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2 years ago

Write a system of equations that could be used to solve the situation described below.

1 answer:

3 0

If there are 12 coins under the couch and every coin is either a nickel or a penny and together they are forming 32 cents then the equations which represent the problem will be x+y=12, 0.01x+0.05y=0.32. The correct option is B which is x+y=12, 0.01x+0.05y=0.32.

Given There are 12 coins and total money is 32 cents.

Let the number of pennies be x and the number of nickels be y.

According to question there are 12 coins so the first equation becomes:

x+y=12.

Then we have been told that together they amount to 32 cents.

We know that 1 penny is 1 cent coin and 1 nickel is 5 cent coin so the equation becomes :

1*x+5*x=32

x+5y=32

converting into dollar

0.01x+0.05y=0.32.

Hence the right equations showing the problem of nickel and pennies are x+y=12, 0.01x+0.05y=0.32.

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Eight times the sum of 8 and some number is 17. What is the number?

OverLord2011 [107]

Edited answer: The number is: "- 6" .
_______________________________________________

8 (8 + x) = 16 ;

in which "x" represents the number for which to be solved ;

8*8 + 8*x = 16 .

Edit: 64 + 8x = 16 ;

Subtract "64" from each side of the equation:

Edit: 64 + 8x − 64 = 16 − 64 ;

to get: 8x = - 48 ;

Divide EACH SIDE of the equation by "8" ; to isolate "x" on one side of the equation ; and to solve for "x" ;

Edit: 8x / 8 = -48 / 8 ;

Edit: x = - 6 .
______________________________________________
The number is: "- 6" .
______________________________________________
Let us check our answer, by plugging in "-6" for "x" in the original equation:
______________________________________________
8 (8 + x) = 16 ;

→ 8 [8 + (-6) ] =? 16 ?? ;

→ 8 (8 − 6 ) =? 16 ?? ;

→ 8 (2) =? 16 ?? ;

→ 16 = ? 16 ?? Yes!
_________________________________________________

4 0

3 years ago

Read 2 more answers

Express the confidence interval (0.036, 0.086) in the form of p-e< p

lina2011 [118]

Answer:

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

Step-by-step explanation:

Given;

Confidence interval CI = (a,b) = (0.036, 0.086)

Lower bound a = 0.036

Upper bound b = 0.086

To express in the form;

p-e< p < p+e

Where;

p = mean Proportion

and

e = margin of error

The mean p =( lower bound + higher bound)/2

p = (a+b)/2

Substituting the values;

p = (0.036+0.086)/2

Mean Proportion p = 0.061

The margin of error e = (b-a)/2

Substituting the given values;

e = (0.086-0.036)/2

e = 0.025

Re-writing in the stated form, with p = 0.061 and e = 0.025

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

6 0

3 years ago

What is the greatest number that can be divided evenly into 78 and 104 without leaving a remainder?

irga5000 [103]

Answer:

26 can be divides evenly into 78 and 104 without leaving a remainder

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The distance between two cities is 145 miles. A truck can cover this distance in 2. 5 hours. A car is 1. 5 times as fast as the

Sophie [7]

The relative speed of the car to the truck while moving towards each other is the sum of the speed of both vehicles.

The time it takes them to meet is 1 hour

Reasons:

The distance between the cities, d = 145 miles

The time it takes a truck to cover the distance = 2.5 hours

The speed of the car = 1.5 × Th speed of the truck

Required:

The time it takes them to meet if they are moving towards each other.

Solution:

$\displaystyle Speed = \mathbf{ \frac{Distance}{Time}}$

$\displaystyle Speed \ of \ the \ truck, \ v_{truck} = \frac{145 \ miles}{2.5 \ hours} = \mathbf{58 \ mph}$

Therefore;

The speed of the car, $v_{car}$ = 1.5 × 58 mph = 87 mph

At the time, t, the truck and the car meet, we have;

$\mathbf{v_{car} \times t + v_{truck} \times t = d}$

Which gives;

87 × t + 58 × t = 145

$\displaystyle t = \mathbf{\frac{145}{87 + 58}} = 1$

The time it takes them to meet, t = 1 hour

Learn more about distance, time and speed here:

brainly.com/question/17609639

8 0

2 years ago

The equation of a line that goes through the points (0,0) and (300000,365)

olga_2 [115]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 0 &,& 0~) 
% (c,d)
&&(~ 300000 &,& 365~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{365-0}{300000-0}\\\\\\ \cfrac{365}{300000}\implies \cfrac{73}{60000}$

$\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-0=\cfrac{73}{60000}(x-0)\implies y=\cfrac{73}{60000}x$

4 0

3 years ago