Answer:
C. 17.3
Step-by-step explanation:
Using Pythagoras theorem
Divide the triangle into half
c^2=a^2+b^2
20^2=a^2+10^2
400=a^2+100
400-100=a^2
300=a^2
17.32=a^2
The height of the equilateral triangle to the nearest tenth is 17.3
Given that:
An equilateral triangle has sides of length 20.
Equilateral triangles are the type of triangles which has all the sides equal to each other.
That is, three sides will have equal length.
So all the side of the triangle is 20.
The height of the triangle is the perpendicular line drawn from any of these vertices.
Since this is an equilateral triangle, the height divides the base into equal lengths.
So each half will be 20/2 = 10.
Here, a right angle is formed.
Using Pythagoras theorem,
h = √(20² - 10²)
= √(400 - 100)
= √300
= 17.3
Hence the correct option is C.
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A classroom is 24 metres long and 21 metres wide. Find the area of the classroom
Answer:
504 m²
Step-by-step explanation:
21 m * 24 m = 504 m²
So, the answer is 504 m²
The formula for the area of a rectangle is:
Length × Width
OR
L × W
In this case...
L = 24 m
W = 21
^^^Plug these numbers into the formula for the area of a rectangle
24 × 21
504
The area of this class room is 504 [tex]m^{2}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the median of the following data set?
{6, 3, 9, 1, 7}
ANSWER ASAP
Answer: the median is 9
Step-by-step explanation:
Because we have to find but the in in the middle
Answer: 6
Step-by-step explanation: list numbers in normal order and go through to find middle
which of these ordered pairs is a solution to the linear inequality y ≤ 4x - 3
Answer:
(2,5) is a solution of the inequality
Step-by-step explanation:
we have
[tex]y\leq4x-3[/tex]
The solution of the inequality is the shaded area below the solid line [tex]y=4x-3[/tex]
Remember that if a ordered pair is a solution of the linear inequality, then the ordered pair must lie on the shaded region of the inequality
Let
A(-2,5),B(2,5),C(1,5),D(1,4)
Plot each point
The point B(2,5) lie on the shaded region
therefore
(2,5) is a solution of the inequality
see the attached figure
what is the mean of the following data value 53,71,89,10,62
Answer: 57
Step-by-step explanation:
53+71+89+10+62=285
285/5=57
Answer: 57
Step-by-step explanation:
Order the data least to greatest: 10, 53, 62, 71, 89
then add them to get the sum of: 285
now divide that by how many numbers are in the data set so: 285/5
= 57
Amit is going to guess on all
2
0
2020 questions of his multiple-choice test. Each question on the test has
4
44 answer options, and only one is correct.
What is the best prediction for the number of questions that Amit will answer correctly?
Choose 1 answer:
Answer:
The best prediction for the number of questions that Amit will answer correctly is 5.
Step-by-step explanation:
Each question can be considered as an independent Bernoulli trial. This implies that we have 20 independent trials.
Now, the probability of making a correct guess on each question is;
1/4. This is because we have 4 choices per question and only 1 is correct.
If we now let the random variable X denote the number of questions that Amit will answer correctly, then X is a Binomial random variable with parameters;
20 and 1/4.
The expected number of correct answers is simply the product of these two values;
20 * (1/4) = 5
Therefore, the best prediction for the number of questions that Amit will answer correctly is 5
e^ln(6x)=
A: 6ln(x)
B: 6x
C: ln(6)
D: ln(x)
Answer:
B: 6x
Step-by-step explanation:
e^ln(6x) = 6x . . . . . . . . comes from the definition of the logarithm function
___
q = ln(p) is the value that makes e^q = p. That is, e^ln(p) = p.
In this problem, p=6x.
on friday the farmers hens laid 25 eggs. there were 15 white eggs and 10 brown eggs. what is the probability that the first egg randomly selected will be white?
A. 1/25
B. 1/15
C. 10/25
D. 15/25
E. 10/15
Answer:
The answer is d
Step-by-step explanation:
The probability that the first egg randomly selected will be white is 15/25, the correct option is D.
What is the probability?The chance that something will happen.
On Friday the farmer's hens laid 25 eggs.
There were 15 white eggs and 10 brown eggs.
The probability that the first egg randomly selected will be white is;
[tex]\rm Probability=\dfrac{White \ egg}{White \ egg + Brown \ egg}[/tex]
Substitute all the values in the formula
[tex]\rm Probability=\dfrac{White \ egg}{White \ egg + Brown \ egg}\\\\ Probability=\dfrac{15}{15+10}\\\\ Probability=\dfrac{15}{25}[/tex]
Hence, the probability that the first egg randomly selected will be white is 15/25, the correct option is D.
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Describe in your own words the characteristics of linear equations that determine whether a system of linear equations will be Intersecting, Parallel, or Coincident? (2 points, 0.5 for clarity of response, 0.5 for each type of system (intersecting, parallel, and coincident)).
Step-by-step explanation:
i) An intersecting system of linear equations
A system of linear equations comprises of two or more linear equations. Linear equations are simply straight line equations with a given slope and a unique y-intercept .
Solutions to systems of linear equations can be determined using a number of techniques among them being;
Elimination method
Substitution method
Graphical method
The graphs of a system of linear equations will intersect at a unique single point if the lines are not parallel.
An example of intersecting system of linear equations;
y = 2x -5 and y =5x + 4
The two lines will intersect at a particular single point since the slopes are not identical. The attachment below demonstrates this aspect.
ii) A parallel system of linear equations
Two lines are said to be parallel if they have an identical slope but unique y-intercepts. Parallel lines never intersect at any given point since the perpendicular distance between them is always constant.
Thus a parallel system of linear equations has no solution. An example of parallel system of linear equations;
y = 3x - 4 and y = 3x + 8
The attachment below demonstrates this aspect.
iii) A coincident system of linear equations
A system of linear equations is said to be coincident if the two straight lines are identical. That is the lines have an identical slope and y-intercept. Basically, we are just looking at the same line. Two parallel lines can also intersect if they are coincident, which means they are the same line and they intersect at every point.
Therefore, this system of linear equations will have an infinite number of solutions.
The question is in the picture
For this case we have by definition that if two lines are parallel, then their slopes are equal.
We have the following line:
[tex]-2x + 4y = 8[/tex]
Manipulating algebraically we have:
[tex]4y = 8 + 2x[/tex]
[tex]y = \frac {2x} {4} + \frac {8} {4}\\y = \frac {1} {2} x + 2[/tex]
Thus, the slope is [tex]m = \frac {1} {2}[/tex]
Then, a parallel line will be of the form:
[tex]y = \frac {1} {2} x + b[/tex]
We find the cut point "b" replacing the point:
[tex]-1 = \frac {1} {2} (- 5) + b\\-1 = - \frac {5} {2} + b\\b = -1 + \frac {5} {2}\\b = \frac {-2 + 5} {2}\\b = \frac {3} {2}[/tex]
Finally, the line is:
[tex]y = \frac {1} {2} x + \frac {3} {2}[/tex]
ANswer:
Option A
Select the correct answer. Which transformation will always map a parallelogram onto itself? A. a 90° rotation about its center B. a reflection across one of its diagonals C. a 180° rotation about its center D. a reflection across a line joining the midpoints of opposite sides
Answer:
C. a 180° rotation about its center
Step-by-step explanation:
The question is on rotation of an object about the origin through 180°
When a point B, (h,k) is rotated about the origin 0 through 180° both clockwise and anticlockwise directions , the new position is B'(-h,-k)
Example, if we have point K (5,8) rotated through 180°, clockwise or anti-clockwise about the origin the new position will be; K'(-5,-8)
A 180° rotation about the center of a parallelogram will always map the parallelogram back onto itself due to the shape's symmetry.
Explanation:The transformation that will always map a parallelogram onto itself is a 180° rotation about its center. This is because a 180° rotation essentially flips the shape over, but, because a parallelogram is symmetrical, it would still look the same. For example, imagine a parallelogram ABCD with point A at the top and AB as the base. If you rotate it 180°, point A was at the top and now is at the bottom, but the shape is still a parallelogram. Similarly, the other transformations may not necessarily map the shape back onto itself.
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Beijing has 20.720.720, point, 7 million people and an area of 16,400\text{ km}^216,400 km 2 16, comma, 400, space, k, m, start superscript, 2, end superscript. Shanghai has 23.723.723, point, 7 million people and an area of 6300\text{ km}^26300 km 2 6300, space, k, m, start superscript, 2, end superscript. How many times as great is the population density of Shanghai as Beijing?
Answer:
The population density of Shanghai is 2.98 times greater than the population density of Beijing
Step-by-step explanation:
we know that
To find the population density, divide the total number of people by the area
step 1
Find the population density of Beijing
[tex]\frac{20,700,000}{16,400}=1,262.2\frac{people}{km^{2}}[/tex]
step 2
Find the population density of Shanghai
[tex]\frac{23,700,000}{6,300}=3,761.9\frac{people}{km^{2}}[/tex]
step 3
Divide the population density of Shanghai by the population density of Beijing
[tex]3,761.9/1,262.2=2.98[/tex]
therefore
The population density of Shanghai is 2.98 times greater than the population density of Beijing
Which is a better buy—100 sheets of binder paper at $2.50, or 150 sheets at $3.50?
Answer:
150 sheets is the better buy.
Step-by-step explanation:
Cost of each sheet when buying 100 = $2.50 / 100 = $0.0250'
If you buy 150 cost per sheet = $3.50 / 150 = $0.0233.....
So buying 150 sheets is the better buy.
Final answer:
After calculating the unit price for both options, the 150 sheets at $3.50 offer a lower unit price of approximately $0.0233 per sheet compared to $0.025 per sheet for 100 sheets at $2.50, making it the better buy.
Explanation:
To determine which is a better buy between 100 sheets of binder paper at $2.50 and 150 sheets at $3.50, we need to calculate the unit price for each option.
For the first option, 100 sheets at $2.50, the unit price would be $2.50 divided by 100 sheets, which equals $0.025 per sheet.For the second option, 150 sheets at $3.50, the unit price would be $3.50 divided by 150 sheets, which equals approximately $0.0233 per sheet.Comparing the two unit prices, the 150 sheets at $3.50 offer a lower unit price and thus represent a better value for your money.
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When a system of equations appears on a graph, what are the characteristics of a system with one solution? No solution? Infinite solutions?
Answer:
One solution graph is when the graphs of the equations intersect, then there is one solution that is true for both equations.
One solution = lines intersect
No solution graph is when the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
No solution: lines are parallel
Infinitive solution graph is when the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.
Infinitive solutions: One line
How would you graph the solution to x/3 ≤ -2? Draw a closed circle on -6 and shade to the right. Draw a closed circle on -6 and shade to the left. Draw an open circle on -6 and shade to the right. Draw an open circle on -6 and shade to the left.
Answer:
Draw a closed circle on -6 and shade to the left.
solve by factoring
p² + 16p +64 = 0
i like highkey don’t know how to do this
Answer:
-8
Step-by-step explanation:
When you factor, you just find two numbers that add to be the first number (16) and multiply to be the second number (64). 8 and 8 both do this. So when we factor, we also add the variable into each equation because it also has been divided into two equations, and we get: (p + 8)(p +8). Notice that the equations are "+8" and not "-8" because two +8s add to give us a +16 and multiply to give us a +64. After that, we just solve the two equations to find the solutions. Subtract 8 from each equation (we do the opposite operation because 8 is positive) to get -8. Because the answer for each equation is the same our answer is -8.
Answer:
That factors into:
(p +8) * (p +8) =0
Therefore, p = -8 and p = -8
Step-by-step explanation:
Rita's hourly wage increased from $7.50 to
$8.25. What was the percent of increase?
A. 10%
B. 75%
C. 100%
D. 107.5%
Answer:
A. 10%
Step-by-step explanation:
percent change = (new number - old number)/(old number) * 100%
The new number is the increased wage, $8.25, and the old number is the original wage, $7.50.
percent change = ($8.25 - $7.50)/($7.50) * 100%
percent change = ($0.75)/($7.50) * 100%
percent change = 0.1 * 100%
percent change = 10%
Since the percent change is a positive number, it is a percent increase.
The percent increase was 10%.
Answer: A. 10%
Dominic is looking over his spending pattern for the past week to try to determine how much money he had on Sunday. This is Dominic’s spending pattern:
Day
Debit ($)
Credit ($)
Monday
158
---
Tuesday
69
44
Wednesday
175
---
Thursday
131
38
Friday
---
53
Saturday
22
14
If the bank charges Dominic an overdraft fee of $25 every time he overdraws his account, and Dominic overdrew his account on Thursday but not on Saturday, which of the following is a possible amount of money that Dominic could have had in his account last Sunday? Assume that the only debits and credits not listed are overdraft fees.
a.
$500
b.
$480
c.
$435
d.
$400
Please select the best answer from the choices provided
A
B
C
D
Answer:
THE ANSWER IS C.435
Step-by-step explanation:
Answer:
The correct answer would be option C, $435
Explanation:
In real financial banking transactions, Debits are basically the withdrawals and credits are deposits.
Because the problem states that there was an over withdrawal on Thursday but not on Saturday, this means that the ending balance on Thursday was a negative balance. On Saturday, the remaining balance was a positive balance. 500 and 480 as a beginning balance doesn't give a negative balance on Thursday. 400 as a beginning balance gives a negative balance on Thursday as well as Saturday.
Debit Credit Balance
Sunday 435
Monday 158 277
Tuesday 69 44 252
Wednesday 175 77
Thursday 131 38 -16
25 -41 Overdraft fee
Friday 53 12
Saturday 22 14 4
So the correct answer is option C, $435
For the following question, what is the value of x to the nearest tenth?
(1 point)
3.6
4.2
06.6
O 10.4
O 11.6
Answer:
Unit 4(circles) Lesson 2 (chords and arcs)
Step-by-step explanation:
1. The circles are congruent. Which conclusion can you draw?
answer: <AEB=<QUR
2. JG is the diameter of M. Which conclusion cannot be drawn from the diagram?
answer: KN=NI
3. For the following question, what is the value of x to the nearest tenth?
answer: 6.6
4. For the following question, what is the value of x to the nearest tenth?
answer: 11.5
5. If <AFB=<DFE what must be true
answer: AB=DE
hope this helpppss
The value of x to the nearest tenth by the Pythagoras theorem is 6.57.
It is given that
Length of the chord = 11
Distance of chord from the center of the circle = 3.6
As we know that perpendicular drawn from the center of a circle to its chord bisects the chord.
Using Pythagoras theorem
What is Pythagoras theorem?The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
[tex]x^{2} = 3.6^{2} + (11/2)^{2}[/tex]
[tex]x^{2} = 12.96 + 30.25\\\\x^{2} = 43.21\\\\x = 6.57[/tex]
Therefore, the value of x to the nearest tenth is 6.57.
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What is the value of x?
Answer:
17 1
3
Step-by-step explanation:
= 675+ 3 x = 53
100 8 4
------------------------- × 1000
6,750+ 375x = 13,250
375x = 6,500
x = 6,500 = 260 = 52 = 17 1
375 15 3 3
graph D Which graph represents the system 3x + 5y ≤ 9 and 2x + y ≥ 5?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]3x+5y\leq 9[/tex] ----> inequality A
The solution of the inequality A is the shaded area below the solid line [tex]3x+5y=9[/tex]
[tex]2x+y\geq 5[/tex] -----> inequality B
The solution of the inequality B is the shaded area above the solid line [tex]2x+y=5[/tex]
Using a graphing tool
The solution of the system of inequalities is the shaded area indicated in the attached figure
Use 3.14 for pi to estimate the area of a circle the diamater is given round your answer to the nearest hundredth if nessesary (please help I don’t remember how to do this and I’d like to know how if you could help I’d appreciate it)
Answer: 221.56
Step-by-step explanation: (3.14)(r)^2
r = half diameter
Solve 2sin2(x) – 5sin(x) – 3 = 0. Let u = sin(x). Which of the following is equivalent to the given equation?
Answer:
(2u + 1)(u – 3) = 0 is equivalent to the given equation
For the second part of the question, the solutions to the equation are C and D, 7π/6 +2kπ and 11π/6 + 2kπ
Step-by-step explanation:
∠ABC measures 124° and ∠MNO measures 56°. Therefore, the two angles are
A) complementary.
B) supplementary.
C) congruent.
D) vertical.
B) supplementary are two angles that add up to 180.
124+56= 180
How do u write 5(2x - 1) in a distributive property
Answer:
5(2x-1) = 5(2x) - 5(1)
Step-by-step explanation:
The distributive property states that multiplying a sum or difference of two terms by a number is equal to multiplying the same number with each term of the sum or difference separately and then adding the products.
It can be written as:
a(b+c) = ab + ac
or
a(b-c) = ab - ac
So, for the given question,
=>5(2x-1) = 5(2x) - 5(1)
Answer:
5(2x)+5(-1)
Step-by-step explanation: You need to distribute the numbers from left to right. : 5x2+5x-1
Travis is buying Mushrooms at the grocery store mushrooms cost five dollars for 9 ounces how much will 13 ounces of mushroom cost to the nearest cent
For this case we make a rule of three, based on the fact that 9 ounces of mushrooms cost $ 5.
9 oz --------------> 5 $
13oz ------------> x
Where "x" represents the amount of dollars that cost 13 ounces of mushrooms.
[tex]x = \frac {13 * 5} {9} = \frac {65} {9} = 7.222222[/tex]
Rounding out, we have that 13 ounces of mushrooms cost $ 7 with 22 cents.
Answer:
$ 7 with 22 cents
Answer:
Step-by-step explanation:
9 oz cost $5 therefore you want to find the cost per oz which would be $5/9oz= 0.55555556 per oz
0.55555556 x 13oz = $7.222222 which is $7.22
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Find the length of AC if AB is 8, BC is 13, and B is between A and C?
Answer:
21
Step-by-step explanation:
Since B is between A and C, we can simply add 8 and 13 to get the length of AC becauswe B is on line AC. This gives us 8+13 or 21 as the distance between A and C.
A and C is 6 because 2 sides have to be bigger than the other
Write 3/ 8 as a percentage
Step-by-step explanation: To write 3.8 as a percent multiply 3.8 by 100 to obtain 380. Then append the percent sign (%). To learn about the spacing check out the reference section of decimal to percent.
What are the coordinates of the image of vertex G after a
reflection across the line y= x?
(4,-5)
(4,5)
(-5, 4)
(5, 4)
Answer:
(- 5, 4)
Step-by-step explanation:
Under a reflection in the line y = x
a point (x, y) → (y, x)
Hence
G(4, - 5) → G'(- 5, 4)
If the vertex G is reflected across the line y= x, the resulting coordinate will be (-5, 4)
Reflection of coordinate
Reflection creates a mirror image of each other. If the coordinate (x, y) are reflected across the line y = x, the resulting coordinate is (y, x)
Given the coordinate G(4, -5). If the vertex G is reflected across the line y= x, the resulting coordinate will be:
G(4, -5) = G'(-5, 4)
Note that the coordinate points are only interrchanged
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Kiran bought 6 yards of ribbion for $3.90 . which ratio is proportional to 6 yards at $3.90 ?
The lowest proportion would be 1 yard at .65¢
We can get this by dividing $3.90 by 6, since we divided 6 by 6 to get 1.
Answer:
any option which has 0.65 as a unit rate
Step-by-step explanation:
since 3.90/6=0.65
divide the $ by the amount of fabric and you should get 0.65, if u get 0.65 thats ur answer
hope this helps!