Answer:
y-intercept: (0,5); x-intercept: (5/2, 0)
Step-by-step explanation:
The equation of the line is given: -4x + 7 = 2y - 3.
To find the x-intercept, set y = 0 and solve for x:
-4x + 7 = 0 - 3. This becomes -4x = -10, or x = 5/2. The x-intercept is (5/2, 0).
To find the y-inercept, set x = 0 and solve for y:
0 + 7 = 2y - 3, or 2y = 10, or y = 5. Then the y-intercept is (0, 5).
The factors of 26 are one, two, 13 and 26. One and the number itself, in this case 26, are always factors. Since 26 is an even number, which means that it ends in zero, two, four, six or eight, it's evenly divisible by two. Two times 13 equals 26.
No numbers between two and 13 divide evenly into 26, so there are no more factors other than the four listed. Because two and 13 are both prime numbers, which are numbers that are only divisible by one and themselves, the prime factorization of 26 is 2 x 13. The prime factorization of a number refers to the prime numbers that multiply together to make that given number
Answer:
The infant mortality rate in Korea based on equality provided is:
Step-by-step explanation:
Since the text mentions that the infant mortality rate in Korea is equal to the criminal success rate, the two expressions must equalize and clear the variable m, which is the rate in each of the expressions:
- 7 (m + 3) - 2 = 8m + 17.2
- 7m + 21 - 2 = 8m + 17.2
- 7m + 19 = 8m + 17.2
- 19 - 17.2 = 8m - 7m
- <u>1.8 = m</u>
As you can see, once the equality of the expressions is solved, <u>a rate of 1.8 is obtained</u>.
Answer:
One of the obvious non-trivial solutions is 
.
Step-by-step explanation:
Suppose the matrix A is as follows:
![A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&3_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B11%7D%26a_%7B12%7D%26a_%7B13%7D%5C%5Ca_%7B21%7D%26a_%7B22%7D%263_%7B23%7D%5C%5Ca_%7B31%7D%26a_%7B32%7D%26a_%7B33%7D%5Cend%7Barray%7D%5Cright%5D)
The observed system 
after multiplying looks like this
![Ax=0 \iff \left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right] \cdot \left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right] =0 \iff \\ \\a_{11}x_1+a_{12}x_2+a_{13}x_3=0\\a_{21}x_1+a_{22}x_2+a_{23}x_3=0\\a_{31}x_1+a_{32}x_2+a_{33}x_3=0\\\\](https://tex.z-dn.net/?f=Ax%3D0%20%5Ciff%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B11%7D%26a_%7B12%7D%26a_%7B13%7D%5C%5Ca_%7B21%7D%26a_%7B22%7D%26a_%7B23%7D%5C%5Ca_%7B31%7D%26a_%7B32%7D%26a_%7B33%7D%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_1%5C%5Cx_2%5C%5Cx_3%5Cend%7Barray%7D%5Cright%5D%20%3D0%20%5Ciff%20%5C%5C%20%5C%5Ca_%7B11%7Dx_1%2Ba_%7B12%7Dx_2%2Ba_%7B13%7Dx_3%3D0%5C%5Ca_%7B21%7Dx_1%2Ba_%7B22%7Dx_2%2Ba_%7B23%7Dx_3%3D0%5C%5Ca_%7B31%7Dx_1%2Ba_%7B32%7Dx_2%2Ba_%7B33%7Dx_3%3D0%5C%5C%5C%5C)
Since we now that 
, where 
are the columns of the matrix A, we actually know this:
![-2\cdot \left[\begin{array}{ccc}a_{11}\\a_{21}\\a_{31}\end{array}\right] +3\cdot \left[\begin{array}{ccc}a_{12}\\a_{22}\\a_{32}\end{array}\right] -5\cdot \left[\begin{array}{ccc}a_{13}\\a_{23}\\a_{33}\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right]](https://tex.z-dn.net/?f=-2%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B11%7D%5C%5Ca_%7B21%7D%5C%5Ca_%7B31%7D%5Cend%7Barray%7D%5Cright%5D%20%2B3%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B12%7D%5C%5Ca_%7B22%7D%5C%5Ca_%7B32%7D%5Cend%7Barray%7D%5Cright%5D%20-5%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B13%7D%5C%5Ca_%7B23%7D%5C%5Ca_%7B33%7D%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
Once we multiply and sum up these 3 by 1 matrices, we get that these equations hold:
This actually means that the solution to the previously observed system of equations (or equivalently, our system ) has a non-trivial solution .
Answer:
h = 4.22 cm
Step-by-step explanation:
Mathematically, we have the volume of a cylinder as;
V = pie * r^2 * h
We have it that the radius is 6 cm
V = pie * 6^2 * h
for the sphere, we have it that;
V = 4/3 * pie * r^3
V = 4/3 * pie * 4.5^3
We can proceed to equate both volumes;
pie * 6^2 * h = 5/3 * pie * 4.5^3
pie on both sides cancel out
6^2h = 5/3 * 4.5^3
36h = 151.875
h = 151.875/36
h = 4.22 cm
