Answer:
49
Step-by-step explanation:
If the smaller number is
x
, then the larger number is
2
x
−
3
Explanation:
(
x
)
+
(
2
x
−
3
)
=
75
3
x
−
3
=
75
3
x
=
78
x
=
26
The numbers are 26 and 49.
The value of the larger number will be 26.
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 sum of two numbers is 75.
And, The second number is three less than twice the first.
Now,
Let the larger number = x
So, The second number = 2x - 3
Since, The sum of two numbers is 75.
Hence, We can formulate;
⇒ x + 2x - 3 = 75
⇒ 3x - 3 = 75
⇒ 3x = 78
⇒ x = 26
Thus, The value of the larger number will be 26.
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__:11= 1/3 :6
Pls fill in the blank number
Answer:
x=11/18 or 0.61
Step-by-step explanation:
Let x represent the blank
[tex]As\ x:11::1/3:6\ form\ a\ proportion,\ we\ may\ use\ the\ ratio\ method\ to\ find\ x.\\\\Hence,\\x:11::1/3:6\\6x=1/3*11\\x=11*1/3*1/6\\x=11*1/18\\x=11/18[/tex]
Let the polynomial p be the function of x. The graph of the polynomial has four zeros at
3, -4/3, -1, and 0. Select all the expressions that could represent p.
A. – 2x(x − 3)(x+3)(x + 1)^2
B. 2x(x + 3)(x + 3)(x+1)
C. - x(x − 3)(3x + 4)(2x + 2)
D. - *x(x − 3)(4x + 3)(x + 1)
E. 2x(x − 3)(3x + 4)(x - 1)^2
Which problem situation best matches the equation 10 + 2x = 16?
Situation A: Angie bought peaches for $2 per pound and laundry detergent
for $10. She spent a total of $16. How many pounds of peaches did Angie buy?
Situation B: Angie bought peaches for $10 per pound and laundry detergent
for $2. She spent a total of $16. How many pounds of peaches did Angie buy?
Answer:
situation a and she bought 3 pounds
Step-by-step explanation:
Answer: I would say A because $10 per pound seems to much and laundry detergent to turn out as $16
round 1.456 to nearest hundredths
Answer:
1.46
Step-by-step explanation:
Answer:
Solution steps:
Step 1: Locate and underline the whole number place (.) and look to the right (4):
1.456
Step 2: The digit to the right (4) is 4 or below. So, we replace it by a 0 (zero), then we get 1 as the answer.
In short: 1.456 rounded to the nearest whole number is 1.
QUESTION 9 1 Let A = (2²). 21 9.1 Find the eigenvalues of A. (3) 9.2 Find bases for the eigenspaces of A. (6) 9.3 Is A diagonalisable? Give reasons. (1) 9.4 Find a matrix P and a diagonal matrix D such that P-¹AP = D. (2) 9.5 Find A²3. (You may write 223, for example, as it is without calculating its value.) (4) 9.6 Use the above to solve the following system of differential equations: (6) 3/₁ = x₁ + 2x₂ 3/₂ = 2x1 + x₂
1. The eigenvalues of matrix A are 2 and 3.
2. The bases for the eigenspaces of A are {(1, -1)} and {(3, 1)}.
3. A is diagonalizable because it has distinct eigenvalues and the sum of the dimensions of its eigenspaces is equal to the dimension of the matrix.
4. The matrix P is [1, 3; -1, 1], and the diagonal matrix D is [2, 0; 0, 3], such that P^(-1)AP = D.
5. A^23 is equal to 2^23, which can be written as 223.
6. The system of differential equations can be solved using the matrix equation X' = PX, where X is the vector [x1; x2] and P is the matrix [1, 2; 2, 1].
1. To find the eigenvalues of matrix A, we solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue. By calculating the determinant, we get (2-λ)(2-λ) - 1 * 1 = 0, which simplifies to λ^2 - 4λ + 3 = 0. Solving this quadratic equation, we find the eigenvalues λ = 2 and λ = 3.
2. To find the eigenspaces of A, we solve the equations (A - λI)X = 0, where X is a non-zero vector in the eigenspace corresponding to eigenvalue λ. For eigenvalue λ = 2, we have (A - 2I)X = 0, which gives the equation [0, 1; -1, 0]X = 0. The solution is X = [1, -1]. Similarly, for eigenvalue λ = 3, we have (A - 3I)X = 0, which gives the equation [-1, 1; -1, 1]X = 0. The solution is X = [3, 1].
3. A matrix is diagonalizable if it has a complete set of eigenvectors. In this case, since A has distinct eigenvalues and the sum of the dimensions of its eigenspaces (2) is equal to the dimension of the matrix (2x2), A is diagonalizable.
4. To find the matrix P and diagonal matrix D, we need to find the eigenvectors corresponding to the eigenvalues of A. The matrix P is formed by taking the eigenvectors as its columns, i.e., P = [1, 3; -1, 1]. The diagonal matrix D is formed by placing the eigenvalues on its diagonal, i.e., D = [2, 0; 0, 3]. Then, we can verify that P^(-1)AP = D.
5. A^23 means raising the matrix A to the power of 23, which is equivalent to raising each element of A to the power of 23. Since A is a 2x2 matrix, A^23 is represented as 223.
6. The system of differential equations can be solved using the matrix equation X' = PX, where X is the vector [x1; x2], X' is the derivative of X with respect to t, and P is the matrix [1, 2; 2, 1]. By solving this equation, we can find the solution for x1 and x2 as functions of t.
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Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!!!
5/6 ÷ 15/3 x 2/3 (multiplying and dividing fractions)
Answer:
25/27
Step-by-step explanation:
because
5/6÷15/3×2/3
in BODMAS =5/6×15/3×2/3
=150/54=25/27
Find the key numbers of the inequality. (Enter your answers as a comma-separated list.) x² - 2x - 24 > 0 X = Need Help? Read It Viewing Saved Work Revert to Last Response Submit Answer 3. [-/0.41 Points] DETAILS LARCOLALG10 1.8.011. Find the key numbers of the inequality. (Enter your answers as a comma-separated list.) 1 X-3 +120 X = Need Help? Read It
To find the key numbers of the inequality x² - 2x - 24 > 0, we need to determine the values of x that make the inequality true. The key numbers are the points where the expression changes sign. In this case, the key numbers are -4 and 6.
To find the key numbers, we can factor the quadratic expression x² - 2x - 24 > 0. The factored form is (x - 6)(x + 4) > 0. The inequality is satisfied when either both factors are positive or both factors are negative.
Setting each factor equal to zero, we get x - 6 = 0 and x + 4 = 0. Solving these equations, we find that x = 6 and x = -4.
Now, we need to determine the intervals on the number line where the inequality is true. We choose test values from each interval and substitute them into the inequality. For example, testing x = -5 gives (-5 - 6)(-5 + 4) > 0, which is true. Similarly, testing x = 0 gives (0 - 6)(0 + 4) < 0, which is false.
By considering the sign changes, we find that the inequality is true for x < -4 and x > 6. Therefore, the key numbers are -4 and 6, which divide the number line into three intervals: (-∞, -4), (-4, 6), and (6, ∞).
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X-1 How to solve this equation (x-1) using the difference between two cubes formula
By applying the difference between two cubes formula, the solutions to the equation (x-1) are x = 1 and the complex solutions obtained from solving x² + x + 1 = 0.
The difference between two cubes formula states that a³ - b³ = (a - b)(a² + ab + b²). In this case, we have (x³ - 1³) = 0. By applying the difference between two cubes formula, we get (x - 1)(x² + x + 1) = 0.
To solve for x, we set each factor equal to zero and solve the resulting equations:
x - 1 = 0, which gives x = 1
x² + x + 1 = 0, which can be solved using the quadratic formula or factoring methods.
The equation x² + x + 1 = 0 represents a quadratic equation, and its solutions can be obtained using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 1, b = 1, and c = 1. Substituting these values into the quadratic formula, we get:
x = (-1 ± √(1 - 4(1)(1))) / (2(1))
Simplifying further:
x = (-1 ± √(-3)) / 2
Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, the only solution to the original equation (x - 1) = 0 is x = 1.
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the set of all positive integers which leaves remainder 5 when divided by 7
On average, 4 customers per hour use the public telephone in the sheriff's detention area, and this use has a Poisson distribution. The length of a phone call varies according to a negative exponential distribution. with a mean of 5 minutes. The sheriff will install a second telephone booth when an arrival can expect to wait 3 minutes or longer for the phone
a. By how much must the arrival rate per hour increase to justify a second telephone booth?
b. Suppose the criterion for justifying a second booth is changed to the following: install a second booth when the probability of having to wait at all exceeds 0.6 Under this criterion, by how much must the arrival rate per hour increase to justity a second booth?
A. The arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone boothe.
B. The arrival rate per hour must increase by at least 1.6 customers per hour to justify a second telephone booth under the new criterion.
How to calculate arrival rateTo get the how much arrival rate must increase, we must get the expected waiting time for a customer.
Assuming;
X is the number of customers who arrive per hour
Y is the length of a phone call in minutes.
Then, X follows a Poisson distribution with λ = 4 (since 4 customers per hour use the phone on average)
Y follows a negative exponential distribution with mean μ = 5 (since the mean length of a phone call is 5 minutes).
Total time is given as sum of waiting time and length of call;
T = W + Y
The waiting time W is the difference between the time a customer arrives and the time that the phone becomes available. waiting time follows a uniform distribution where mean= 1/λ (since the arrivals follow a Poisson process);
Then we have;
E(W) = 1/(2λ) = 1/8 hours
The expected total time T that a customer spends at the phone booth is:
E(T) = E(W) + E(Y) = 1/8 + 5/60 = 11/48 hours
For a second telephone booth to be justifiable, new customer that arrives must wait 3 minutes or longer for the phone.
E(W) ≥ 1/20
To get λ,
1/(2λ) ≥ 1/20
λ ≤ 10
This means that, the arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone booth.
b. Getting how much the arrival rate per hour must increase to justify a second telephone booth under the new criterion,
we need to find the probability that a customer has to wait at all.
Let P(W > 0) be the probability that a customer has to wait.
P(W > 0) = 1 - P(W = 0)
The waiting time W follows a uniform distribution with mean 1/λ, so we have:
P(W = 0) = 1 - λ/4
The length of a phone call Y follows a negative exponential distribution with mean 5 minutes = 1/12 hours, so we have:
P(Y > t) = e^(-μt) = e^(-t/12)
The probability that a customer has to wait is given as;
P(W > 0) = 1 - P(W = 0) = λ/4
To justify a second telephone booth, the probability of having to wait at all must exceed 0.6. so we have;
P(W > 0) > 0.6
λ > 2.4
The arrival rate per hour must increase by at least 2.4 - 4 = 1.6 customers per hour to justify a second telephone booth under the new criterion.
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if 0.06(10000)+0.08x = 0.072(10000+x) , then the value of x is
Step-by-step explanation:
To solve for x, we can begin by simplifying both sides of the equation:
0.06(10000) + 0.08x = 0.072(10000 + x)
600 + 0.08x = 720 + 0.072x
0.08x - 0.072x = 720 - 600
0.008x = 120
x = 120 / 0.008
x = 15,000
Therefore, the value of x is 15,000.
If f(x) = 2x2 + 1, what is f(x) when x = 3?
O 1
O 7
O 13
O 19
Answer:
19
Step-by-step explanation:
f(x) = 2x^2 + 1
Let x= 3
f(3) = 2 * (3)^2 +1
Exponents first
= 2 * 9+1
Then multiply
= 18+1
Add
= 19
Answer:
THE ANSWER IS 19 JUST TOOK THE UNIT TEST
Step-by-step explanation:
What is slope of the line that passes through the point (0,7)and(2,9)?
solve the inequality for x ...
-5x + 20 5
a. x>5
b. x 3
d. x < -5
Answer:
a
Step-by-step explanation:
Factor completely
4x^2-1
Answer:
(2x - 1)(2x + 1)
Step-by-step explanation:
Difference of Squares: (ax + b)(ax - b) = (ax² - b²)
Answer:
4×^2-1=(2× +1)(2× -1)
Step-by-step explanation:
using a^2 - b^2 =(a+b)(a-b)
I GIVE BRAINLY. Chelsea recorded in the table below the number of minutes she spent practicing her basketball skills,
Chelsea's Basketball Practice Times
Monday Wednesday
15,35 min
12.6 min
24.666 min 30.05 min
Dubbling
Shooting
Friday
14.125 min
22.9 min
How much longer did Chelsea spend practicing her shooting on Wednesday than she spent practicing her dribbling on
Wednesday
1745 min
17.99 min
28.45 min
42.65 min
Answer:
17.45
Step-by-step explanation:
I just took the quiz good luck! :)
Answer:
17.45
Step-by-step explanation:
edge 2022
Kenya is reserving a room in a hotel in France where they use euros (€). The room charge is €75. Suppose the conversion rate is €1 = $1.298. What is the cost of the room in dollars?
Answer:
The answer is $97.35
Step-by-step explanation:
This because you would need to multiply 75x1.298 to get your answer and your conversion method is multiplying so your answer is $97.35
Hope this helps and have a great day!!
Answer:
r u indian??
Step-by-step explanation:
wow bro m an indian too
find a so that the point (1,1) is on the graph of f(x)ax)^2 3
Given that the graph of f(x) = ax² + 3 passes through the point (1,1). We are supposed to find the value of a.Since the point (1, 1) lies on the graph of the function, we can say thatf(1) = 1That is:a(1)² + 3 = 1a + 3 = 1a = 1 - 3a = -2
Therefore, the value of a is -2. Thus, the graph of the function f(x) = -2x² + 3 passes through the point (1, 1).The solution is done in 88 words.
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In order for quantity supplied to equal 6 units, the price per unit must be: a) $1. b) $2. c) $3. d) $4.
To determine the price per unit at which the quantity supplied equals 6 units, we need additional information such as the supply function or the relationship between price and quantity supplied. The price and quantity relationship in the supply function can vary depending on various factors such as production costs, market conditions, and technology.
Therefore, it is crucial to have more context or data to determine the specific price per unit required for the quantity supplied to be 6 units. In summary, without the supply function or more information, it is not possible to determine the exact price per unit at which the quantity supplied equals 6 units.
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How do I know how to determine whether a relation is a function? What is a function?
Input: Output:
-3 11
0 5
3 -1
6 -7
9 -13
Answer:
all are functions
Step-by-step explanation:
a function is when each x has a y
a relation is when 1 x has more than 1 y which makes it invalid therefore not a function
what is the slope of the line?
Answer:
15
Step-by-step explanation:
Its y2 - y1 over x2-x1
How to graph y=1/2x on a coordinate plane
Answer:
steps below but I recommend the graphing calculator on demos
Step-by-step explanation:
y= mx + b....... y= 1/2x+ 0
our b is 0 so first plot that
our slope is 1/2 so go up one and to the right twice
keep doing that and you will have your line. USE DESMOS
PLEASE HELP ME!!!!!
In △MNP, point Q is on side MN so that PM=PQ. Prove that PN>PM.
Answer:
What kind of proof do you need?
M, Q, and N are collinear, with Q between M and N.
Triangle QPM is isosceles (PM=PQ).
That makes PN greater than PQ.
If you need a formal proof, it looks as if you can use trigonometry and the law of sines.
If you need a formal two-column proof using Euclidean geometry, I'm not sure how you would do it....
Step-by-step explanation:
Rectangle A has length 3 and width 5. Rectangle B has length 12 and
width 20. Is Rectangle B a scaled copy of Rectangle A? If so, what is the
scale factor?
No, Rectangle B is not a scaled copy of Rectangle A.
Yes, the scale factor is 9.
Yes, the scale factor is 4.
Yes, the scale factor is 3.
Yes, the scale factor is 15.
Answer:
Yes, the scale factor is 4.
Step-by-step explanation:
If you times the length, 3, and the width, 5, by 4, you'll get 12 as your length and 20 as your width.
Which sequence has a common difference of four?
Answer:
An arithmetic sequence has first term 4 and common difference 8
Step-by-step explanation:
PLEASE HELP ME WITH THIS AND SHOW UR WORK PLEASEEEEEE
Answer: the answer is X=-6
Step-by-step explanation:
5x-14=8x+4 - move variable to the left-hand side and change its sign
5x-8x-14=4 - first switch it you are going to have a better understanding
5x-8x= 4=14 move constant to the right-hand side and change its sign
-3x=4+14 collect like term
-3x=18 add the numbers/ then divide both sides of the equation by -3
x=-6
A car drives 60 miles per hour. Write and solve an equation to find the number of hours it takes the
car to travel 720 miles.
Answer:840 hours
Step-by-step explanation:You have to Add to get your answer.This is how I got 840:
60+60=120
120+720=840
Your answer is:840 hours
hope this was helpful :)
What Is X? 16 times x = 1.49
16× X = 1.49
=> X = 1.49 ÷ 16
=> X = 0.093125−4 4/5÷4 i need a good answer so who can get it will get 10 credits
Answer:
we use BODMAS
-4 x 4 /5÷ 4=-16/5÷4
=-16÷1[tex]1/4[/tex]
=-16 ÷ 5/4
=-16 x 4/5
=-64/5
=12[tex]4/5[/tex]
Step-by-step explanation:
