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3 years ago

Sue has $2.80 in dimes and nickels. If she has 13 more dimes than nickels, how many of each coins does she have?

1 answer:

5 0

I have seen this question before and I think you meant 10 more dimes than nickels.

We can use substitution to answer this question. The value of a nickel is 5 cents, and we can use the variable n to represent the number of nickels. The value of a dime is 10 cents, and we can use the variable d to represent the number of dimes.

First lets figure out the equations.
.10d+.5n=2.80 (the number of nickels (n) multiplied by .5 will tell us their money value. Same thing for the dimes)
d-n=10 (since there are 13 more dimes than nickels, the number of dimes value (d) minus the number of nickels value (n) will give us 10)

Now lets isolate a variable in one of the equations, preferably the second one because it doesn't have any visible coefficients,

d-n=10
-n=10-d (subtracted the d from both sides)
n=-10+d (made the n positive)

Now that we have the value of n, we can plug it into the other equation.

.10d+.05n=2.80
.10d+.05(-10+d)=2.80 (we replaced the n with the value that we previously got)
.10d-.5+.05d=2.80 (did the multiplication)
.15d-.5=2.80 (combined like terms)
.15d=3.30 (added the .5 to both sides)
d=22 (divided both sides by the .15)

Now that we know that there are 22 dimes and we also know that there are 10 less nickels than dimes, so we can subtract 10 from 22 to get the number of nickels. 22-10=12

d=22
n=12

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3 years ago

XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3

nataly862011 [7]

<h2>Answer:</h2>

4π

<h2>Step-by-step explanation:</h2>

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = $\frac{1}{2}$ x b x h -------------(i)

Where;

A = 18 $\sqrt{3}$

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

<em>Substitute these values into equation(i) and solve as follows:</em>

18 $\sqrt{3}$ = $\frac{1}{2}$ x b x 6

18 $\sqrt{3}$ = 3b

<em>Divide through by 3</em>

6 $\sqrt{3}$ = b

Therefore, b = XZ = 6 $\sqrt{3}$

<em>Now, assume that the circle is centered at O;</em>

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180° [sum of angles in a triangle]

=> XOZ + 30° + 30° = 180°

=> XOZ + 60° = 180°

=> XOZ = 180° - 60°

=> XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

$\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}$

$\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}$

$\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}$

$\frac{1}{12} = \frac{1}{2|OZ|}$

$\frac{1}{6} = \frac{1}{|OZ|}$

|OZ| = 6

The radius of the circle is therefore 6.

<em>Now, let's calculate the length of the arc XZ</em>

The length(L) of an arc is given by;

L = θ / 360 x 2 π r ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

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3 years ago

The cells of a bacteria doubles in every 15 minutes. A scientist begins with a single cell. How many cells will be there after (

Anastaziya [24]

Step-by-step explanation:

Given that:-

1 cell = 15 minutes

So, we can concert 15 minutes to hours.

So,

60 minutes = 1 hour

1 minute = 1/60

15 minutes =

$\frac{15}{60} = 0.25 \: hrs$

Okay, now we will apply first for 0.4 hours.

$0.25 \: hrs= 1 \: cell$

$1 \: hr = \frac{1}{0.25}$

$0.4 \: hrs = \frac{0.4}{0.25}$

$= 1.6 \: cells$

$= 16 \times {10}^{ - 1} \: cells$

Now, second one:-

$10 \: hrs = \frac{10}{0.25}$

$= 40 \: cells$

$= 0.4 \times {10}^{2} \: cells$

Hope it helps :D

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3 years ago