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4 years ago

Annette has 5more dimes than quarters, the total amount is $3.30. How many of each coin does she have?

Mathematics

1 answer:

faust18 [17]4 years ago

7 0

Step-by-step explanation:the answer is you have 8 quarter and 13 dimes .

Because you have 5 more dimes than quarters which will equal 3 dollars and 30 cents

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If the polygon shown below is a regular nonagon what is the value of x?

jeyben [28]

The sum of the measures of the angles of a polygon is given by (n - 2)(180), where n is the number of sides. In this case we would have (9-2)(180)=7(180)=1260. This is the sum of the angles. Since it is a regular nonagon, that means that all sides are congruent and all angles are congruent. Therefore we find the measure of each individual angle by dividing the sum, 1260, by the number of sides, 9. 1260/9=140. x forms a linear pair with one of the interior angles; that means that the interior angle, 140, added to x would give us 180. Therefore we find x by subtracting 180-140. x = 40.

3 0

3 years ago

What is the total resistance of a parallel circuit that has three loads? Load one has a resistance of 6 ohms. Load two has a res

gizmo_the_mogwai [7]

Answer:

The total resistance of these three resistors connected in parallel is $1.7143\Omega$

Step-by-step explanation:

The attached image has the circuit for finding the total resistance. The circuit is composed by a voltage source and three resistors connected in parallel: $R_1=6\Omega$ , $R_2=3\Omega$ and $R_3=12\Omega$ .

First step: to find the source current

The current that the source provides is the sum of the current that each resistor consumes. Keep in mind that the voltage is the same for the three resistors ( $R_1$ , $R_2$ and $R_3$ ).

$I_{R_1}=\frac{V_S}{R_1}$

$I_{R_2}=\frac{V_S}{R_2}$

$I_{R_3}=\frac{V_S}{R_3}$

The total current is:

$I_S=I_{R_1}+I_{R_2}+I_{R_3}=\frac{V_S}{R_1}+\frac{V_S}{R_2}+\frac{V_S}{R_3}=\frac{R_2\cdot R_3 \cdot V_S+R_1\cdot R_3 \cdot V_S+R_1\cdot R_2 \cdot V_S}{R_1\cdot R_2\cdot R_3}$

$I_S=V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}$

The total resistance ( $R_T$ ) is the source voltage divided by the source current:

$R_T=\frac{V_S}{I_S}$

Now, replace $I_S$ by the previous expression and the total resistance would be:

$R_T=\frac{V_S}{V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}}$

Simplify the expression and you must get:

$R_T=\frac{R_1\cdot R_2\cdot R_3}{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}$

The last step is to replace the values of the resistors:

$R_T=\frac{(6\Omega )\cdot (3\Omega)\cdot (12\Omega)}{(3\Omega)\cdot (12\Omega)+(6\Omega)\cdot (12\Omega)+(6\Omega)\cdot (3\Omega)}=\frac{12}{7}\Omega=1.7143\Omega$

Thus, the total resistance of these three resistors connected in parallel is $1.7143\Omega$

4 0

3 years ago

6372(52836y)+46x=665x(637y+57)

alex41 [277]

Answer:

$x=\frac{336670992y}{423605y+37859};\quad \:y\ne \:-\frac{37859}{423605}$

Step-by-step explanation:

$6372\left(52836y\right)+46x=665x\left(637y+57\right)\\6372\cdot \:52836y+46x=665x\left(637y+57\right)\\336670992y+46x=665x\left(637y+57\right)\\336670992y+46x=423605xy+37905x\\336670992y+46x-336670992y=423605xy+37905x-336670992y\\46x=423605xy+37905x-336670992y\\46x-\left(423605xy+37905x\right)=423605xy+37905x-336670992y-\left(423605xy+37905x\right)\\-423605xy-37859x=-336670992y\\-x\left(423605y+37859\right)=-336670992y\\$ $\frac{-x\left(423605y+37859\right)}{-\left(423605y+37859\right)}=\frac{-336670992y}{-\left(423605y+37859\right)}\\x=\frac{336670992y}{423605y+37859};\quad \:y\ne \:-\frac{37859}{423605}$