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Sveta_85 [38]
2 years ago
5

Write the prime factorization of 315.

Mathematics
1 answer:
Klio2033 [76]2 years ago
6 0

3 exponent 2 × 5 exponent 1 × 7 exponent 1

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Solve the system of equations using matrices. Use the Gauss- Jordan elimination method And find a solution set
KATRIN_1 [288]
\begin{gathered} x+y+z=4 \\ x-y-z=0 \\ x-y+z=8 \\ \text{The system using matrix is} \\ \begin{bmatrix}{1} & {1} & {1}, & {4} \\ {1} & {-1} & {-1,} & {0} \\ {1} & {-1} & {1,} & {8}{}{}\end{bmatrix}\rightarrow F2=F2-F1=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {-2} & {-2,} & {-4} \\ {1} & {-1} & {1,} & {8}{}{}\end{bmatrix} \\ \rightarrow F3=F3-F1=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {-2} & {-2,} & {-4} \\ {0} & {-2} & {0,} & {4}{}{}\end{bmatrix}\rightarrow F2=-\frac{1}{2}F2 \\ =\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {-2} & {0,} & {4}{}{}\end{bmatrix}\rightarrow F3=F3+2F2=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {0} & {2,} & {8}{}{}\end{bmatrix}\rightarrow F3=\frac{1}{2}F3 \\ =\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {1,} & {2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix}\rightarrow F2=F2-F3=\begin{bmatrix}{1} & {1} & {1}, & {4} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix} \\ \rightarrow F1=F1-F3=\begin{bmatrix}{1} & {1} & {0}, & {0} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix}\rightarrow F1=F1-F2 \\ =\begin{bmatrix}{1} & {0} & {0}, & {2} \\ {0} & {1} & {0,} & {-2} \\ {0} & {0} & {1,} & {4}{}{}\end{bmatrix} \\ \text{Therefore, the solution is }x=2,\text{ y=-2 and z=4} \end{gathered}

6 0
1 year ago
In ΔJKL, the measure of ∠L=90°, JL = 24, LK = 7, and KJ = 25. What is the value of the sine of ∠K to the nearest hundredth?
Shalnov [3]

Hi the picture has the answer and work, if you have any questions feel free to ask!!

7 0
3 years ago
A plane is scheduled to complete a 1,792-mile flightin 3.5 hours. In order to complete the trip on time, what should be the plan
deff fn [24]

Answer:

  512 mph

Step-by-step explanation:

The relevant relation is ...

  speed = distance/time

  speed = 1792 mi/(3.5 h) = 512 mi/h

The plane's average rate of speed should be 512 miles per hour.

5 0
3 years ago
A fourth degree polynomial equation is shown below.
natita [175]
<span> 4x^2-8x-12 =
(x -3) * (x +1)

4x^2-24x+32
</span><span>(x -4) * (x -2)

</span>Factored Form
(x -3) * (x +1) * <span>(x -4) * (x -2) = 0

x = 3
x = -1
x = 4
x = 2

All four roots are real numbers and so the graph crosses the x-axis four times.  The graph of the equation would resemble a "W".


</span>
6 0
3 years ago
Find the value of x. Round to the nearest tenth
VladimirAG [237]

Answer:

36.869 or 36.87

Step-by-step explanation:

first, you find which trig function you are using. in this case, tangent.

then, you put calculate the arctan(3/4) which is 36.96989765

7 0
3 years ago
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