Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A.
A. 1/2x + 3y = 11 → 1/2x + 3y = 11
5x − y = 17 → 15x − 3y = 51
15 1/2x = 62
B. 1/2x + 3y = 11
151/2x = 62
Answers
A=(3,4)
B=(3,5)
C=(4,3)
D=(5,3)
Answer: C (4,3)
Step-by-step explanation:
How to work with negative exponents
Final answer:
Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. When multiplying or dividing with negative exponents, add or subtract them accordingly. In scientific notation, divide the coefficients and subtract the exponents to divide numbers.
Explanation:
Working with negative exponents is an essential skill in mathematics, where a negative exponent indicates the inverse or reciprocal of the base raised to the corresponding positive exponent. For example, 2-1 equals 1/2, which means that we are finding the reciprocal of 2. In operations involving exponents, such as multiplication and division, we follow certain rules with negative exponents:
When multiplying numbers, add the exponents (negative exponents included).
When dividing numbers, subtract the exponents (again, include negative exponents).
To convert a negative exponent into a positive one, take the reciprocal of the base with the corresponding positive exponent.
Here's an example of division in scientific notation: 106 ÷ 103 = 10(6-3) = 103. If you need to divide two numbers using scientific notation, you divide the coefficients and subtract the exponents.
Remember, a number like 3-4 is equivalent to 1/34, or 1 divided by 3 multiplied by itself four times. In general, negative exponents flip the base to the denominator, signifying a division rather than multiplication.
Explain why rational number is either a terminating or repeating decimal?
Plz someone help me
90% of students at a university use a backpack, while the rest do not. Of all the students, 50% carry their laptops with them and 5% carry neither a backpack nor laptop. What percentage of students carry their laptops and use a backpack?
The percentage of students who carry their laptops and use a backpack is 45%.
Explanation:To find the percentage of students who carry their laptops and use a backpack, we need to subtract the percentage of students who carry neither a backpack nor laptop from the percentage of students who carry their laptops.
Given that 5% carry neither a backpack nor laptop, we can subtract this from the 50% who carry their laptops to find that 45% of students carry their laptops and use a backpack.
If m C=66, find the values of x and y.
A) x = 24, y = 66
B) x = 90, y = 66
C) x = 90, y = 24
D) x = 66, y = 24
Answer:
C) x=90°, y=24°
Step-by-step explanation:
The two sections into which A is split, are the same size as indicated. Sides AB and AC are the same length. Because of those reasons, it can be concluded that B and C are the same size.
The corners of a triangle adds up to 180°. For ΔABC:
[tex]A+B+C=180\\A+2(66)=180\\A=48[/tex]
y° is half of A:
∴y° = 24°
Now add up the corners of triangle ABD:
[tex]y+x+B=180\\24+x+66=180\\x=90[/tex]
∴x° = 90°
Plz Someone Help Me.
I got to pass this piece of homework to school tomorrow.
characteristics of the graph of the absolute value parent function
55 divided by 2044 i need help for my summer packets
Final answer:
To divide 55 by 2044, use long division. The quotient is 0.027.
Explanation:
To divide 55 by 2044, you can use long division. Here is the step-by-step process:
Start by dividing 55 by the first digit of 2044, which is 2. The quotient is 27 and the remainder is 1.Bring down the next digit of 2044, which is 0.Divide 10 by 2044. The quotient is 0 and the remainder is 10.Bring down the next digit of 2044, which is 4.Divide 104 by 2044. The quotient is 0 and the remainder is 104.Bring down the next digit of 2044, which is 4.Divide 1044 by 2044. The quotient is 0 and the remainder is 1044.At this point, you have reached the end of the division process. The final quotient is 0.027 and there is no remainder. Therefore, 55 divided by 2044 is approximately 0.027.
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13.
(08.06 LC)
Variable g is 8 more than variable w. Variable g is also 2 less than w. Which pair of equations best models the relationship between g and w? (1 point)
g= 8w
g = w + 2
w = g + 8
w = g – 2
w = 8g
w = g + 2
g= w + 8
g = w – 2
The two equations are:
g= w +8
g= w +2
^_^
find the apporximate side length of a square game board with an area of 151 in2
To find the approximate side length of a square game board with an area of 151 in², take the square root of 151.
Explanation:To find the approximate side length of a square game board with an area of 151 in2, we can use the formula for the area of a square, which is length x width. Since all sides of a square are equal, we can represent the side length as 's'. So, s x s = 151. To find the side length, we can take the square root of 151, which is approximately 12.29 inches. Therefore, the approximate side length of the square game board is 12.29 inches.
please solve x+9.72=21
Angle DAB measures ( 2x4 )°− and angle BCD measures 47°. Find x.
Nina has 5 bills and 10 bills in her wallet. She has a. total of 7 bills with a value of $55. How many of each type of Bill does she have?
Answer:
4 tens3 fivesStep-by-step explanation:
If all were $5 bills, the total would be $35. It is $20 more than that. Each time a $5 bill is replaced by a $10 bill, the total goes up $5. Since the total is $20 higher, there must be $20/$5 = 4 such replacements.
There are 4 $10 bills and 3 $5 bills.
mr. lee had a bag of red beans and a bag of black beans. 20% of the total number of beans were black, and there were 180 ounces more red beans than black beans. he transferred some red beans to the bag containing black beans, so that, the bag now contained 30% of the total number of beans. How many ounces of beans were there in the bag of mixed beans
Final answer:
After finding the total weight of beans based on the given percentages and difference in weight between red and black beans, we determine that there are 90 ounces of beans in the mixed bag.
Explanation:
The question asks us to find out how many ounces of beans are now in the bag of mixed beans, given certain percentages before and after mixing. We know that initially, 20% of the total beans are black, and the rest are red. After Mr. Lee transferred some red beans to the bag containing black beans, the bag contained 30% of the total number of beans.
To solve this, let's denote the total number of beans by T, the number of black beans by B, and the number of red beans by R. According to the information provided:
20% of T is black beans: B = 0.20TThere are R = B + 180 oz of red beans.After transferring, the mixed bag contains 30% of T.First, we use the initial conditions to write an equation for the total number of beans T. Since R is 180 ounces more than B:
T = B + R
T = B + (B + 180)
T = 2B + 180
Given that B is 20% of T, we can also write this as:
T = 2(0.20T) + 180
T = 0.40T + 180
We can now solve for T:
T - 0.40T = 180
0.60T = 180
T = 180 / 0.60
T = 300 ounces
Since we know that the mixed bag contains 30% of the total, we calculate 30% of 300 ounces:
30% of T = 0.30 x 300
30% of T = 90 ounces
Therefore, after transferring, there are 90 ounces of beans in the mixed bag.
Simon used a probability simulator to roll a 12-sided number cube 100 times. His results are shown in the table below:
Number on
the Cube Number of
Times Rolled
1
18
2
5
3
16
4
12
5
10
6
5
7
8
8
14
9
2
10
5
11
2
12
3
Using Simon's simulation, what is the frequency of rolling a 3 on the number cube? (5 points)
100 over 16
100 over 84
16 over 100
84 over 100
The probability would be 16 over 100.
We can tell this because by the table, the number 3 was rolled 16 total times. You can state the probability by expressing with the number of times rolled over total times rolled. Since it was rolled a total of 100 times, we are left with 16/100.
Answer:
The probability would be 16/100
Step-by-step explanation:
I took the test and got it right!! :)
Solve 4w = 2w - 12. Plis help me with that
When Emma was born she was 20.5 inches long. At her 6-month checkup, she was 26.25 inches long. what was the approximate percentage change in her length?
Answer:
28% and she increased by 5.75 inches. Hope this helped
Step-by-step explanation:
Greg bought 2 boxes of balloons he used half of them to decorate his yard he used 40 to decorate his porch he used the rest inside his house how many balloons did he use
It says to find each product
Suppose Lisa places $8500 in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
At the end of 1 year, the amount in the account will be $9860. At the end of 2 years, the amount in the account will be $11437.6. This is calculated using the formula for compound interest.
Explanation:Lisa is placing $8500 in an account that pays 16% interest compounded annually. To solve for part (a) and part (b) which ask for the amount in the account at the end of 1 year and 2 years respectively, we use the formula for compound interest: A = P *(1 + r/n)^(nt).
Here, P is the principal amount ($8500), r is the annual interest rate (16% or 0.16 as decimal), n is the number of times that interest is compounded per unit t (n = 1 as it's compounded annually), and t is the time the money is invested for.
For (a), t = 1 year. Inserting these values into the formula, we get:
A = $8500 * (1 + 0.16/1)^(1*1) = $8500 * 1.16 = $9860.
Therefore, at the end of 1 year, the amount in the account will be $9860.
For (b), t = 2 years. Using the same formula, we get:
A = $8500 * (1 + 0.16/1)^(1*2) = $8500 * 1.16^2 = $11437.6.
Therefore, at the end of 2 years, the amount in the account will be $11437.6.
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Which of the following describes the graph of a linear function?
It is V shaped and passes through the origin.
Its y-values increase at a constant rate as its x-value increases.
It is a straight line in one portion and a curve in another portion.
Its y-values increase at a nonconstant rate as its x-value increases.
Answer:
Option B is the correct option.
Step-by-step explanation:
The Linear function is always in the form of y = mx + c
Where m defines the slope which is rate of change of y-values or change in y-values with the change in x-values.
Therefore, Option B is the correct option.
What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)?
How many 2/3- cup servings are in 6 cups of yogurt
Answer: The required number of servings in 6 cups of yogurt is 9.
Step-by-step explanation: We are given to find the number of [tex]\dfrac{2}{3}[/tex] cup servings in 6 cups of yogurt.
We will be using the UNITARY method to solve the given problem.
We have
Number of servings in [tex]\dfrac{2}{3}[/tex] cups of yogurt = 1.
So, the number of servings in 1 cup of yogurt will be
[tex]\dfrac{1}{\frac{2}{3}}=\dfrac{3}{2}.[/tex]
Therefore, the number of servings in 6 cups of yogurt is given by
[tex]\dfrac{3}{2}\times6=9.[/tex]
Thus, the required number of servings in 6 cups of yogurt is 9.
is 4/2 an integer?
I am stumped, so that is why I want to know
3 litters were born last year and each litter had 7 puppies how many puppies were born last year
Which line has an undefined slope? A y = 0 B y = 2 C x = y D x = 2
Line x =2 has undefined slope.
What is slope?" Slope is defined as the ratio of the difference in the increase of y-coordinates to the difference in the increase of x-coordinates."
Formula used
Equation of the line
y = mx + c
c = y-intercept
m = slope
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
According to the question,
1. y = 0
Compare it with standard equation of the line
y = 0x + 0
slope = 0
It is not a correct answer.
2. y =2
Compare it with standard equation of the line
y = 0x + 2
slope = 0
It is not a correct answer.
3. x= y
Compare it with standard equation of the line
y = 1x + 0
slope = 1
It is not a correct answer.
4. x=2
It is vertical line , x value remain constant.
Therefore,
[tex]x_{1}=2\\x_{2}=2[/tex]
Slope = [tex]\frac{y_{2}-y_{1}}{2-2}[/tex]
= [tex]\frac{y_{2}-y_{1}}{0}[/tex]
Zero in the denominator therefore, undefined slope
Hence, line x =2 has undefined slope.
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Final answer:
The line with an undefined slope is D. x = 2, which is a vertical line with a constant x-value for all points on the line.
Explanation:
The question asks which line has an undefined slope. An undefined slope occurs when a line is vertical since slope is defined as the change in y over the change in x, and in a vertical line the change in x is zero. Looking at the options given, the equation representing a vertical line is D. x = 2. This line is vertical because it has the same x-value for all points on the line, meaning there is no change in x as you move along the line, thus creating an undefined slope.
Jacob wants to use an elevator to carry identical packages having the same weight. Each package weighs 3 pounds and Jacob weighs 99 pounds. If the elevator can carry a maximum of 300 pounds at a time, which inequality shows the maximum number of packages, n, that Jacob can carry with himself in the elevator if he is the only passenger?
Answer:
The required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].
Step-by-step explanation:
Consider the provided information.
Each package weighs 3 pounds and Jacob weighs 99 pounds.
let n is the maximum number of package that Jacob can carry with himself in the elevator.
Thus, the total weight of Jacob while having n packages on the elevator is:
[tex]3n+99[/tex]
The elevator can carry a maximum of 300 pounds at a time, therefore.
[tex]3n+99\leq 300[/tex]
Now, subtract 99 from both sides and divide the obtained inequality with 3.
[tex]3n+99-99\leq 300-99[/tex]
[tex]3n\leq 201[/tex]
[tex]\frac{3n}{3}\leq \frac{201}{3}[/tex]
[tex]n\leq 67[/tex]
Thus, the Jacob can carry maximum 67 packages.
Hence, the required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].
A skydiver is falling at about q42 feet per second.How many feet per minute is she falling?
Is 7.6 repeating greater or less than square root 55