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3 years ago

What’s the correct answer?

Mathematics

1 answer:

Julli [10]3 years ago

8 0

Answer: 6 m

This statement:

"Jared has run two-thirds of an 18-kilometer race" can be written as an equation:

$18km.\frac{2}{3}=12km$

This means two-thirds of 18 km is equivalent to 12 km

If we substract this value to the total, we have the values of the kilometers left to run:

$18km-12km=6km$

Therefore the correct option is D

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The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0

4 years ago

I am stuck on this question do you mind checking it for me

nataly862011 [7]

Solution:

Given:

$\frac{a}{b}\cdot\frac{c}{d}$

Since b and d are nonzero elements, then it is the product of two rational numbers.

Multiplying two rational numbers produces another rational number.

Therefore, the product is a rational expression.

OPTION C is the correct answer.

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1 year ago

Sharon bought 100/300/100 policy with a $100 deductible on collision and $100 deductible on comprehensive coverage.

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The answer would be 1,928.85

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3 years ago

It takes 8 men 96 days to build a tower. working at same rate, how long will it take 12 men

Kryger [21]

Answer:

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[(3•2+5)2]2-4 12356789

Gelneren [198K]

Answer:

−49427112 us the correct answer

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3 years ago