The pair of equations show you how to find 16 – 9 is 9+1=10, 10+6=16. Therefore, option B is the correct answer.
The given numerical expression is 16-9.
What is a numerical expression?A numerical expression in mathematics can be a combination of numbers, and integers combined using mathematical operators such as addition, subtraction, multiplication, or division.
Now, the pair of equations show you how to find 16 – 9 is 9+1=10,
10+6=16
Therefore, option B is the correct answer.
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A rectangle has a length of 3x+ 1 and a width of 2x - 9 write an expression for the perimeter of the rectangle
Given the length and width, the expression for the perimeter of the rectangle is 10x - 16.
What is the expression for the perimeter of the rectangle?The perimeter of rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Length l = 3x+ 1Width w = 2x - 9Plug the given values in the equation above
Perimeter = 2( l + w )
Perimeter = 2( (3x+ 1) + ( 2x - 9) )
We can go on and simplify.
Perimeter = 2( (3x+ 1) + ( 2x - 9) )
Perimeter = (6x+ 2) + (4x - 18)
Perimeter = 6x+ 2 + 4x - 18
Perimeter = 10x - 16
Given the length and width, the expression for the perimeter of the rectangle is 10x - 16.
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Graph the line with slope -1 passing through the point (-1, -2).
Step-by-step explanation:
find point (-1,-2)
go down one
go to the right one
repeat
draw line with arrows at each end
done!
angle EFG and angle GFH are a linear pair, angle EFG=2n + 25 and angle GFH=4n + 17 what are angles EFG and GFH?
The angles EFG and GFH are 71 and 109 degrees
How to determine the angles EFG and GFH?The given parameters are:
EFG =2n + 25
GFH = 4n + 17
Linear pair angles are supplementary angles
So,we have
2n + 25 +4n + 17 = 180
Evaluate the like terms
6n= 138
Divide by 6
n = 23
Substitute n = 23 in EFG =2n + 25 and GFH = 4n + 17
EFG = 2 * 23 + 25 =71
GFH = 4 * 23 + 17 = 109
Hence, the angles EFG and GFH are 71 and 109 degrees
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Oscar buys a bag of cookies that contains 7 chocolate chip cookies, 8 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies.
What is the probability that Oscar reaches in the bag and randomly selects a peanut butter cookie from in the bag and randomly selects a peanut butter cookie from
the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie?
Give your answer as a fraction, or accurate to at least 4 decimal places.
The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how probable an event is to do, or how likely it's that a proposition is true. The probability of an event is a number between 0(zero)(zero) and 1(one), where, roughly speaking, 0(zero) indicates the impossibility of the event and 1(one) indicates certainty.The more advanced the probability of an event, the more likely it's that the event will do.These generalities have been given a self-evident fine formalization in probability proposition, which is used extensively in areas of study similar to statistics, mathematics, wisdom, finance, gambling, artificial intelligence, etc.
P(sugar | oatmeal) = (7/25)(6/24) = 0.07
The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.
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Find the slope of the line shown on the graph to the right.
Question content area bottom left
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
The slope would be [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Answer:
-4/-5
Step-by-step explanation:
Remember the formula to slope:
(y2 - y1)/(x2-x1) given two points on the line that are (x1, y1) and (x2, y2).
The two points given on this line are: (2,2) from the top left and (-3,-2) from the bottom left. Let's say (2,2) = (x1, y1) and (-3,-2) = (x2, y2). Plug the points into the formula:
(-2 - 2)/(-3-2) = -4/-5
FINAL ANSWER: -4/-5
There are 6 faces on a standard die. How many faces are on 5 dice?
Answer: 30
Step-by-step explanation: just do 6*5, 6 faces for five die is thirty faces
There are 30 faces on 5 dice in total.
Given that a standard die has 6 faces on it, we need to determine the number of the faces on 5 dice.
A standard die has 6 faces. If you have 5 dice, each with 6 faces, you can calculate the total number of faces by multiplying the number of dice by the number of faces on each die:
Total number of faces = Number of dice × Number of faces on each die
Total number of faces = 5 dice × 6 faces/die
Total number of faces = 30 faces
So, there are 30 faces on 5 dice.
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If it is given that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S , then concluding that m ∠ J K L = m ∠ Q R S is an example of:
Concluding that m∠ J K L = m ∠ Q R S is an example of: substitution property of equality
What is Substitution Property of Equality?The substitution property of equality states that 'If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression.
Now, we are told that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S.
Thus, concluding that m ∠ J K L = m ∠ Q R S is an example of: substitution property of equality
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Consider the following linear program.
Min 3A + 4B
s.t.
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
Answer:
Minimum z =22 at A =6, B=1
See the graph below variable A is on the horizontal axis and variable B on the vertical axis
Step-by-step explanation:
We can solve using the graphical method
Min z = 3A + 4B
s.t.
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
Draw two lines using the constraint equations
1A + 3B = 9
1A + 1B = 7
The feasible region for the inequality constraints is the region that satisfies all 4 constraints below
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
This is the heavily shaded region in the graph. The minimum will be at one of the corner points
There are three corner points on the graph
(0,7), (6,1) and (9,0)
Plug in these coordinate values with A being the first and B being second in the parentheses and see which set of values makes the objective function the minimum
Point (7,0) ==> z = 3(0) + 4(7) = 28
Point (6,1) ==> z = 3(6) + 4(1) = 22
Point (9,0) ==> z = 3(9)+4(0) = 27
Four thousand five hundred eleven ten-thousandths in standard decimal form?
HELPP!!
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 15 gallons of water. Ryan used 6.8 gallons to water his garden in June and 5 and one-eighth gallons in July. How much water is left in the barrel?
1.) 3.075 gallons
2.) 5.125 gallons
3.) 5.178 gallons
4.) 16.675 gallons
Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation:
If x > 3,, which of the following is equivalent to
1
1
1
+
x+ 2 x+3
?
I
If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].
As per the question statement, we are provided with a mathematical expression in the form of a fraction which goes as [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex].
We are required to calculate an equivalent simplified form of the above mentioned expression.
To solve this question, we simply have to add the fractions in the denominator part and then perform a reciprocal of the overall fraction, and simplify it further in that format only, to obtain our final desired answer. The process is shown below as:
[tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\\=\frac{1}{\frac{(x+3)+(x+2)}{(x+2)(x+3)} } \\=\frac{1}{\frac{(2x+5)}{(x+2)(x+3)} }\\=\frac{(x+2)(x+3)}{(2x+5)} \\=\frac{x^{2}+3x+2x+6 }{2x+5} \\=\frac{x^{2}+5x+6 }{2x+5}[/tex]
Hence, If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].
Expression: In Mathematics, expressions are mathematical statements that have at least two terms, comprising of numbers or variables, or both, and being connected by an operator in between.To learn more about Expressions, click on the link below.
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what is the length of the conjugate axis? (y-2)^2/16 -(x+1)^2/144=1
Answer: 24
A hyperbola is the locus of a point in a plane which moves in the plane in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed line is always constant, which is always greater than unity.
the fixed point is called the focus and the fixed line is directrix and the ratio is the eccentricity.
The general equation for the vertical hyperbola is
[ (y-k)^2 / a^2 ] – [ (x-h)^2 / b^2 ] = 1
The conjugate axis of the vertical hyperbola is y = k
Length of the conjugate axis = 2b
According to the question k = 2, h = -1, a = 4, b = 12
Length of the conjugate axis = 2b = 2 * 12 = 24
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One person earns $58,000 per year. Another person earns $3450 per month.
How much more does the first person earn in a year than the second?
The first person earns $ more than the second person in one year.
Answer:
There are 12 months per year so:
58000 - 12(3450) = $________ more
Just plug into calculator or otherwise
work the arithmetic.
Hope this helps.
please help with this question the question is in the attached image
The coefficient matrix for the given system of equations is as follows:
[tex]\left[\begin{array}{ccc}2&-6&-1\\-10&9&5\\3&0&5\end{array}\right][/tex]
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The augmented matrix of a system is composed as follows:
The first column has the coefficients of x.The second column has the coefficients of y.The last column has the results, that is, the values of the other side of the equality.In standard notation, this system is given as follows:
2x - 6y = -1.-10x + 9y = 5.3x + 0y = 5.Hence the augmented matrix is given by:
[tex]\left[\begin{array}{ccc}2&-6&-1\\-10&9&5\\3&0&5\end{array}\right][/tex]
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If f(x) = 2ax + b/x-1, lim x→0 f(x) = -3, lim x→∞ f(x)=4, prove that: f(2)= 11.
If
[tex]f(x) = \dfrac{2ax+b}{x-1}[/tex]
Note that
[tex]f(2) = \dfrac{4a+b}{2-1} = 4a+b[/tex]
From the given information we have
[tex]\displaystyle \lim_{x\to0} f(x) = \lim_{x\to0} \frac{2ax+b}{x-1} = \frac{0+b}{0-1} = -b = -3 \\\\ ~~~~ \implies b=3[/tex]
and
[tex]\displaystyle \lim_{x\to\infty} f(x) = \lim_{x\to\infty} \frac{2ax+b}{x-1} = \lim_{x\to\infty} \frac{2a+\frac bx}{1-\frac1x} = \frac{2a+0}{1-0} = 2a = 4 \\\\ ~~~~ \implies a=2[/tex]
It follows that
[tex]f(2) = 4\cdot2+3 = 11[/tex]
as required.
Can someone please help me with This question? I don’t understand it. Please and thank you I would really appreciate it!! :)
(A∩B)∪(A∩C) using roster method is as follows:
(A∩B)∪(A∩C) = {a, e, f}
What are sets?Sets are an organized collection of objects that can be represented in set-builder form or roster form.
Therefore,
The universal sets is as follows:
U = {a, b, c, d, e, f, g, h}
The subsets are as follows:
A = {c, e, f}
B = {a, e, f}
C = {a, b, d, g, h}
Therefore, let's find (A∩B)∪(A∩C) using roster method.
The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
Hence,
(A∩B) = {e, f}
(A∩C) = {a}
Finally,
(A∩B)∪(A∩C) = {a, e, f}
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ans : 27.......................
[tex] \frac{(243 {)}^{2n/5} . {3}^{2n + 1} }{ {9}^{n + 1}. {3}^{2(n - 2)} } \\ [/tex]
please give step by step explanation...
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{((243 {)}^{2n/5} ) \sdot( {3}^{2n + 1}) }{ ({9}^{n + 1}) \sdot( {3}^{2(n - 2)} )}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{5(2n/5)} ) \sdot( {3}^{2n + 1}) }{ ({3 }^{2(n + 1)}) \sdot( {3}^{2(n - 2)} )}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{2n} \sdot( {3}^{2n + 1}) }{ ({3 }^{(2n + 2)}) \sdot( {3}^{(2n - 4)} )}[/tex]
let's break it up :
[tex] \sf 3 {}^{2n} = (3 {}^{2n -4} ) \sdot(3 {}^{4} )[/tex][tex] \sf 3 {}^{(2n + 1)} = (3 {}^{2n -4} ) \sdot(3 {}^{5} )[/tex][tex] \sf 3 {}^{(2n + 2)} = (3 {}^{2n -4} ) \sdot(3 {}^{6} )[/tex]now let's take [tex]{ \sf {3}^{(2n-4)}} [/tex] common here ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{(2n - 4)} (3 {}^{4} \sdot{3}^{5}) }{ {(3 )}^{(2n - 4)}(3 {}^{6} \sdot1)}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{{} (3 {}^{4} \sdot{3}^{5}) }{ (3 {}^{6} \sdot1)}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{{} 3 {}^{9} }{ 3 {}^{6} }[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 27[/tex]
Answer:
27Step-by-step explanation:
[tex]\sf \cfrac{243^{\frac{2n}{5}}\cdot \:3^{2n+1}}{9^{n+1}\cdot \:3^{2\left(n-2\right)}}[/tex]
[tex]\sf 9^{n+1}\cdot \:3^{2\left(n-2\right)}[/tex]
Simplify:-
[tex]\sf 3^{4n-2}[/tex][tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{\boxed{\bf 3^{4n-2}}}[/tex]
Now, Factor:-
[tex]\sf 243^{\frac{2n}{5}}[/tex][tex]= \boxed{\bf 3^{2n}}[/tex][tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{3^{4n-2}}[/tex]
Now, let's simplify:-
[tex]\sf \cfrac{3^{2n}}{3^{4n-2}}[/tex][tex]=\boxed{\bf 3^{-2n+2}}[/tex][tex]\sf 3^{-2n+2}\cdot \:3^{2n+1}[/tex]Simplify:-
[tex]\sf 3^{-2n+2}\cdot \:3^{2n+1}[/tex]Apply the exponent rule:-
[tex]\sf 3^{-2n+2+2n+1}[/tex][tex]\sf 3^3[/tex][tex]\sf 27[/tex]Therefore, your answer is 27.
______________________
Hope this helps!
Have a great day!
how to solve this ; 4(x + y) = 48
Answer:
Step-by-step explanation:
First I would begin by dividing both sides by 4
4(x+y) = 48 4/4 = 1 48/4 = 12
x + y = 12
next I'm going to assume this is needed in y = mx+b format so I will solve for y by subtracting the x:
y = -x + 12
this line has a slope of -1 and has a y-intercept at 12.
If an individual makes $4,000 in salary per month and has a side job making $20 per hour for 10 hours a week for 4 weeks in a
month, and they receive $1,000 per month in rent from a roommate, what is their gross income?
O $4,000
O $4,800
O $5,800
O Cannot be determined, because taxes and deductions are not provided
The gross income will be $5,800.
It is given that per month salary of an individual is $4000 and from a side job he makes $20 per hour for 10 hours a week for 4 weeks and rent he got is $1000.
We have to calculate the gross income.
What do you mean by gross income ?
Gross income refers to the total income of a person or business from all resources.
As per the question ;
Per month salary = $4000
Earning from side job is given $20 per hour for 10 hours a week for 4 weeks.
i.e.,
= 20 × 10 × 4
= $800 for 4 week
and
the rent they receive = $1000
So ;
The gross income will be ;
= 4000 + 800 + 1000
= $5,800
Thus , the gross income will be $5,800.
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Round 0.007492 to the nearest hundredth
Answer:
0.01
Step-by-step explanation:
Nearest hundredth is the second digit after the decimal point.
If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit.
I NEED HELP ASAP WITH THESE QUESTIONS
1. The sum of twice a number and 5
2. Twice the sum of a number and 5
3. The square of five more than a number
Answer:1.2x+5 2.2(x+5) 3.(x+5)^2
Step-by-step explanation:
could someone please help answer this.
Answer:
+ 12 yards
Step-by-step explanation:
8-3 = 5
5 + 12 - 5 = 12
At a school concert the total value of tickets sold was $3888. Student tickets sold for $7 and adult tickets sold for $10. The number of adult tickets sold was 6 less than 4 times the number of student tickets. Find the number of student tickets sold.
Number of student tickets sold = 84
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
Let the number student tickets sold = x
Let the number adult tickets sold = y
7x+10y = 3888 -----------i
y = 4x-6 ----------------------ii
Substituting eq ii in i
7x + 10 ( 4x -6) = 3888
7x + 40x - 60 = 3888
47x = 3888+60
x = 3948 / 47
= 84
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Sterling already owes his parents $40. He asks to borrow money from them to purchase candy bars for his friends that cost $1.50 each. The rule in Sterling's house is that he can owe his parents no more than $50. How many candy bars can he purchase and still stay within the maximum borrowing amount?
Answer: 6
Step-by-step explanation: 6 because then he would owe his parents 49 dollars
00:00
Which equations show you how to find 13 - 6?
A. 7 + 3 = 10, 10+ 3 = 13
B. 6 + 4 = 10, 10+ 4 = 14
C. 6+4 = 10, 10+ 3 = 13
D. 8+2 = 10, 10+ 3 = 13
If the number 12,345x is divisible by 11, the lest digit of x must be....
Answer:
The last digit you multiplied by.
Step-by-step explanation:
It's not that hard, but here you go :)
If you multiplied 12 by 11 you would get 2 as your last digit, because 2 is the last digit of 12. (12x11=132)
So for 123 by 11, following this pattern, 3 is the last digit of 123 so the answer must end in 3. (123x11=1353)
If you still don't get the pattern I'll give you a few more examples here:
If you multiply 1234 by 11 you would get a number ending in 4 because the last digit of 1234 is 4! (1234x11=13574)
So what would be the last digit of 12345?
Hope this was helpful!
(The answer was 5 btw)
IV. Are these ratios equivalent? 12 birds to 60 animals 17 birds to 85 animals Yes No
Answer:
True
Step-by-step explanation:
Both fractions simplify to 1/5 and thus are equivalent
solve for x. 2/2+x=1/x+5
Answer:
Step-by-step explanation:
its 8 duh jk its your mom XD
Hey bestieee!!!
What is a^2 + 3b
When a = 2
And b = 3
Answer:13
Step-by-step explanation:(2)²+3(3)=4+9=13
Answer:
2a^n+ 3b
Differentiate w.r.t a
2na^n - 1
= 13
Helpppppppppp
Urgenttttt
Pleaseeeee!
Answer:
The first set is a set of linear equations.
The way to figure this out is pretty easy. If you want to see it visually, go search up desmos graphing calculator and put in these equations.
A linear equation is a function that has a constant slope, meaning that the rate it increases or decreases will never change. The first one is a set of linear equations because it is 2 equations with constant slopes, meaning that the slopes will never change no matter what y and x are.
The second set is not, because while the first equation is linear, the second is an inequality. While it is a straight line, it doesn't count as a linear equation.
The third set, both equations have exponents on the x, which means that the slope will change depending on x. This means that both of these are not linear equations.
The only set that is a linear set is the one that has only linear equations.