derivatives of the surface equation with respect to u and v, respectively.
In this case, we have:
f(u, v) = (24 + 0,u - 40, 8u)
f_u = <0, 1, 8>
f_v = <1, 0, 0>
Therefore, at the point (u, v) = (24, 9), we have:
n(u, v) = <0, 1, 8> x <1, 0, 0> = <-8, 0, 1>
Finally, let's find the equation of the tangent plane at the point (u, v) = (24, 9). The equation of a plane can be written as:
Ax + By + Cz = D
where A, B, and C are the components of the normal vector, and D can be found by plugging in the coordinates of the point on the plane. In this case, we have:
A = -8
B = 0
C = 1
D = -8(24) + 1(9) = -183
Therefore, the equation of the tangent plane at the point (u, v) = (24, 9) is:
-8x + z = -183
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A contractor is building a rectangular patio. If
t^2+19t+84/4t-4 represents the length of the patio
and 2t-2/t^2+9t+14 represents the width, write and
simply an expression that represents the area of
the patio. Leave simplified answers in factored form
The expression that represents the area of the rectangular patio in factored form is: area = [(t + 4)(t + 21) / 2(t + 7)(t + 2)]
What is an expression?An expression is a grouping of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division in mathematics.
Exponents, functions, and other mathematical symbols may also be included.
In mathematical equations and formulas, expressions are used to represent numbers, calculations, and relationships.
The length of the rectangular patio is given by the expression:
length = (t^2 + 19t + 84) / (4t - 4)
The width of the rectangular patio is given by the expression:
width = (2t - 2) / (t² + 9t + 14)
The area of the rectangular patio is given by the product of its length and width:
area = length x width
By substituting, we get:
area = [(t² + 19t + 84) / (4t - 4)] x [(2t - 2) / (t² + 9t + 14)]
We can factor the numerator and denominator of both fractions to simplify the expression:
area = [(t + 4)(t + 21) / 4(t - 1)] x [2(t - 1) / (t + 7)(t + 2)]
We can then simplify the expression by canceling out the common factors of (t - 1) in the numerator and denominator:
area = [(t + 4)(t + 21) / 4] x [2 / (t + 7)(t + 2)]
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Find the amount of tin needed to make a milk can that has a diameter of 4cm and height of 5cm
In the surface area, the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here we know that the tin is in the shape of cylinder.
Now to find the amount we need to determine the surface area of the cylinder.
Now Height h = 5 cm, Diameter = 4 cm then radius r = d/2 = 4/2 = 2 cm.
Now using formula then,
Surface Area = 2[tex]\pi\\[/tex]r(h+r) square unit.
=> Surface area = [tex]2\times3.14\times2(5+2)=2\times3.14\times2\times7[/tex] = 87.92 [tex]cm^2[/tex]
Hence the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].
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Determine if the sequence is a geometric sequence. If it is, find the common ratio and write the explicit formula and recursive definition. 45, 15, 5, 5/3
The type of sequence is a geometric sequence with a common ratio of 1/3
Checking the type of sequenceTo determine whether the given sequence is a geometric sequence, we need to check if there is a common ratio between any two consecutive terms.
The common ratio, denoted by "r", is calculated by dividing any term of the sequence by its preceding term.
Let's check if there is a common ratio between any two consecutive terms of the given sequence:
15/45 = 1/3
5/15 = 1/3
5/3 / 5 = 1/3
Since the ratio between any two consecutive terms is the same (1/3), the sequence is a geometric sequence.
To find the explicit formula for a geometric sequence, we use the formula:
an = a1 * r^(n-1)
So, we have
an = 45* (1/3)^(n-1)
For the recursice sequence, we have
an = a(n - 1) * 1/3
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Kevin has three classes in a row. Eight classes two hours long. Kevin’s first class is at seven. When will Karen’s last class and?
Karen's last class will end at three in the afternoon.
At what time will Karen’s final class conclude?Given that Kevin has three classes in a row, each lasting two hours, we can calculate the total duration of his classes. Three classes, each two hours long, amount to a total of 6 hours.
Since Kevin's first class starts at seven in the morning, we add 6 hours to that time, resulting in the conclusion of Karen's last class at three in the afternoon.
Understanding schedules and timetables is essential for effective time management. In academic settings, students often have multiple classes with varying durations throughout the day.
Calculating the end time of a class or event based on its start time and duration helps individuals plan their activities and allocate their time efficiently.
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will mark brainlist to the correct person who does the step by step correctly and also the correct answer
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Answer:
answer choice C
Step-by-step explanation:
The playground is a rectangle.
To find the area of a rectangle, we use the formula:
Area = Length x Width
The length is 25 yards.
The width is 68 yards.
Plugging these into the area formula:
Area = 25 x 68 = 1,700 square yards
Of the options, the closest choice is:
1,710 square yards
The area is 1,710 square yards.
Emir earned some money doing odd jobs last summer and put it in a savings account that earns 10% interest compounded monthly. After 9 years, there is $400. 00 in the account. How much did Emir earn doing odd jobs?
Round your answer to the nearest cent
Emir earned approximately $207.05 doing odd jobs.
Let x be the amount that Emir earned doing odd jobs. We can use the formula for compound interest, A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we have P = x, r = 0.1, n = 12 (since interest is compounded monthly), t = 9, and A = 400. Solving for x, we get:
x = A/(1+r/n)^(nt) = 400/(1+0.1/12)^(12*9) ≈ $207.05
Therefore, Emir earned approximately $207.05 doing odd jobs.
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How do I do number 3?
3.) The volume of the triangular prism = 6,480 mi³
The surface area of the triangular prism = 1,872mi²
How to calculate the surface area of the triangular prism?To determine the surface area of the given triangular prism, the formula that should be used is given as follows:
Surface area = bH + (b1+b2+b3)×l
where ;
b= 8 mi
b1 = 18 mi
b2 = 24 mi
b3 = 30 mi
Height = 18 mi
length = 24 mi
Surface area = 8×18 + ( 18+24+30)× 24
= 144 + 1728
= 1,872mi²
To calculate the volume of a triangular prism, the formula the should be used is given as follows;
Volume = 1/2 × b× h × L
where;
b = 24 ni
h = 18 mi
l = 30 mi
volume = 1/2 ×24×18×30
= 6,480 mi³
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Please find x ASAP please please please
Answer:
GiveN:-Sides of triangles are √80 , 8 and xTo FinD:-Value of x = ??SolutioN:-we know that given triangle is right angled triangle.
➢ By using Phythagoras Theorem:-
[tex] \sf \longrightarrow \: (AC)^2 = (AB)^2 + (BC)^2[/tex]
[tex] \sf \longrightarrow \: ( \sqrt{80} )^2 = (x)^2 + (8)^2[/tex]
[tex] \sf \longrightarrow \: 80 = (x)^2 + (8)^2[/tex]
[tex] \sf \longrightarrow \: 80 \: = x^2 \: + \: 8^2[/tex]
[tex] \sf \longrightarrow \: 80 \: = x^2 \: + \: 64[/tex]
[tex] \sf \longrightarrow \: 80 \: - 64 = x^2 \:[/tex]
[tex] \sf \longrightarrow \: 16 = x^2 \:[/tex]
[tex] \sf \longrightarrow \: x^2 \: = 16[/tex]
[tex] \sf \longrightarrow \: x \: = \sqrt{16} [/tex]
[tex] \sf \longrightarrow \: x \: = 4 \: units [/tex]
PLEASE HELP ME IMMEDIATELY!!!!!
The intervals where f is decreasing are given as follows:
None of the above.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented by y also increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.Hence the decreasing intervals of the function are given as follows:
-3.5 < x < -1.x > 2.5.Which are none of the options given in the problem.
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How many outcomes are there in a 5 digit license plate if the first 2 digits must be letters and the last 3 digits are numbers?
The letters and numbers can be repeated.
100
B 260
676,000
D 1,757,600
Find the perimeter of the rectangle, in feet.
L: 3 1/4 FT
W: 7/8 FT
Answers:
A. 8 1/4 ft
B: 8 1/5 ft
C: 8 1/2 ft
D: 8 1/3 ft
The perimeter of the rectangle is 8 1/4 feet. the correct answer is A.
Perimeter is the total length of the sides of a two-dimensional shape. In a rectangle, opposite sides are equal in length, so the perimeter can be found by adding the lengths of all four sides. To find the perimeter of a rectangle, we use the formula:
Perimeter = 2(length + width)
In this case, the length is given as 3 1/4 feet and the width is given as 7/8 feet. To find the perimeter, we substitute these values into the formula:
Perimeter = 2(3 1/4 + 7/8)
To simplify, we need to convert the mixed number to an improper fraction and find a common denominator for the fractions:
Perimeter = 2(13/4 + 7/8)
Perimeter = 2(26/8 + 7/8)
Perimeter = 2(33/8)
Now we can simplify the expression by multiplying 2 by the fraction:
Perimeter = 66/8
We can reduce this fraction by dividing both the numerator and denominator by 2:
Perimeter = 33/4
Therefore, the perimeter of the rectangle is 8 1/4 feet, which is answer choice A.
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Find the average rate of change for the given function. f(x) = x² x + 6x between x = 0 and x = 7 The average rate of change is 13. (Simplify your answer.)
The average rate of change for the function f(x) = x² + 6x between x = 0 and x = 7 is 13.
To find the average rate of change for the given function f(x) = x² + 6x between x = 0 and x = 7, you can follow these steps: Calculate the value of the function at the given points.
f(0) = 0² + 6(0) = 0
f(7) = 7² + 6(7) = 49 + 42 = 91
Use the average rate of change formula, which is (f(b) - f(a)) / (b - a), where a and b are the given points.
Substitute the values into the formula:
Average rate of change = (f(7) - f(0)) / (7 - 0) = (91 - 0) / 7 = 91 / 7 = 13
Therefore the average rate of change for the function f(x) = x² + 6x between x = 0 and x = 7 is calculated to be 13.
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A translation is applied to the square formed by the points A(−3, −4) , B(−3, 5) , C(6, 5) , and D(6, −4) . The image is the square that has vertices A′(−3, −6) , B′(−3, 3) , C′(6, 3) and D′(6, −6) . Select the phrase from the drop-down menu to correctly describe the translation. The square was translated Choose... .
The square was translated 2 units downwards.
Describing the transformationFrom the question, we have the following parameters that can be used in our computation:
Points A(−3, −4) , B(−3, 5) , C(6, 5) , and D(6, −4) . The image is the square that has vertices A′(−3, −6) , B′(−3, 3) , C′(6, 3) and D′(6, −6)The square was translated 2 units downward since all the y-coordinates of the vertices of the image square are 2 units less than the corresponding y-coordinates of the vertices of the pre-image square.
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9.
What is the solution set for this inequality?
negative five D plus five and one over two symbol seventeen.
Answer:
Step-by-step explanation:
If x = 3 centimeters, y = 5 centimeters, and z = 5 centimeters, what is the area of the object?
A. 40 square centimeters
B. 50 square centimeters
C. 45 square centimeters
D. 25 square centimeters
The area of the object is 40 square centimeters
The correct answer is an option (B)
We know that the formula for the area of trapezoid is,
A = ((a + b)/2) × h
where a and b are the two parallel bases
h is the height of the trapezoid
From the attached figure, first we determine the length of the two parallel bases.
Let us assume that 'a' represents the length of the upper base and 'b' represents the length of the bottom side of the trapezoid
We can observe that a = 2x
so the length of a = 6 centimeters
And b = 2z
So, the length of b = 2(5)
= 10 cm
Here, the height h of the trapezoid is given by y = 5 cm
Using above formula for the area of trapezoid, the area of the object would be,
A = ((a + b)/2) × h
A = ((6 + 10)/2) × 5
A = (16/2) × 5
A = 40 cm²
Therefore, the correct answer is an option (B)
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Find the complete question below.
Consider the vector field F(x, y, z) = (yz, -5xz, –4xy). Find the divergence and curl of F. div(F) = V.F= = curl(F) = V XF =( ). B) Consider the vector field F(x, y, z) = (-x?, -(x + y)
a) The divergence of F is -4x - 2y,
b) The curl of F is (-2(x+y), 0, -2x).
A) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:
div(F) = ∇ · F = ∂(yz)/∂x + ∂(-5xz)/∂y + ∂(-4xy)/∂z
= 0 - 5z - 4x
= -5z - 4x
To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:
curl(F) = ∇ × F = ( ∂(-4xy)/∂y - ∂(-5xz)/∂z, ∂(yz)/∂z - ∂(4xy)/∂x, ∂(-yz)/∂x - ∂(-5xz)/∂y )
= (-5z, y, -5x)
B) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:
div(F) = ∇ · F = ∂(-x²)/∂x + ∂(-(x+y)²)/∂y + ∂(0)/∂z
= -2x - 2(x+y)
= -4x - 2y
To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:
curl(F) = ∇ × F = ( ∂(0)/∂y - ∂(-(x+y)²)/∂z, ∂(0)/∂z - ∂(-x²)/∂x, ∂(-(x+y))/∂x - ∂(-x²)/∂y )
= (-2(x+y), 0, -2x)
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What is the value of 6x*2 +17 when x=8
Answer:
113 or 401: see below for explanation
Step-by-step explanation:
x = 8
The way you wrote it with the " * " symbol, it means the multiplication of 6x and 2. This is what I did in the line below.
6x × 2 + 17 = 6 × 8 × 2 + 17 = 48 × 2 + 17 = 113
If by " * " you actually meant an exponent, such as 6x², then here is the calculation using 2 as an exponent. For exponent, we normally use ^, such as 6x^2 to mean 6x².
6x² + 17 = 6 × 8² + 17 = 6 × 64 + 17 = 384 + 17 = 401
A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the standard deviation of X, the number of draws until the first red marble? 0. 4852 0. 9704 2. 0770 1. 5172
The standard deviation of X to be approximately 0.4852. The correct answer is option (A).
To calculate the standard deviation of X, we need to first calculate the probability of drawing a red marble on the first draw, which is 11/29. The probability of not drawing a red marble on the first draw is 18/29. The probability of drawing a red marble on the second draw, given that we did not draw a red marble on the first draw, is 11/29. Using the formula for the geometric distribution, which models the number of trials until the first success, we can calculate the expected value of X, which is 1/p, where p is the probability of success (11/29 in this case).
Therefore, the expected value of X is 29/11. To calculate the standard deviation of X, we use the formula sqrt(q/p^2), where q is the probability of failure (18/29) and p is the probability of success (11/29). Plugging in these values, we get the standard deviation of X to be approximately 0.4852. Therefore, the correct answer is option A, 0.4852.
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Find the critical value t Subscript c for the confidence level c=0.90. and sample size n=26
The critical value t Subscript c for a confidence level of 0.90 and sample size of 26 is 1.708. A t-value greater than or less than 1.708 in absolute value would lead to rejection of the null hypothesis at the 0.10 level of significance.
To find the critical value t Subscript c for the confidence level c=0.90 and sample size n=26, we can use a t-distribution table or calculator.
Since we have a sample size of n=26, we have n-1 = 25 degrees of freedom. Using a t-distribution table or calculator with 25 degrees of freedom and a confidence level of 0.90, we get
t Subscript c = 1.708
Therefore, the critical value t Subscript c for the confidence level c=0.90 and sample size n=26 is 1.708. This means that if we calculate the t-value from our sample data and it is greater than or less than 1.708 in absolute value, we can reject the null hypothesis at the 0.10 level of significance.
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the following list shows the number of goals scored by a soccer team in each of 9 games. 0 0 1 1 1 3 3 4 5 how does the median number of goals scored compare with the mean number of goals scored? responses
The median number of goals scored is 1, and the mean number of goals scored is 2. The median is less than the mean, indicating a right-skewed distribution.
To find the median, we need to first put the numbers in order
0, 0, 1, 1, 1, 3, 3, 4, 5
There are an odd number of values, so the median is the middle value, which is 1.
To find the mean, we add up all the values and divide by the number of values
(0 + 0 + 1 + 1 + 1 + 3 + 3 + 4 + 5) / 9 = 2
So the mean number of goals scored is 2.
Since the median (1) is less than the mean (2), we can say that the distribution is skewed to the right. This is because the high value of 5 pulls the mean up, while the median is not affected as much by outliers.
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PLEASE HELP ME ASAP
Can you please make a copy and put dots in eachone that goes where its supposed to go
Answer:
1
1
1
2
2
2
2
Step-by-step explanation:
6. A certificate of deposit (CD) pays 2. 25% annual interest compounded biweekly. If you
deposit $500 into this CD, what will the balance be after 6 years?
The balance of the CD after 6 years will be $678.35.
To calculate the balance of the CD after 6 years, we need to use the formula:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A = the balance after 6 years
P = the initial deposit of $500
r = the annual interest rate of 2.25%
n = the number of times the interest is compounded per year (biweekly = 26 times per year)
t = the number of years (6)
Plugging in the values, we get:
A = [tex]500(1 + 0.0225/26)^{(26*6)[/tex]
A = 500(1.001727)¹⁵⁶
A = 500(1.3567)
A = $678.35
Therefore, the balance of the CD after 6 years will be $678.35.
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Quadrilateral ABCD is a square with diagonals AC and BD. If A(4, 9) and C(3, 2), find the slope of BD.
Using the given information from #13, find the length of BD. Give your answer in simplest radical form.
B
the location of point 0 on directed line segment PS such that PO: OS is divided into a ratio of 3:2
The length of BD is √(65)) and the slope of BD is 1/7.
What does Quadrilateral means ?
In geometry, a quadrilateral is a four-sided polygon with four sides (sides) and four angles (vertices). The word is derived from the Latin words quadri, the form of four, and latus, meaning "side". Different types of quadrilaterals include trapezoid, parallelogram, rectangle, rhombus, square, kite
To find the slope of the diagonal BD of square ABCD, you must first find the coordinates of points B and D. Since ABCD is a square, all sides are the same length and the diagonals bisect each other at 90 degrees.
The midpoint M of AC is the intersection of the diagonals, so we can find the coordinates of M by taking the average of the x-coordinates and the average of the y-coordinates:
M = ((4 +3)/2, (9+ 2)/2) = (3.5, 5.5)
Since BD bisects AC, the coordinates of the midpoint M are also the coordinates of both B and D. Hence we have:
B = D = (3.5, 5.5)
The slope of the line passing through points A and C is:
m_AC = (2-9)/(3-4) = -7
Since the diagonals of the square are perpendicular, the slope of BD is the negative inverse of m_AC:
m_BD = -1/m_AC = 1/7
We can use the Pythagorean theorem to find the length of BD. Let x be the length of BD. Then we have:
AC² + BD² = 2x²
Since AC is the diagonal of the square, its length is:
AC = square((3-4)²+ (2-9)²) = square(65)
Substituting this into the above equation and solving for x, we get:
√(65) x² = 2x²
x² = square(65)
x = square (square(65))
Therefore, the length of BD is √(65) and the slope of BD is 1/7.
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() Jamison works as a server at a local restaurant. He made $42.80 in tips on
Thursday night. He made 2 1/4 times that amount in tips on Friday night. How much
in tips did he earn on Friday?
Therefore, Jamison made $96.30 in tips on Friday night.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.
Here,
Jamison made $42.80 in tips on Thursday night.
To find out how much he made in tips on Friday night, we need to multiply the Thursday amount by 2 1/4, which is the same as multiplying it by 9/4.
$42.80 x 9/4 = $96.30
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