A train travels 120 km in 2 hours and 30 miniutes. what is the average speed in km/h ?

Help with matrice equations

Tasya [4]

Answer:

21) x=1, y=-1, z=2 and 23) x=3, y=-1, z=-1

Step-by-step explanation:

there are 3 equations in 21)

1) x+y-z=-2

2)2x-y+z=5

3)-x+2y+2z=1

solve for x by adding equation 2) and 1)

2)2x-y+z=5 + 1) x+y-z=-2 = 3x=3, then divide by 3 and x=1

solve for z by adding equation 1) and 3)

1) x+y-z=-2 + 3)-x+2y+2z=1

we then get a new equation, 4), by isolating z

3y+z=-1 which is 4) z=-1-3y

substitute our new equation, 4) z=-1-3y, and x=1 into equation 1) to get y

(1)+y- (-1-3y)=-2

isolate y to get y=-1

then substitute y=-1 into equation 4) to get z=2

check by substituting x=1, y=-1, and z=2 into all 3 equations

there are 3 equations

1)x+3y=0

2)x+y+z=1

3)3x-y-z=11

add equation 3) and 2) together to get x

3)3x-y-z=11 + 2)x+y+z=1

4x=12, x=3

substitute x=3 into equation 1) (3)+ 3y=0 to get y

3y=-3, y=-1

substitute x=3 and y=-1 into equation 2) to get z

(3)+(-1)+z=1, z=-1

4 0

2 years ago

Tom Johnson worked 32 hours this week for $9.25 per hour. What is Tom’s gross pay for the week?

Dominik [7]

Answer:

296 dollars

Step-by-step explanation:

5 0

2 years ago

Which expression is equivalent??? help!

dexar [7]

Answer:

The equivalent expression for the given expression $\sqrt[3]{256x^{10}y^{7} }$ is

$4x^{3} y^{2}(\sqrt[3]{4xy} )$

Step-by-step explanation:

Given:

$\sqrt[3]{256x^{10}y^{7} }$

Solution:

We will see first what is Cube rooting.

$\sqrt[3]{x^{3}} = x$

Law of Indices

$(x^{a})^{b}=x^{a\times b}\\and\\x^{a}x^{b} = x^{a+b}$

Now, applying above property we get

$\sqrt[3]{256x^{10}y^{7} }=\sqrt[3]{(4^{3}\times 4\times (x^{3})^{3}\times x\times (y^{2})^{3}\times y )} \\\\\textrm{Cube Rooting we get}\\\sqrt[3]{256x^{10}y^{7} }= 4\times x^{3}\times y^{2}(\sqrt[3]{4xy}) \\\\\sqrt[3]{256x^{10}y^{7} }= 4x^{3}y^{2}(\sqrt[3]{4xy})$

∴ The equivalent expression for the given expression $\sqrt[3]{256x^{10}y^{7} }$ is

$4x^{3} y^{2}(\sqrt[3]{4xy} )$

5 0

3 years ago

Calculate the value of each expression:<br> (-8)•(-2/3)<br> SHOW YOUR WORK:

inna [77]

Answer: $\frac{16}{3}$

Step-by-step explanation:

For this exercise it is important to remember the multiplication of signs:

$(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-$

In this case, given the following expression:

$(-8)(-\frac{2}{3})$

You can idenfity that both factors are negative. Then, the product (The result of the multiplication) will be positive.

Then, in order to get the product, you need to multiply the numerator of the fraction by -8. So, you get:

$\frac{(-2)(-8)}{3}=\frac{16}{3}$

You can notice that the numerator and the denominator of the fraction obtained cannot be divided by the same number; therefore, the fraction cannot be simplified.

3 0

2 years ago

A movie theater sends out a coupon for 85% off the price of a ticket. Write an equation for the situation, where y is the pri

ra1l [238]

Answer:

$y=0.15x$

Step-by-step explanation:

Given:

Original price of the ticket is $x$

Price after using the coupon is $y$

Coupon discount is 85% of $x=0.85x$

Therefore, the price after applying coupon is given as the difference of the original price and the coupon discount. That is,

$y=x-0.85x=x(1-0.85)=0.15x\\\therefore y=0.15x$

The graph is shown below. The graph passes through the origin as the above relationship is a proportional relationship.

The line $y=0.15x$ strictly remains in the first quadrant as both $x$ and $y$ can't be negative as they represent price of tickets and price can never have negative values. Hence, only the first quadrant has both the values of $x$ and $y$ positive.

3 0

3 years ago

A train travels 120 km in 2 hours and 30 miniutes. what is the average speed in km/h ?​

A train travels 120 km in 2 hours and 30 miniutes. what is the average speed in km/h ?