11/12+(−7/12). Write your answer as a fraction in simplest form.
The result of the operation 11/12 + (-7/12) simplifies to 1/3, because the sum of the numerators is 4, and we keep the same denominator of 12, giving us 4/12. In simplest form, this fraction is 1/3.
Explanation:The question is asking us to perform an addition operation on two fractions. Specifically, we are asked to add 11/12 and -7/12. When adding or subtracting fractions, the most important thing is that they have the same denominator, which our fractions do. Here's how you perform the operation:
Add the numerators of the fractions: 11 + (-7) = 4.
You keep the same denominator: 12.
So, 11/12 + (-7/12) = 4/12.
To simplify this fraction, we find the greatest common divisor of 4 and 12, which is 4, and divide both the numerator and denominator by it. So, 4/12 simplifies to 1/3.
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-3(m-2n) = 5m
solve for m
Answer:
n=3n/4
Step-by-step explanation:
Pqr is a right angle. If pq=8 what is equivalent
Why cant you take the inverse of a matrix with det = 0?
A matrix with a determinant of zero is called a singular matrix and doesn't have an inverse because it indicates the system of equations it represents doesn't have a unique solution, and the transformation it performs is not reversible.
When a matrix has a determinant of zero (det A = 0), it is classified as a singular matrix and is not invertible. This characteristic implies that the matrix cannot be used to find unique solutions for a set of linear equations because such a matrix corresponds to a system of equations that has either no solution or an infinite number of solutions.
The ability to have an inverse matrix is crucial as it allows us to solve matrix equations and essentially 'undo' the transformations applied by the original matrix.
The reason why a zero determinant indicates the absence of an inverse lies in the mathematics of linear transformations.
A determinant of zero suggests that the transformation associated with the matrix collapses the dimensionality of the space, which means some information about the original vectors is lost, and hence, an inverse operation to recover the original vectors cannot exist.
To further illustrate this, consider the matrix equation AB = I, where A is our original matrix and B is its supposed inverse yielding the identity matrix I. It follows from the properties of determinants that det(AB) = det(A) x det(B).
If det(A) is zero, then the product det(A) x det(B) will also be zero, not equal to 1, which is the determinant of the identity matrix. Therefore, B cannot serve as the inverse of A.
In other words, having a non-zero determinant is a prerequisite for a matrix to have an inverse, as it ensures that the system of equations it represents is solvable and that the matrix transformation is reversible.
The sum of 4 consecutive even integers is 36, what is the 3rd largest integer in the set?
The sum of four consecutive even integers that equal 36 is broken down to find the smallest integer. Once the smallest integer is found (6), we can determine that the third largest integer in the sequence is 8.
Explanation:To solve for the third largest integer in a set of four consecutive even integers that sum to 36, we can define the smallest integer as x. The next integers would be x + 2, x + 4, and x + 6. Setting up the equation:
x + (x + 2) + (x + 4) + (x + 6) = 36
Combining like terms, we get:
4x + 12 = 36
Subtracting 12 from both sides:
4x = 24
Dividing by 4:
x = 6
Now we have our integers: 6, 8, 10, 12. The third largest integer, which is the second smallest, is 8.
In a triangle, the measure of the first angle is three timesthree times the measure of the second angle. the measure of the third angle is 80 degrees80° more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180degrees° to find the measure of each angle.
Find the coordinates of the midpoint of the segment whose endpoints are given . e(4,-4) , f (1,7)
I made a clay snake 9 5/8 inches long, but a section 1 7/8 inches long broke off. How long is the snake now?
Find the least common multiple of 3,4,5,6,10,15
The steps to do it. It says "solve for x. Each figure is a parallelogram. Show your work.
The value of x is 4.
To solve for x, we'll use the property of parallelograms that opposite angles are supplementary.
Given that one angle is [tex]\(140^\circ\)[/tex], we can set up the equation:
140 + 10x = 180
Now let's solve for x:
10x = 180 - 140
10x = 40
[tex]x = \frac{40}{10}[/tex]
x = 4
Therefore, the value of x is 4. Adjacent angles in a parallelogram are indeed supplementary.
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. time (hours) 4, 6, 8, 10 distance (miles) 212, 318, 424, 530
Answer:
The car travels 53 miles per hour.
Step-by-step explanation:
time (hours) 4 6 8 10
distance (miles) 212 318 424 530
The rate of change can be given as:
[tex]\frac{318-212}{6-4}[/tex] = [tex]\frac{106}{2}[/tex] = 53 mph
[tex]\frac{424-318}{8-6}[/tex] = [tex]\frac{106}{2}[/tex] = 53 mph
Hence, the rate of change is 53 mph or we can say the car travels 53 miles per hour.
A car travels 100 meters in 5 seconds. What is the speed of the car/7281023/14f0e74f?utm_source=registration
14. For the equation 5x + 36 = x, which value could be a solution? A)–9 B) 5 C)9 D)–5
The length of a rectangle is four more than five times its width. its perimeter is 4444 inches. find its dimensions (length and width).
What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?
3,−6,12,−24,...
You can rewrite this as:
(−1)n3⋅(1,2,4,8,...)
If we focus on 1,2,4,8...
an+1=2an
with a0=1.
This can be written out as a nice sum:
N∑n=02n=20+21+22+23+...
=1+2+4+8+...
Thus, now we can recombine everything to get:
3N∑n=0(−1)n2n
does the set of numbers form a pythagorean triple explain 24 , 10 ,26
If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor of 4, what is the equation of the new function?
A. g(x) =1/4 x2
B. g(x) = (1/4x)2
C. g(x) = 4x2
D. g(x) = (4x)2
Answer:
B is your answer
Step-by-step explanation:
g(x)=(1/4x)^2
Suppose you drop a ball from a window 10 meters above the ground. The ball bounces to 80% of its previous height with each bounce. What is the total number of meters (rounded to the nearest tenth) the ball travels between the time it is dropped and the 10th bounce?
79.3 meters
73.2 meters
89.3 meters
77.5 meters
Two slices of Dans Famous pizza have 230 calories how many calories would you expect to be in 5 slices of the same pizza
Find the GCF of the given polynomial.
16a⁴b⁴ + 32a³b⁵ - 48a²b⁶
Can someone help me with this question?
The sum of the two numbers is 50 and their difference is 4 what are the two numbers
Brandon has 7/1/2gallon of paint. He plans on using 1/1/2 gallon on each room. How many rooms will he be able to paint.
A local civic group is selling t-shirts to raise funds for Relay to Life. They plan to sell
2500 t-shirts for $10. They consider raising the t-shirt price in order to earn more
profit. For each $1 increase, they will sell 100 fewer t-shirts. Let x represent the
number of $1 increases.
a. Write a function,
Write a function, c(x), to represent the cost of one t-shirt based on the number
of increases.
b. Write a function, t(x), to represent the number of t-shirts sold based on the
number of increases.
c. Write a revenue function, r(x), for the t-shirt sell that could be used to maximize
a. Let us say that c(x) is the cost of one t shirt based on the number of increases therefore:
c = 10 + x
b. Say that t(x) is the number of t shirts sold based on the number of increases so:
t = 2500 – 100 x
b. The revenue is simply the product:
r(x) = (10 + x) (2500 – 100 x)
Combining:
r(x) = 25000 – 1000 x + 2500 x – 100 x^2
r(x) = 25000 + 1500 x – 100 x^2
Taking the 1st derivative and setting dr / dx = 0 to get the maxima:
dr / dx = 1500 – 200 x
1500 = 200 x
x = 7.5
t = 2500 – 100 x = 2500 – 100 (7.5) = 1750
Hence 1750 shirts should be sold.
A car travels 95 miles on 5 gallons of gas. give the ratio of miles to gallons as a rate in miles per gallon.
The parent function of a graph is f(x) = x2. The graph shifts a units to the left and down b units. Which function models the transformed function?
A) y = x2 - a + b
B) y = (x - a)2 - b
C) y = (x + a)2 - b
D) y = (x - b)2 - a
Answer:
Option c
Step-by-step explanation:
A parent function is given by f(x) = x²
If the graph of the parent quadratic function is shifted a units to the left then new function will become
f'(x) = (x+a)²
Now the new function f'(n) is shifted b units down then the shifted function will be
f" (x) = (x + a)² - b
Therefore, Option c. is the answer.
please help me with my math homework??
Two numbers are between 20 and 30. their greatest common factor is 4.Which two numbers could they be?
Rectangle EFGH is graphed on a coordinate plane with vertices at E(-3,5), F(6,2), G(4,-4), and H(-5,-1). Find the slopes of each side. What do you notice about the slopes of opposite sides? What do you notice about the slopes of adjacent sides?
In sakura's garden for every 5 red flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden. How maNY red flowers are in sakura'sgarden?
Answer:
25 red flowers
Step-by-step explanation:
yeah