Answer:
The expression E (3B + A) is defined. The size of the resulting matrix is (1 x 1).
Step-by-step explanation:
Let's consider the following operations between matrices.
E (3B + A)
B is a matrix of (4 x 1), that is, it has 4 rows and 1 column. Let F = 3B. This is the product of a scalar by a matrix, which results in a matrix of the same size as the original. Then, F is a matrix of (4 x 1).
Now, let's consider the sum F + A, which we well call G. We can sum F and A because they are of the same size and we will get G, a matrix of the same size, (4 x 1).
Finally, we have the product E . G. We can multiply 2 matrices of sizes (m x k) and (k x n), that is, the number of columns of the first matrix must be equal to the number of rows of the second matrix, and the resulting matrix has a size (m x n). This is the case because E is (1 x 4) and G is (4 x 1), and the resulting matrix will be (1 x 1).
Ezra has to throw a beanbag 17 feet far to reach Allie
According to the question,
The distance between Allie and Ezra's flagpoles is 15 feet
length of Allie's flagpole = 35 feet
length of Ezra's flagpole = 27 feet
Difference between Allie and Ezra's flagpole = (35 - 27) feet
= 8 feet
Now, there forms a right angled triangle, where hypotenuse is the distance that Ezra's bean bad has to cover.
Using Pythagoras theorem,
![H^{2} = B^{2} + A^{2}](https://tex.z-dn.net/?f=H%5E%7B2%7D%20%3D%20B%5E%7B2%7D%20%2B%20A%5E%7B2%7D)
where H = hypotenuse,
B= Base of the triangle
A = Altitude of the triangle
we are given,
B = 15 feet,
A = 8 feet
On substituting the values,
![H^{2} = 15^{2} + 8^{2}](https://tex.z-dn.net/?f=H%5E%7B2%7D%20%3D%2015%5E%7B2%7D%20%2B%208%5E%7B2%7D)
![H^{2} = 225 + 64\\H^{2} = 289\\H = \sqrt{289} \\H = 17\\](https://tex.z-dn.net/?f=H%5E%7B2%7D%20%3D%20225%20%2B%2064%5C%5CH%5E%7B2%7D%20%3D%20289%5C%5CH%20%3D%20%5Csqrt%7B289%7D%20%5C%5CH%20%3D%2017%5C%5C)
So hypotenuse = 17 feet
Ezra has to throw the beanbag 17 feet far in order to reach it to Allie.
To learn more about Pythagoras theorm from the given link
brainly.com/question/343682
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All three of them do exist on the line y = 2.5x + 4
In order to find the answer to this question, start by finding the line for two points. For this example, we'll use A and C.
First we need to find the slope.
(y1 - y2)/(x1 - x2)
(9 - -1)/(2 - -2)
(9 + 1)/(2 + 2)
10/4
2.5
Now using slope intercept form and point A, we can determine the intercept of that line as well.
y = mx + b
-1 = 2.5(-2) + b
-1 = -5 + b
4 = b
So now we know A and C form the line y = 2.5x + 4. We can then check if B fits that line.
y = 2.5x + 4
4 = 2.5(0) + 4
4 = 0 + 4
4 = 4 (TRUE)
Therefore, it also falls on that line.
Answer:
114.99
18 percent of 97.45 is 17.541
add them together and u get 114.99
You have to convert the lengths 3 feet in a yard and 12 inches in a foot.
10×3=30 feet
168÷12=14 feet
Then subtract, so 30-14=16
Hope this helps!!