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3 years ago

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Marie has a small copy of rene magritte's famous painting, the schoolmaster. Her copy has dimensions 2 inches by 1.5 inches. The

scale of the copy is 1 in :40 cm. Find the dimensions of the original painting

1 answer:

Andrej [43]3 years ago

4 0

We just multiply the scale to the dimensions
2 in to original is: 2×40= 80 cm
or do proportions:
$\frac{2}{x}$ = $\frac{1}{40}$
= $\frac{2*40}{1}$ =x
=80 cm=x the original dimension.
Same thing to the other side.
1.5×40=60 cm
or proportions again:
$\frac{1.5}{y}$ = $\frac{1}{40}$
$\frac{1.5*40}{1}$ =y
60 cm=y
60 cm is the original dimension
80 cm times 60 cm ORIGINAL DIMENSION

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a quadrilateral has 2 right angles. the measure of the third angle is 73, what is the measure of the forth angle?

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Answer: 107 degrees.

Step-by-step explanation:

A quadrilateral is defined as a 2-dimensional closed shape which has four sides and four vertices.

By definition the interior angles of a quadrilateral add up 360 degrees.

We know that this quadrilateral has 2 right angles (which are angles that measure 90 degrees) and we know that the measure of the third angle is 73 degrees.

Let be "x" the measure of the fourth angle.

Then you can write this expression:

$360\°=90\°+90\°+73\°+x$

And finally solve for "x":

$360\°=253\°+x$

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2 years ago

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7 vinegar, and the second brand con

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Answer:

78 ml of 7% vinegar and 312 ml of 12% vinegar.

Step-by-step explanation:

Let x represent ml of 7% vinegar brand and y represent ml of 12% vinegar brand.

We have been given that chef wants to make 390 milliliters of the dressing. We can represent this information in an equation as:

$x+y=390...(1)$

$y=390-x...(1)$

We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be $0.07x$ .

The second brand contains 12 vinegar, so amount of vinegar in y ml would be $0.12y$ .

We are also told that the chef wants to make 390 milliliters of a dressing that is 11% vinegar. We can represent this information in an equation as:

$0.07x+0.12y=390(0.11)...(2)$

Upon substituting equation (1) in equation (2), we will get:

$0.07x+0.12(390-x)=390(0.11)$

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$-0.05x+46.8-46.8=42.9-46.8$

$-0.05x=-3.9$

$\frac{-0.05x}{-0.05}=\frac{-3.9}{-0.05}$

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Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.

Upon substituting $x=78$ in equation (1), we will get:

$y=390-78$

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Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.

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3 years ago

The half-life of cesium-137 is 30 years. Suppose we have a 180-mg sample. (a) Find the mass that remains after t years. (b) How

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Answer:

a) $Q(t) = 180e^{-0.023t}$

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c) 225.8 years.

Step-by-step explanation:

The following equation is used to calculate the amount of cesium-137:

$Q(t) = Q(0)e^{-rt}$

In which Q(t) is the amount after t years, Q(0) is the initial amount, and r is the rate at which the amount decreses.

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The half-life of cesium-137 is 30 years.

This means that Q(30) = 0.5Q(0). We apply this information to the equation to find the value of r.

$Q(t) = Q(0)e^{-rt}$

$0.5Q(0) = Q(0)e^{-30r}$

$e^{-30r} = 0.5$

Applying ln to both sides of the equality.

$\ln{e^{-30r}} = \ln{0.5}$

$-30r = \ln{0.5}$

$r = \frac{\ln{0.5}}{-30}$

$r = 0.023$

So

$Q(t) = Q(0)e^{-0.023t}$

180-mg sample, so Q(0) = 180

$Q(t) = 180e^{-0.023t}$

(b) How much of the sample remains after 120 years?

This is Q(120).

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$Q(120) = 180e^{-0.023*120}$

$Q(120) = 11.4$

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(c) After how long will only 1 mg remain?

This is t when Q(t) = 1. So

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$1 = 180e^{-0.023t}$

$e^{-0.023t} = \frac{1}{180}$

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$\ln{e^{-0.023t}} = \ln{0.00556}$

$-0.023t = \ln{0.00556}$

$t = \frac{\ln{0.00556}}{-0.023}$

$t = 225.8$

225.8 years.

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Answer:

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