The perimeter of the figure is 5.0.
What is a perimeter?
The perimeter of a two-dimensional shape is the distance around the outside of the shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is the sum of the lengths of all four sides. The perimeter of a triangle is the sum of the lengths of all three sides.
To reflect a point across the line y=x, we can use the following formula:
(x', y') = (y, x)
Where (x', y') is the reflected point and (x, y) is the original point.
Using this formula, we can find the coordinates of the reflected points A' and B':
A' = (4, 4) -> (4, 4) -> (4, 4)
B' = (5, -1) -> (-1, 5) -> (-1, 5)
Therefore, the image of AB is A'B' with endpoints A'(4, 4) and B'(-1, 5).
To find the perimeter of the figure formed by the segments AB, B'B, and A'B', we can add up the lengths of these three segments. The length of AB can be found using the distance formula:
[tex]AB = \sqrt{((5-4)^2 + (-1-4)^2)}\\\\= \sqrt{(1^2 + (-5)^2)}\\\\= \sqrt{(1 + 25)}\\\\= \sqrt{26}[/tex]
The length of B'B can be found using the same formula:
[tex]B'B = \sqrt{((-1-(-1))^2 + (5-5)^2)}\\\\= \sqrt{(0^2 + 0^2)}\\\\= 0[/tex]
The length of A'B' can also be found using the distance formula:
[tex]A'B' = \sqrt{((-1-4)^2 + (5-4)^2)}\\\\= \sqrt{(-5)^2 + (1)^2}\\\\= \sqrt{25 + 1}\\\\= \sqrt{26}[/tex]
The perimeter of the figure is AB + B'B + A'B' = √26 + 0 + √26 = 2√26. To the nearest tenth, this is 5.0.
Hence, the perimeter of the figure is 5.0.
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What is the numerator of the simplified sum?
StartFraction x Over x squared + 3 x + 2 EndFraction + StartFraction 3 Over x + 1 EndFraction
Therefore, the numerator of the given equation comes out to be 4x+6
what is fraction?A fraction denotes a component of a whole or, more generally, any number of equal parts. In conversational English, a fraction, such as one-half, eight-fifths, or three-quarters, denotes the quantity of a specific size of portions.
Given
[tex]\frac{x}{x^{2} +3x+2} + \frac{3}{x+1}[/tex]
A common denominator must exist for the fractions before we can add them.
Factor the denominator of the first fraction
[tex]\frac{x}{(x+1) (x+2)} + \frac{3}{x+1}[/tex]
Subtract (x + 2) from the second fraction's numerator and denominator.
[tex]\frac{x}{(x+1) (x+2)} + \frac{3(x+2)}{(x+2)(x+1)}[/tex] ← Currently, fractions share a common denominator.
Add the numerators leaving the denominators
= [tex]\frac{(x+2)(x+3)}{(x+2)(x+1)}[/tex]
= [tex]\frac{x^{2} +3x+6}{(x+2)(x+1)}[/tex]
= [tex]\frac{4x+6}{(x+2)(x+1)}[/tex]
simplified sum with numerator 4x + 6
Therefore the numerator of the given equation comes out to be 4x+6.
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Expand and simplify (2x + 1)(x-2)(x + 3)
Optional working
+
Answer
+
Answer:2x^3+3x^2-11x-6
Step-by-step explanation:
Rony spent 20% of his salary on a wallet. He bought a bag which cost $20 more than the wallet. He also bought a pair of shoes. The ratio of the cost of the wallet to the cost of the pair of shoes was 5:6. He then had $844 left.
(a) What was his monthly salary?
(b) Express the amount of money he spent on the pair of shoes as a fraction of his monthly salary in its simplest form.
The 20% Tony spends from his monthly salary on the wallet, the bag which cost $20 more than the wallet and the ratio of the wallet to shoe cost of 5:6, which expressed as a fraction is 5/6, indicates;
(a) Tony's monthly salary is $2,400
(b) The amount spent on the pair of shoes is (6/25) of his monthly salary
What is a fraction?A fraction is a part of a whole item, expressed as a quotient.
Let x represent Tony's salary, from the details of the question, we get;
The amount Tony spent on the wallet = 20% of his salary
The cost of the bag Tony bought = $20 + The cost of the wallet
Ratio of the cost of the wallet to the cost of the pair of shoes = 5:6
The amount Tony had left = $844
Therefore;
The amount Tony spent on the wallet = 20% of x = 0.2·x
Amount spent on the bag = 20 + 0.2·x
Ratio of the cost of the wallet to the cost of the pair of shoes = 5:6
Therefore;
Cost of the pair of shoes = (6/5)×(0.2·x)
Therefore;
x - 0.2·x - (20 + 0.2·x) - (6/5) ×(0.2·x) = 844
0.36·x - 20 = 844
x = (844 + 20)/0.36 = 2400
Tony's monthly salary, x = $2400(b) The amount Tony spends on the pair of shoes = (6/5) × (0.2·x)
(6/5) × (0.2·x) = (6/5) × (2/10) × x = (12/50)·x = (6/25)·x
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Hugo decided to pay $2 a week to his brother to buy a bicycle. The equation y – 10 = –2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
How much did the bicycle cost?
Hugo needs 15 weeks to pay back his brother completely if he pays $2 a week.
What is an equation?
An equation is written in the form of variables and constants separated by the operation of multiplication and division.
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
According to the given question:
Hugo decided to pay $2 a week to his brother to buy a bicycle.
The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
To pay back to the brother he must owe no money which is y = 0.
∴ The weeks needed is,
0 - 10 = -2(x - 10).
- 10 = -2x + 20.
2x = 30.
x = 15.
He needs 15 weeks to pay back completely.
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A Question 9 (2 points) Retake question
Evaluate the function f(x), if f(x) = 4x - 2, what is the value of f(3)?
Enter your answer in the box below.
f(3) =
A
The value of f(3) is 10.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Here, we have
Given function :
f(x) = 4x - 2
We have to find the value of f(3).
Now we put x = 3 and we get
f(3) = 4 × 3 - 2
f(3) = 12 - 2
f(3) = 10
Hence, the value of f(3) is 10.
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hey i would appreciate it if someone could help
Answer:
x^3y^2√xy
Step-by-step explanation:
First, you calculate what's in the square root. x^2 becomes x and y^4 becomes y^2.
Then you distribute the 1/2 to the x^5 and the y so they become x^5/2 and y^1/2.
Next, you combine the like terms. x and x^5/2 becomes x^7/2. y^2 and y^1/2 become y^5/2.
So you have x^7/2 y^5/2
To get rid of the 2 on the bottom of the exponents you square root both variables.
So you get √x^7 y^5 (square rooted x^7 and y^5)
Simplify the square rooted problem to x^3 y^2 √xy
You get x to the third power y to the second power and square rooted xy.
Create a probability model for the outcome of performing 2 spins. What is the probability of landing on red once and yellow once?
Using the concept of probability, the probability of not landing on yellow or red at all is 1/4.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Creating a square model of the two spins :
Red(R) ; Blue(B) ; Green(G) ; Yellow(Y)
___ R ___ B ___ G ___ Y
R_ RR __ RB __ RG __ RY
B_ BR __ BB __ BG __ BY
G_ GR __GB __ GG __GY
Y_ YR __ YB __ YG __ YY
Sample space = 4² = 16
Combinations without red and yellow :
{BB, BG, GB, GG}
Number of selections without red or yellow = 4
Recall :
Probability = required outcome / Total possible outcomes
P(without Red or Yellow) = 4/16 = 1/4
Hence, the probability of not landing on yellow or red at all is 1/4.
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What are the other two factors of this polynomial x^3-4x^2-17x+60x-3
The factors of y =x³-4x²-17x+60x are (x−3), (x−5) and (x+4)
What is Polynomial?An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
Given:
y =x³-4x²-17x+60x
Let us assume that the factors are
(x−a), (x−b) and (x- c)
So, if x is either equal to a or b or c, y=0
and a⋅ b⋅ c=−60, which means a or b and c are factors of 60.
Thus, which factor of 60 (such as 2, 3, 5, 6, 10 etc.) makes y=0.
It is given that (x−3) is a factor of y
and, When we divide y by (x−3), we get x²−x−20
Similarly x=5 makes x²−x−20 equal and Dividing x2−x−20 by (x−5), we get (x+4)
Hence, the factors of y =x³-4x²-17x+60x are (x−3), (x−5) and (x+4)
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How do I do this question about angles in circles
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100100100 pieces of sushi in total. Sofia had already ordered and paid for 242424 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 121212 pieces and costs \$8$8dollar sign, 8. Let rrr represent the number of additional rolls that sofia orders. 1) which inequality describes this scenario? choose 1 answer: choose 1 answer:.
In linear equation, Sofia will order 7 more rolls of sushi (84 pieces) and pay $56.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
They need at least 100 pieces of sushi
Sofia had ordered and paid for 24 pieces of sushi already
Sushi comes in rolls
Each roll=12 pieces at $8
R=additional rolls that Sofia orders
Additional sushi= Needed sushi - ordered sushi
=100-24
=76 pieces of sushi
Each roll has 12 pieces
76/12=6.33
Sofia has to order in rolls
So, she will order 7 more rolls of sushi of 12 pieces each
12*7=84 pieces
Recall, that they needed at least 100 pieces, so the number of pieces could be more than 100
If Sofia orders 84 pieces + the already ordered 24 pieces
Total pieces=108 pieces
She has paid for 24 pieces (3 rolls) at $8 per roll
7 rolls=$8*7
=$56
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A fox can run at a peed of 10 kmph, and a wolf can run at a peed of 11 mph. Which animal i fater?
If fox run at speed of 10 kmph and wolf run at 11 mph , then the animal that runs faster is wolf .
In the question ,
it is given that ,
the speed at which the fox runs is = 10 kmph
the speed at which the wolf runs is = 11mph ,
for comparison , the units should be same ,
So , we need to convert 11 mph to kmph .
we know that , 1 mile per hour = 1.60934 kmph ,
So , 11 mph = 17.7028 kmph .
So , the speed at which the wolf runs is = 17.7028 kmph .
On comparison , we get that speed of wolf is greater than speed of fox .
Therefore , wolf runs faster than fox .
The given question is incomplete , the complete question is
A fox can run at a speed of 10 kmph, and a wolf can run at a speed of 11 mph. Which animal is faster ?
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Answer: the Answer is wolf
Step-by-step explanation:
the wolf can peed so it is fater
Tess wants to make throw pillows for her couch. She has 6 yards of fabric. Each pillow uses 2/3 of a yard of fabric. How many pillows can she make?
Answer:
4
Step-by-step explanation:
[tex] \frac{2}{3} \times 6 = 4[/tex]
I think she can make 4 throw pillows if she should use 6 yards of fabric
i hope this helped
Which statement is a proportion?
a. 3/4 = 5/8
b. 3/4 = 4/8
c. 3/4 = 6/8
d. 3/4 = 7/8
The statement that is proportion is 3/4 = 6/8
What is statement ?
Depending on the context, the term "statement" in logic can refer to either a proposition or a coherent declarative utterance that can be true or untrue. Which is the claim a true or untrue declarative phrase makes.
A sentence that asserts something to be true is called a statement.
In the fields of law, banking, and government, there are more types of statements. Every statement makes a claim or a point. If you see an accident, you have to tell the police what you observed in a statement.
A statement is a directive issued to the computer that tells it to carry out a specific task, like display something on the screen or gather input. A succession of assertions make up a computer program.
3/4 = 5/8
3:4 ≠ 5:8
3/4 = 4/8
3/4 = 1/2
3:4 ≠ 1:2
3/4 = 6/8
3/4 = 3/4
3:4 = 3:4
3/4 = 7/8
3:4 ≠ 7/8
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Ethan uses the function f(x) = 2x2 + 2x + 4 to track the temperature of a substance over 8 hours. You know that
f(3) = 28 meaning that the temperature of the substance is 28°C when you plug in a 3 for x. What is the domain
of Ethan's function?
The domain of f(x) = 2x² + 2x + 4 is (-∞, ∞).
What is a Quadratic equation?A quadratic equation, or quadratics, is a polynomial equation with a maximum degree of two. It will be in the form of ax² + bx + c = 0.
When a quadratic function is represented in a graph on the x and y grid, It will represent a parabola. Either it will open upwards or downwards.
The domain of a parabola is the entire set of real numbers [ Without any restrictions ]
Here we have
Ethan uses the function, f(x) = 2x² + 2x + 4
As we know all quadratic functions are parabolas
And its domain is the set of real numbers
Therefore,
The domain of f(x) = 2x² + 2x + 4 is (-∞, ∞).
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9x - 7 = -7
Solve For X
Answer:
the answer to this should be no solution
Step-by-step explanation:
the first step would be adding seven to both sides, but all that does is leave a zero on the other side, so the equation ends up being 9x=0.
The value of x in the expression is 0.
We have,
Expression: 9x - 7 = -7
To solve for x.
Add 7 on both sides.
9x - 7 + 7 = -7 + 7
9x = 0
x = 0
Thus,
The value of x in the expression is 0.
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An ice cube is freezing in such a way that the side length s, in inches, is s of t equals one half times t plus 2 comma where t is in hours. The surface area of the ice cube is the function A(s) = 6s2.
Part A: Write an equation that gives the volume at t hours after freezing begins. (2 points)
Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points)
Part C: After how many hours will the surface area equal 216 square inches? Show all necessary calculations, and check for extraneous solutions. (4 points)
a) The equation for the volume of the cube after t hours is of: V(t) = (0.5t + 2)³.
b) The equation for the surface area of the cube after t hours is of: S(t) = 6(0.5t + 2)².
c) The surface area will be of 216 in² after 8 hours.
How to obtain the volume and the surface area of a cube?Considering a cube of side length s, the surface area and the volume are given as follows:
Surface Area: S(s) = 6s².Volume: V(s) = s³.In this problem, the side length is a function of the time, as follows:
s(t) = 0.5t + 2.
Hence the equations are given as follows:
Surface Area: S(t) = 6(0.5t + 2)².Volume: V(t) = (0.5t + 2)³.The surface area will be of 216 in³ when:
6(0.5t + 2)² = 216
(0.5t + 2)² = 216/6
(0.5t + 2)² = 36.
Taking the square root from both sides, the time is given as follows:
0.5t + 2 = 6
0.5t = 4
t = 4/0.5
t = 8 hours.
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What is the solution to the system of equations graphed below? y = –2x – 4 y = x + 2 A. (0, 2) B. (–2, 0) C. (0, –2) D. (2, 0)
The solution to the system of equations is ( -2, 0)
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
y = -2x - 4 ------------1
y = x + 2--------------2
Equating equation 1 and 2 we have
-2x - 4 = x + 2
collect like terms
-2x - x = 2 + 4
-3x = 6
x = 6/-3
x = -2
but y = x + 2
substitute x = -2
y = -2 + 2, y = 0
In conclusion the solution of the system of linear equations is (-2, 0 )
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I need help with these two questions!
Question 1
C. Congruent by ASA.
Question 2
The reason is 'definition of isosceles triangle'.
What is StartFraction 2 tangent (10 degrees) Over 1 minus tangent squared (10 degrees) EndFraction expressed as a single trigonometric ratio?
As a single trigonometric ratio (2tan(10 degrees))/(1 - tan² (10 degrees)) = tan 2x = tan 20 degree
What is Trigonometric Ratios ?
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions.
The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
The expression given is
(2tan(10 degrees))/(1 - tan² (10 degrees))
By the property of Tan 2x
Tan 2x = 2tanx /(1 - tan² x)
Therefore from the formula ,
x = 10 in the given expression
Therefore as a single trigonometric ratio (2tan(10 degrees))/(1 - tan² (10 degrees)) = tan 2x = tan 20 degree
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Answer: yes tan(20°) option 4
Step-by-step explanation:
The sum of the 12th square number and the 4th cube number is:
Answer:
144 + 64 =208
Step-by-step explanation:
you see the 12th square number is 12 × 12 which is 144 then the 4th cube number is 4 × 4 ×4 make it 64 and the sum of all of this is 204
Suppose trains leave from New York for Atlanta every 20 minutes starting at 1 a.m., and trains leave Atlanta for New York every 30 minutes starting at 1:10 a.m. If it takes each train 10 hours to travel from one city to the other, how many trains traveling from Atlanta to New York are passed by the train that leaves New York at 1 p.m. and arrives in Atlanta at 11 pm?
The trains leaving atlanta for new york every 30 minutes....it takes 10 hours so there is 20 trains on the track when YOUR
NY to ATL train leaves......during the 10 hour trip ANOTHER 20 trains will launch from ATL going to NY
so you will pass 40 trains that are going from ATL to NY while you are travelling to ATL
This assumes that the trains go every 30 minutes around the clock.
If they do not go around the clock , you will only pass trains that launch for the 10 hours after your departure from NY
that would be 20 trains
Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is 0.
R′(x) = 0.06x^2 − 0.05x + 138
The demand function for the marginal revenue function is p(x) = 0.02x² - 0.025x + 138.
Define Marginal revenue
Marginal revenue is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit.
Given expression is,
R′(x) = 0.06x² − 0.05x + 138
To make R'(x) to R(x) just integrate R'(x),
R(x) = ∫ R'(x) dx
= ∫ (0.06x² − 0.05x + 138) dx
= 0.06x³/3 − 0.05x²/2 + 138 x + C
We get, R(x) = 0.02x³ − 0.025x² + 138 x + C
It's given, the revenue is 0 means no items sold so R(0) = 0.
Now, put x = 0 and find C
R(0) = 0.02(0)³ − 0.025(0)² + 138 (0) + C
0 = 0 + C
C = 0
So, R(x) = 0.02x³ − 0.025x² + 138 x, since C = 0
Now, take x common from R(x) will give us,
R(x) = x( 0.02x² − 0.025x + 138 )
so, R(x) = x p(x)
so, p(x) = 0.02x² − 0.025x + 138
Hence, the demand function for the marginal revenue function is p(x) = 0.02x² - 0.025x + 138.
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Christopher buys 1/2 pound of cheese for $3.60. How much would it cost per pound of cheese?
Answer:
$ 7.2
Step-by-step explanation:
½ pound = $3.60
1 pound = x
just cross multiply.
½x = $ 3.60
0.5x = $ 3.60
x = $3.60/0.5
x = $7.2
Answer:
[tex]\huge\boxed{\sf \$ 7.20}[/tex]
Step-by-step explanation:
Given that,
1/2 pound of cheese = $3.60
Using unitary method.Multiply 2 to both sides
1 pound of cheese = $3.60 × 2
1 pound of cheese = $7.20[tex]\rule[225]{225}{2}[/tex]
help please
What is the Range of the function?
The range of the function f(x) = 3x - 4, having domain x ≥ 1 is x ≥ -1 and the graph is attached below so, option D is correct.
What is range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given:
The function, f(x) = 3x - 4,
Domain = x ≥ 1
When domain = 1,
Range = 3 × 1 - 4 = -1
When domain = 2
Range = 3 × 2 - 4 = 2
Thus, you can conclude the range of the function as x [-1, ∞) or x ≥ -1
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Question
You go down 8 floors in an elevator. Your friend goes up 5 floors in an elevator. Write each amount as an integer.
you will be on floor no. -8 and your friend will be in floor no. 5 if you and your friend started at floor no. 0
YOU CAN ALSO VISUALISE THIS WAY
given 2n = m + h h = n + m prove n = 2m
See steps below for proving n = 2m:
Step-by-step explanation:An equation is formed of two equal expressions. n=2m can be proved by solving the two of the given equation for h and then equating them together as shown below.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign ''=''.
Given the two equations, 2n=m+h, and h=n+m. Now, solve the two of the equations for h as shown below:
Equation 1.
2n = m + h
2n - m = h
h = 2n - m
Equation 2.
h = n + m
Further, equate the value of h from both the equation,
h = h
2n - m = n + m
Bring the like terms on the same side of the equation,
2n - n = m + m
n = 2m
Hence, proved n=2m.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Use the 2016 marginal tax rates to compute the income tax owed by the following person. Single male, no dependents. Gross income: $88,000 Adjustments: $2000 Deductions:$27,000 mortgage interest $4036 property taxes $2000 charitable contributions
The taxable income in marginal tax rates for 2016 is $44964.
What is marginal tax rate?
The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate. With a marginal tax rate of 10%, tax would be deducted from the following dollar of income at a rate of 10%.Gross income = $88000
Adjustments = $2000
Deductions interest = $27000
Property taxes = $4036
Charitable contribution = $2000
Taxable income = 88000 - (2000 + 27000 + 4036 + 2000)
= 88000 - 35036
= 44964
Hence, the taxable income in marginal tax rates for 2016 is $44964.
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375 ÷ 3 = n. what do you guys think it is answers?????
Answer:125=n
Step-by-step explanation: 375 divided by 3 is 125
A group consisting of 35 aggressive zombies quadruples in size every hour. Which
equation matches the number of zombies after 7 hours?
OZ = 4(35)7
OZ = 35(1+4)7
OZ = 35(4)7
OZ=35(4) (4)(4)
Submit Answer
Answer: Z=35(4)^7
Step-by-step explanation:b = multiplier = 4b = multiplier = 4a = starting amount = 35a = starting amount = 35t = time = 7 hourst = time = 7 hours. a⋅b^t
35(4)735(4)7Equivalent forms:Equivalent forms:35(4)(4)(4)(4)(4)(4)(4)35(4)(4)(4)(4)(4)(4)(4)
Julius operates an athletic apparel stor. His records indicate that he had sales of 97,000. Customer return $ 2000 worth of clothing and shoes because of various reason. His cost of good sold was $ 25,000. What is Julius schedule c ( form) gross profit
Julius's Schedule C gross profit is $72,000
($97,000 sales - $2,000 returns - $25,000 cost of goods sold = $70,000 gross profit).
What does the profit actually mean?income from trade or business after covering the costs of generating and disbursing goods and services: Selling scraps to textile businesses brings her a sizable profit.
The purpose of profit calculationA business's primary goal should be to earn a profit. Understanding where your business is producing money and where you are spending it can help you assess your level of success. Calculating your profit can also provide you this information.
What does profit math look like?Income less all costs. As an illustration, Sam's Bakery collected $900 yesterday, but its expenses, including salaries, food, and power, were $650. Profit was therefore $900 divided by $650 to equal $250.
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