Answer:
Choice B
Step-by-step explanation:
For a triangle to be true, the longest side has to be shorter than the two shorter sides combined. The only answer that fits this is choice be. 70<40+60
PLEASE HELP! WILL MARK BRAINLIEST!
Let f(x) = 5 - x and g(x) = 2x - 1. Perform the following operation: (g - f)(x).
Answer:
(g - f)(x) = 3x - 6
Step-by-step explanation:
Step 1: Define
f(x) = 5 - x
g(x) = 2x - 1
Step 2: Find (g - f)(x)
(g - f)(x) = 2x - 1 - (5 - x)
(g - f)(x) = 2x - 1 - 5 + x
(g - f)(x) = 3x - 6
Answer:
3x-6
Step-by-step explanation:
f(x) = 5 - x
g(x) = 2x - 1
(g - f)(x) = 2x - 1 - (5 - x )
Distribute the minus sign
=2x - 1 - 5 + x
Combine like terms
= 3x-6
How much t-shirts does the business man need to sell in order to break even or make a profit
-81 ÷ (-9)× 23(3/4)
ANSWER: 155.25
EXPLANATION: -81 ÷ (-9)× 23(3/4)
9×69/4
621/4
155.25 answer
please mark as brainliest if it helps
Answer:
[tex] \frac{621}{4} [/tex]
or
[tex]155.25[/tex]
Dapper Dan's Dancing School charges $85 for enrollment plus $6 per class, whereas Leaping Larry's Dancing School charges $40 for how many classes will leaping larry’s dancing school be more expensive
enrollment plus $12 per class. For how many classes will Leaping Larry's Dancing School be more expensive?
Answer:
The Leaping Larry's Dancing School will be more expensive for a number of classes above 7.5 or equal to and above 8 classes
Step-by-step explanation:
The given information are;
The amount Dapper Dan's Dancing School charges for enrollment = $85
The amount Dapper Dan's Dancing School charges per class = $6
The amount Leaping Larry's Dancing School charges for enrollment = $40
The amount Leaping Larry's Dancing School charges per class = $12
Therefore, we have for X number of classes, when the cost of Dapper Dan's Dancing School and Leaping Larry's Dancing School are equal
$85 + X × $6 = $40 + X × $12
$85 - $40 = X × $12 - X × $6
$45 = X × $6
X = $45/$6 = 7.5
From which we have at X = 7.5 classes, the cost of the two dancing schools will be equal
However below 7.5 classes, for 7 classes for example, we have;
Cost of Dapper Dan's Dancing School = $85 + 7 × $6 = $127
Cost of Leaping Larry's Dancing School = $40 + 7 × $12 = $124
Therefore, for the number of classes below 7.5, Dapper Dan's Dancing School is more expensive than Leaping Larry's Dancing School
Above 7.5 classes, for 8 classes for example, we have;
Cost of Dapper Dan's Dancing School = $85 + 8 × $6 = $133
Cost of Leaping Larry's Dancing School = $40 + 8 × $12 = $136
Therefore, for the number of classes below 7.5, Dapper Dan's Dancing School is less expensive than Leaping Larry's Dancing School
Therefore, Leaping Larry's Dancing School will be more expensive for a number of classes above 7.5 or equal to and above 8 classes.
Which of the following terms are part of the "Sum of Minterms" form of the function F = xy + xz +
yz? (All correct answers should be chosen for full credit; no partial credits). ( x'y'z' O xy'z ( x'yz' x'yz ( xy'Z' (
xyz' xyz
In the "Sum of Minterms" form of the function F = xy + xz + yz, the terms that are part of this form are: x'y'z', xy'z, x'yz', and xyz.
x'y'z' is part of the "Sum of Minterms" form because it represents the minterm where x', y', and z' are complemented (negated).
xy'z is also part of the "Sum of Minterms" form because it represents the minterm where x, y', and z are complemented.
x'yz' is included in the form as it represents the minterm where x', y, and z' are complemented.
Lastly, xyz is part of the "Sum of Minterms" form because it represents the minterm where x, y, and z are not complemented.
These terms represent the individual minterms that are summed together to express the function F in the "Sum of Minterms" form. Each term corresponds to a specific combination of input variables (x, y, and z) where the function evaluates to true.
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The Wallace family split a 17¾ pound bag of dog food between their three dogs. How much dog food does each dog receive?
Answer:
about 9.92 each
Step-by-step explanation:
17.75÷3= 9.91666666666.... I rounded to get 9.92.
a radio station has a daily contest in which a random listener is asked a trivia question. on the first day, the station gives $300 to the first listener who answers correctly. on each successive day, the winner receives 95% of the winnings from the previous day. what is the total amount of prize money the radio station gives away during the contest?
The radio station gives away a total of $315.79 during the contest.
In the first day of the contest, the radio station gives a prize of $300 to the first listener who answers the trivia question correctly. The amount of the prize decreases by 5% for each day that passes. We are required to find the total amount of prize money the radio station gives away during the contest.Let X be the total amount of prize money given away during the contest. Then we can write the following equation:X = $300 + $285 + $270.75 + $257.21 + …After solving this infinite geometric series, we can find the total amount of prize money that the radio station gives away during the contest.X = a1 / (1 - r), where a1 is the first term and r is the common ratio.Substituting the values of a1 and r, we get:X = $300 / (1 - 0.05) = $300 / 0.95 = $315.79 (rounded to two decimal places)
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Question 1 (20%) (a) If Matrix A and B are orthogonal, determine whether the following are orthogonal or not. Give full justifications for your answer. (i) AT, (ii) B-¹, (iii) B-¹ A B. (b) Consider the transformation f: R² → R³ given by f(x, y) = (x+2y, x − y, −2x+3y). Show that f is a linear transformation. Find a matrix form of this transformation.
In part (a) of Question 1, we are asked to determine whether certain matrices are orthogonal or not, given that matrices A and B are orthogonal. We need to justify our answers. Specifically, we need to determine if AT (transpose of A), B-¹ (inverse of B), and B-¹AB are orthogonal matrices.
In part (b), we are given a transformation f from R² to R³ and asked to show that it is a linear transformation. Additionally, we need to find a matrix representation of this transformation.
(a) To determine if AT, B-¹, and B-¹AB are orthogonal matrices, we need to recall the properties of orthogonal matrices. An orthogonal matrix is a square matrix whose transpose is equal to its inverse.
(i) For AT, since A is orthogonal, we know that AAT = I, where I is the identity matrix. Taking the transpose of both sides, we have (AAT)T = IT, which simplifies to ATA = I. Therefore, AT is also orthogonal.
(ii) For B-¹, if B is orthogonal, then BB-¹ = I. Taking the transpose of both sides, we have (BB-¹)T = IT, which simplifies to (B-¹)TBT = I. Therefore, B-¹ is orthogonal.
(iii) For B-¹AB, we can rewrite it as (B-¹A)B. Since A and B are orthogonal matrices, B-¹A is also orthogonal. Multiplying an orthogonal matrix (B-¹A) by another orthogonal matrix (B) results in another orthogonal matrix. Therefore, B-¹AB is orthogonal.
(b) To show that f is a linear transformation, we need to verify two properties: additivity and homogeneity.
Additivity: f(u + v) = f(u) + f(v) for any vectors u and v in R².
Let u = (x₁, y₁) and v = (x₂, y₂). Then f(u) = (x₁ + 2y₁, x₁ - y₁, -2x₁ + 3y₁) and f(v) = (x₂ + 2y₂, x₂ - y₂, -2x₂ + 3y₂). Adding these two vectors, we get f(u + v) = (x₁ + x₂ + 2(y₁ + y₂), x₁ + x₂ - (y₁ + y₂), -2(x₁ + x₂) + 3(y₁ + y₂)). By comparing f(u + v) with f(u) + f(v), we see that they are equal. Hence, f satisfies additivity.
Homogeneity: f(cu) = cf(u) for any scalar c and vector u in R².
Let u = (x, y). Then f(u) = (x + 2y, x - y, -2x + 3y). Multiplying this vector by scalar c, we get f(cu) = (cx + 2cy, cx - cy, -2cx + 3cy). By comparing f(cu) with cf(u), we see that they are equal. Hence, f satisfies homogeneity.
To find the matrix representation of f, we can write the coordinates of f(u) as a linear combination of the standard basis vectors in R³:
f(u) = x(1, 1, -2) + y(2, -1, 3)
The matrix representation of f is then:
[1 2]
[1 -1]
[-2 3]
This matrix can be used to perform vector operations on u directly.
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a right circular cylinder with radius 2 is inscribed in a hemisphere with radius 5 so that its bases are parallel to the base of the hemisphere. what is the height of this cylinder?
Answer:
Step-by-step explanation:
We can use the Pythagorean Theorem to find the height of the cylinder
We have
height = √ [ 5^2 - 2^2 ] = √[25 - 4] = √21 units
Someone help. Will give brainliest
Answer:
Step-by-step explanation:
3/4 is 0.75 and 1 1/2 is 1.5
plot the numbers:
1.1, 3/4 , -0.9 , -1, 1 1/2 ( the line is not up to scale)
_|_______|__|_______|_____|___|__|_____|____|_
-2 -1 -0.9 0 3/4 1 1.1 1 1/2 2
the number the least is -1
the number greatest 1 1/2
the correct order from least to greatest is
-1 , -0.9 , 3/4 , 1.1 , 1 1/2
On a coordinate plane, 4 points are plotted. Point A is on the y-axis, Point B is at the origin, Point C is at (1, 2), and point D is on the x-axis. Which statements are true? Select all that apply. C is on the y-axis. B is on the y-axis. D is at the origin. B is at the origin. D is on the x-axis. A is on the x-axis.
Answer:
B is at the origin. D is on the x-axis.
Step-by-step explanation:
For a point to be at the origin, it lies at the intersection of both the x- axis and the y - axis. Both axes intersect at the origin. So, point B is at the origin.
For a point to be on the x - axis, its coordinate on the y- axis is zero. So, for a point on the x- axis with coordinate, x, it is the point (x,0) and it lies on the x axis. So, point D is on the x - axis.
For a point to be on the y - axis, its coordinate on the x - axis is zero. So, for a point on the y- axis with coordinate, y, it is the point (0,y) and it lies on the x axis. So, point A is on the y - axis.
The point C which is at (1,2) lies in the plane x-y since it has both x and y coordinates.
The correct option is B is at the origin. D is on the x-axis.
The following information should be considered:
For a point to be at the origin, it lies at the intersection of both the x- axis and the y - axis. Both axes intersect at the origin. So, point B is at the origin.
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A Buggatti can reach a top speed of 300 mph. At this rate, how many more hours would it take for the bugatti to travel 1500 miles if they have already traveled 600 miles?
Subtract miles traveled from total miles:
1500 - 600 = 900 more miles to go
Divide miles to go by speed:
900 / 300 = 3 hours
3 more hours
Answer:
3 more hours
Step-by-step explanation:
Did I do this right?
please someone help for geometry !
Answer:
1st one
Step-by-step explanation:
Rotation: Turn
Clockwise: The direction a clock turns, right.
2, 3, and 4 are not correct because 2 is a translation, or a slide. 3 includes more than one rigid transformations, and 4 is a reflection.
When you turn bottom left triangle one more time to the right, it will fit into the top left triangle. There is no need to reflect or translate the shape.
Evaluate 5/8 × 7/15 Give your answer in its simplest form.
Answer:
The answer to your question is 7/24. 7/24 is in simplest form.
Hope this helps, have a nice day, have a wonderful weekend and stay safe!
Also Happy Halloween! :) :D :3
Helpppo:)))))) pleaseeee
Answer:
32
Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 5x - 4
g(x) = -4x - 12
Step 2: Find f(g(x))
f(g(x)) = 3(-4x - 12)² - 5(-4x - 12) - 4
f(g(x)) = 3(16x² + 96x + 144) + 20x + 60 + 4
f(g(x)) = 48x² + 288x + 432 + 20x + 64
f(g(x)) = 48x² + 308x + 496
Step 3: Find f(g(-4))
f(g(-4)) = 48(-4)² + 308(-4) + 496
f(g(-4)) = 48(16) - 1232 + 496
f(g(-4)) = 768 - 736
f(g(-4)) = 32
x2-5x+10=0 is it quadratic equation? how can i identify the value of a,b,c? help
Name three collinear points.
D
А
B)
N
OS
OD
ON
ОА
ОС
DB
answer _------Three or more points , , , ..., are said to be collinear if they lie on a single straight line. .
a regular polygon has n sides Each exterior angle is 5n/2 degrees find the value of n.
Answer:
12
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
Since there are n sides and each exterior angle = [tex]\frac{5n}{2}[/tex] , then
n × [tex]\frac{5n}{2}[/tex] = 360 ( multiply both sides by 2 to clear the fraction )
5n² = 720 ( divide both sides by 5 )
n² = 144 ( take the square root of both sides )
n = [tex]\sqrt{144}[/tex] = 12
The polygon has 12 sides
100 square feet of denim for $18.50 OR 150 square feet of denim for $26.75
Answer:
150 for 26.75
Step-by-step explanation:
26.75/150 is .178
18.5/100 is .185
Greatest common factor of 66 and 77, will mark brainlist to the first 1 who gets it right
Answer:
D (11)
Step-by-step explanation:
77 / 11 = 7
66/11 = 6
Answer:
the factors and prime factorization of 66 and 77. The biggest common factor number is the GCF number. So the greatest common factor 66 and 77 is 11.
Step-by-step explanation:
Dina is making a logo and she decides to use a regular polygon. Each interior angle of the polygon measures 140°. What is the number of sides of this polygon?
Answer:
The polygon has 9 sides (a regular nonagon).
Step-by-step explanation:
Angles in a Regular Polygon
A polygon with n sides has a total sum of internal angles equal to 180°(n-2). This means that each angle (in a regular polygon) measures
[tex]\displaystyle \frac{180(n-2)}{n}[/tex]
The regular polygon used by Dina for the logo is such that each interior angle measures 140°, thus:
[tex]\displaystyle \frac{180(n-2)}{n}=140[/tex]
Multiply by n:
[tex]180(n-2)=140n[/tex]
Operate:
[tex]180n-360=140n[/tex]
Reducing:
[tex]40n=360[/tex]
Solving:
n=9
The polygon has 9 sides (a regular nonagon).
There are 3 pink marbles, 5 orange marbles, and 8 blue marbles. What is the ratio of blue marbles to the total amount of marbles? Make sure your ratio is in simplest form. *
Answer:
1:2
Step-by-step explanation:
The total number of marbles is
3+5+8 = 16
blue : total
8 : 16
Divide each side by 8
8/8 : 16/8
1:2
Answer:
1:2
Step-by-step explanation:
There are 16 marbles in total. 3+5+8=16
8 of them are blue so it is 8:16 simplify 1:2
help pls im strugglin
66 is the correct answer
Solve the quadratic equation x(x+1)=8-x. Write your answer as a whole number or fraction
Answer:
x=-4 or 2
Step-by-step explanation:
x(x+1)=8-x
x^2+x=8-x
x^2+2x-8=0
x^2+4x-2x-8=0
x(x+4)-2(x+4)
(x-2)(x+4)=0
x-2=0
x=2
or
x+4=0
x=-4
A pit at a recreational center contains a total of 2600 red and purple balls. There are 200 more purple balls than three times the amount of red balls in the pit. Write a system of linear equations that represents this situation.
Answer:
Step-by-step explanation:
P=2975 + r and 4= p - 225
In the diagram, mAngleFLI is 106°, mAngleFLG = (2x – 1)°,
mAngleGLH = (x + 17)°, and mAngleHLI = (4x – 15)°.What is the measure of the smallest angle in the diagram?
15°
29°
32°
45°
Answer:
29o
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
edge 2020
2x+10=3x-9 solve for x
Answer:
19 = x :)
Step-by-step explanation:
(see attachment for explanation)
Sierra is getting her car fixed at a mechanics. The total cost after tax is represented by 0.065(30h) + 30h, where h represents the number of hours it takes to repair the car. What part of the expression represents the amount of money she will have to pay in tax? Explain.
Given :
Sierra is getting her car fixed at a mechanics. The total cost after tax is represented by 0.065(30h) + 30h, where h represents the number of hours it takes to repair the car.
To Find :
What part of the expression represents the amount of money she will have to pay in tax.
Solution :
Total cost , T = 30h( 1 + 0.065)
T = 30h + 30h(0.065)
T = (30h) + (30h )× 6.5 %
Here, 30h is the cost of repairing the car.
Other part shows the tax she have to pay which is 6.5% of the total amount.
Hence, this is the required solution.
