The mid-point of the sides of this quadrilateral are the vertices of a parallelogram.
How to find the mid-side of the parallelogram?
You should know that in every parallelogram, the opposite sides are equal and parallel.
The given vertices are (2,4), (5,8), (9,5) and (6,1).
Let the vertices be A,B,C,D And the midpoints of the sides be M, N, O, P
Coordinates of A (2+5)/2 , (4+8)/2 = (3.5 , 6)
Coordinates of B (5+9)/2 , (8+5)/2 = (7,6.5)
Coordinates of C (9+6)/2 , (5+1)/2 = (7.5, 3)
Coordinates of D (6+2)/2 , (1+4)/2 = (4 , 2.5)
The distance between the vertices is denoted by the formula
distance = [tex]\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2} }[/tex]
AB= √(3.5-7)²+(3-6.5)² = √12.5 = 3.5
BC= √(7-7.5)²+(6.5.3)² = √6.5 = 2.5
CD= √(7.5-4)²+(3-2.5)² = √12.5 = 3.5
DA= √(4-3.5)²+(2.5-6)² = √6.5 = 2.5
From the calculations, it is clear that the opposite side of the quadrilateral are equal
This means that quadrilateral is a parallelogram
Learn more about distance between two points on a quadrilateral on https://brainly.com/question/24485622
#SPJ1
The correct question:
A quadrilateral has the vertices at the point (2,4), (5,8), (9,5) and (6,1). Show that the mid-point of the sides of this quadrilateral are the vertices of a parallelogram.
Josephine started to watch a movie the movie starts at 18:30 the movie was 1 hour and 53 minutes long but part way through it she paused it for 16 minutes what time did the movie end?
Answer:
The movie ended at 7:39 a.m.
Step-by-step explanation:
She started at 6:30. 53 minutes added to that would be 7:23. Another 16 minutes added to that would be 7:39.
The movie will end at 20:39.
What is time conversion?Conversion Time means a time which falls after the Calculation Time and is the time at which the admission of the Ordinary Shares arising on Conversion to the Official List becomes effective.
Given that, Josephine started to watch a movie the movie starts at 18:30 the movie was 1 hour and 53 minutes long but part way through it, she paused it for 16 minutes
The total time taken = 1 hour + 53 minutes + 16 minutes = 1 hours + 69 minutes
= 1 hour + 60 minutes + 9 minutes
= 1 hours + 1 hours + 9 minutes
= 2 hours + 9 minutes
Therefore, total time she took for movie is 2 hr 9 min
Since, the movie started at 18:30,
Therefore, 18:30 + 2 hour 9 minute
= 20 hours + 39 minutes
Hence, The movie will end at 20:39
For more references on time conversion, click;
https://brainly.com/question/7985747
#SPJ2
Mr.green Is putting lights around 8 windows; each window is 3 and 1/2 feet wide and 5 feet long. How many feet of light does he need?
Answer:
The answer is 140
Step-by-step explanation:
The first step is simple L x W which will give us.
L being 5 and W being 3.5 The equation is 5 × 3.5 = 17.5.
With that being said I just need to multiply that answer by 8 which gives us 140.
This means that he will need 140 ft of light in order to put light around each window.
Hope this helped :)
What is the slope of y = − 5 + 4x
one of the 4 choices
The translation from the parent function is defined according to the following option:
A translation of 5 units to the right.
How to define the translation?The four possible translations are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function in this problem is defined as follows:
f(x) = x².
The translated function is given as follows:
g(x) = (x - 5)².
Meaning that the translated function can be written as follows:
g(x) = f(x - 5).
Thus the transformation to the parent function is given as follows:
x -> x - 5.
Thus it was a translation right of five units, and the third option is the correct option.
More can be learned about translations at brainly.com/question/29211183
#SPJ1
The expression - 270 +18.3y represents a submarine that began at a depth of 270 feet below sea level and ascended at a rate of 18.3 féet par minute. What was the depth
of the submarine after 8 minutes?
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. The submarine ___ was feet below sea level after 8 minutes.
(Type an integer or a decimal:)
B. The submarine will have reached sea level after 8 minutes.
The depth of the submarine after 8 minutes is -123.6 feet below sea level.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Depth of the submarine after y minutes.
= -270 + 18.3y
The depth of the submarine after 8 minutes.
= -270 + 18.3 x 8
= -270 + 146.4
= -123.6
Thus,
The submarine is at -123.6 feet below sea level.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
The library at your school has MP3 players pre-loaded with audio and digital books
to check out. When the librarian starts downloading new books at 11:00 am, there
are 15 already loaded. When she checks at noon, there are 25 books completely
loaded. Assuming that the computer downloads books at a consistent rate, how
many complete books will have downloaded at 2:45 pm?
Write a function of books downloaded, y, based on time passed, x (in hours), as well
as the total number of books that will be completed by 2:45 pm.
The total number of books completed by 2:45 pm will be 42.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that when the librarian starts downloading new books at 11:00 am, there are 15 already loaded. When she checks at noon, there are 25 books completely loaded.
The number of books loaded in 1 hour is calculated as,
N = 25 - 15
N = 10 books
Now from 12 noon to 2:45 pm, the time in hours will be,
T = 165 minutes or 165 / 60 = 2.75 hours
The equation for the number of books loaded will be written as,
y = 15 + 10T
y = 15 + ( 10 x 2.75)
y = 15 + 27.5
y = 42.5 or 42
The completely loaded books are 42 in number.
To know more about an expression follow
https://brainly.com/question/26310043
#SPJ1
Two angles form complements. One angle measure is eight more than twice the other. Find both angles measures.
Answer:
41° and 49°
Step-by-step explanation:
Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:
2x + 8 = 90
Solving for x, we get:
2x = 82
x = 41
Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.
Therefore, the two angles have measures of 41 and 49 degrees.
Given: segment BD bisects angle ABC and segment BD bisects angle ADC. Prove: segment AD is congruent to segment CD
If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.
What is bisector of an angle?
In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..
Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.
Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.
AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.
Consider △ABD and △DBC:
∠ABD = ∠DBC
∠ADB = ∠BDC
Therefore, △ABD ≅ △DBC
According to CPCT, AD ≅ CD.
To learn more about congruent triangle, click on below link:
https://brainly.com/question/15064982
#SPJ1
One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs $0.91. There are 3.8 liters in one gallon. How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
Answer: One gallon of gas in Toronto would cost approximately $3.43. To find this, first convert the price of gasoline in Buffalo to liters. Since there are 3.8 liters in one gallon, one gallon of gas in Buffalo costs $2.29 * 3.8 liters = $8.69. Next, divide the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.91 / 3.8 liters/gallon = $0.24/liter. Finally, multiply the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.24/liter * 3.8 liters/gallon = $0.91/gallon. Round this to the nearest cent to find that one gallon of gas in Toronto costs $0.91/gallon = $<<0.91/gallon=0.91>>0.91.
which analysis technique simulates a model's outcome many times to provide a statistical distribution of the calculated results?
The answer is that the Monte Carlo analysis simulates a model’s outcome many times to provide a statistical distribution of the calculated results.
Now, what is Monte Carlo analysis technique?
Monte Carlo Analysis is a risk management technique used to conduct a quantitative analysis of risks.
This mathematical technique is used to analyze the impact of risks on your project — in other words, if this risk occurs, how will it affect the schedule or the cost of the project?
So, Monte Carlo Analysis gives you a range of possible outcomes and probabilities to allow you to consider the likelihood of different scenarios.
For example, let’s say you don’t know how long your project will take. You have a rough estimate of the duration of each project task. Using this, you develop a best-case scenario (optimistic) and worst-case scenario (pessimistic) duration for each task.
You can then use Monte Carlo to analyze all the potential combinations and give you probabilities of when the project will complete.
Other major benefits of this technique is -
1. It Provides early indication of how likely you are to meet project targets.
2. Can be used to create a more real budget and schedule.
3. Predicts the likelihood of schedule .
4. Gives quantitative measure of risks to assess impacts
5. Provides objective data for decision making.
To learn more about monte carlo analysis, visit link - brainly.com/question/15350591
#SPJ4
Which one. Multiple choice.
In the given relation, 1 is not a domain.
What is domain?The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.
All the values that go into a function. The output values are called the range.
The domain of a function is the set of all possible inputs for the function.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.
Given that, a function,
{(5, 1), (4, -3), (3, -1)}
We know, a domain is the set of all "x" values.
Therefore, domain of the function are, 5, 4 and 3
But, if we see, 1 is one of the values of y.
Hence, 1 is not a domain.
For more references on domain, click,
https://brainly.com/question/28135761
#SPJ1
You recently joined a gym. You had to pay a joining fee of $40, and you will pay $20 per month to maintain the membership.
What is the one-time charge? What does it represent in slope-intercept form?
What is the recurring charge? What does it represent in slope-intercept form?
What does x represent?
What does y represent?
The number 40 represents the one-time charge which is the y-intercept. And the number 20 presents the fee for gym per month. The x-intercept represents that you need to pay 14 monthly fees for a year.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' represents the number of months and 'y' be the total cost. Then the equation is given as,
y = 20x + 40
The number 40 addresses the one-time charge which is the y-capture. Also, number 20 presents the charge for the exercise center each month. The x-block addresses that you really want to pay 14 month-to-month charges for a year.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ1
What is the name given to the exponent to which 3 must be raised to obtain 11?
The number which can be raised by 3 to give the value of 11 is 2.224.
What are exponential functions?The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.
Given:
The exponent to which 3 must be raised to obtain 11,
Assume the number is x then, According to the statement,
x³ = 11
x = ∛11
x = 2.224
Thus, the number is 2.224.
To know more about exponential functions:
https://brainly.com/question/15352175
#SPJ1
x = [?]
4x-2 3x + 14
Write a cosine function that has a midline of 3, an amplitude of 5 and a period of 2.
Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.
What is a Cosine Function?A crucial periodic function in trigonometry is the cosine function.
Utilizing the unit circle will make understanding the cosine function the simplest.
Draw a unit circle on the coordinate plane, center the angle at the origin, and label one side as the positive x-axis for the supplied angle measure.
The point where the other side of the angle intersects the circle has an x-coordinate of cos(), and a y-coordinate of sin().
According to our answer-
B = 2pi/T, where T is the period and T = 1/f is the frequency; T is the period
Determines horizontal phase shift by using
C =determines vertical shift.
When solving the given issue, D = midline = 5
A = amplitude = 2.
B = 2pi/T = 2pi/(2/3) = 3pi since frequency = 3/2 means that the period is T = 2/3, which is the reciprocal of the frequency.
C = 0.
The result of adding everything up is A = 2, B = 3pi, C = 0, and D = 5.
so,
A*cos(B(x-C)) + D = y
y = 2*cos(3pi(x-0)), plus 5.
y = cos(3pi*x) * 2 * + 5
Hence, Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.
learn more about cosine function click here:
https://brainly.com/question/12617989
#SPJ1
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
Learn more about area of similar figures on:
https://brainly.com/question/17132861
#SPJ1
Kiera's lemon cookie recipe calls for 5 cups of sugar. How much sugar would Kiera use to make 3 5/8 batches of cookies?
Answer:18 1/8
Step-by-step explanation:
5x3=15
5x5/8=25/8=3 1/8
15+3 1/8=18 1/8
40 PTS
TWO PART QUESTION NEED! :)))
You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula:A = P(1 + r/n) ^nt to give:
Part a. The future value in 4 years.
Part b. The interest gained in 4 years.
The future value of investment is $560.30, and interest gained in 4 years is 136.8%
What is compound interest?The interest regarding loan or investment that increases exponentially with respect to time is called compound interest.
Why is compound interest used?We use compound interest so as to enhance our investment in a large scale.
Given, Amount invested, P= $500
compound interest rate, r= 2.85%
number of time period, t = 4 years
number of times interest applied per time period, n =12 (as interest compound monthly)
Final amount, A
we used compound interest formula, A= P(1+r/n)∧nt
A= 500(1+0.0285/12) ∧12×4
Final amount, A= $560.30
The future value = $560.30
Interested gained in 4 years with compound monthly =2.85x12x4 =136.8%
to know more about compound interest visit:
https://brainly.com/question/14295570
#SPJ1
Write a rule for the glide reflection that maps ABC with vertices A(-4,-2), B(-2, 6).
and C(4, 4) to A'B'C' with vertices A'(4, -2), B(6, -6), and C'(12,-4).
The glide reflection that maps ABC to A'B'C' is given as follows:
Reflection over the line y = x - 9.Translation right 8 units.What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.
The midpoint of segment A'B' is given as follows:
x = (4 + 6)/2 = 5.y = (-2 - 6)/2 = -4.The slope of this segment is given as follows:
m = (-6 - (-2))/(6 - 4) = -1.
Then the slope of the reflection line is of:
m = 1.
(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).
Then:
y = x + b.
When x = 5, y = -4, then the intercept b is calculated as follows:
-4 = 5 + b
b = -9.
Thus the reflection line is of:
y = x - 9.
Then the translation is given subtracting the coordinates of one of the vertices, as follows:
4 - (-4) = 4 + 4 = 8 units right.-2 - (-2) = -2 + 2 = 0 units vertically.More can be learned about glide reflections at https://brainly.com/question/5612016
#SPJ1
Witch expression is equivalent to (-10/9t+1/8)-(-6/18t+3/4) (I NEED THIS FAST!)
Answer: ( -56 - 45t ) / 72t
Step-by-step explanation:
attached a picture for explaination.
hope that helps...
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.
What is a sphere?
The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.
Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.
The radius of a sphere is the half of its diameter.
The radius of the bottom ball is 3/2 feet =1.5 feet
The radius of the middle ball is 2/2 feet = 1 feet.
The radius of the top ball is 1/2 feet = 0.5 feet.
The volume of a sphere is 4/3 × ∏r³.
The volume of bottom ball is 4/3 × ∏ × (1.5)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (1)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (0.5)³ cubic foot.
The total amount of snow is
4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³
= 4/3 × ∏ [1.5³ +1³ + 0.5³ ]
= 4/3 × ∏× 4.5
= 18.84
≈ 19 cubic foot
To learn the volume of a sphere, click on below link:
https://brainly.com/question/7473395
#SPJ1
Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of f(x)=x^2-5x+1 . Write a rule for g .
Answer:We may rewrite f(x) = (x-1)^2
We stretch by having 3(x-1)^2
We reflect about the y axis by changing x to -x: 3(-x-1)^2 = 3(x+1)^2
We move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2
Step-by-step explanation:A way to verify this: Consider y = x^2 to be the unit parabola. f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1; moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2
We may write g(x) = 3x^2 + 18x + 27, also.
PLEASE EXPLAIN AND SHOW YOUR WORK THANK YOU!!
Solve as a MIXED NUMBER:
-2.25 + 0.4x = -2.8
THANK YOU!!!
Answer:
x=-1 3/8
Step-by-step explanation:
-2.25 + 0.4x = -2.8
-2.25 + 2.25 + 0.4x = -2.8 + 2.25 ==> add 2.25 on both sides to isolate x
0.4x = -0.55
(0.4x = -0.55)*20 ==> multiply the equation by 20 to remove decimals
8x = -11
x=-11/8
x=-(3+8)/8 ==> turn x into a mixed number
x=-3/8 - 8/8
x=-3/8 - 1 ==> simplify
x=-1 - 3/8
x=-(1 + 3/8)
x=-1 3/8
Work out:
(1.2 × 10′²) × (2 × 10ª)/3 x 10-5
Give your answer in standard
form.
The standard form of the expression is [tex]0.000286 \times 10^a[/tex].
What is a standard form?
A standard form is a document that contains predetermined information in a specific format, such as a contract or agreement. Standard forms are often used to ensure uniformity and efficiency among different parties. Standard forms may include a variety of information, including contact details, payment information, and other important details related to a transaction. By utilizing a standard form, individuals and organizations are able to save time and effort when completing administrative tasks. Standard forms can also be used to ensure that all parties involved in a transaction are aware of the terms and conditions.
The given expression is
[tex]=(1.2 \times 10^2) \times \frac{(2 \times 10^a)}{3} \times 10^{-5}\\\\=129 \times\frac{2}{3}\times\frac{10^a}{3}\times0.00001\\\\=0.000286 \times 10^a[/tex]
Hence, the standard form of the expression is [tex]0.000286 \times 10^a[/tex].
To learn more about the standard form, visit:
https://brainly.com/question/19169731
#SPJ1
1,000 individuals total: 900 are fully susceptible (fs) to methicillin, meaning they die early in the course of treatment. 90 are somewhat susceptible (ss) to methicillin, meaning they have some resistance to methilicillin. 10 are killed only by a full treatment with methicillin (ft), meaning they have the greatest degree of resistance. what is the percentage of each type of s. aureus?
The percentage of each types of s. aureus
Fully susceptible (fs) to methicillin = 90% Somewhat susceptible (ss) to methicillin = 9% Killed only by a full treatment with methicillin = 1%Total number of individuals = 1000
Number of individuals susceptible (fs) to methicillin = 900
The percentage = (Number of individuals susceptible (fs) to methicillin / Total number of individuals) × 100
= (900/1000) × 100
= 90%
90 are somewhat susceptible (ss) to methicillin
The percentage = (90 /1000) × 100
= 9%
10 are killed only by a full treatment with methicillin (ft)
The percentage = (10/1000) × 100
= 1%
Therefore, the percentage of each types of s. aureus are 90%, 9% and 1%
Learn more about percentage here
brainly.com/question/12715980
#SPJ4
a car manufacturer wants to learn more about the brand preferences of electric car owners. there are millions of electric car owners in the world. who should the company survey? 1 point the entire population of electric car owners a sample of car owners who have owned more than one electric car a sample of all electric car owners a sample of car owners who most recently bought an electric car
A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.
What is Survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.
As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.
To know more about Survey:
https://brainly.com/question/17373064
#SPJ1
Geometry is hard help
A college student is deciding how many hours to work at a part time job(x) and how many hours to work at an internship (y). The job pays $24 and hour, and the internship pays $12 an hour. The student needs to work less than 15 hours a week but needs to earn at least $240 a week to pay expenses. Write 2 systems of inequalities to represent all the combinations of number of hours the student can work at the job and internship
Answer:
x + y < 152x + y ≥ 20-------------------------------
Total hours worked is x + y.
Earning from the part time job is 24x, from the internship is 12y.
Inequality for the number of hours:
x + y < 15Inequality for the earning:
24x + 12y ≥ 240This can be simplified by dividing all terms by 12:
2x + y ≥ 20Answer:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
Step-by-step explanation:
Part-time job
Let x be the number of hours worked.$24 = pay per hour.Internship
Let y be the number of hours worked.$12 = pay per hour.The student needs to work less than 15 hours a week:
[tex]\implies x+y < 15[/tex]
The student needs to earn at least $240 a week:
[tex]\implies 24x+12y \geq 240[/tex]
Therefore, the system of inequalities is:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
The second inequality can be simplified by dividing each term by 12:
[tex]\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}[/tex]
[tex]\implies 2x+y \geq 20[/tex]
Therefore, a second system of inequalities is:
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
To solve the system of equalities, graph both inequalities and shade the overlapping region.
Any (x, y) point in the overlapping region is a solution to the system of inequalities.
Look at the triangles shown below.
5
Which statement is TRUE?
Answer: B
Step-by-step explanation:
vertical angles are =
Triangle A'B'C' is a reflection of triangle ABC across line BC. Prove that ray BC is the angle bisector of angle ABA'.
Proof of ray BC is the angle bisector of angle ABA' is given.
What are angle bisectors?Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.
A graph will move exactly to the other side of an axis, such as the x-axis, as if it were a mirror when it is reflected along that axis.
Because it is symmetrical, each point is as far from the axis of reflection as its mirror counterpart.
Triangle A'B'C' is a mirror of triangle ABC over line BC, as shown by the provided issue.
Therefore, <A'B'C' = <ABC
by virtue of congruent triangles' characteristics. Means that if the sides' lengths are equal, the angles' measures are equal, and they may be overlaid.
Therefore, the ray BC is the angle, bisector of angle ABA'.
Learn more about angle bisector here;
https://brainly.com/question/12896755
#SPJ1
