Answer:
Its the Adding a quantity one or the bottom right
Adding equations is a legitimate method in solving systems because it utilizes the elimination process to simplify the system. It also respects the fundamental properties of equations and provides a precise analytical technique for finding solutions, which can be more accurate than graphical methods.
Explanation:Adding equations, known as the method of elimination, is a valid method for solving a system of equations. This approach works because it leverages the property that if two equations both equal the same variable, they can be added together to eliminate one of the unknowns, simplifying the system. For instance, suppose we have equation a: x + 2y = 6, and equation b: 3x - y = 4. Adding them gets 4x + y = 10, which is a new equation that can help solve for one of the variables more directly. This takes advantage of the fact that equations describe relationships between variables that hold true under various mathematical operations, including addition.
Another key aspect is the understanding that solutions to equations are often not unique when they include an unknown squared, leading to two potential solutions. However, contextual knowledge can determine which solution is reasonable, such as in physics problems where time or velocity must make sense in the real world.
Moreover, while analytical methods of solving systems are precise, solving equations graphically can offer a visual understanding but may lack accuracy due to potential scaling and drawing inaccuracies. Therefore, analytical techniques, like adding equations, are generally more accurate but can be complemented with graphical methods for a better conceptual grasp.
You have 4/6 cup of cocoa in your cupboard. A recipe for cookies calls for
2/5 cup of cocoa. How much cocoa would you have left if you made the cookies?
Answer:
4/15 cocoa would be left if we made cookies
Step-by-step explanation:
4/6- 2/5
= 4(5)- 2(6)/30
= 20-12/30
=8/30
=4/15
After making the cookies using 2/5 cup of cocoa from the initial 4/6 cup, you would subtract 12/30 cup from 20/30 cup to find that you would have 4/15 cup of cocoa left.
Explanation:To determine how much cocoa you would have left after making the cookies using 4/6 cup of cocoa and using 2/5 cup for the recipe, you would need to subtract the amount used from the initial amount. To perform the subtraction, you first need to have the quantities expressed with a common denominator. The least common denominator for 6 and 5 is 30.
Convert 4/6 cup to an equivalent fraction with a denominator of 30: (4 × 5) / (6 × 5) = 20/30 cup.
Convert 2/5 cup to an equivalent fraction with a denominator of 30: (2 × 6) / (5 × 6) = 12/30 cup.
Now you can subtract the amount of cocoa used for the cookies from the total amount you have:
Remaining cocoa = Initial amount - Amount used = 20/30 cup - 12/30 cup.
Remaining cocoa = (20 - 12) / 30 = 8/30 cup of cocoa.
To simplify this, divide both the numerator and denominator by their greatest common divisor, which is 2:
Remaining cocoa = 4/15 cup. So you would have 4/15 cup of cocoa left after making the cookies.
how do you know a mixed number in a decimal
which is the graph of the cube root function f(x)=3 square root x
The student is probably asking about the cube root function multiplied by 3, which is an increasing function and is defined for all real numbers, including negative values.
Explanation:The phrase 'f(x)=3 square root x' seems to be a typo. Assuming this refers to the cube root function, such as 'f(x) = 3 √x,' then this function represents the cube root of 'x' multiplied by 3. To graph this function, start by plotting points, taking the cube root of various values of 'x' and scaling these by 3.
The graph will pass through the origin and rise less steeply than a linear function; it will be an increasing function for all 'x' as the cube root of a real number is always real. This also means that the function will be defined for all real numbers, including negatives, as cubing can produce both positive and negative results.
Which function is the inverse of y = 2x+5/2?
Answer:
y=1/2x-5/4
Step-by-step explanation:
y=2x+5/2
x=2y+5/2
2y=x-5/2
y=1/2x-(5/2)/2
y=1/2x-(5/2)(1/2)
y=1/2x-5/4
There are 2.54 centimeters in every inch. If a bug moves at a rate of 3.5 inches per second, then Which of the following is closest to its speed in meters per second?
The bug's speed is approximately 5.33 meters per minute, which is closest to option (2).
To find the bug's speed in meters per minute, we need to convert its speed from inches per second to meters per minute.
First, let's convert the bug's speed from inches per second to inches per minute:
[tex]\[3.5 \text{ inches per second} \times 60 \text{ seconds per minute} = 210 \text{ inches per minute}\][/tex]
Now, let's convert inches to meters:
[tex]\[210 \text{ inches} \times \frac{2.54 \text{ centimeters}}{1 \text{ inch}} \times \frac{1 \text{ meter}}{100 \text{ centimeters}} = 5.33 \text{ meters per minute}\][/tex]
So, the bug's speed is closest to option (2) 5.33.
Complete Question:
There are 2.54 centimeters in every inch. If a bug moves at a rate of 3.5 inches per second, then which of the following is closest to its speed in meters per minute?
(1) 3.86
(3) 6.25
(2) 5.33
(4) 7.19
Estimate a 10% tip on a bill of $143.17 by first rounding the bill amount to the nearest ten dollars.
Estimated tip: $il
x
6
?
Answer:
Step-by-step explanation:
143.17
round the bill to the nearest $ 10..
that would make it $ 140
a 10% tip......its the same thing as multiplying by 0.1
and when u multiply any number by 0.1 ur actually starting at the decimal ( or the end of the number) and move one space to the left.
examples :
10% of 245 = 24.5
10% of 5010 = 501
10% of 76 = 7.6
10% of 88.5 = 8.85 .....if there is a decimal, start at the decimal
so.....10% of 140
start at the end of the number and move 1 space to the left...
ur answer is 14 <==
What is the remainder R when the polynomial p(x) is divided by (x - 2)? Is (x - 2) a factor of p(x)?
p(x) = -4x4 + 6x3 + 8x2 - 6x - 4
Answer:
The answer can be calculated by doing the following steps;
Step-by-step explanation:
The Reminder is 0 and (x -2) is the factor of polynomial p(x).
What is polynomials?Polynomials are mathematical articulations that comprise of factors and coefficients. In other cases, variables are referred to as indeterminates. We can perform math activities like expansion, deduction, increase, and furthermore sure number types for polynomial articulations yet not division by factor.
Given polynomials p(x) = -4x⁴ + 6x³ + 8x² - 6x - 4
to divide by (x - 2)
We choose long division and look for what will multiply with (x-2) to make the polynomial
(x - 2)(-4x³) = -4x⁴ + 8x³
We subtract this from the original -4x⁴ + 6x³ + 8x² - 6x - 4 - (-4x⁴ + 8x³)
this leaves -2x³ + 8x² - 6x - 4
repeat the same process
(x - 2)(-2x²) = -2x³ + 4x²
subtract this from -2x³ + 8x² - 6x - 4 we get
-2x³ + 8x² - 6x - 4 - (-2x³ + 4x²) = 4x² - 6x - 4
again repeat the process
(x - 2)(4x) = 4x² - 8x
subtract this from 4x² - 6x - 4 we get
4x² - 6x - 4 - (4x² - 8x) = 2x - 4
repeat again
(x - 2)(2) = 2x - 4
subtract this from 2x - 4 we get
2x - 4 - (2x - 4) = 0
Hence the reminder of polynomials p(x) = -4x⁴ + 6x³ + 8x² - 6x - 4 is 0 and (x - 2) is factor of p(x).
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Rachel hikes at a steady rate from a ranger station to a campground that is 20 mi away. After 2 h, she is 13 mi from the campground. After 4 h, she is 6 mi from the campground. A graph shows her distance y from the campground, in miles, after x hours. What is the slope of the graph, and what does it represent?
From 2 hours to 4 hours she traveled 7 miles.
7 miles / 2 hours = 3.5 miles per hour.
The slope is 3.5 , which is 3.5 miles per hour, which is how fast she is walking.
The average test score of RSM students in September increased by 10%. In October it increased by another 15%. By what percent did the average score on the test increase during the two months? PLEASE HELP I NEED THE ANSWER QUICK
Answer:
26.5%
Step-by-step explanation:
Increasing Percentages
When sequential percentages increasing are computed, each increase applies to the previous result, instead of the first quantity. That is why sometimes the final results may be confusing. For example, increasing 10% and then 15% will not be the same as increasing a total of 25%.
The average test scores of RSM students first increased by 10%. It means that some quantity C increased by
[tex]10C/100=0.1C[/tex]
Now the average test scores are
[tex]C+0.1C=1.1C[/tex]
A new increasing occurred by 15%, and the previous quantity must be multiplied by 1.15, so the final average test scores are
[tex]1.15(1.1C)=1.265C[/tex]
It means that the total increasing was [tex]100(1.265-1)=26.5\%[/tex]
Answer:
26.5%
Step-by-step explanation:
IM SMART! :D
What is the solution of the inequality below for y ?
2x − 5y ≤ 15
The solution for y in 2x − 5y ≤ 15 is [tex]y \geq \frac{2x}{5} - 3[/tex]
Solution:
Given that we have to find solution for given inequality for y
2x − 5y ≤ 15
Let us solve above equation for "y"
[tex]2x - 5y \leq 15[/tex]
Add -2x on both sides
[tex]-2x + 2x - 5y\leq 15 - 2x\\\\-5y \leq 15 - 2x[/tex]
Divide by -5 on both sides
Remember that You can perform on operations on both sides of inequality, and have its truth value unchanged
But if we multiply or divide by a negative number, we must flip the sign
[tex]\frac{-5y}{-5} \geq \frac{15}{-5} - \frac{2x}{-5}\\\\y \geq -3 + \frac{2x}{5}\\\\y \geq \frac{2x}{5} - 3[/tex]
Thus solution for "y" is found
A coin collector has 31 dimes and nickels with a total face value of $2.40. (They are actually worth a lot more.) How many of each coin does she have?
Answer:
The number of each coin she have are 17 dimes and 14 nickels.
Step-by-step explanation:
Given:
A coin collector has 31 dimes and nickels with a total face value of $2.40.
Now, to find each does she have.
Let the number of dimes be [tex]x[/tex].
Let the number of nickels be [tex]y[/tex].
So, total number of coins are:
[tex]x+y=31[/tex]
[tex]x=31-y.............(1)[/tex]
Value of a dime = 10 cents
Value of a nickel = 5 cents
Total face value = 240 cents
(1$ = 100 cents. $2.40×100 =240 cents)
Now, total value of coins:
[tex]10x+5y=240[/tex]
Putting the equation (1) in the place of [tex]x[/tex]:
[tex]10(31-y)+5y=240[/tex]
[tex]310-10y+5y=240[/tex]
[tex]310-5y=240[/tex]
Moving variables on one side and the numbers on other:
[tex]310-240=5y[/tex]
[tex]70=5y[/tex]
Dividing both sides by 5 we get:
[tex]14=y[/tex]
The number of nickels = 14.
Now, putting the value of [tex]y[/tex] in equation (1) we get:
[tex]x+y=31[/tex]
[tex]x+14=31[/tex]
Subtracting both sides by 14 we get:
[tex]x=17.[/tex]
The number of dimes = 17.
Therefore, the number of each coin she have are 17 dimes and 14 nickels.
Which polynomial is factored completely?
121x2 + 36y2
(4x + 4)(x + 1)
2x(x2-4
3x4 – 151° +12
Answer:
121x2 + 36y2
Step-by-step explanation:
= (4x + 4)(x + 1)
= 4(x + 1)(x + 1)
= 4(x + 1)2 and is hence the fully factored form
not sure bout the rest though...... it may have mistakes in the question forms.
Polynomials given to us can be factored except 121x² + 36y²,
so we can say that 121x² + 36y² is factored completely.
What do we mean by factorization of a polynomial?Factorization of a polynomial is the method by which we write the given polynomial as a product of two or more factors, which when multiplied gives back the same Polynomial.
How do we solve the given question?
We will analyze all the given polynomial.
121x² + 36y², cannot be factored further(4x + 4)(x + 1) = 4(x+1)(x+1) = 4(x+1)², factored further2x(x²-4) = 2x(x+2)(x-2), factored furtherCannot be determined∴ After checking all the options, we can say that 121x² + 36y² was completely factored.
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State weather the equation represents exponential growth, exponential decay or neither, 30 POINTS EASY
Answer:
Exponential Decay
Step-by-step explanation:
It's exponential growth when your base value is > 1. Example:
1.3ˣ, 2ˣ, 7ˣ, 999ˣ
It's exponential decay when the base value is < 1. Example:
0.9ˣ, 0.45ˣ, (1/2)ˣ, 0.79ˣ, .999ˣ
It's neither when the base value = 1. Example:
1ˣ
Which graph represents the solution to the given system ? Y=- 6X - 2Y +2=- 6X
Answer: The graph is attached.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the first equation:
[tex]y=- 6x - 2[/tex]
You can identify that:
[tex]m=-6\\b=-2[/tex]
By definition, the line intersects the x-axis when [tex]y=0[/tex]. Then, subsituting this value into the equation and solving for "x", you get that the x-intercept is:
[tex]0=- 6x - 2\\\\2=-6x\\\\x=-\frac{1}{3}\\\\x=-0.333[/tex]
Now you can graph it.
Solve for "y" from the second equation:
[tex]y +2=- 6x\\\\y=-6x-2[/tex]
You can identify that:
[tex]m=-6\\b=-2[/tex]
Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations has Infinitely many solutions.
See the graph attached.
Jordan bikes at a speed of 8 2/3 mph. How many miles will he bike in:
45 minutes?
Answer:
6 1/2
Step-by-step explanation:
So basically 8 2/3 is equally to 26/3 so 45 minutes is 45/60.
45/60=3/4
26/3*3/4=6 1/2
Jordan, with a speed of 8 2/3 miles per hour, will cover a distance of 6.5 miles in a 45 minute bike ride.
Explanation:First, we need to understand that Jordan is biking at a speed of 8 2/3 miles per hour. This means in 1 hour, or 60 minutes, he covers that distance. If we want to know how much he covers in a different timeframe - 45 minutes in this case - we have to adjust proportionally.
As a step-by-step calculation, first change 8 2/3 to a decimal, which equal to 8.67.
To find out how far Jordan bikes in 45 minutes, you need to multiply his speed (8.67 mph) by the time in hours. Since 45 minutes is 0.75 of an hour (45/60), the mathematical calculation will be:
Distance = Speed x Time = 8.67 miles/hour x 0.75 hour = 6.5 miles
Therefore, Jordan will bike 6.5 miles in 45 minutes.
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25 POINTS!
Which answer is an equation in point-slope form for the given point and slope?
point: (−3,5) ; slope: 4
y−5=4(x−3)
y+5=4(x+3)
y+5=4(x−3)
y−5=4(x+3)
Answer:
y-5=4(x+3)
Step-by-step explanation:
y-y1=m(x-x1)
y-5=4(x-(-3))
y-5=4(x+3)
perfect cube
.
[tex]7.4[/tex]
Answer:
405.224
Step-by-step explanation:
2. What are the next two terms of the following sequence?-2,4,-8, 16, ...
A. -32, 64 D . 32, – 64
B. -32, 64
C. 32, 64
Answer:
(A.B.)-32, 64Step-by-step explanation:
[tex]-2\\(-2)(-2)=4\\(-2)(4)=-8\\(-2)(-8)=16\\-----------------\\(-2)(16)=-32\\(-2)(-32)=64\\\vdots[/tex]
Each next term is created by multiplying the previous term by (-2).
Answer:
It's the geometric sequence so the following numbers are:
-32,64
d= -2(multiplication number)
Answer: i did not fully understand,since there are two similar answer options(it's wether A or B)
Good luck!
Intelligent Muslim,
From Uzbekistan.
Jessica's monthly gross pay is $5,660. Each month she has $355 in deductions,
plus state tax of 3% of her gross pay, Social Security taxes of 6.2%, and Medicare takes
of 1.45%. What is her net pay?
Answer:
The net pay of her will be $4702.21
Step-by-step explanation:
The State Tax plus Social Security Taxes plus Medicare takes (3 + 6.2 + 1.45) = 10.65% from Jessica's monthly gross pay.
If the gross pay is $5660 then the after the above deduction the remaining pay will be [tex]5660(1 - \frac{10.65}{100}) = 5057.21[/tex] dollars.
Now, again there is a deduction of $355 from her payment each month.
Therefore, the net pay of her will be = $(5057.21 - 355) = $4702.21 (Answer)
A group of friends bought 7 tickets to a dog show for $30 each. How much did they spend on the tickets?
Answer:
$210
Step-by-step explanation:
1 ticket= 30
7 tickets = 7*30=$210
PLEASE HELP!! Will mark brainliest!!
Answer: 12 small candles and 16 large candles.
Step-by-step explanation:
Notice that an small candle costs $4 and a large candle costs $6.
Let be "s" the number of small candles you sold and "l" the number of large candles you sold.
Set up a System of equations:
[tex]\left \{ {{4s+6l=144} \atop {s+l=28}} \right.[/tex]
Use the Elimination Method to solve it:
- Multiply the second equation by -4.
- Add the equations.
- Solve for "l".
Then:
[tex]\left \{ {{4s+6l=144} \atop {-4s-4l=-112}} \right.\\.......................\\2l=32\\\\l=16[/tex]
- Substitute the value of "l" into the second equation and solve for "s":
[tex]s+16=28\\\\s=12[/tex]
Evaluate Ic2 + b2l, given a = 5, b = -3, and c= -2.
Answer:
Ic² + b²l = 13 units.
Step-by-step explanation:
We have to evaluate the expression Ic² + b²l with unknowns b and c and having the values of b and c respectively - 3 and - 2.
Now, Ic² + b²l
= I(- 2)² + (- 3)²l {Putting the values of b and c}
= I4 + 9l
= I13l
= 13 units.
Therefore, Ic² + b²l = 13 units. (Answer)
A car travels at 30 1/5 miles in 2/3 of an hour. What is the average speed in miles per hour of the car
Answer:
Adverage of 20 mph
30 1/5 = 30.2
2/3 = .6667
30.2 x .6667 = 20.13
Answer:
45.3 miles/hour
Step-by-step explanation:
the information we have is:
distance:
[tex]d=30\frac{1}{5}miles=30.2miles[/tex]
time:
[tex]t=\frac{2}{3} hour[/tex]
the formula for the average speed is:
[tex]v=\frac{distance}{time} =\frac{d}{t}[/tex]
substituting all the known values we get:
[tex]v=\frac{30.2miles}{2/3hour} =\frac{3(30.2miles)}{2hour}= 45.3miles/hour[/tex]
the average speed in miles per hour is: 45.3
which equation is equivalent to log^x36=2?
The equation which is equivalent to [tex]\log _{x} 36=2[/tex] is [tex]x^{2}=36[/tex] or x = 6 ([tex]\log _{6} 36=2[/tex]).
Step-by-step explanation:
Given Equation:
[tex]\log _{x} 36=2[/tex]
As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:
[tex]b^{y}=a[/tex]
Then, the base b logarithm of x is equal to y
[tex]\log _{b}(x)=y[/tex]
Now, use the logarithmic rule for the given equation by comparing with above equation. We get b = x, y = 2, and x = 36. Apply this in equation,
[tex]b^{y}=a[/tex]
[tex]x^{2}=36[/tex]
When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as [tex]\log _{6} 36=2[/tex]
Answer:D
Step-by-step explanation:
i got it right
A local flower shop is selling $1 raffle tickets and is donating all proceeds to the children's hospital. They sold 5,500 tickets and plan to give away 20 flower arrangements valued at $70 and 20 gift certificates valued at $25. Find the expected value of purchasing a raffle ticket.
Round to the nearest cent. Do not round until the final calculation.
The expected value of purchasing a raffle ticket is -0.647.
What is the Expected Value of a Probability & Statistical Analysis?The expected value is derived in probability analysis by the multiplication of each of the potential possibilities by the likelihood that each result will occur and then adding all of those values together.
Using the formula below, we can calculate the expected value as follows:
[tex]\mathbf{ E(X)= \sum^{n}_{i=1}X_i P(X_i)}[/tex]
However, the probability (Pr) of each event can be categorized as follows:
Pr (to win a flower arrangement ) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]Pr (to gift a certificate) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]Pr (no win) ) [tex]\mathbf{=\dfrac{5500 - 20 - 20}{5500}=\dfrac{5460}{5500}}[/tex]Thus;
[tex]\mathbf{E(X) = 70(\dfrac{20}{5500} \times 25 ((\dfrac{20}{5500} )- 1(\dfrac{5460}{5500} )}[/tex]
[tex]\mathbf{E(X) =-0.647}[/tex]
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I need this please 64 points!
Answer:
None. Wanda's work is correct.
Step-by-step explanation:
The first is correct.
Answer:
Wanda converted the percent to a decimal incorrectly. It should be 0.73
Step-by-step explanation:
It has to be move two decimal place.
What are the x and y-intercepts of the line described by the equation?
-6x + 3y = 18.9
Answer:
x-intercept - x = 1/2y - 3.15
y-intercept - y = 2x + 6.3
Step-by-step explanation:
For x,
-6x + 3y = 18.9
-6x = -3y + 18.9
x = -3y/-6 + 18.9/-6
x = 1/2y - 3.15
For y,
-6x + 3y = 18.9
3y = 6x + 18.9
y = 6x/3 + 18.9/3
y = 2x + 6.3
Solve for x when m LKM=90
Answer:
x= -15
Step-by-step explanation:
3x+10=2x-5
3(-15)+10=2(-15)-5
-45+10=-30-5
-35=-35
Each side of the angle is equal, that's how i knew the two were supposed to be equal. <3 Hope this helps!
(I found the picture.)
Answer:
17
Step-by-step explanation:
L 3x + 10 5875 =90 2x - 5 x=_17 5 5 - x =17 Use the image to answer questions 6-7. 125 Given that Xll Y use the figure below to answer questions 8 - 11. -40-40 normal Unit 2: Equations & Exponents Directions: 1. Solve each problem.
Marla will paint 48 pots . She plans to paint 9 pots each week . Draw an array to find how many weeks it will take Marla to paint all of the pots . Explain
Answer:
The number of weeks Marla will take to paint all the pots is 5 weeks and 3 days .
Step-by-step explanation:
Given as :
The number of pots Marla will paint = 48 pots
The number of pots she plans to paint each week = 9 pots
Let The number of weeks Marla needs to paints all pots = n weeks
Now, According to question
The number of weeks = [tex]\dfrac{number of pots Marla will paints}{\textrm The number of pots Marla will paints each week}[/tex]
Or , n = [tex]\dfrac{48}{9}[/tex]
∴ n = 5.3
So The number of weeks = n = 5 weeks and 3 days
Hence The number of weeks Marla will take to paint all the pots is 5 weeks and 3 days . Answer
Bob can body paint 12 cars in 3 weeks. How many cars can Bob body paint in 8 weeks?
Answer:
32 cars
Step-by-step explanation:
we know that he can paint 12 cars in 3 weeks.
that means that he can paint 4 cars per week.
4cars x 8weeks = 32 cars in 8 weeks
Answer:
Step-by-step explanation:
12 cars in 3weeks
Then in 1week he will paint= 12/3 car
= 4 cars
so in 8weeks = 4 × 8 cars
= 32cars