Prove that:
A-(A-B)⊆B
how can we multiply 2 equations
Answer:
Given equations:
a = x + yb = x - yTo multiply 1 and 2;
[tex]{ \tt{a \times b = (x + y)(x - y)}} \\ = { \tt{(x.x) + (x. - y) + (y.x) + (y. - y)}} \\ = { \tt{ {x}^{2} - xy + xy - {y}^{2} }} \\ = { \tt{ {x}^{2} - {y}^{2} }}[/tex]
Round this number to the
nearest tenth.
6.3579
Answer: 6.4 :)
Step-by-step explanation:
6.358
Step-by-step explanation:
To round a number to the nearest tenth, look at the hundredth number .If that number is greater than 5,add 1 to the tenth value.If is less than 5 , leave the tenth place value as it is, and remove all the numbers present after the tenth's place.
5 friends went out to a tapas restaurant and ordered from the menu that included $4, $6 and $7 options. They ordered a total of 24 items. The number of $4 items was twice the $6 and $7 items combined. When they split the bill at the end, they each owed $23. How many of each type of item did they order?
The 5 friends ordered 16 items of $4 , 5 items of $6 , 3 items of $7 .
How to find solution of system of equations in two variables by substitution?Let p and q be two variables and
a₁p+ b₁q=c₁
a₂p+ b₂q =c₂
Where a₁, a₂, b₁, b₂, c₁, c₂ are constants then we can solve these simultaneous equations by substitution take value of p from equation (1) and then put it in (2) to get an equation for q only and then solve for q. Put value of q in equation (1) to get value of p.
Let the 5 friends ordered x number of $4 items , y number of $6 and z number of $7 items
They ordered total a total of 24 items.
Then, x+ y + z = 24 ....(1)
Given that $4 was twice the $6 and $7 items combined
Then, x =2( y+ z )
Put this expression of x in (1),we get
2(y+ z)+ y + z =24
3y + 3z =24
y + z =8 ....(2)
Also given that they split the bill at the end, they each owed $23
Therefore total bill will be 5 times $23 = 5*23 = $ 115
Total money spent on bill = $ 4x+6y+7z
Thus, 4x+6y+7z = 115
Again put x =2(y+ z) here and get
8(y+ z) +6y+ 7z =115
8y +8z + 6y +7z = 115
14y +15z = 115 ....(3)
Therefore, (2) and (3) is the system of equations we have to solve.
From (2) we get y =8 -z
Put this value of y into (3) and get
14(8-z)+15z =115
112 - 14z +15z =115
z= 115-112 = 3
Then, y = 8-z = 8-3 = 5
x = 2(y+ z)= 2(3+5) =16
Therefore x= 16 , y = 5, z=3 from system of equations generate by (2) and (3)
The 5 friends ordered 16 items of $4 and 5 items of $6 and 3 items of $7.
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How many liters each of a 10 % acid solution and a 40 % acid solution must be used to produce 60 liters of a 35 % acid solution? (Round to two decimal places if
necessary.)
Hence , 10 liters of a 10% acid solution and 50 liters of a 40% acid solution must be used.
System of Equations: Setting up a system of equations containing the 2 unknown values, the substitution technique is also accustomed acquire associate degree equation with just one of the unknowns. The ensuing equation could then be resolved to search out the worth of the remaining unknown. From here, the second worth is also obtained by subbing the primary worth back to at least one of the equations.Let the amount of 10 % acid solution be " x " and the amount 40 % acid solution be " y " .
The total volume of the resulting solution is 60 L which can be given by
x + y = 60 .....(1)
The total acid in the resulting solution is 35 % acid solution which is given by 0.10 x + 0.40 y = 0.35(60) .....(2)
Multiplying by 100 in equation (2) , we get
10 x + 40 y = 2100 .....(3)
Putting x = 60 - y in equation (3) , we get
10 ( 60 - y ) + 40 y = 2100
600 - 10y + 40y = 2100
30y = 1500
y = 50
Putting y = 50 equation (1) , we get
x = 60 - 50 = 10
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Given the function g(x)=
3×2+5×+6
×+3
determine the equation for the slant asymptote.
Check the picture below.
Do someone have the answers
1. y = 5x + 15.
2. y = total cost
x = number of calendar
m = cost per calendar = slope = 5
b = initial value/y-intercept = 15
3. $1,015.
4. The equation in slope-intercept form is: y = 5x + 15
5. Slope (m) = 5
6. y-intercept (b) = 15; x-intercept = -3.
7. See attachment below for the graph.
How to Write an Equation that Models a Situation?Using the information given, we can create an equation in slope-intercept form y = mx + b, where m would be the slope and b would be the y-intercept of the linear equation.
Let,
y = total costx = number of calendarm = cost per calendar = slope = 5b = initial value/y-intercept = 151. To create an equation that models the situation, substitute m = 5 and b = 15 into y = mx + b:
y = 5x + 15.
2. The variables and numbers in the equation are:
y = total cost
x = number of calendar
m = cost per calendar = slope = 5
b = initial value/y-intercept = 15
3. Substitute x = 200 into y = 5x + 15
y = 5(200) + 15
y = 1,015
Total cost = $1,015.
4. The equation in slope-intercept form is: y = 5x + 15
5. The slope (m) = 5
6. The y-intercept (b) = 15
To find the x-intercept, substitute y = 0 into y = 5x + 15
0 = 5x + 15
-5x = 15
x = 15/-5
x = -3
The x-intercept = -3.
7. See attachment below for the graph.
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Are the functions of g(x)=(x-4)^2 and h(x)=x^2-4 equivalent? Explain your reasoning.
Answer:
[tex]g(x) = (x-4)^2\; and \;h(x)= x^2-4 \;are\;\bold{not}\;equivalent[/tex]
Step-by-step explanation:
For two functions g(x) and h(x) to be equivalent, they must have the same domain and range.
Domain is the set of all values of x(inputs) that result in a real and defined value for the function
Range is the set of all values of the function that it can take given the values of x in the domain
[tex]g(x)=(x-4)^2=16-8x+x^2\\[/tex]
Can be rewritten as
[tex]g(x) = x^2 -8x + 16[/tex] The domain of g is unrestricted, g can be any value so the
Domain of g: [tex]-\infty < x < \infty[/tex]
Range of g: Since [tex](x-4)^2[/tex] is always positive including 0, the range of g(x) is g(x) ≥ 0
[tex]h(x) = x^2 - 4[/tex]
Domain of h : [tex]-\infty < x < \infty[/tex] since x can be any value and we will still get a real number as function output
However x² is always zero or a positive number so we have the restriction
x² ≥ 0
Subtract 4 on both sides
x²-4 >= -4
But the above is nothing but the outputs of h(x)
So h(x) >= -4 and can be written as -4 ≤ x ≤ ∞
So we can see that, while the domains of the two functions are the same, their ranges are different
Hence the two functions g(x) and h(x) are not equivalent
Tip
If you have difficulty determining domain and range, take a specific value of x for both functions and check if the function output values are the same. It may not always be easy choosing an appropriate x value depending on the function
For x = 0
g(0) = (0-4)² = (-4)² = 16
h(0) = 0^2 -4 = 0-4 = -4
So we get different output values for the same input value for both functions and therefore they are not equivalent
You can this latter explanation to the above explanation
Hope that helps and is understandable :)
N/12 = 300 N=? what is the answer please
Answer:
3600
Step-by-step explanation:
N = 300 x 12 =3600
help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee !!
Answer:
21, -4, 5
Step-by-step explanation:
In the function we are changing x into -5 :
So :
(-5)² - 4
25 - 4 = 21
f(0) will be :
0² - 4
0 - 4 = -4
f(3) will be :
(3)² - 4
9 - 4 = 5
Hope this helped and have a good day
The square in the middle has an area of 1 square unit. What is the area of the entire
rectangle in square units? Explain your reasoning.
Mrs Peh paid $1438 for 1 drum set and 1 keyboard. Tim paid $690 for 1 flute
and 1 keyboard. The drum set cost thrice as much as the flute. How much would
1 drum set and 1 flute cost?
Answer:
flute=374, drum=1122, keyboard=316
Rewrite (132 + 228) using factoring.
4(32 + 57)
6(22 + 222)
4(33 + 57)
16(116 + 14)
Answer:
can u help me with my homework
Answer:
Farmers are the backbone of our society. They are the ones who provide us all the food that we eat. As a result, the entire population of the country depends upon farmers. Be it the smallest or the largest country. Because of them only we are able to live on the planet. Thus Farmers are the most important people in the world. Though farmers have so much importance still they do not have proper living.
Here are weights (in pounds) of sample of 12 male eleventh graders. 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165
The mean weight of the male graders will be 151 pounds.
How will you calculate the mean?It should be noted that from the information, the sample of 12 male eleventh graders are: 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165.
We will add the values together and this will be 1812. Also, there are 12 students.
Therefore, the mean will be:
= Total weight / Number of students
= 1812 / 12
= 151 pounds.
Therefore, the mean weight will be 151 pounds.
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Here are weights (in pounds) of sample of 12 male eleventh graders. 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165. Calculate the mean weight.
Find the measurement of the angle indicated for each trapezoid.
Answer:
∠ C = 50°
Step-by-step explanation:
• each lower base angle is supplementary to the upper base angle on the same side.
then
∠ C + ∠ D = 180°
∠ C + 130° = 180° ( subtract 130° from both sides )
∠ C = 50°
BROS HELPPP Oh my god I NEED HELPP
Answer:
Ok, so all you have to do, is substitute the numbers in for x.
Step-by-step explanation:
For example substitute -3 in for x and solve. I hope this helps some!
Convert R57 894 to dollars if the exchange rate is R7,30 = 1 dollar.
Main answer:R57 894 is 79.3 dollors.
Concept and definitions should be there:
The formula for calculating exchange rates is: Starting Amount (Original Currency) / Ending Amount (New Currency) = Exchange Rate. For example, if you exchange 100 U.S. Dollars for 80 Euros, the exchange rate would be 1.25.
Given data
Convert R57 894 to dollars if the exchange rate is R7,30 = 1 dollar.
Soving part
The formula for exchanging rates
R (57894/730)
now dividing the starting amount and ending amount we get exchange rate.
Final Answer : 79.3 dollers.
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Can someone help me with this problem!
The probability that a randomly selected person from the survey plays pokemon go who belongs to the Age group 26 - 35 is 0.33.
We have the table for the survey,
Age 18 - 25 Age 26 - 35 Total
Plays Pokemon Go 17 39 56
Does not play Pokemon Go 37 25 62
Total 54 64 118
From the table,
We have,
The number of people in the age group 18 - 25 who play pokemon go is 17.
The number of people in the age group 18 - 25 who play don't pokemon go is 37.
The number of people in the age group 26 - 35 who play pokemon go is 39.
The number of people in the age group 26 - 35 who don't play pokemon go is 25.
The total number of people participated in the survey are 17 + 39 + 37 + 25 = 118
The total number of people in the Age group 18 - 25 is 54.
The total number of people in the Age group 26 - 35 is 64.
The total number of people that play pokemon go is 56.
The total number of people who do not play pokemon go is 62.
Now,
The probability of choosing a random person from the survey from the age group 26 - 35 who plays pokemon go will be:
= ( no. of people of age group 26 - 35 that play pokemon go) / total no. of people in the survey.
= 39/ 118
= 0.33
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help me asap im in a dba back to basics exam and didnt study
Answer:
is this flvs full flex? I'm in this as well, whats your grade?
also im doing 12th grade math if you havent gotten to that point yet you will be working in Aleks for math and phewww, good luck i hate this
Step-by-step explanation:
Circle P has a circumference of approximately 75
inches.
Mark this and return
T
What is the approximate length of the radius, r? Use 3.14
for T. Round to the nearest inch.
O 12 inches
24 inches
O 38 inches
46 inches
Save and Exit
Subroit
Answer: ≈12 inches
Step-by-step explanation:
Lengh a circumference L=2πR
Divide both parts of the equation by 2π:
[tex]\displaystyle\\R=\frac{L}{2\pi } \\\\R=\frac{75}{(2)(3.14)} \\\\R=\frac{75}{6.28} \\\\R\approx12\ inches[/tex]
Answer the following subject
Thanks
The function is decreasing at [3, 13], increasing at [0, 3] U [ 13, 18 ], maximum value is 2.6, the minimum value is 0.6, the domain is [0, 18] and the range is [0.6, 3].
We have been given the graph of the function.
We need to find the increasing and decreasing intervals by analyzing the graph.
So, we get that:
The function is decreasing at the interval:
[3, 13]
The function is increasing at the intervals:
[0, 3] and [13, 18]
= [0, 3] U [ 13, 18 ]
The maximum value is:
= 2.6
The minimum value is:
= 0.6
The domain of the function is:
D = [0, 18]
The range of the function is:
R = [0.6, 3]
Therefore, we get that, the function is decreasing at [3, 13], increasing at [0, 3] U [ 13, 18 ], maximum value is 2.6, the minimum value is 0.6, the domain is [0, 18] and the range is [0.6, 3].
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Piano lessons with Ms. Bell cost $30 for
3/4
of an hour. What is Ms. Bell's hourly rate?
Answer:
$40
Step-By-Step Explanation:
The wavelength of a seventh wave is recorded. The wavelength is greater than 4/100 nanometer, but less than 4 x 10^-1 nanometer. write the answer with a denominator of 100 is it possible to have more than 1 correct answer
Using inequalities, we can say that Yes, there are more than 1 possible ways to get the answer of inequalities.
What are inequalities?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Given,
the wavelength is greater than 4/100 nanometer and
less than 4 x 10^-1 nanometer
Let wavelength = λ
4/100 ≤ λ ≤ 4/10
0.04 ≤ λ ≤ 0.4
or
1/50 ≤ λ ≤ 2/5
So, from the above three equations, we can conclude that there can be more possible ways to have more than 1 correct answer.
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six million, ninety-six thousand, sixty-one
in standard notation
Can anyone help me with this?
Answer: y=40x
Step-by-step explanation:
HELP IM TIMED ILL MAKE AS BRAINLIEST
Answer: 26
Step-by-step explanation: 208/8=26
3. What is this number in standard form? (1 point)
5.75 x 109
O5,750,000,000
O 575,000,000,000
O
0.00000000575
O 0.575000000000
4
HELP PLSSSSSSSS
Answer:
5,750,000,000
Step-by-step explanation:
Find the intersection of the two lines by solving the system of equations.
x + y = -8
-x + y = -2
Answer:
(-3, -5)
Step-by-step explanation:
Adding the equations, we get 2y = -10, and thus y = -5.
Substituting this back into the first equation gives us that x = -3.
So, the point of intersection is (-3, -5).
Fill in the blank of any operations and make sure to use ().
4 ? 2 ? 3 = -2
Answer:
4-2*3=-2 At first we have to do multiple of2 and 3
then subtract with 4
Michael and Lauren each have a coin collection.
The number of coins in Michael's collection can be represented by x.
The number of coins in Lauren's collection is 5 times the number in Michael's collection.
The total number of coins in both collections is 366.
What is x, the number of coins in Michael's collection?
If the number of coins in Lauren's collection is 5 times the number in Michael's collection and the total number of coins in both collection is 366, then the number of coins in Michael's collection is 61
The number of coins in Michael's collection = x
The number of coins in Lauren's collection is 5 times the number in Michael's collection
Then the number of coins in Lauren's collection = 5x
The total number of coins in both collection = 366
Combine the values and the equation will be
x+5x=366
Add like terms
6x= 366
x=[tex]\frac{366}{6}[/tex]
x=61
Hence, if the number of coins in Lauren's collection is 5 times the number in Michael's collection and the total number of coins in both collection is 366, then the number of coins in Michael's collection is 61
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