To find the highest common factor (HCF) between two numbers , first to take HCF of both the numbers.
[tex] \purple {\Large\begin{array}{r | l}2&\underline{12}\\3& \underline{6}\\2&\underline{2}\\&\underline{1}\\\end{array}} \: \: \: \: \: \: \: \: \: \: \: \: \purple {\Large\begin{array}{r | l}2&\underline{40}\\2& \underline{20}\\5&\underline{10}\\2&\underline{2} \ \\ &\underline{1}\\\end{array}}[/tex]
Take every common prime factor between 12 and 40[tex] \red {\large \implies} \large \: 12 \: = \: 2 \: \times \: 3 \: \times \: 2 \: \: \: \: \: \: \: \: \: \: \\ \\ \red {\large \implies} \large \:40 \: = \: 2 \: \times \: 2 \: \times \: 5 \: \times \: 2 \: [/tex]
Finally, identify the factors common to each number and multiply those common factors together.
[tex] \rm\orange {\large \implies} \large \:Common \: factors \: = \: 2 \: \times \: 2[/tex]
[tex]\rm\orange {\large \implies} \large \:HCF = 4[/tex]
Can someone look at this image ?
Answer:
3x-2y=13
Step-by-step explanation:
Someone help me : The Venn diagram below shows the number
of customers in a restaurant who ordered
starters and desserts. There were 23
customers in total.
What is the probability that a customer
picked at random ordered a starter but did
not order a dessert?
Give your answer as a fraction in its
simplest form.
Answer:
5/23
Step-by-step explanation:
▪︎ There are 23 customers in total.
▪︎ Only 5 of them ordered a starter but not a dessert.
▪︎ => 5/23
The probability that a customer picked at random ordered a starter but did not order a dessert = 5/23
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total Customers= 23
and, Customer like starter=5
Customer like Dessert =8
Customer like both =7
So, probability that a customer picked at random ordered a starter but did not order a dessert = 5/23
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only a genius can solve it !!
[tex] \frac{ \cos(A) }{1 - \sin(A) } + \frac{ \sin(A) }{1 - \cos(A) } + 1 = \frac{ \sin(A) \cos(A) }{(1 - \sin(A)(1 - \cos(A)} [/tex]
[tex]\text{L.H.S}\\\\=\dfrac{\cos A}{1-\sin A} + \dfrac{\sin A}{1-\cos A} +1\\\\\\=\dfrac{\cos A(1-\cos A) + \sin A(1-\sin A) + (1-\sin A)(1 - \cos A)}{(1-\sin A)(1 -\cos A)}\\\\\\=\dfrac{\cos A - \cos^2 A + \sin A - \sin^2 A + 1 - \cos A - \sin A + \sin A \cos A}{(1 -\sin A)(1 - \cos A)}\\\\\\=\dfrac{-(\sin^2 A + \cos^2A) +1 + \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\dfrac{-1 + 1 + \sin A \cos A }{(1 - \sin A)((1 - \cos A)}\\\\\\=\dfrac{0+ \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\[/tex]
[tex]=\dfrac{\sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x+4y=-28
Answer:
y=-x-7
Step-by-step explanation:
Slope-intercept form is y=mx+b
We have the equation 4x+4y=-28 and must put it into the form above. To do this first subtract 4x from both sides.
4x-4x+4y=-28-4x
This equals 4y=-4x-28. Now, divide 4 from both sides.
4y/4=-4x/4-28/4
y=-x-7
Hope this helps!
If not, I am sorry.
which statements could be an interpretation of the graph x intercept or y intercept
Answer:
If you attach the answers i can help you better
Step-by-step explanation:
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to the following linear inequality in the coordinate plane.
5x - y > -3
27
Drawing Tools
Select
Line
Dashed Line
Shaded Region
Click on a tool to begin drawing.
10
8
6
The solution to the inequality 5x - y > -3 is shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An inequality shows the non equal comparison of two or more variables and numbers.
The solution to the inequality 5x - y > -3 is shown in the graph.
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Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
Answer:
-2x - 1 = 3^(-x); 2^(-x) + 2 = -5^x + 3
Step-by-step explanation:
for this question you are choosing the lines that do not touch
the graphs for the second third and fourth ones all touch
but
the first and last one do not
therefore those are the ones with no solution
Answer:
Graph 1 and Graph 5
Step-by-step explanation:
As the first and final graphs do not intersect at any points on their graphs, they have no solution.
48 + what gives you 180
Answer:
132
Step-by-step explanation:
180-48=132
Answer: 132
Step-by-step explanation:
let x = unknown amount
48 + x = 180
————————————————————————
Solve for x by subtracting 48 from both sides
48 - 48 + x = 180 - 48
x = 132
The sum of two numbers is 48. If one number is three more than twice the second number, which of the following is the
smaller number?
O 24
O 15
O 30
O 33
Answer:
15 (second option listed)
y = 15
x = 30
Step-by-step explanation:
setting up this statement algebraically:
[where x = one of our numbers, y = other number]
x + y = 48
x = (2y + 3)
x = 2y + 3
plug x [now in terms of y] into the original equation
(2y + 3) + y = 48
3y + 3 = 48
- 3 - 3
3 y = 45
÷3 ÷3
y = 15
from this value, we can plug it back into the y-value of the original equation to find our x-value
x + y = 48
x + 15 = 48
- 15 - 15
x = 33
{to check: 33 is 2y + 3}
we know that y = 15 (smaller number) and that x = 33 (larger number)
so, the solution to the question of which is the smaller number is 15
What is the area of ruth's mural?
Answer:
Step-by-step explanation:
Comment
The shape consists of a rectangle on the bottom and a trapezoid on the top.
Rectangle
A rectangle has a very simple Area formula. It is Area = L*W. In this case the L = 14 m and is horizontal. The width is at right angles to the length and is marked as 3.
Area = L * w
L = 14
w = 3
Area = 14 * 3 = 42 m^2
Trapezoid
The trapezoid is a bit more complicated and some things have to be found. First of all b1 is the first base of the trapezoid. It is parallel to and equal to the Length of the rectangle. b2 is marked 10 meters. The height is just a bit more complicated. The total height of the figure is 8 m. You can't count the 3 m of the rectangle as part of the height because b1 comes only to the top of the rectangle. The height is 8 - 3 = 5
Area = 1/2(b1 + b2)*h/2
b1 = 14
b2 = 10
h = 8 - 3 = 5
Area = 1/2 ( 14 + 10) * 5 / 2
Area = 1/2 (24)*5
Area = 12 * 5
Area = 60 m^2
Total Area 102 m^2
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. persons taking a 70-hour review course average a score of 780. based on these two data points, create a linear equation for the function that describes how score varies as a function of time. use this function to predict an average score for persons taking a 43-hour review course. round your answer to the tenths place.
Answer:
Answer for linear equation: y=4x+500 and Avg score for persons taking 43-hour review course is 672
5)Express in standard form: (i)4809000 (ii)0.00849
Answer:
I hope it helps .in case you don't understand any part ,feel free to ask.
Classify the following polynomials. Combine any like terms first.
2x-x²+4x+x²
x^3-5x^2 + 3-2
x^3-x^3+x²-x²+3
7x-x^2+x³+4x²
-6x-x^3 +6x-4x
Answer:
A resposta certa é:
[tex]6x \\x^3 - 5x^2 + 1 \\3 \\x^3 + 3x^2 + 7x \\-x^3 - 4x[/tex]
Step-by-step explanation:
1° equação:
Como há um x² positivo e um negativo, ambos irão se anular, sobrando apenas as incógnitas de potência 1 (ou, 6x)
2° equação:
Esta resulta em uma equação de 3° grau incompleta, já que há uma incógnita de potência 3, uma de potência 2, não há uma incógnita de potência 1 mas há as constantes, que as unindo forma a constante 1.
3° equação:
As incógnitas presentes há uma negativa e uma positiva de mesma potência, anulando-as e sobrando apenas a constante 3.
4° equação:
Considerando que há um 4x² e um -x² na equação, unindo-os forma o 3x², após isso é só repetir a equação.
5° equação:
Há -10x (-6x -4x = -10x) e 6x, resultando em um -4x, e então é só repetir a equação
Nota: I'm Brazilian, so I found it more practical to write the entire explanation in Portuguese, so if you can't understand, I ask you to use the translator, thanks for understanding :)
Which distance measures 7 units? L 50+5 7 -8 -7 -6 5 4 3 -2 -1 0 1 2 O the distance between points L and M O the distance between points L and N O the distance between points M and N the distance between points M and P 3 4 OL 5 6 s 8
The distance that measures 7 units is the distance between points M and P
How to determine the distance?The complete question is in the attached image
The points are given as:
L= -7
M = -1
N = 2
P = 6
The distance between any points A and B is calculated using:
AB = |B - A|
Using the above formula, we have:
MP = |6 -(-1)|
Evaluate the difference
MP = |7|
Remove absolute bracket
MP = 7 units
Hence, the distance that measures 7 units is the distance between points M and P
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. So the correct answer is option B.
What is inequality?inequality the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
We can start by dividing the inequality by 3 to get ...
8 -4x < 2(x -5)
And we can divide by 2 to simplify further to ...
4 -2x < x -5
Now, we can add 2x+5, which gives ...
9 < 3x
and then divide by 3 again:
3 < x
Therefore number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. So the correct answer is option B.
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Line q and m are cut by transversal lines j and k. The line and the measures of some of the angles created by the intersections of the lines are shown in the diagram below. What is the measure, in degrees, of angle 1?
Answer:
70
Step-by-step explanation:
180 minus 110 is 70
straight lines are 180 degrees
. An elevator in a building starts with five passengers and stops at seven floors. Say every passenger is equally likely to get off at each floor and all the passengers leave independently of each other. a. How many ways are there for the passengers to be assigned a floor? b. How many ways are there for the passengers to be assigned a floor but no two passengers are on the same floor?
There are 16807 number of ways the passengers to be assigned a floor and there are 2520 number of ways the passengers to be assigned a floor but no two passengers are on the same floor.
Given that an elevator starts with five passengers and stops at the seven floors of a building.
From the given information, the total number of floors n=7.
The number of passengers r = 5.
(a) Compute the number of ways that 5 passengers can be assigned to seven floors.
Here, repetition is allowed.
From the known information, if r numbers are selected from n number of observations then the total number of observations that can be drawn from n number of observations is [tex]n^r[/tex].
If 5 passengers can be assigned to seven floors is 7⁵ = 16807.
(b) Compute the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor.
Here, repetition is not allowed.
If 5 passengers can be assigned to seven floors but no two passengers are on the same floor is 7x6x5x4x3 = 2520.
Hence, the number of ways that 5 passengers can be assigned to seven floors is 16807, and the number of ways that the passengers to be assigned a floor but no two passengers are on the same floor is 2520.
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PLEASE HELP ME!!! I'M ON A SERIOUS TIME CRUNCH!!!
Given the graph of trapezoid FOUR and its reflection. Use the coordinates of the images’ vertices, U and U' to to algebraically find the line of reflection.
x = -1
y = 1
x = 1
y = -1
Answer:
y = -1
Step-by-step explanation:
Because the coordinate of U and U' is (5, 0) and (5, -2), the line that is right in the middle would be y = -1.
Or you can compare two of the coordinates to create the line of reflection.
For example: R (0,0), R'(0, -2)
U(5, 0), U'(5, -2)
The middle points are (0, -1) (5, -1).
In this case, y = -1.
Help would be appreciated
Answer:
625 × 48 = 30,000
[tex]\sqrt[4]{30000} = 10 \sqrt[4]{3} [/tex]
answer = third option
HELP ITS ABOUT ANGLES :((((
Answer:
its D. 2 and 3
Step-by-step explanation: supplementary angles are angles that add up to 180 (or that make a straight line) the angle pairs that make a straight line are 1 and 2, 2 and 3, 3 and 4, and 4 and 1.
So D would be correct
I dive to 17 metres for 23 minutes. after a 30 minute surface interval, i plan to dive to 16 metres. what is the maximum allowable time for the second dive
Answer:
i don't know
Step-by-step explanation:
i don' know
One polygon has a side of length 2 feet. A similar polygon has a corresponding side of length 4 feet. The
ratio of the perimeter of the smaller polygon to the larger is
021
01/2
014
Answer:
the largest is 014 because I did it and the teacher said it is correct
Step-by-step explanation:
teacher checked work
X^2 + y^2 = 169 and y = -5 as a graph and where are the coordinates of intersection
Step-by-step explanation:
please mark me as brainlest
A/n ____ is a part of a circle that represents an angle.
Answer:
An Arc is a part of a circle that represents an angle.
Calculate the sum of each expression. Arrange the expressions in the order of their value from largest to smallest.
92 + ( -5 )
2+2
Answer:
6
Step-by-step explanation:
Answer:
92 + ( -5 ) , 2+2
Step-by-step explanation:
1) 92 + ( -5 )
= 92 - 5
= 87
2) 2 + 2 = 4
What is the factored form of the following expressions?
x2 – x – 42
Answer:
(x-7)(x+6)
Step-by-step explanation:
find the inverse of the given function f(x) = (-2x+1)^2 where x _< 1/2
Answer:
((√x) - 1 )/-2 = y (3rd answer)
Step-by-step explanation:
Swap the x and y in the original equation:
x = (-2y+1)^2
√x = -2y + 1
((√x) - 1 )/-2 = y
I believe the final answer is the third answer.
Rayonnia is buying cans of frozen lemonade concentrate to make punch for a holiday party with each can she can make 6  cups of lemonade write an equation which gives the number of cups of lemonade that can be made with any number of cans of frozen lemonade concentrate
The number of cups of lemonade, y that can be made with any number of cans of frozen lemonade concentrate, x is y=6x.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that with a single can of frozen lemonade concentrate 6 cups of lemonade can be made. Therefore, the number of cups that can be made with x number of cans is,
Number of cups that can be made, y = 6x
Hence, the number of cups of lemonade, y that can be made with any number of cans of frozen lemonade concentrate, x is y=6x.
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A gas mixture has a total pressure of 0.56 atm and consists of He and Ne. If the partial pressure of the He in the mixture os 0.27 atm. What is the partial pressure of the Ne in the mixture?
The partial pressure of the Ne in the mixture is 0.29 atm if the as mixture has a total pressure of 0.56 atm and consists of He and Ne.
What is Dalton's law?Dalton's law states that the total partial pressures of all the gases in a mixture of non-reacting gases at a constant temperature equal the pressure the mixture exerts.
We have:
A gas mixture has a total pressure of 0.56 atm and consists of He and Ne. If the partial pressure of the He in the mixture os 0.27 atm.
According to Dalton's law
Total pressure = partial pressure of He + Partial pressure of Ne
0.56 = 0.27 + P(Ne)
P(Ne) = 0.29 atm
Thus, the partial pressure of the Ne in the mixture is 0.29 atm if the as mixture has a total pressure of 0.56 atm and consists of He and Ne.
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7litres of petrol cos t £3.50. Find the cost of 23 litresof petrol of the same grade.
Answer:
£11.50
Step-by-step explanation:
7litres of petrol cos t £3.50. The cost of 1 liter will be:
= £3.50/7
= £0.50
The cost of 23 litres of petrol of the same grade will be:
= £0.50 × 23
= £11.50
