Answers
The answers are given as follows:
2
a)
A = 8
b = 10
x = 118°
y = 62°
b)
a = 8
b = 15
y = 50
x = 100°
3)
(a)
∠2 = 25°
∠3 = 65°
∠4 = 65°
∠5 = 90°
(b)
since SL = 10,
i) LT 10
ii) TM = 10
iii) SM = 10
4)
a) Since m∠118
∠2 = 18°
∠3 = 72°
∠4 = 72°
If FA = 27, then LO = 13.5
The above are resolved using the properties of Parallelograms; Rhombus, and Rectangle
What is the Justification for the above responses?
Since the above answers are justified by the qualities or properties of :
Parallelograms; Rhombus, and Rectangle, lets look at them one by one.
2
a)
A = 8 - opposite sides of a parallelogram are equal in length
b = 10 -opposite sides of a parallelogram are equal in length
y = 62° - opposite angles of a parallelogram are of equal measure.
x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2
= 118°
3)
(a) Here we have a Rhombus.
∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2
∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°
∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3
∠5 = 90° - [properties of a Rhombus]
(b)
since SL = 10,
i) LT 10 - All sides of a Rhombus are equal
ii) TM = 10 - All sides of a Rhombus are equal
iii) SM = 10 - All sides of a Rhombus are equal
4) Here we have a Rectangle.
a) Since m∠18
∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)
∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ = 90-18 = ∠72°
∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)
If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,
LO = FA/2
LO = 27/2
LO = 13.5
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Related Questions
(-2, 2) and (4, -1) lie on a line, what is the equation of the line?
Answers
As (-2, 2) and (4, -1) lie on a line the equation of the line is: y = (-1/2)x + 1
We can use the slope-intercept form of a linear equation,
which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope of the line using the two given points. The slope formula is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the values, we get:
m = (-1 - 2) / (4 - (-2)) = -3/6 = -1/2
Now we have the slope (m = -1/2), and we can use either of the two given points to find the y-intercept (b).
Let's use the first point (-2, 2):
y = mx + b
2 = (-1/2)(-2) + b
2 = 1 + b
b = 1
So the equation of the line is:
y = (-1/2)x + 1
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Is the product of (x − 3)2 a perfect square trinomial? Explain your reasoning
Answers
Yes, the product of (x - 3)^2 is a perfect square trinomial because it can be written as the square of the binomial (x - 3).
A perfect square trinomial is a trinomial of the form a^2 + 2ab + b^2, where a and b are terms that can be squared. When we expand the square of a binomial, we get a perfect square trinomial.
In this case, the binomial is (x - 3), and its square is (x - 3)^2. When we expand this expression, we get:
(x - 3)^2 = (x - 3)(x - 3) = x^2 - 6x + 9
This is a perfect square trinomial, because it can be written as the square of the binomial (x - 3). Specifically, we can write:
(x - 3)^2 = (x - 3)(x - 3) = (x - 3)^2
Therefore, the product of (x - 3)^2 is a perfect square trinomial.
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through: (0,-5) and (-2,-3)
Answers
The equation of the linear function is y = x - 5
How to determin the equation of the linear functionFrom the question, we have the following parameters that can be used in our computation:
The ordered pairs (0,-5) and (-2,-3)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
This means that
y = mx - 5
Using the other point (-2, -3), we have
-2m - 5 = -3
Evaluate the like terms
-2m = 2
Divide by 2
m = 1
Substitute the known values in the above equation, so, we have the following representation
y = x - 5
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Complete question
Find the equation of the linear function represented by the line that goes through: (0,-5) and (-2,-3) in slope-intercept form.
y = ___?___
draw a coordinate plane and find points A(-2;0) B(1;4) C(-5;-1) D(5;0) E(0;0)
pls help me
20 points
Answers
A weeping willow that is
15
1515 feet in height grows to a maximum height of
35
3535 feet in
�
yy years at a constant rate of
24
2424 inches per year. Which of the following equations best describes this situation?
1
foot
=
12
inches
1foot=12inches
Answers
The value of the equation is 35 = 15 + 2y , where y is the number of years and the y = 10 years
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the initial height of the weeping willow be = 15 feet
Let the final height of the weeping willow be = 35 feet
The height in feet the weeping willow grows each year = 24 inches = 2 feet
Let the number of years be = y
On simplifying the equation , we get
35 = 15 + 2y
Subtracting 15 on both sides of the equation , we get
2y = 20
Divide by 2 on both sides of the equation , we get
y = 10 years
Hence , the equation is y = 10 years
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Find all remaining roots for 3x³- 7x² - 7x + 3 = 0; x = 3
Answers
The roots of the polynomial equation are x = −1, 1/3, and 3.
Finding Roots of a polynomial equationA polynomial equation is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.
Finding the value(s) of 'x' that satisfy the polynomial equation p(x) = 0 is all that is required to solve the problem. A number "a" is a polynomial p(x) "zero" if and only when p(a) = 0.
Given that:
3x³- 7x² - 7x + 3 = 0
Factor the left side of the equation.
(x + 1) (3x − 1)(x − 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x + 1 = 0
3x − 1 = 0
x − 3 = 0
Set x + 1 equal to 0 and solve for x; x = - 1
Set 3 x − 1 equal to 0 and solve for x; x = 1/3
Set x − 3 equal to 0 and solve for x; x = 3
The final solution is all the values that make (x + 1)(3 x − 1)( x − 3) = 0 true is x = −1, 1/3, 3.
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Shawna is playing a game that involves rolling a black numbered cube and a red numbered cube. The result of a red numbered cube represents a negative number, and the result of a black numbered cube represents a positive number. Shawna’s current score is 4. Then, Shawna rolls a red 5 and a black 3. Write and solve an equation to represent Shawna’s new score
Answers
Shawna's new score can be represented by the equation is New Score = Current Score + (Result of Black Cube) + (Result of Red Cube). So, Shawna's new score is 2.
In the game that Shawna is playing, rolling the black cube results in a positive number, while rolling the red cube results in a negative number. We are told that Shawna's current score is 4, which means that she has accumulated 4 points up to this point in the game.
Next, we are told that Shawna rolls a red 5 and a black 3. This means that the red cube resulted in a negative 5 and the black cube resulted in a positive 3.
To calculate Shawna's new score, we can add the results of these two rolls to her current score. However, we need to be careful to subtract the negative number, rather than adding it. This is because a negative number is actually a decrease in score.
Therefore, we can use the following equation to calculate Shawna's new score:
New Score = Current Score + (Result of Black Cube) + (Result of Red Cube)
Substituting in the values that we know, we get:
New Score = 4 + 3 + (-5)
Simplifying, we can combine the positive and negative numbers:
New Score = 4 - 2
Therefore, Shawna's new score is 2. This means that after rolling a red 5 and a black 3, her score has decreased by 2 points from her original score of 4.
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Leila had 1 3/4 of a bag of chips. Her brother gave her 1 1/2bags of chips. How many
does Leila have altogether?
Answers
COULD SOMEONE PLEASE HELP ME WITH #2!!
Answers
2: 115
3: 65
4: 65
5: 115
6: 65
what would the shape of the graph b if the speed of the objects decreased from 50m/s at 30s to 30m/s at 40s
Answers
The shape of the graph b will be linear with an immediate decrease in speed.
What is a position vs time graph?In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled by an object from its starting position with respect to the time when it is started moving.
Generally speaking, the position or distance traveled by a physical object in a position vs time graph is always plotted on the y-coordinate while time is always plotted on the x-coordinate (x-axis).
In this scenario, the rate of change of the shape's position can be calculated as follows:
Rate of change = (30 - 50)/(40 - 30)
Rate of change = -20/10
Rate of change = -2.
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How can I find the population of the town? Many thanks
Answers
X•0.12=522
Then you divide by 0.12 which gives you
X=4350
Please Help! I Have Limited Time! A scatter plot is shown on the coordinate plane.
Which two points would a line of fit go through to best fit the data?
A. (3, 6) and (7, 3)
B. (3, 7) and (9, 1)
C. (1, 9) and (10, 1)
D. (1, 7) and (2, 5)
Answers
The two points that a line of fit will go through to best fit the data are;
B: ( 3, 7) and (9, 1)
How to Interpret the Scatter Plot?Scatter plots are defined as the graphs that present the relationship between two variables in a data-set. It is used to represent data points on a two-dimensional plane or on a Cartesian system. The independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.
A line of best fit is a straight line drawn through the maximum number of points on a scatter plot. It should have an equal number of points above and below that line. This is best represented on the blue line on the attached graph. It touched 4 points and is between the green and red line.
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the town's population has increased for 80,000 to 90,000 in the past 10 years. what was the present increase.
Answers
The percentage increase in the population of the town is 12%.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Increase in population = 90,000 - 80,000 = 10,000
Percentage increase = 10,000/80,000 * 100 = 100/8 = 12.5%
Hence the percentage increase in the population of the town is 12%.
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[tex]20x+18=58[/tex]
Answers
20x+18=58
Answer is 2
For a classical infinite square-well potential of width a. How does the classical result compare with the quantu
Answers
For small particles such as atoms and subatomic particles, quantum mechanics produces more accurate results than classical mechanics. As the particle size decreases, the differences between classical and quantum mechanical results become more pronounced.
The particle in an infinite square well potential is treated as a point particle with well-defined position and momentum in classical mechanics. The classical solution to the infinite square well problem involves a particle bouncing back and forth between the well's walls, its energy being provided by the kinetic energy associated with its motion inside the well.
In quantum mechanics, on the other hand, the particle in an infinite square well potential is treated as a wave function that solves the Schrödinger equation. The probability distribution of the particle's position and momentum inside the well is described by the wave function. The allowed energy levels of the particle are quantized and can be calculated using the problem's boundary conditions.
The following formula gives the classical result for a particle's energy in an infinite square well potential:
[tex]n2*h2/(8ma2) = E n[/tex]
where n is an integer, h is Planck's constant, and m is the particle's mass. According to this formula, energy levels are continuous and can take any value.
The quantum mechanical result for a particle's energy in an infinite square well potential, on the other hand, is given by the formula:
[tex]E n = (n2 * pi2 * h2) / (2ma2).[/tex]
n must be a positive integer. According to this formula, energy levels are quantized and can only take on discrete values.
As a result, the classical result for the energy of a particle in an infinite square well potential differs greatly from the quantum mechanical result. The classical result predicts continuous energy levels, whereas the quantum mechanical result predicts quantized energy levels.
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3 Hassan recorded the number of people in 60 passing cars.
Here are his results. Find:
a the missing frequency
b the modal number of people in a car
c the median
d the mean.
Answers
a) The missing frequency is 20
b) The modal number of people in a car is 1
c) The median is 3
d) The mean is 0.95
The sum of the frequencies must be 60.
The missing frequency by subtracting the sum of the other frequencies from 60
60 - (28 + 3 + 7 + 1 + 1) = 20
To find the median, we need to arrange the data in order from smallest to largest:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6
There are 60 numbers in total, so the median is the average of the 30th and 31st numbers:
median = (3 + 3)/2 = 3
The mode is the value with the highest frequency, which is 1.
mean = (1 x 28 + 2 x 20 + 3 x 3 + 4 x 7 + 5 x 1 + 6 x 1) / 60
= (28 + 40 + 9 + 28 + 5 + 6) / 60
= 0.95
Therefore, the missing frequency, mode, median and mean has been found
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The given question is incomplete, the complete question is
Hassan recorded the number of people in 60 passing cars
people 1 2 3 4 5 6
frequency 28 ? 3 7 1 1
a)find the missing frequency
b)median
c)modal
d)mean
help me out please i
Answers
Answer: 2 *(3+4)= (2x3)+ (2x4)
Step-by-step explanation:
La masse d’un atome est de 1,05•
Answers
Answer:La masse d'un atome de cuivre est de 1,05 x 10^-25 kg. Un atome de cuivre comporte 29 électrons. Ces electrons constituent le nuage electronique de l'atome. chaque electron a une masse de 9,11 x 10^-311.
Step-by-step explanation:
you are skiing down a mountain with a vertical height of 900 feet. the distance from the top of the mountain to the base is 1800 feet. what is the angle of elevation from the base to the top of the mountain?
Answers
Can some one help me find y I have already found x
Answers
Step-by-step explanation:
Since y is on a straight line, it'll be easy
The degree of a straightine is 180
You have one angle of 57, so all we do is subtract 57 from 180
180-57 = 123
what is the surface area of a right cylinder with a radius of 6 units and a height of 14 units?
Answers
The surface area of a right cylinder with a radius of 6 units and a height of 14 units is equal to 753.6 square units.
How to calculate surface area of a cylinder?Mathematically, the surface area (SA) of a right cylinder can be calculated by using this formula:
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the surface area of a right cylinder formula, we have;
Surface area (SA) of cylinder = (2 × 3.14 × 6 × 14) + 2 × 3.14 × 6²
Surface area (SA) of cylinder = 527.52 + 226.08
Surface area (SA) of cylinder = 753.6 square units.
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Question 3 Complete the following word problems by showing all your calculations: 3.1) Thato bought a bicycle for R 8 000 on a loan at Cycle lab. If the interest rate was 14% per annum for 3 years. a) What is the interest he will pay? b) What is the final amount he will pay for the bicycle? 3.2) The florist bought 200 roses for R900. If she sells the roses in a bouquet of five for R 35. a) What was the cost price per rose? b) What is the selling price per rose? c) What is the profit that she will make per rose? 3.3) The shopkeeper buys oranges and apples at a ratio of 4:3. How many apples will he buy, if he buys 96 oranges? (3) 3.4) Mr Dingaan started practicing the 1st of January to run a marathon of 140 km on the 1st of June. He practices every day for 3 hours and runs at a speed of 35km/hour. a) What is the distance that he runs in one day? b) What is the total distance he runs during the time that he practices, from January to June?
Answers
1a. The interest that Thato will pay equals to R3,840.
1b. The final amount he will pay for the bicycle will be R 11 840.
1a What is the interest he will pay?a) To calculate the interest that Thato will pay, you can use the following formula:
Interest = Principal * Rate * Time
Interest = R 8,000 * 0.14 * 3
Interest = R3 840
1b What is the final amount he will pay for the bicycle?Final amount = Principal + Interest
Final amount = R 8,000 + R 3,840
Final amount = R 11,840
2a What was the cost price per rose?Cost price per rose = Total cost of roses / Number of roses
Cost price per rose = R 900 / 200
Cost price per rose = R 4.50
2b. What is the selling price per rose?Selling price per rose = Price of bouquet of 5 roses / Number of roses in the bouquet
Selling price per rose = R 35 / 5
Selling price per rose = R 7.00
2c. What is the profit that she will make per rose?Profit per rose = Selling price per rose - Cost price per rose
Profit per rose = R 7.00 - R 4.50
Profit per rose = R 2.50
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hi can have help with this please i can’t figure out what c is :)
Answers
Answer: octagon
Step-by-step explanation:
Answer:
Step-by-step explanation:
No. c will be decagon because it has 10 sides
Please find the degree of angle x!
Answers
Answer:22.61 degrees
Step-by-step explanation:
Use reverse tangent
Ms. Rod rolls a 6-sided die . If she rolls the die 57 times, how many times should she expect to roll a composite number?
Answers
By understanding what composite numbers are and how they relate to rolling a die, we can determine the expected number of times Ms. Rod will roll a composite number in 57 rolls.
A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is a number that can be factored into smaller positive integers.
To find the number of times Ms. Rod should expect to roll a composite number, we need to know how many numbers from 1 to 6 are composite. Only two numbers are prime in this range, namely 2 and 3. This means that the other four numbers (4, 5, and 6) are composite. Therefore, out of the 6 possible outcomes of rolling the die, 4 of them are composite numbers.
We can use this information to calculate the expected number of times Ms. Rod will roll a composite number. We know that she is rolling the die 57 times, and each roll has a probability of 4/6 (or 2/3) of resulting in a composite number. Therefore, we can use the formula for the expected value of a discrete random variable, which is:
Expected value = (number of trials) x (probability of success)
Plugging in the values, we get:
Expected value = 57 x 2/3
Expected value = 38
Therefore, we can expect Ms. Rod to roll a composite number about 38 times out of 57 rolls. However, it's important to note that this is just an expected value, and the actual number of times she rolls a composite number may vary.
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25kg= blank lb i need help plese i have 2 min left
Answers
Answer: 25,000 grams
Step-by-step explanation:Really sorry if im wrong.
at a cricket match there are 27500 people correct to the nearest 100
calculate the upper bound for the difference between the number of people at the football match and at the cricket match
Answers
The upper bound for the difference between the number of people at the football match and at the cricket match is 29750<=p<=29849 .
p = number of people
The true value of p is unknown, but we know that it rounds to 29800 when rounding to the nearest hundred people.
The smallest p could be is 29750 since that rounds to 29800.
The largest is 29849; note that 29850 rounds to 29900.
We have this interval 29750<=p<=29849
r = the rate in which the people leave
This rate is in "people per minute".
Like p, the true value of r is unknown.
The midpoint of 350 and 400 is (350+400)/2 = 375, which represents the smallest value r could be if we round to the nearest 50.
The value 374 would round to 350.
On the other side of the spectrum, (400+450)/2-1 = 425-1 = 424 rounds to 400 as well when rounding to the nearest 50.
The value 425 rounds to 450.
To wrap this section up, you have this interval 375<=r<=424
Summary so far:
29750<=p<=29849
375<=r<=424
where p is the number of people and r is the rate in which they leave (in people per minute).
If we have the smallest number of people (29750) and the highest rate in which they leave (424), then we'll get the lower bound of how long it takes everyone to leave.
This can be thought of as the floor value.
time = (number of people)/(rate)
time = (29750)/(424)
time = 70.1650943396227
time = 70.165
Hence, the upper bound for the difference between the number of people at the football match and at the cricket match is 29750<=p<=29849 .
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Tanya went to the store and bought a box of spaghetti noodles for $4. She also bought x pounds of ground beef for $3.52 per pound. The total amount of money Tanya spent can be represented by the equation 18 = 3.52x + 4. How many pounds of ground beef did Tanya buy?
Answers
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note for this question, we will have to make x the subject and solve for x.
x is equal to 3.97
It takes an older computer twice as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 5 minutes to
send out the email. How long will it take the newer computer to send out the email on its own?
Do not do any rounding.
minutes
Answers
The time taken by the new computer to send an email found using the unitary method, is 7.5 minutes.
What is a unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Let,
Time taken by new computer to send 1 email = x
Time taken by the old computer to send same mail = 2x
Using unitary method
In 1 minute
Work done by new computer = 1/x
Work done by old computer =1/2x
Given the time taken when both computers work together = 5 minutes
Work done in 1 minute by both = 1/5
So we can write,
1/x + 1/2x = 1/5
3/2x = 1/5
x = 7.5 minutes
Therefore the time taken by the new computer to send an email found using the unitary method, is 7.5 minutes.
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Macy spent 2hours working on homework she spent 1/4 of that time working on math
Answers
Time for working for history is 50 minutes.
First we need to multiply to make the fractions have equal denominators so we can add/subtract.
Science: 1/3 x 4/4=4/12
Math: 1/4 x 3/3=3/12
Now we can find the time she spent on history (I assume this is what you are looking for)
Total time-math time-science time=history time
12/12-4/12-3/12
=5/12
Macy spent 5/12 of her time working on history.
so totak fo 2 hours she spent 5/12 time to work on history
so 2 hours*5/`12 = 5/6 hours = 50 minutes
Q- Macy spent 2 hours working on homework she spent 1/4 of that time working on math he spent 1/3 of her time working on science find time for working for history.
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