By elimination, the solution of the system of equations, 2r + s = 3 and 4r - s = 9, is (r , s) = (2 , -1).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in r and s, a variable should be eliminated by adding/subtracting the two equations.
Adding the two equations will eliminate the variable s.
2r + s = 3 (equation 1)
4r - s = 9 (equation 2)
6r = 12
r = 2
Substitute the value of r to any of the two equations and solve for s.
2r + s = 3 (equation 1)
2(2) + s = 3
s = 3 - 4
s = -1
Hence, the solution of the system of equations is (r , s) = (2 , -1).
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Which can of Spaghettios is the better deal?
26.25 oz because it costs $.066 per ounce.
14.75 oz because it costs $.066 per ounce.
A rental car company charges $37.93 per day to rent a car and $0.11 for every mile driven. Taylor wants to rent a car, knowing that:
She plans to drive 50 miles.
She has at most $300 to spend.
Which inequality can be used to determine dd, the maximum number of days Taylor can afford to rent for while staying within her budget?
5.5d + 37.93 ≥ 300
5.5 + 37.93d ≤300
5.5 + 37.93d ≥ 300
5.5d + 37.93 ≤ 300
The inequality [tex]5.5+37.93d\leq300[/tex] should be used to calculate the number of days.
What is an inequality?
The relationship between two non-equal expressions, denoted by a symbol such as 'not equal to, 'greater than' or 'less than' is known as inequality.
She drives 50 miles and per mile it costs $0.11.
So, for 50 miles, cost = 50 x $0.11 = $5.5
and per day cost = $37.93
Thus, the inequality that must be used to calculate number of days is
[tex]5.5+37.93d\leq300[/tex]
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Solve negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity.
two thirds
18 over 54
negative two ninths
negative two and 42 over 54
The value of the expression given as negative one sixth times the quantity 3 minus 15 times the quantity one third squared is 2/9
How to solve the expression?The expression is given as:
negative one sixth times the quantity 3 minus 15 times the quantity one third squared
Rewrite the above expression properly as
-1/6(3 - 15) * (1/3)^2
Evaluate the square in the above expression
-1/6(3 - 15) * 1/9
Evaluate the difference in the above expression
-1/6 * - 12 * 1/9
Evaluate the product in the above expression
2/9
Hence, the value of the expression given as negative one sixth times the quantity 3 minus 15 times the quantity one third squared is 2/9
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Answer:
The value of the expression given as negative one sixth times the quantity 3 minus 15 times the quantity one third squared is 2/9
Maya bought 3 chicken wings for $8.80. If Maya spent $25.30, how many chicken wings did she buy?
Answer:
She bought 8.625 wings
Step-by-step explanation:
We can use a ratio to solve
3 x
------- = ----------
8.80 25.30
Using cross products
3 * 25.30 = 8.80x
75.9 = 8.80x
Divide each side by 8.8
75.9/8.8 = 8.8x/8.8
8.625 = x
She bought 8.625 wings
Christina bought 1and4 of 1and2 of pizza how much pizza did Christina buy how much did she pay
The cost of the pizzas that Christina bought will be $4.30.
How to calculate the value?From the information, The cost of a large pizza is $0.90 and the cost of a small pizza is $0.70. Christina bought 4 large pizzas and 1 small pizza.
The number of pizzas will be:
= 4 + 1
= 5 pizzas
The cost will be:
= 4($0.90) + 1($0.70)
= $3.60 + $0.70
= $4.30
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The cost of a large pizza is $0.90 and the cost of a small pizza is $0.70. Christina bought 4 large pizzas and 1 small pizza. How much pizza did Christina buy how much did she pay?
What is the inverse of f(x) =4x + 5?
Answer:[tex]x= \frac{f (x) - 5}{4}[/tex]
Step-by-step explanation:
f(x) = 4x+5
- 5 for both
f(x) - 5 = 4x+5 -5
4x = f (x) - 5
divided 4 for both
(4x)/4 = (f (x) - 5) / 4
[tex]x= \frac{f (x) - 5}{4}[/tex]
A number, n, is 9.27 when rounded to 2 decimal places.
Complete the inequality to show the lower and upper bounds of n.
9.27 rounded to 2 decimal places is 9.27
The important thing to remember is that you should round 9.270 to two digits or places after the decimal point. As a result, we wish to do rid of the final digit in 9.270. We utilize the following Two Decimal Places Rules to find the answer by removing the final digit in 9.270:
Rule #1 for two decimal places: If the final digit in 9.27 is less than 5, it should be removed.
Two Decimal Places Rule #2: If the second-to-last digit in 9.27 is less than 9 and the previous digit is 5 or greater, the last digit must be removed and one added to the second-to-last digit.
Three Decimal Places Rule #3: If the final digit in a number, such as 9.27, is five or more, the second to last digit is nine, and the third to last digit is less than nine, the last digit is eliminated, the second to last digit is changed to zero, and the third to last digit is increased by one.
Fourth Rule of Two Decimal Places: Add 1 to the value on the left side of the decimal point and change the right side of the decimal point to 00 if the final digit in 9.270 is 5 or more, the next-to-last digit is 9, and the next-to-last digit is 9.
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Given f(x)= 5(3−x), what is the value of f(−2)?
A truck can be rented from Company A for $110 a day plus $0.20 per mile. Company B charges $70 a day plus $0.40 per mile to rent the same truck. Find the
number of miles in a day at which the rental costs for Company A and Company B are the same.
The number of miles in a day at which the rental costs for Company A and Company B are the same will be 200 miles.
We are given that:
For Company A:
Fixed cost = $ 110
Variable cost = $ 0.20 per mile
For Company B:
Fixed cost = $ 70
Variables cost = $ 0.40 per mile
Let the number of miles in a day be x.
So, the equation for rental cost for company A will be:
Rental cost = 110 + 0.20 x
The equation for rental cost for company B will be:
rental cost = 70 + 0.40 x
Now, put both rental cost equal.
110 + 0.20 x = 70 + 0.40 x
0.40 x - 0.20 x = 110 - 70
0.20 x = 40
x = 40 / 0.20
x = 200 miles.
Therefore, the number of miles in a day at which the rental costs for Company A and Company B are the same will be 200 miles.
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in the figure below helppp
Find the percent increase or decrease from 200 to 460.
57% increase
130% decrease
57% decrease
130% increase
The percent increase from 200 to 460 is 130% increase
How to find the percent increase or decrease?The numbers are given as
200 and 460.
460 is greater than 200
So, the percentage is an increment
The percentage increment is then calculated as
Percentage = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation
Percentage = (460 - 200)/200 * 100%
Evaluate the difference
So, we have
Percentage = 260/200 * 100%
Evaluate the quotient
So, we have
Percentage = 1.3 * 100%
Evaluate the product
So, we have
Percentage = 130%
Hence, the percent increase from 200 to 460 is 130% increase
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A line y=mx+b is translated using the vector . Write the equation of the translated line. What is the value of the y -intercept?
The found value are-
Equation of the translated line: y = mx − am + 2b.The value of the y -intercept: 2b − am.What is general form of straight line?A straight line's general equation is y = mx + c, in which m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.
Now, as per the given question;
The general equation of the line is given as;
y = mx + b
Each point (x,y) of the line is moved to the point (x+a, y+b) by the translation:
(x,y) ---> (x+a, y+b)
We find the original line's x and y intercepts:
Put y=0 in general equation of the line
⇒mx+b = 0
⇒x = −b/m
When, x=0
⇒y = m⋅0 + b
⇒ y = b
A, (0,b) and B( -b/m, 0)
We find the translational coordinates of the points A,B:
A(0,b) ---> A′ (0+a,b+b)
A(0,b) ---> A′ (a,2b)
And,
B( -b/m, 0) ----> B'( -b/m + a, 0 + b)
B( -b/m, 0) ----> B'( -b/m + a, b)
To find the equation of the line's translation, we use the points A and B ′:
m' = (2b - b)/[a - (-b/m +a)]
m' = b/(b/m)
m' =m
And,
y−yA' = m' (x−xA')
y−2b=m(x−a)
y=mx−am+2b
The translation of the line's x and y intercepts are:
Put x=0
⇒y = m⋅0−am+2b
⇒y = 2b−am
And, put y=0
⇒0 = mx−am+2b
⇒x = a - (2b/m)
Therefore, the equation of the translate line is found to be y = mx − am + 2b.
And, the value of the y-intercept is found to be 2b−am.
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solve 3/5w-1/5w+10=4
3/5w - 1/5w +10 = 4
First, simplify 3/5w - 1/5w
2/5w + 10 = 4
Then, subtract each side by 10
2/5w = -6
Multiply each side by the denominator
2w = -30
Then divide each side by 2
w = -15
Given the number n as input, print the first n odd numbers starting from 1. for example if the input is 4 the output will be: 1 3 5 7
Pseudocode algorithms are used as prototypes of an actual program.
The required pseudocode algorithm is as follows:
1. Start
2. Input n
3. Odd = 1
4. For i in range(n):
4.1 Print Odd 4.2 Odd = Odd + 2
How to write the pseudocode that prints the first n odd numbers starting from 1?The pseudocode that prints the first n odd numbers starting from 1 is as follows:
1. Start
2. Input n
3. Odd = 1
4. For i in range(n):
4.1 Print Odd 4.2 Odd = Odd + 2
The above pseudocodes would print the first n odd numbers starting from 1, given that n is the input
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Which list shows the students in order from the student with the shortest plant to the student with the tallest plant
Answer: B
Step-by-step explanation:
What is the slope of the line that contains the points R(-2,1) and S(10,6)? Express your answer as a fraction.
The slope of the line that contains the given points R(-2,1) and, S(10,6) is 5/12 .
It is given in the question that the line contains the points R(-2,1) and S(10,6).
We know that:-
The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-
m = (d-b)/(c-a)
Here, we have
m = slope of the line
(a,b) = (-2,1)
(c,d) = (10,6)
Hence, putting the values of (a,b) and (c,d) , we get
Slope of the line that contains the given points R(-2,1) and, S(10,6) is given by:-
(6-1)/(10-(-2)) = 5/12=
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Sarah has two bags, each
containing x counters and
another bag containing y
counters.
Write an expression for the
number of counters Sarah has.
Answer:
2x+y
Step-by-step explanation:
They have 2 bags containing "x" counters and 1 containing "y" counters. So 2 multiply the number of x since there are 2 bags + y because y also contains counters we need to add. (I'm pretty sure)
Which is an equivalent expression for (3^2 • 5^4)^3?
3^2 • 5^12
3^5 • 5^7
3^6 • 5^12
15^18
Hey there!
(3^2 * 5^4)^3
= (3 * 3 * 5 * 5 * 5 * 5)^3
= (9 * 25 * 25)^3
= (9 * 625)^3
= (5,625)^3
= 5,625 * 5,625 * 5,625
= 31,640,625 * 5,625
= 177,978,515,625
= 3^6 * 5^12
Therefore, your answer should be:
Option C. 3^6 * 5^12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Write a recursive formula for each sequence. 1,4,9,16, . . . . . . .
The recursive formula for sequence 1,4,9,16, . . . is a(n) = 2 a(n-1) - a(n-2) + 2
The recursive formula of a sequence is a formula that relates the nth term of the sequence with the preceding term(s), (n-1)th, (n-2)th, and so on.
The given sequence is: 1,4,9,16, . . .
So, we must ask ourselves:
How can we get 4 from 1?
How can we get 9 from 4 and 1?
and so on.
Notice that:
4 = 1 + 3
9 = 4 + 5
16 = 9 + 7
Notice that the differences (3, 5, 7) increase by 2.
Therefore, we can write:
4 = 1 + 3
= 1 + (1 - 0) + 2
9 = 4 + (4 - 1) + 2 (9 is a(3), and 4 is a(2))
a(3) = a(2) + a(2) - a(1) + 2
= 2 a(2) - a(1) + 2
16 = 9 + (9 - 4) + 2
a(4) = a(3) + a(3) -a(2) + 2
a(4) = 2 a(3) - a(2) + 2
Continue this process, we get:
a(n) = 2 a(n-1) - a(n-2) + 2
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Match the polynomial on the left with the corresponding polynomial on the right.
Add: (-4x²-3x+6) + (6x² - 2x + 1)
Find the opposite of: 2x² + x-7
Subtract: (-4x²+2x-1)-(-2x² + 3x+6)
-2x²-x-7
-2x²-x+7
-2x² - 5x+7
2x²-x+7
2x²-5x+7
(-4x2-3x+6) + (6x2 - 2x + 1) = 2x2-5x + 7, the opposite of 2x2 + x-7 is -2x2 - X+ 7 and (-4x2+2x-1) - (-2x2 + 3x+6) = -2x-x - 7
1. (-4x2-3x+6) + (6x2 - 2x + 1)
= -4x2+ 6x2- 3x- 2x + 1+ 6
= 2x2- 5x + 7
Thus, adding gives us 2x2- 5x + 7 and thus (-4x2-3x+6) + (6x2 - 2x + 1) will be matched with the 5th equation.
2. opposite of: 2x2 + x-7
The opposite of 2x2 + x-7 can be found if we just reverse the signs of each of the term. This means that + becomes - and - becomes -
Thus the opposite is: -2x2 - X+ 7
Thus, it will be matched with the second option.
3. (-4x2+2x-1) - (-2x2 + 3x+6)
= -4x2+2x-1 + 2x2 - 3x - 6
= -4x2+ 2x2 +2x - 3x - 6-1 = -2x-x - 7
Thus, this equation will be matched with the 1st option.
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Luna has consumed 900 calories so far today. She has also burned 500 calories in dance class. She wants to keep her daily calorie total to 1,500 calories per day. How many calories does she have left to consume for the day? Is 1,200 a viable solution to this problem?
No; 1,200 is more than the 500 she burned dancing.
No; 1,200 will cause her to exceed 1,500.
Yes; 1,200 is less than 1,500.
Yes; 1,100 is less than 1,500.
Luna already had,
→ consumed 900 cal
→ burned 500 cal
She wants to keep her daily calorie,
→ 1,500 cal/day
Calories she have left to consume,
→ 1500 - (900 - 500)
→ 1500 - 400
→ 1100 cal
Therefore, 1,200 cal will cause her to exceed 1,500 cal/day.
3. Find the value of the variables for which the shape must be a parallelogram.
please help
Answer:
x = 2
y = 17
Step-by-step explanation:
Rule that applies to this question: Opposite sides of a parallelogram are equal.
Therefore:
x+2 = 4
x = 4 - 2
x = 2
y-5 = 12
y = 12 + 5
y = 17
z = x+m+y, solve for x
u = bak, solve for a
help please i really need to get this done
Answer:
C. The classmate was supposed to multiply the exponents.
Step-by-step explanation:
[tex] { ({2}^{3}) }^{2} = {2}^{6} = 64[/tex]
Answer:
C
Step-by-step explanation:
your classmate multiplied the exponenets
what is the inverse of the function y=5x+30?
The inverse of the function is y = ( 1/5 )x - 6.
An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Consider the function,
y = 5x + 30
To find the inverse of the function we interchange x and y then find the equation for y.
Therefore, after interchanging x and y:
x = 5y + 30
Subtracting 30 from each side of the equation.
x - 30 = 5y + 30 - 30
x - 30 = 5y
Now, dividing the whole equation by 5
( x - 30 ) / 5 = 5y / 5
y = ( 1/5 )x - 30/ 5
y = ( 1/5 )x - 6
Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.
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Given a focal length of a mirror and an object distance, you determine that s' < 0. from this you can conclude that:_________
The image seen in the compact mirror is not of the same size as seen in the plane mirror. This compact mirror is concave on one side and convex on the other side.
The size of the image as compared to the object is related to the magnification. The size of an object’s image is larger (or smaller) than the object itself by its magnification, The level of magnification is proportional to the ratio of and An image that appears to be double the size of the actual object would have magnification
The radius of curvature of a mirror is twice its focal length.
All distances measured to the right of the origin (along the positive x-axis) are taken as positive while those measured to the left of the origin (along the negative x-axis) are taken as negative.
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The time needed to roast a chicken depends on its weight. Allow at least 20 min/lb for a chicken weighing as much as 6 lb . Allow at least 15 min/lb for a chicken weighing more than 6 lb .
a. Write two inequalities to represent the time needed to roast a chicken.
The two inequalities are:
y = 20x when x ≤ 6 and y = 15x when x > 6
The scenario given here is of a chicken that is being roasted. To solve this problem, we will take y as the time required to roast the chicken and x as the lbs of the chicken. (weight)
Now two different conditions are applied depending upon the lbs of the chicken the taken to roast the chicken will vary,
20min/lb for a chicken weighs as much as 6lb.
y = 20x when x ≤ 6
15 min/lb for a chicken weighs more than 6lb.
y = 15x when x > 6
The above two equations are the two inequalities that represent time needed to roast both the chicken.
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-10.4 + 8a = -20 + 5a
-5a+8a=-20+10.4
-3a=-10.4a
How many numbers from 1 through 400 have a 2 in the units place (ones place) and are divisible by 4?
Answer:
2 6 9 7 4 7 66 46 66 74 89 84 653 88
Line graphs that indicate time along the x-axis can be used to predict what would happen to dependent variables in an experiment at a later point in time
only if the existing line shows an upward trend.
only if the existing line shows a downward trend.
if a new variable was introduced to the experiment.
if the experiment continued under the same conditions.
Answer:
if the experiment continued under the same conditions.
Answer: if the experiment continued under the same conditions.
Step-by-step explanation:E2022
