Answer:
The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.
Step-by-step explanation:
Example: What is the HCF of {12,42,14}
Answer: The HCF is 2 as the biggest number they can all be divided by is 2. {12,42,14} = {2^2*3,2*3*7,2*7} The factors in each number is 2.
A farmer has 45 horses and 20 cows.
(i) Write this as a ratio horses : cows.
Give your answer in its simplest form.
Answer: 9 : 4
Step-by-step explanation:
45 : 20
simplify
9 : 4
Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance
Answer:
Step-by-step explanation:
Define two ways of painting to be in the same class if one can be rotated to form the other.We can count the number of ways of painting for each specific class .
Case 1: Black-white color distribution is 0-6 (out of 6 total faces)
Trivially [tex]1^{2}[/tex]=1 way to paint the cubes.
Case 2: Black-white color distribution is 1-5
Trivially all [tex]\frac{6}{5}[/tex] =6 ways belong to the same class , so [tex]6^{2}[/tex] ways to paint the cubes.
Case 3: Black-white color distribution is 2-4
There are two classes for this case: the class where the two red faces are touching and the other class where the two red faces are on opposite faces. There are 3 members of the latter class since there are 3 unordered pairs of 2 opposite faces of a cube. Thus, there are [tex]\frac{6}{4}[/tex]-3=12 members of the former class . Thus, [tex]12^{2} + 3^{2}[/tex] ways to paint the cubes for this case.
Case 4: Black-white color distribution is 3-3
By simple intuition, there are also two classes for this case, the class where the three red faces meet at a single vertex, and the other class where the three red faces are in a "straight line" along the edges of the cube. Note that since there are 8 vertices in a cube, there are 8 members of the former class and [tex]\frac{6}{3} -8=12[/tex] members of the latter class. Thus, [tex]12^{2} - 8^{2}[/tex] ways to paint the cubes for this case.
Note that by symmetry (since we are only switching the colors), the number of ways to paint the cubes for black-white color distributions 4-2, 5-1, and 6-0 is 2-4, 1-5, and 0-6 (respectively).
Thus, our total answer is[tex]\frac{2*(6^{2} + 1^{2}+ 12^{2}+ 3^{2})+12^{2}+8^{2}}{2^{12} } =\frac{588}{4096} = \frac{147}{1024}[/tex]
A suitcase measures 24 inches long and the diagonal is 30 inches long. What is the area of material that is needed to cover one side of the suitcase
Answer:
706.858347
Step-by-step explanation:
Find the midpoint of points A(10,-7) and B(6, 1) graphically.
Answer:
(8,-3)
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x^{1}+x^{2} }{2}, \frac{y^{1} +y^{2} }{{2} } )[/tex]
Plug in your numbers from the coordinates:
(10+6/2, -7+1/2)
(16/2, -6/2)
(8,-3)
If x is inversely proportional to y, then as x decreases, y decreases.
Answer:
Yes
Step-by-step explanation:
Let's assume that x=1/y.
For y=1, x=1
For y=2, x=0.5
For y=4, x=0.25
And so on
If 3x + 7 =22, what is the value of x
Answer:
x=5
Step-by-step explanation:
solution,
3x+7=22
or,3x=22-7
or,3x=15
or,x=15/3
:×=5
The value of x in the equation 3x + 7 = 22 is x = 5.
To find the value of x in the equation 3x + 7 = 22, we can solve for x as follows:
Subtract 7 from both sides of the equation:
3x + 7 - 7 = 22 - 7
3x = 15
Divide both sides of the equation by 3 to isolate x:
(3x)/3 = 15/3
x = 5
Therefore, the value of x in the equation 3x + 7 = 22 is x = 5.
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PLEASE HELP!!!!!!!!!!!!!!
Answer:
The first answer is correct:
[tex]\{\frac{1}{3},-3.45,\sqrt{9}\}[/tex]
Step-by-step explanation:
Since [tex]\frac{1}{3}, -3.45, \sqrt{9}=3[/tex] are all rational numbers, the set that contains those numbers is the set of rational numbers.
In the second set, number [tex]\sqrt{37}[/tex] is irrational number since it can not be written as quotient.
Also in the third and fourth set, numbers [tex]\sqrt{44}[/tex] and [tex]\sqrt{2}[/tex] are irrational numbers.
Therefore, the first answer is correct.
4. Point P is not on line . Describe the shortest distance from the point to the line
P
8
Answer:
a line that is perpendicular to the line l
Minerva starts a savings account with $50. The interest on the account balance is compounded annually. The graph below shows the account balance in terms of x ,the number of years since the account was opened.
After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account.
Cannot be determined from the information given.
False
True
Minerva's account balance will be about $100 , it is True and Option A is the correct answer.
What is meaning of Compounded annually ?Compounded Annually means when the interest is given even on the interest accrued from the principal amount . This is done once a year.
It is given that
Principal Amount = $50
From the graph attached in the answer which was missing in the question ,
It can be confirmed that after 12 years
Minerva's account balance should be about $100.
Therefore it is True and Option A is the correct answer.
The graph missing is attached
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Determine whether the stated conclusion is valid based on the given information. If not,
write invalid. In either case, explain your reasoning.
A. Given: If a point is the midpoint of a segment, then it divides the segment into two
congruent segments. R is the midpoint of QS
Conclusion: QR = RS.
Both the given statements are true. The figure is given below.
We need to determine whether the stated conclusion is valid based on the given information.
What is the midpoint of the line segment?In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. R is the midpoint of QS.
Conclusion: QR=RS.
Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. AB=BC
Conclusion: B divides AC into two congruent segments
Both the given statements are true. The figure is given below.
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Find the number, d, if the sum of five times d and five times five is a
hundred.
The value of d from the given expression is 15
Word problem leading to equationFrom the given statement the sum of five times d and five times five is a
hundred is interpreted as;
5d + 5(5) = 100
5d + 25 = 100
Subtract 25 from both sides
5d = 100 - 25
5d = 75
d =15
Hence the value of d from the given expression is 15
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If the zeros of a quadratic equation are 7 and - 4 , what would be the factors?
Answer:
(x - 7) , (x + 4)
Step-by-step explanation:
given the zeros of a quadratic equation x = a and x = b , then
the corresponding factors are (x - a) and (x - b)
here the zeros are x = 7 and x = - 4 then factors are
(x - 7) and (x - (- 4) ) , that is
(x - 7) and (x + 4)
What is the circumference of the given circle in terms of л
Answer:
30π in
Step-by-step explanation:
Circumference of a circle = 2πr
Where r is the radius
In the given diagram, the radius is 15 in
2×π×15 in = 30π in
Casey was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:
−8, which represents the depth of water in the swimming pool
+7, which represents the height of the slide at the pool
Part A: What does 0 represent in this situation? (3 points)
Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)
Part C: Casey held a pole in the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)
The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that −8 represents the depth of water in the swimming pool. Hence:
The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.
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Suppose that $x$ is a multiple of 6 (not necessarily positive). If the square of $x$ is less than 200, how many possible values of $x$ are there
All multiple of 6 under 14 are: -12, -6, 0, 6, 12
How do we get 14 here:
√200= 14.142 (Round to thousandth place)
This is how many x we have found.
A multiple in math is the number you get when you multiply a certain number by using an integer. for example, multiples of 5 are: 10, 15, 20, 25, 30…, and so forth. Multiples of 7 are 14, 21, 28, 35, 42, 49…and many others.
In math, the meaning of a multiple is the product result of one number multiplied by another number. Here, 56 is a multiple of the integer 7. Here is an example of multiples: Fun facts. 0 is a multiple of every number as the product of 0 multiplied by any number is 0.
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A trapezoid has bases measuring 5cm and 9cm, and an area of 42cm. Find the height
The height of the trapezoid is 6 cm
How to find the height?The given parameters are:
Bases = 5cm and 9cm
Area = 42 square cm
The height is calculated using
Area = 0.5 * (Sum of bases) * Height
So, we have:
42 = 0.5 * (5 + 9)* Height
This gives
42 = 7* Height
Divide through by 7
Height= 6
Hence, the height of the trapezoid is 6 cm
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Write an equation in slope intercept form for the line with slope -1/2 and y-intercept -5
Answer: -1/2x - 5 = Y
Step-by-step explanation:
- slope intercept form is mx + b = Y
- m is the slope
- b is the y intercept
- leave x and y as variables
- since your y intercept is negative the + will be a -
- so the equation becomes -1/2x - 5 = Y
hope this helps :)
An article marked to give 120% profit originally cost $60. what is the marked price?
Evaluate 3 × 5². A. 30 B. 75 C. 150 D. 225
Answer:
B: 75
Step-by-step explanation:
5^2 is 5 times itself twice, so 5 times 5 = 25
3 times 25 is 75
Answer:
Hello! The answer to your question is B. 75.
Step-by-step explanation:
To solve this question, you have to first convert the exponents:
[tex]5^2 = 25[/tex]
Now that you have converted the exponents, you can multiply:
3 × 25 = 75
Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
The answer will be either 8 or 4 or 0.
What is a riddle?
A riddle is an intentionally framed ambiguous question or statement that requires ingenuity and critical thinking to solve or understand.
In the given riddle, all the two dogs, four horses, one giraffe and a duck are lying on the bed. Three chickens are flying over a chair.
Assumptions:
1) Bed is placed on the ground.
2) Bed and chair considered are of standard type.
case1:
If we consider the legs of only living organisms, the number of legs on the ground at the given instant will be 0.
case2:
If that's not the case, then a typical chair will have four legs, and a standard bed will also have four legs. So a total of 8 legs will be on the ground or floor of the room.
case3:
And if we consider the possibility of the chair being placed on the bed, then the legs of the chair will not touch the ground. So a total of 4 legs will be on the ground or floor of the room.
∴ From different perspectives, the number of legs on the ground will be either 8 or 4 or 0.
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Select the correct answer.
The product of two numbers is 21. If the first number is-3, which equation represents this situation and what is the second number?
OA The equation that represents this situation is x-3=21. The second number is 24.
OB. The equation that represents this situation is 3x=21. The second number is 7.
OC. The equation that represents this situation is-3x=21. The second number is-7.
OD. The equation that represents this situation is -3+x=21. The second number is 18.
Option B is correct
Why
3x=21
3(7) =21
21=21
Step-by-step explanation:
Answer:
[tex]-3x=21 , -7[/tex]
Step-by-step explanation:
[tex]-3x=21\\x=\frac{21}{-3} =-7[/tex]
The area and one side of a rectangle are given. Determine the missing dimension
The missing dimension is x + 4
How to determine the missing dimension?The given parameters are:
Area = 4x^2 + 13x - 12
Length = 4x - 3
The width is calculated using:
Width = Area/Length
This gives
Width = (4x^2 + 13x - 12)/(4x - 3)
Expand
Width = (4x^2 + 16x - 3x - 12)/(4x - 3)
Factorize
Width = (4x(x + 4) - 3(x + 4)/(4x - 3)
Factor out x + 4
Width = (4x - 3)(x + 4)/(4x - 3)
Cancel out the common factor
Width = x + 4
Hence, the missing dimension is x + 4
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A survey of 150 people at a local high school about playing video games was conducted, and the results are posted in the table.
Play Video Games Do Not Play Video Games
Juniors 48 12
Seniors 45 25
Teachers 6 14
What is the probability of choosing a person at random who is a teacher and plays video games? Are these independent events?
The P(teacher and video games) = 4%; the two events are not independent.
The P(teacher and video games) = 4%; the two events are independent.
The P(teacher and video games) = 9%; the two events are not independent.
The P(teacher and video games) = 9%; the two events are independent.
The P(teacher and video games) = 4%; the two events are not independent.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
P(teacher and video games) = number of teachers who play video game / total number of respondents
6/150 = 0.04 = 4%
Independents events are events whose occurrence do not depend on each other. They are random events.
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Answer:
The P(junior and video games) = 32%; the two events are not independent.
Step-by-step explanation:
i got it right aswell
At a meeting attended by 23 people, the females exceeds the males by 7. how many males were there?
Number of males in the meet were 8.
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.
Let the number of males be x.
∴ Number of females = x + 7
Total number of people attending meet = Number of male +
Number of females
23 = x + x + 7
23 = 2x + 7
16 = 2x
x = 8.
Thus number of males in the meet were 8.
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He length of the hypotenuse of a right triangle is 24 inches. if the length of one leg is 8 inches, what is the approximate length of the other leg? 16.0 inches 18.4 inches 22.6 inches 25.3 inches
Answer:
22.6
Step-by-step explanation:
a^2 + b^2 = c^2 We know one of the legs and the hypotenuse. The hypotenuse must be c. The leg that we do know can be a or b. It is our choice. I am going to let it be a
8^2 + b^2 = 24^2 Plug in the numbers that I know
64 + b^2 = 576 Square the numbers that I know
b^2 = 512 Subtract 64 from both sides
b = 22.6 Put this in your calculator to find the square root and round.
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Considering the definition of an inequality and system of inequalities, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
System of inequalitiesA system of inequalities is made up of two or more inequalities.
The solution will be formed by the intersection of the half-planes of each of the inequalities, that is, it will be the enclosure that all the inequalities have in common. That is, the solution of the system is given by the region of the common plane of the half-planes that define each one of the inequalities.
System of inequality in this caseIn this case:
c represents child bikes.a represents adult bikes.Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. The company is able to have up to 120 hours of building time and 100 hours of testing time for a week.Then, the system of inequality is:
[tex]\left \{ {{4c+6a\leq 120} \atop {4c+4a\leq 100}} \right.[/tex]
On the other hand, the company can build 20 child bikes and 6 adult bikes in the week. So, checking the equations, for given c=20 and a=6:
4×20 + 6×6= 116 < 120
4×20 + 4×6= 104 >100
Finally, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."
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Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.
Which explains whether ΔFGH is congruent to ΔFJH?
They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
They are congruent because opposite sides of a parallelogram are congruent.
They are not congruent because only one pair of corresponding sides is congruent.
They are not congruent because only two pairs of corresponding sides are congruent.
Answer:
They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words.
The graphs of functions f and g are shown.
Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.
Function g is defined as . What is the value of k?
The value of k is
.
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words.
The graphs of functions f and g are shown.
Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.
Function g is defined as . What is the value of k?
The value of k is
(1,0)
For the following exercises, find the x- and y-intercepts of the graphs of each function.
28. f(x) = −2| x +1 | + 6
The x- and y-intercepts of the graphs of the function described are; (2,0) and (4,0) respectively.
What are the x- and y-intercepts of the graph of the function?It follows from the task content that the function given is; f(x) = −2| x +1 | + 6.
Since the x- and y-intercepts corresponds to x and y values for which y and x are zero respectively, it follows that;
x -intercept is;
0 = -2(x+1) + 6
2x = -2 +6
2x = 4
x = 4/2 = 2
y-intercept is;
y = -2(0+1) +6
y = 4.
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In the diagram, JKLM∼EFGH. Find the perimeter of each polygon.
The perimeter of polygon JKLM = 85 units
The perimeter of polygon EFGH = 34 units.
What is the Perimeter of a Polygon?The perimeter of polygon JKLM = JK + KL + LM + JM
The perimeter of polygon EFGH = EF + FG + GH + EH
Find the missing lengths using the similarity theorem:
JK/EF = KL/FG = LM/GH = JM/EH
Plug in the values
20/8 = KL/11 = LM/3 = 30/EH
20/8 = KL/11
KL = (20 × 11)/8 = 27.5
20/8 = LM/3
LM = (20 × 3)/8
LM = 7.5
20/8 = 30/EH
EH = (30 × 8)/20
EH = 12
The perimeter of polygon JKLM = 20 + 27.5 + 7.5 + 30 = 85 units
The perimeter of polygon EFGH = 8 + 11 + 3 + 12 = 34 units.
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