The solution to a system equations is (5,-19). Chose two equation that might make up the system
Answers
The system of equations that might make up the system is
Equation 1: y = 2x - 29
Equation 2: y = -3x - 4
To determine two equations that could make up the system of equations with the solution (5, -19), we can consider the general form of a linear equation: y = mx + b, where m represents the slope and b represents the y-intercept.
Equation 1: Let's consider an equation with a slope of 2 and a y-intercept of -29:
y = 2x - 29
Equation 2: Let's consider an equation with a slope of -3 and a y-intercept of -4:
y = -3x - 4
Both equations are linear and can form a system of equations. By substituting x = 5 and y = -19 into these equations, we can verify if they indeed yield the solution (5, -19).
For Equation 1:
-19 = 2(5) - 29
-19 = 10 - 29
-19 = -19 (true)
For Equation 2:
-19 = -3(5) - 4
-19 = -15 - 4
-19 = -19 (true)
Therefore, the system of equations that might make up the system is:
Equation 1: y = 2x - 29
Equation 2: y = -3x - 4
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Related Questions
if a fair die is rolled 5 times, what is the probability, rounded to the nearest thousandth, of getting at least 2 fours?
Answers
So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.
What is the simple definition of probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
According to the given information:The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:
P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)
Using the binomial formula, we can calculate each of these probabilities:
P(X=k) = (n choose k) p^k (1-p)^(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.
P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608
P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322
P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013
P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003
Therefore,
P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943
So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.
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The equation w(w + 6) = 40 represents the area of a rectangle where w represents the width. What are the dimensions of the rectangle?
Answers
Answer:
The dimensions are thus 4 by 10 units
Step-by-step explanation:
Rewrite w(w + 6) = 40 in standard quadratic form ax^2 + bx + c = 0:
w^2 + 6w - 40 = 0
This factors as follows:
w^2 + 6w - 40 = 0 => (w + 10)(w - 4) = 0.
Solving for w, we get w = 4 (and also the unhelpful w = -10).
The width of the rectangle is 4 and the length is 4 + 6, or 10.
The dimensions are thus 4 by 10 units, with area = 40 units^2
the boxplot shows the fuel economy ratings for 67 subcompact cars with the same model year. some summary statistics are also provided. the extreme outlier is an electric car whose electricity usage is equivalent to 112 miles per gallon. if that electric car is removed from the data set, how will the standard deviation be affected? the iqr?
Answers
The IQR measures the spread of the middle 50% of the data.
Without knowing the actual values of the fuel economy ratings or the summary statistics, we cannot provide an exact answer. However, we can make some general observations about the effects of removing an extreme outlier on the standard deviation and the interquartile range (IQR).
First, the standard deviation measures the spread of the data around the mean. Removing an extreme outlier that is far from the mean could potentially decrease the standard deviation, as the remaining values may be more tightly clustered around the mean. However, the effect on the standard deviation will depend on the exact values of the data points and how much they vary from the mean.
Second, the IQR measures the spread of the middle 50% of the data. Removing an extreme outlier that is far from the bulk of the data may not have a significant effect on the IQR, as the remaining.
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can someone help me pls !!!!!!!
Answers
2-3
3-50
4- -5
5-32
6-18
7- (-96)
8-48
11-78
12-42
13- (-12)
14-37
15-1159
16-27
17-9
18-72
Mark as brainliest took so long pls
An online office supply store has 30 boxes of white printer paper, 10 boxes of colored
printer paper, 5 ink printer cartridges, 7 laser printer cartridges. Thomas selects an
item at random. Based on the given information, which statement is true?
Answers
Quadrilateral WXYZ is a rectangle. Find each measure if m<1 = 30 . (Lesson 6-4 )
m<8
Answers
In a rectangle WXYZ, if the measure of angle 1 is 30 degrees, then the measure of angle 8 can be determined.
A rectangle is a quadrilateral with four right angles. In a rectangle, opposite angles are congruent, meaning they have the same measure. Since angle 1 is given as 30 degrees, angle 3, which is opposite to angle 1, also measures 30 degrees.
In a rectangle, opposite angles are congruent. Since angle 1 and angle 8 are opposite angles in quadrilateral WXYZ, and angle 1 measures 30 degrees, we can conclude that angle 8 also measures 30 degrees. This is because opposite angles in a rectangle are congruent.
Since angle 3 and angle 8 are adjacent angles sharing a side, their measures should add up to 180 degrees, as they form a straight line. Therefore, the measure of angle 8 is 180 degrees minus the measure of angle 3, which is 180 - 30 = 150 degrees.
So, if angle 1 in rectangle WXYZ is 30 degrees, then angle 8 measures 150 degrees.
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Let v
1
=
⎣
⎡
1
2
1
−2
3
⎦
⎤
,v
2
=
⎣
⎡
2
5
−1
3
−2
⎦
⎤
,v
3
=
⎣
⎡
1
3
−2
5
−5
⎦
⎤
,v
4
=
⎣
⎡
3
1
2
−4
1
⎦
⎤
,v
5
=
⎣
⎡
5
6
1
−1
−1
⎦
⎤
Let W:={w∈R
5
∣w=a
1
v
1
+a
2
v
2
+a
3
v
3
+a
4
v
4
+a
5
v
5
} 1- Find bases Q of W. 2- What is the dimension of W. 3- Orthogonalize Q using Gram-Schmit orthogonalization. 4- Let B=
⎣
⎡
1
2
1
−2
3
2
5
−1
3
−2
1
3
−2
5
−5
3
1
2
−4
1
5
6
1
−1
−1
⎦
⎤
find the range(B), the columns space of B, the rank of B and the null space of B.
Answers
1- The basis Q of W is Q = {v1, v2, v3, v4, v5}. 2- The dimension of W is 5. 3- The orthogonalized vectors of Q using Gram-Schmidt orthogonalization are q1, q2, q3, q4, and q5. 4- The range of B, the column space of B, is the entire space spanned by the columns of B. 5- The rank of B is 5. 6- The null space of B is the trivial solution, as there is no non-zero vector x that satisfies Bx = 0.
1- To find a basis Q of W, we need to find linearly independent vectors in W. We can start by considering the given vectors v1, v2, v3, v4, and v5 and check if any linear combination of these vectors can be written as zero. If not, then these vectors form a basis for W.
By performing row operations on the augmented matrix [v1 | v2 | v3 | v4 | v5], we can row reduce it to obtain the following row-echelon form:
⎣ ⎡ 1 2 1 −2 3 ⎦ ⎤ * a1 + ⎣ ⎡ 2 5 −1 3 −2 ⎦ ⎤ * a2 + ⎣ ⎡ 1 3 −2 5 −5 ⎦ ⎤ * a3 + ⎣ ⎡ 3 1 2 −4 1 ⎦ ⎤ * a4 + ⎣ ⎡ 5 6 1 −1 −1 ⎦ ⎤ * a5 = w
The row-echelon form shows that the vectors v1, v2, v3, v4, and v5 are linearly independent since there are no non-zero rows without a pivot. Therefore, a basis Q of W is Q = {v1, v2, v3, v4, v5}.
2- The dimension of W is equal to the number of vectors in a basis of W. In this case, the dimension of W is 5 since Q = {v1, v2, v3, v4, v5} contains 5 linearly independent vectors.
3- To orthogonalize Q using Gram-Schmidt orthogonalization, we can apply the Gram-Schmidt process to the vectors in Q. Starting with v1 as the first vector, we can compute the orthogonal vectors by subtracting the projection of the vectors onto the previous orthogonal vectors.
After applying the Gram-Schmidt process, we obtain the following orthogonal vectors:
q1 = v1
q2 = v2 - proj(v2, q1)
q3 = v3 - proj(v3, q1) - proj(v3, q2)
q4 = v4 - proj(v4, q1) - proj(v4, q2) - proj(v4, q3)
q5 = v5 - proj(v5, q1) - proj(v5, q2) - proj(v5, q3) - proj(v5, q4)
4- Let B be the matrix with columns v1, v2, v3, v4, and v5:
B = [v1 | v2 | v3 | v4 | v5]
The range of B, also known as the column space of B, is the span of the columns of B. In other words, it is the set of all possible linear combinations of the columns of B. Since B has linearly independent columns, the range of B is the entire space spanned by the columns.
The rank of B is equal to the number of linearly independent columns in B. In this case, since the columns of B are linearly independent, the rank of B is 5.
The null space of B, also known as the kernel of B, is the set of all vectors x such that Bx = 0. In this case, the null space of B is the trivial solution since the columns of B are linearly independent and there is no non-zero vector x that satisfies Bx = 0.
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Which of the following shapes are quadrilaterals?
please help asap I'll make brainliest
Answers
Explanation:
A quadrilateral has four sides, and each side is a straight line.
Quad = 4
Lateral = side
This means we go for choices A and C.
Choice B is ruled out because of the curved side on the right.
Choice D is ruled out because it has 5 sides instead of 4.
Determine whether the Mean Value theorem can be apolied to f on the closed interval (a,b) ( (5elect all that appiy.) f(x)=[x 3
,(1,2) Wes, the Mean Vake Theorem can be applied, No, because f is nok continucus on the cloted interval {a,b} No, because fis not differentiable in the open interyal (a,b). None of the above. If the Mean Value Theorem can be appiled. find all values of cin the open interval (a,b) such that f(C)=f(b)=f(a). Enter vour answern as a coinma-strarated list. Hi the Mean Value Theorero eannot be applied, enter Na.)
Answers
The only value of `c` in the open interval `(1, 2)` such that `f(c) = f(b)
= f(a)` is
`c = 1`.
`a = 1` and
`b = 2`.Continuity: The function
\(`f(x) = x^3`\) is continuous everywhere, so it is continuous on the closed interval `[1, 2]`.Differentiability: The function
\(`f(x) = x^3`\) is differentiable everywhere, so it is differentiable on the open interval `(1, 2)`.
Therefore, by the Mean Value Theorem, there exists a number `c` in the open interval `(1, 2)` such that `f(b) - f(a) = f'(c)(b - a)`. So the Mean Value Theorem can be applied to \(`f(x) = x^3`\) on the closed interval `[1, 2]`.Now, we need to find all values of `c` in the open interval `(a, b)` such that `f(c) = f(b)
= f(a)`.So,
`f(a) = f(1)
\(= 1^3\)
= 1` and
`f(b) = f(2)
\(= 2^3\)
= 8`.To find `c`, we need to solve the equation
`f(c) = f(b)
= f(a)` i.e.,
\(`c^3 = 1^3`.\) So,
`c = 1`.Therefore, the only value of `c` in the open interval `(1, 2)` such that
`f(c) = f(b)
= f(a)` is
`c = 1`.
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A slushy machine at 7-Eleven holds 39 liters of wild cherry slushy. How many 0.6 liter slushies can be dispensed before the machine is completely empty?
PLS HELP!!!!
Answers
Answer:
65
tep-by-step explanation:
Brainliest tysmmm you are my 5000 points tysmmmmm
Compare the expressions if a is less than b
-12.7a...-12.7b
What sign should be between -12.7a and -12.7b?
Answers
The required sign between -12.7a and -12.7b should be greater than sign (>).
If a is less than b, then -12.7a will be greater than -12.7b, because multiplying a smaller number by a negative constant (-12.7 in this case) will result in a larger negative value than multiplying a larger number by the same constant.
To see this, suppose we have two positive numbers x and y such that x < y. Then, multiplying both by a negative constant c will result in two negative numbers with magnitudes that are greater for x:
cx < cy, because c is negative and (x < y)
Therefore, if a is less than b, then:
-12.7a > -12.7b
So the sign between -12.7a and -12.7b should be greater than sign (>).
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what is the answer of 3/5013
Answers
Answer:
0.0006 or 1/1671
I hope it helps.
Answer:
Step-by-step explanation:
Test the exactness of ODE, if not, use an integrating factor to make exact and then find general solution: (2xy-2y^2 e^3x)dx + (x^2 - 2 ye^2x)dy = 0.
Answers
It is requred to test the exactness of the given ODE and then find its general solution. Then, if the given ODE is not exact, an integrating factor must be used to make it exact.
This given ODE is:(2xy - 2y²e^(3x))dx + (x² - 2ye^(2x))dy = 0.To verify the exactness of the given ODE, we determine whether or not ∂Q/∂x = ∂P/∂y, where P and Q are the coefficients of dx and dy respectively, as follows: P = 2xy - 2y²e^(3x) and Q = x² - 2ye^(2x).Then, we have ∂P/∂y = 2x - 4ye^(3x) and ∂Q/∂x = 2x - 4ye^(2x).Thus, since ∂Q/∂x = ∂P/∂y, the given ODE is exact.To solve the given ODE, we have to find a function F(x,y) that satisfies the equation Mdx + Ndy = 0, where M and N are the coefficients of dx and dy respectively. This is accomplished by integrating both P and Q with respect to their respective variables. We have:∫Pdx = ∫(2xy - 2y²e^(3x))dx = x²y - y²e^(3x) + g(y), where g(y) is a function of y. We differentiate both sides of this equation with respect to y, set it equal to Q, and then solve for g(y). We have:(d/dy)(x²y - y²e^(3x) + g(y)) = x² - 2ye^(2x)Thus, g'(y) = 0 and g(y) = C, where C is a constant.Substituting the value of g(y) in the equation above, we get:x²y - y²e^(3x) + C = 0, as the general solution.The given ODE is exact, so we can solve it by finding a function that satisfies the equation Mdx + Ndy = 0. After integrating both P and Q with respect to their respective variables, we find that the general solution of the given ODE is x²y - y²e^(3x) + C = 0.
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4×5+-8÷(7×9) what is the answer?
Answers
Answer:
19.87301587
Step-by-step explanation:
Answer:
Step-by-step explanation:
Ok, so you would use PEMDAS, which is the correct order in which you would need to solve an equation. The idea is that the operations that come first would have to be solved first.
If you don't know it, PEMDAS is:
Parentheses
Exponents
Multiplication/division
Addition/subtraction
In this case, you would need to solve the parentheses. (7x9) is 63.
It would be rewritten as 4x5-8/63
There are no exponents, so you can skip the next operation.
Then you would do multiplication next, which would be 4x5 = 20
The equation would be rewritten as 20-8/63
-0.126984127 is -8/63
Lastly, 19.8730159 is the result of 20-0.126984127
Hope this helps!
The mean of 16, X, 3, 14,57 is 22. Find
Х
Answers
Answer:
20
Step-by-step explanation:
Given,
The mean of 16, X, 3, 14, 57 is 22.
Therefore,
(16+X+3+14+57)/5 = 22
(16+X+3+14+57) = 110
(90+X) = 110
X = 110-90
X = 20
The value of x will be 20.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The mean of set 16, X, 3, 14, 57 is 22.
Now,
Since, The mean of 16, X, 3, 14, 57 is 22.
Hence, By definition of mean we get;
⇒ 16 + X + 3 + 14 + 57 / 5 = 22
Solve for x as;
⇒ 90 + X / 5 = 22
⇒ 90 + X = 22 × 5
⇒ 90 + X = 110
⇒ X = 110 - 90
⇒ X = 20
Thus, The value of x will be 20.
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The enrollment at MSU i decribed by the function
f(x) = 250x 6000, where x i the number of year ince 2010. I. Find the enrollment in 2016. II. In what year will the enrollment reach
10,000?
Answers
(i) The enrollment in 2016 year will be 7500.
(ii)In 2026 the enrollment will reach 10000.
The act of putting yourself or someone else onto the official list of members of a course, college or university, or group.To build support among women, politicians can propose and implement a number of different programmes that directly or indirectly affect female enrolment.During the enrolment period on average 3700 of the eligible 4822 persons were available for screening.
Given,
f(x) = 250x + 6000, where x is the number of years since 2010
(i) In 2016 the value of x will be = 6 years
So, f(x) = 250*6 + 6000
f(x) = 1500+6000
f(x) = 7500
Thus, the enrollment in 2016 year will be 7500.
(ii) Given the enrollment will be 10000
So, f(x) =10000
250x + 6000 =10000
x=16
Therefore, in 2026 year the enrollment will reach 10000.
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Select all the statements about the number 2-^3 that are true. 2-^3 is equal to -8
Answers
The true statement about the number 2^(-3) is that it is equal to 0.125, not -8
I'm sorry, but the statement "2-^3 is equal to -8" is not true. The correct calculation for 2 raised to the power of -3 is as follows:
2^(-3) = 1 / (2^3) = 1 / 8 = 0.125
The exponent of -3 signifies that we are calculating the reciprocal or inverse of the base number raised to the power of 3. In this case, the base number is 2, and raising it to the power of -3 results in the reciprocal, which is 1/8 or 0.125.
It's important to note that negative exponents indicate the use of fractions or decimals in the calculations. In this context, the negative exponent signifies the inverse or reciprocal of the base number raised to a positive exponent.
Therefore, the true statement about the number 2^(-3) is that it is equal to 0.125, not -8.
It's crucial to understand the concept of exponentiation and the rules associated with it. Negative exponents have specific meanings and should be handled correctly to avoid mathematical errors or misunderstandings.
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Given that measure angle 1 is a complement of measure Angle 2 and mAngle2 = 17º, find measure angle 1.
Answers
What is the area of this figure???
Answers
Answer:
24 mm squared
Step-by-step explanation:
3 x 4 x 1/2 = area of the triangle
4 x 3 = area of the rectangular top left
1 x 6 = area of the bottom rectangle
3 x 4 = 12 x 1/2 = 6
4 x 3 = 12
6 x 1 = 6
6 + 12 + 6 =24
Gaste el 60% de lo que no gasté: del resto perdí el 40% de lo que no perdí. De lo que me quedaba no ahorré 50% más de lo que ahorré. Si lo que ahorré es de S/. 70: ¿Cuánto tenia al principio?
Answers
Question in pic! ANSWER ASAP! will give brainliest!
Answers
Answer:
3,-4
Step-by-step explanation:
Please help and explain.
Answers
Answer:
$y=\frac{-2}{9}x+\frac{61}$
Step-by-step explanation:
For two lines to be parallel to each other, it means they have to have the same slope. So, the question is really asking for the line through $(8, 5)$ that has the same slope as the line shown.
We can start by finding the slope of the line shown. Recall that given two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$, the slope of the line between them is $\frac{y_{2}-y_{1}}{x_{2}-x{1}}$, or more commonly remembered as rise over run. Plugging in the points $(-3, 1)$ and $(6, -1)$ into the equation for the slope, we see that the slope of the line shown is $\frac{-1-1}{6-(-3)}=\frac{-2}{9}$.
We recall that the point-slope form of a line is such that given a point $(x_{1}, y_{1})$ and the slope $m$, the equation for a line with that slope through the given point is $y-y_{1}=m(x-x_{1})$(Note: divide by $x-x_{1}$. What does that remind you of?). Plugging in our point and slope, we have that the equation for the line we want is $y-5=\frac{-2}{9}(x-8)$. Expanding the right-hand side gives $y-5=\frac{-2}{9}x+\frac{16}{9}$.
Adding $5$ to both sides gives the desired $\boxed{y=\frac{-2}{9}x+\frac{61}}$
A player in a game must roll a fair six-sided number cube and then flip a coin. What is the probability of a player rolling 4 and then flipping a heads?
Answers
Answer:
Step-by-step explanation:
P(4) = 1/6
P(h) = 1/2
P(both) = 1/2 * 1/6 = 1/12
what is 1500 rounded off to the nearest thousand
Answers
Answer:
2000
Step-by-step explanation:
Look at the number in the hundreds position. It is a 5, so the number will be rounded up. So 2000 will be the answer.
Have a great day! :D
Answer:
2000
Step-by-step explanation:
whenever we round and the \(unit\) is the exact same place as we're rounding to we round the digit after it
1500 ⇒ 2000
whenever the digit is at the halfway point we round up
branliest please :)
Find the equation of the tangent line to y = tan? (2x) at x =-* tan² (2x) = {tan (2x)² J = 2 (tan (2x)) y =2/tan 2x) (sec²(2x 1/2)
Answers
To find the equation of the tangent line to the curve y = tan²(2x) at x = π/4, we need to determine the slope of the tangent line at that point and then use the point-slope form of a line to write the equation.
First, let's find the derivative of y with respect to x. Using the chain rule, we have:
dy/dx = 2tan(2x) sec²(2x).
Now, let's substitute x = π/4 into the derivative:
dy/dx = 2tan(2(π/4)) * sec²(2(π/4))
= 2tan(π/2) * sec²(π/2)
= 2(∞) * 1
= ∞.
The derivative at x = π/4 is undefined, indicating that the tangent line at that point is vertical. Therefore, the equation of the tangent line is x = π/4. Note that the equation y = 2/tan(2x) (sec²(2x) + 1/2) is not the equation of the tangent line, but rather the equation of the curve itself. The tangent line, in this case, is vertical.
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Do YOU currently have earned or unearned income? Where do you get this money from?
Answers
Answer:
Earned Income
Step-by-step explanation:
I get this money from chores I do around the house and my side job of selling sandwiches to my classmates (this is just an example you can personalize it)
the graphic shows a sample 401k investment. a sample 401 (k) investment has an annual contribution of 5,000 dollars, employer match of 5 percent, employer contribution of 2500 dollars, and total contribution of 7500 dollars. based on the graphic, what advantage does this 401k have over other types of investments?
Answers
401(k) investment has over other types of investments is the employer match and contribution.
The graphic shows that for the sample 401(k) investment, there is an annual contribution of $5,000 from the individual. Additionally, there is an employer match of 5% and an employer contribution of $2,500, bringing the total contribution to $7,500.
The advantage of this 401(k) investment is that the employer is providing additional funds towards the individual's retirement savings. The employer match means that for every dollar the individual contributes, the employer contributes an additional 5 cents. This is essentially free money added to the investment, which can significantly boost the overall savings over time.
Furthermore, the employer contribution of $2,500 further enhances the advantage of this 401(k) investment. This contribution is made by the employer without any additional cost to the individual, increasing the overall investment amount.
Compared to other types of investments, such as individual retirement accounts (IRAs) or taxable investment accounts, the employer match and contribution in a 401(k) provide an immediate boost to the individual's retirement savings.
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Triangle ABC ~ triangle DEF. Use the image to answer the question. Determine the measurement of DF.
Answers
Answer:
3.04
Step-by-step explanation:
df/7.6=4.4/11
11df=4.4×7.6
df=4.4×7.6/11
df=3.04
Help with this quistion
Answers
Answer:
3 root 7 the 1st one
Step-by-step explanation:
how can i simplify 11 to the 6th power over 11 to the 4th power?
Answers
Answer:
11² = 121
Step-by-step explanation:
When you divide powers with the same base, subtract the exponents.
\( \dfrac{11^6}{11^4} = 11^{6 - 4} = 11^2 = 121 \)
Answer:
121
Step-by-step explanation:
11 to the 6 power = 1771561
11 to the 4 power = 14641
1771561/14641 = 121