Solve the following system of equations.
2x+y=3
I= 2y - 1
x=
y=
Answers
Note: I am assuming your second equation is:
x = 2y - 1
Answer:
The solution to the system of equations is:
x = 1y = 1Step-by-step explanation:
Given the system of equations
2x+y=3
x = 2y - 1
solving the system of equations using the elimination method
\(\begin{bmatrix}2x+y=3\\ x=2y-1\end{bmatrix}\)
Arrange equation variables for elimination
\(\begin{bmatrix}2x+y=3\\ x-2y=-1\end{bmatrix}\)
Multiply x-2y=-1 by2: 2x-4y=-2
\(\begin{bmatrix}2x+y=3\\ 2x-4y=-2\end{bmatrix}\)
subtracting the equations
\(2x-4y=-2\)
\(-\)
\(\underline{2x+y=3}\)
\(-5y=-5\)
now solve -5y = -5 for y
\(-5y=-5\)
Divide both sides by -5
\(\frac{-5y}{-5}=\frac{-5}{-5}\)
Simplify
\(y=1\)
For 2x+y=3 plug in y=1
\(2x+1=3\)
subtract 1 from both sides
\(2x+1-1=3-1\)
Simplify
\(2x=2\)
Divide both sides by 2
\(\frac{2x}{2}=\frac{2}{2}\)
Simplify
\(x=1\)
Therefore, the solution to the system of equations is:
x = 1y = 1Related Questions
The perimeter of a rectangle is 52 inches, and the area is 160 square inches. Find the length and width of the rectangle.
Answers
Answer:16x16
Step-by-step explanation:
Find the complete factored form of the
polynomial :
-8m²n-7m² nª
Enter the correct answer.
Answers
The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).
To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:
-8m²n - 7m²n = (-m²n) (8 + 7a)
Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.
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Line H has a gradient of 7.
Line K is perpendicular to line H
What is the gradient of line K
Answers
The gradient of the line K that is perpendicular to the line H that has a gradient of 7 is -1/7
What is the perpendicular lines?Perpendicular lines are lines that form a right angle (90 degrees angle) at the point of their intersection, in which the slope of one of lines is the negative reciprocal of the slope of the other line.
The gradient of the line H = 7
The relationship between the lines K and line H is; Line K is perpendicular to the line H
The slope of a line a, which is perpendicular to another line b with slope m is; -1/m
Therefore, the slope of the line K is -1/7
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Can a quadratic equation have no x-intercept?; Which equation has a graph that is a parabola with a vertex at 2 0 )?; Which equation shows the quadratic formula used correctly to solve 7 x 2 9 X for X?; Which equation has the solutions x =- 3?
Answers
Yes, a quadratic equation can have no x-intercept at all. Generally, this happens when the equation is of the \(a^{2}\) + bx + c = 0, where a, b and c are all equal to zero.
The equation that has a graph that is a parabola with a vertex at (2, 0) is: y = - \((x - 2)^2\)
The equation that shows the quadratic formula used correctly to solve 7x2 + 9x for x is: x = [- 9 +/- \(\sqrt{(81 - 28)}\)] / 14
The equation that has the solutions x = -3 is: \(x^2 - 6x + 9 = 0\).
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PLEASE HELP ME ITS DUE IN AN HOUR!!!!!
Answers
Answer:
its would be 1.22
Step-by-step explanation:
Is x greater than, less than, or equal to
73, degrees?
Answers
Answer:
equal
Step-by-step explanation:
it is the same thing as 73 degrees on the other side because it is a vertical angle so therefore its equal
I need help with this question
Answers
Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours
What is the number of hours Sarah and Penelope worked?This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.
Let's assume that Sarah worked x hours.
Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.
Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.
Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.
The total number of shirts ironed by both Sarah and Penelope is 475 shirts.
So, we can write the equation: 30x + (35/2)x = 475.
To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.
Now, we can solve for x: x = (475 * 2) / 95 = 10.
Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.
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A picture called a mosaic was made from 172,435 small clay tiles. What is the value
the digit 2 in 172,435?
A. 200
B. 2.000
C. 20.000
D. 200.000
Answers
Answer:
It would be 2,000
Step-by-step explanation:
let f(r) be the number of riders on a bus r hours after 8 am. Explain the meaning of the statement f(5)=23.
Answers
Answer:
See explanation
Step-by-step explanation:
Given
f(r) => Number of people in the bus after 8am
Required
Interpret f(5) = 23
Going by the analysis in the question, the interpretation goes this:
5 hours after 8 am, there are 23 riders on a bus
We can also interpret as:
There are 23 riders on a bus at 1 pm
Since 1 pm = 5 hours after 8am
the table represents a function.
n: 3, 5, 7, 9, 11
g(n): 0, 2, 4, 6, 8
what is the domain of the function?
-all real numbers greater than or equal to 0
- all real numbers greater than or equal to 3
-(0,2,4,6,8)
-(3,5,7,9,11)
will Brainliest the first answer :)
Answers
The domain of the function is all real numbers greater than or equal to 3
Domain of a function are input values for which the function exists.
Given the table:
n: 3, 5, 7, 9, 11
g(n): 0, 2, 4, 6, 8
We can se that for all value of n there will always be a corresponding output vale. Hence the domain of the function will exist on all real values greater than 3 since the first term of the sequence is 3.
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Convert the following measurements !!
Answers
5 yd= 15 ft
78 in= 0.65 ft
0.5 yd= 18 inch
1 Mile= 1760 yd
4.5 ft= 54 in
Leah and Chris have 3 sushi rolls to share equally for lunch. Leah wants to know how many sushi rolls she will get.
Answers
Answer:
She will get 1.5.
Step-by-step explanation:
Because 3/2 is 1.5 so they are equal
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
Answers
A) The completed table is given as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
B) the graph is attached accordingly.
C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
What is the explanation for the above response?a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.
We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.
D(L) = ceil(L/6)
Using this formula, we can complete the table as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).
b) The graph is attached.
c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.
So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.
In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
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the graph shows the average number of days of rainfall per month in Rome, Italy.
in which of the following intervals is the relationship between the month and average number of days of rainfall decreasing? Select all that apply.
A. June to August
B. August to October
C. December to February
D. February to April
Answers
In the interval June to August and December to February rainfall decreasing.
What is average number of days?
7 days make up a week, there are roughly 365 days in a year, and there are 24 hours in a day. By adding all of your numbers together and dividing by the total amount of numbers, you can arrive at an average. Thus, 132 is the average amount of time periods when joined together.
From the given graph, in the interval June to August and December to February the average number of days of rainfall are decreasing.
Hence, June to August and December to February rainfall decreasing.
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What is the constant in 12r + r/2-19
Answers
Answer:
constant is - 19
Step-by-step explanation:
the constant is the term in an expression with no variable attached to it.
12r + \(\frac{r}{2}\) - 19
the only term without the variable r attached to it is - 19
then the constant term is - 19
Find the particular solution of the differential equation?
/=5^3+9^2, when =1, =8
Answers
Answer:
\(\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} - \frac{9}{4}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Exponential Rule [Rewrite]: \(\displaystyle b^{-m} = \frac{1}{b^m}\)Calculus
Derivatives
Derivative Notation
Solving Differentials - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]: \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Property [Addition/Subtraction]: \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)
Step-by-step explanation:
*Note:
Ignore the Integration Constant C on the left hand side of the differential equation when integrating.
Step 1: Define
\(\displaystyle \frac{ds}{dt} = 5t^3 + \frac{9}{t^2}\)
t = 1
s = 8
Step 2: Integrate
[Derivative] Rewrite [Leibniz's Notation]: \(\displaystyle ds = (5t^3 + \frac{9}{t^2})dt\)[Equality Property] Integrate both sides: \(\displaystyle \int {} \, ds = \int {(5t^3 + \frac{9}{t^2})} \, dt\)[Left Integral] Reverse Power Rule: \(\displaystyle s = \int {(5t^3 + \frac{9}{t^2})} \, dt\)[Right Integral] Rewrite [Integration Property - Addition]: \(\displaystyle s = \int {5t^3} \, dt + \int {\frac{9}{t^2}} \, dt\)[Right Integrals] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle s = 5\int {t^3} \, dt + 9\int {\frac{1}{t^2}} \, dt\)[Right Integrals] Rewrite [Exponential Rule - Rewrite]: \(\displaystyle s = 5\int {t^3} \, dt + 9\int {t^{-2}} \, dt\)[Right Integrals] Reverse Power Rule: \(\displaystyle s = 5(\frac{t^4}{4}) + 9(\frac{t^{-1}}{-1}) + C\)[Right Integrals] Rewrite [Exponential Rule - Rewrite]: \(\displaystyle s = 5(\frac{t^4}{4}) + 9(\frac{1}{t}) + C\)Multiply: \(\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} + C\)Step 3: Solve
Substitute in variables: \(\displaystyle 8 = \frac{5(1)^4}{4} + \frac{9}{1} + C\)Evaluate exponents: \(\displaystyle 8 = \frac{5}{4} + \frac{9}{1} + C\)Divide: \(\displaystyle 8 = \frac{5}{4} + 9 + C\)Add: \(\displaystyle 8 = \frac{41}{4} + C\)[Subtraction Property of Equality] Isolate C: \(\displaystyle \frac{-9}{4} = C\)Rewrite: \(\displaystyle C = \frac{-9}{4}\)Particular Solution: \(\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} - \frac{9}{4}\)
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differentials Equations and Slope Fields
Book: College Calculus 10e
8. Write a paragraph proof.
Proof Given: In a plane, a is perpendicular to b, b id perpendicular to c, and c || d.
Prove: a || d
Answers
To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.
Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.
Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.
By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.
Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.
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What rigid motion maps the solid-line figure onto the dotted-line figure?
A. reflection
Brotation
Ctranslation
Answers
The rigid motion of the solid line figure is translated to the dotted line figure.
How to find the rigid motion maps a solid line?Translation describe a function that moves an object a certain distance.
In a translation, every point of the object must be moved in the same direction and for the same distance.
In translation, the object is not resized, rotated or reflected. The object usually remains the same but it moves a certain distance.
Therefore, the rigid motion maps the solid-line figure onto the dotted-line figure by translation
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A coach of a baseball team orders hats for
the players on his team. Each hat costs
$9.95. The shipping charge for the entire
order is $5.00. There is no tax on the order.
The total cost of the coach's order is less
than $125.00. Which inequality can be
used to determine the greatest number of
hats, h, the coach orders?
Answers
Answer:
9.95h + 5 ≤ 125
Step-by-step explanation:
let 'h' = number of hats
Find what percent 768 is of 3,200.
Answers
Answer:
3200 of 768 is 416.67%
Step-by-step explanation:
There's your answer hope this helps.
X% ————— 768
X= 24%
Austin has $75 to spend on sporting goods. He wants to buy a soccer ball for $12 and spend the rest of the money on soccer shorts. Each pair of soccer shorts costs$19. Which inequality can be used to find s, the number of pairs of soccer shorts he can buy?
Answers
Answer:
4
Step-by-step explanation:
Answer:
4 have a good dayStep-by-step explanation:
If one worker can assemble 9 products per hour, and another worker can assemble 6 products per hour, how long will it take them to assemble 50 products if they both start working at the same time
Answers
Answer:
3 hours 20 minutes
Step-by-step explanation:
Together, the workers can assemble 9 + 6 = 15 products per hour. So the assembly of 50 products will take ...
(50 products)/(15 products/hour) = 50/15 hours = 3 1/3 hours
The two workers can assemble 50 products in 3 1/3 hours.
a bit of help please?
Answers
The value of x for the chord is:
x = 12
How to find the value of x for the chord of the circle?A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.
Recall that: If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords.
Using the above principle, we can say:
3 * x = 4 * 9
3x = 36
x = 36/3
x = 12
Thus, the value of x for the chord is 12.
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Is this relation a function?
Answers
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer: 9 ft
Step-by-step explanation:
24 / (8/3)=9
Answer:
A
Step-by-step explanation:
2 2/3 x 9 =
2 x 9 = 18
2/3 x 9 = 6
6+8 = 14
Josephine is in HR and believes the population mean amount of new employee hires per year in the region is greater than 64. She would like to find evidence of this claim against the standard belief that the population mean amount of new employee hires per year is exactly 64. Josephine gathers a random sample of 56 companies from the region and calculates the sample mean amount of new employees per year to be 64.79 with a sample standard deviation of 2.77. Should the pharmacist reject or fail to reject the null hypothesis given the sample data below? H0:μ=64 versus Ha:μ>64 α=0.05 (significance level) t0=2.13 0.01
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The population mean is p = 64
The sample size is n = 56
The sample mean is \(\= x = 64.79\)
The standard deviation is \(s = 2.77\)
The null hypothesis is \(H_o : \mu = 64\)
The alternative hypothesis is \(H_a : \mu > 64\)
The test statistics \(t = 2.13\)
The level of significance is \(\alpha = 0.05\)
The p-value is \(0.01 < p-value < 0.025\)
Given that the \(p-value < \alpha\) we reject the null hypothesis
Please help with this math question!
Answers
Answer:
5. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Connections Academy Geometry10A semester exam. Does anyone have the answers im 1% away from passing.
Answers
Answer:
probably not, but if you were to post the questions without it saying on it that its an exam (because those get deleted all the time) people could help you through it. :)
Step-by-step explanation:
Evaluate the function for the indicated input
Answers
\(f(0)=0^2+0-6=\boxed{-6}\).
Hope this helps.
what will be the distance travelled at 5 seconds. PLEASE ANSWER IT I WILL MARK BRAINLIEST WHOEVER CAN ANSWER THIS PLEASE
Answers
Answer:
30 m
Step-by-step explanation:
Answer:
it is exactly 80m it is not 30m