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2 years ago

A recipe for punch requires 20 grams of drink mix for 5 liters.

Mathematics

1 answer:

LuckyWell [14K]2 years ago

6 0

4 grams of drink mix is needed per liter of water

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Write an exponential equation in the form y = ab* whose graph passes through points (2, 18) and (5, 60.75).

DochEvi [55]

Let $y=ab^x,$ as described in the problem statement. Plugging in $x=2$ and $x=5$ gives us the equations $18=ab^2$ and $60.75=ab^5.$ Since $a,b$ are nonzero, we divide the second equation by the first to get $\frac{27}{8}=b^3,$ which means that $b=\frac{3}{2},$ after taking the cube root. Plugging this value for $b$ into the first equation, we now have $18=a(3/2)^2=\frac{9a}{4}.$ Solving gives $a=8,$ and our desired exponential equation is $\boxed{y=8\left(\frac{3}{2}\right)^x}.$

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2 years ago

A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the sma

Nata [24]

Answer:

The equations represent the situation is $y=2x+6$ and $y=5+3x$ .

Step-by-step explanation:

Consider the provided information.

First convert the statement into mathematical representation.

Consider the smaller number is x and the larger number is y.

y, is equal to twice the sum of a smaller number and 3.

This information can be written as: $y=2(x+3)$

Which can be further solve as:

$y=2x+6$

The larger number is also equal to 5 more than 3 times the smaller number.

This information can be written as: $y=5+3x$

Thus, the equations represent the situation is $y=2x+6$ and $y=5+3x$ .

Which can be further solve as:

$2x+6=5+3x$

$x=1$

Now, substitute the value of x in $y=5+3x$ .

$y=5+3$

$y=8$

3 0

3 years ago

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45 POINTS* The figure is reflected across the line M and then reflected across the line N. What is the resulting transformation?

Sergio039 [100]

Answer:

Reflection

Step-by-step explanation:

6 0

3 years ago

MONA LISA A visitor to the Louvre Museum in Paris wants to sketch a drawing of the Mona Lisa, a famous painting. The original pa

nydimaria [60]

You need to find a scale factor of dilation (probably contraction) to make the replica.

Given that the units of the original painting are centimeters and the units of the sheet of paper are in inches, you have to convert one of the units.

I choose to covert inches to centimeters.

To do that, use the conversion factor 1 = 2.54 cm / inch

=> 8.5 in * [2.54 cm/in] = 21.59 cm

=> 11 in * [2.54 cm/in] = 27.94 cm

Now determine the scale factor to convert 77 cm to 27.94 cm and 53 cm to 21.59 cm. That just require use of division operation:

77 / 27.94 = 2.76

53 / 21.59 = 2.45

Then the higher scale factor is the relevant one, and you have to reduce the original painting by a factor of (1 / 2.76) which will lead to fit in the sheet of paper.

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2 years ago

Which pair of angles are vertical angles?

Virty [35]

It should be B let me know if im correct

4 0

3 years ago

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