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Nookie1986 [14]
3 years ago
8

Roberta has $4.00 in dimes and quarters. She has 5 more dimes than quarters. Write a system of equations that you could use to f

ind how many dimes and quarters she has.
Mathematics
1 answer:
MakcuM [25]3 years ago
8 0

Answer:

\left\{\begin{array}{l}25x+10y=400\\y=x+5\end{array}\right..

Step-by-step explanation:

Let x be the number of quaters and y be the number of dimes Roberta has.

1. Quater is equal to 25 cents, then x quaters is equal to 25x cents. Dime is equal to 10 cents, then y dimes is equal to 10y cents. $4.00=400 cents, then

25x+10y=400.

2. Roberta has 5 more dimes than quarters, then

y=x+5.

3. The system of equations is

\left\{\begin{array}{l}25x+10y=400\\y=x+5\end{array}\right..

Substitute second equation into the first one:

25x+10(x+5)=400,\\ \\25x+10x+50=400,\\ \\35x=350,\\ \\x=10,\ y=10+5=15.

10 quaters and 15 dimes

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The volume V of a gas varies inversely as the pressure P and directly as the temperature A certain gas has a volume of 10 liters
Ad libitum [116K]

Answer:

Joint variation states that:

If z is directly proportional to x and inversely proportional to y,

i.e, z \propto x , z \propto \frac{1}{y}

then the equation is in the form: z = k\frac{x}{y} where k is the constant of variation.

From the given information: The volume V of a gas varies inversely as the pressure P and directly as the temperature

i.,e V \propto T , V \propto \frac{1}{P}

by definition of joint variation:

V = k\frac{T}{P}  .....[1] where k is the constant of variation.

It is also given that a certain gas has a volume of 10 liters(L) , a temperature of 300 kelvins(K), and a pressure of 1.5 atmosphere(atm).

Substitute these given values in [1] to solve for k;

10 = k\frac{300}{1.5}

Simplify:

10 = 200k

Divide by 200 both sides we have;

k = \frac{10}{200} =\frac{1}{20}

Now, if a gas has a temperature of 400 kelvins and a pressure of 5 atm.

To find the volume (V);

Now substitute the given data and value of k in [1] we have;

V = \frac{1}{20} \cdot \frac{400}{5} = \frac{20}{5} = 4

Therefore, the Volume of a gas is, 4 liters


5 0
3 years ago
rebekah's baby brother weighs 7.71 pounds.How much will her baby brother weigh if he gains 1.3 pounds each week for two weeks?
NemiM [27]

Answer:

10.31 pounds

Step-by-step explanation:

First, we multiply 1.3 x 2 because he is gaining 1.3 for the next TWO weeks.

1.3 x 2 = 2.6

Now, add 7.71 + 2.6 because that is the weight he started with.

7.71 + 2.6 = 10.31‬

Her brother will weight 10.31 pounds if he is 7.71 lbs and continues to gain 1.3 pounds each week for two weeks.

8 0
3 years ago
What is the absolute value of │38│
ale4655 [162]

Answer:

38

Step-by-step explanation:

if there are bars around it its automatically positive even if it was -38 the absolute would still be 38.

7 0
2 years ago
Read 2 more answers
A data set whose original x values ranged from 120 through 351 was used to generate a regression equation of ŷ=0.06x + 14.2. Use
lawyer [7]

Answer:

35.32

Step-by-step explanation:

The regression equation usually demonstrated as

y=a+bx.

In the above equation y is the dependent variable, x is the independent variable, a is the intercept of regression line and b is the slope of regression line.

The given regression equation is

y^=0.06x+14.2

The predicted value of y can be computed by simply putting the value of x in above equation.

So,

y^=0.06(352)+14.2

y^=21.12+14.2

y^=35.32

Thus, the predicted value of y for x=352 is 35.32.

6 0
3 years ago
Cell phone companies estimate that the total number of text messages (t) since the beginning of the month can be modeled by t=40
GalinKa [24]

The desired number is the difference between the number of messages sent by the 16th day and the number sent by the 9th day:

... n = t(16) - t(9)

... n = (40×√16) - (40×√9)

... n = 40×(4 - 3) = 40


40 text messages were sent between the ninth and sixteenth day of the month.

4 0
3 years ago
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