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4 years ago

A rectangle has a length of 60 in and a width of 8 in. Given a scale factor of 4in:5ft. What is the area of the rectangle?

Mathematics

1 answer:

Scilla [17]4 years ago

8 0

Answer:

750ft²

Step-by-step explanation:

Area of rectangle = L*B

Before we find the area of the given rectangle, we need to convert the dimensions using the given scale.

Thus, dimensions of the given rectangle using the scale factor of 4in:5ft would be:

==> Length = 60in = (60*5)/4 = 75ft

Breadth or Width = 8in = (8*5)/4 = 10ft

Therefore, area of rectangle = L * B

= 75ft * 10ft

= 750 ft²

Area of rectangle = 750ft²

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Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=

ladessa [460]

Answer:

(-2, 4, -2)

x=-2, y=4, z=-2.

Step-by-step explanation:

So we have the three equations:

$4x-y-2z=-8\\-2x+4z=-4\\x+2y=6$

And we want to find the value of each variable.

To solve this system, first look at it and consider what you should try to do.

So we can see that the second and third equations both have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all xs.

Therefore, let's first isolate the variable in the second and third equation.

Second Equation:

$-2x+4z=-4$

First, divide everything by -2 to simplify things:

$x-2z=2$

Subtract x from both sides. The xs on the left cancel:

$(x-2z)-x=2-x\\-2z=2-x$

Now, divide everything by -2 to isolate the z:

$z=-\frac{2-x}{2}$

So we've isolated the z variable. Now, do the same to the y variable in the third equation:

$x+2y=6$

Subtract x from both sides:

$2y=6-x$

Divide both sides by 2:

$y=\frac{6-x}{2}$

Now that we've isolated the y and z variables, plug them back into the first equation. Therefore:

$4x-y-2z=-8\\4x-(\frac{6-x}{2})-2(-\frac{2-x}{2})=-8$

Distribute the third term. The -2s cancel out:

$4x-(\frac{6-x}{2})+(2-x)=-8$

Since there is still a fraction, multiply everything by 2 to remove it:

$2(4x-(\frac{6-x}{2})+(2-x))=2(-8)$

Distribute:

$8x-(6-x)+2(2-x)=-16\\8x-6+x+4-2x=-16$

Combine like terms:

$8x+x-2x-6+4=-16\\7x-2=-16$

Add 2 to both sides:

$7x=-14$

Divide both sides by 7:

$(7x)/7=(-14)/7\\x=-2$

Therefore, x is -2.

Now, plug this back into the second and third simplified equations to get the other values.

Second equation:

$z=-\frac{2-x}{2}\\ z=-\frac{2-(-2)}{2}\\z=-\frac{4}{2}\\z=-2$

Third equation:

$y=\frac{6-x}{2}\\y=\frac{6-(-2)}{2}\\y=\frac{8}{2}\\y=4$

Therefore, the solution is (-2, 4, -2)

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3 years ago

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Nuetrik [128]

Answer:

115 degrees

Step-by-step explanation:

The line RQ meets at 115 degrees (Look at the bottom numbers)

It's not 65 degrees because the angle is obtuse.

6 0

3 years ago

Can you rewrite 68/7 as a mixed number

fredd [130]

Answer: 9 5/7

Step-by-step explanation:

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3 years ago

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A triangle has sides with lengths of 43 millimeters, 52 millimeters, and 65 millimeters. Is it a right triangle

Mrrafil [7]

Use pythagora's theorem to test if it is a right triangle

c^2 = a^2 + b^2
65^2 = 52^2 + 43^2
4225 = 2704 + 1849
4225 =/= 4553
therefore it is not a right triangle as it does not comply to pythagora's theorem

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3 years ago

Eight year-old Alex is learning to ride a

cestrela7 [59]

Answer:

The age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years.

Therefore, the age of the horse, in human years, when Alex was born was 42 years.

Step-by-step explanation:

Current age of Alex = 8

Current age of the horse in human years = 50

Since the age of the horse is already stated in human years, it implies there is no need to convert the age of the horse again.

Therefore, since Alex is a human who was born 8 years ago, the age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years as follows:

The age of the horse, in human years, when Alex was born = 50 - 8 = 42

Therefore, the age of the horse, in human years, when Alex was born was 42 years.

This can be presented in a table as follows:

Age of Alex Age of the Horse (in human years)

Eight years ago 0 42

Current age 8 50

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