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3 years ago

Students are going on a field

Mathematics

1 answer:

lara31 [8.8K]3 years ago

6 0

Answer:

5 buses and 3 vans were taken.

Step-by-step explanation:

x+y=8

13x+5y=80

----------------

x=8-y

13(8-y)+5y=80

104-13y+5y=80

104-8y=80

8y=104-80

8y=24

y=24/8

y=3

x+3=8

x=8-3=5

x=5, y=3. (5, 3)

5 buses and 3 vans were taken.

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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

3 years ago

Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this iso

abruzzese [7]

Complete Question

Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a² + b² = c², which in this isosceles triangle becomes a² + a² = c². By combining like terms, 2a² = c². Which final step will prove that the length of the hypotenuse, c, is StartRoot 2 EndRoot times the length of each leg?

a) substitute values for a and c into the original pythagorean theorem equation.

b) divide both sides of the equation by two, then determine the principal square root of both sides of the equation.

c) determine the principal square root of both sides of the equation.

d) divide both sides of the equation by 2.

Answer:

c) determine the principal square root of both sides of the equation.

Step-by-step explanation:

Pythagoras Theorem for a right angled triangles states that:

a²+ b²= c²

But for an Isosceles Triangle, where two sides of the triangle are equal, we have:

a²+ a² = c²

By combining like terms

2a² = c²

We square root both sides of the equation.

√2a² = √c

√2a² = c

The final step will prove that the length of the hypotenuse, c, is StartRoot 2 EndRoot times the length of each leg = √2a² = c is Option c.

4 0

3 years ago

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Jaysonn buys a car and pays by installments. Each installment is $567 per month. After 48 months , Jayson owes $1,250. What was

pogonyaev

Multiply her monthly payment by the number of months she paid so far:

567 x 48 = 27,216 paid so far.

Now add the amount she still owes:

27,216 + 1,250 = $28,466 total price.

8 0

3 years ago

Which absolute value represents a number less than |−0.14|?

____ [38]

Answer:

A- l-0.13l

Step-by-step explanation:

l-0.14l is the same as 0.14

l0.13l is the same as 0.13

l-0.18l is the same as 0.18

l-0.2l is the same as 0.2

l14l is the same as 14

The only value that is less that 0.14 is 0.13, making A the correct answer.

3 0

3 years ago

Find the value of x in the isosceles triangle

SCORPION-xisa [38]

Step-by-step explanation:

Since all 3 sides of the triangle is equal, it is not only an isosceles, but an equilateral triangle.

x = 8sin60° = 6.928 or sqrt48.

4 0

2 years ago

Read 2 more answers