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Harman [31]
3 years ago
7

A mouse traveled a total distance of StartFraction 3 Over 24 EndFraction of a mile in a maze over the past 3 hours. The mouse tr

aveled the same distance each hour. To determine the distance that the mouse traveled each hour, Matt performed the calculations below.
Mathematics
1 answer:
Dvinal [7]3 years ago
8 0

Answer:

Step-by-step explanation:

Using the formula for calculating speed;

Speed = Distance/Time

Given

Speed = 3/24 miles per 3 hours

Required

Distance travelled in an hour

3/24 miles = 3 hours

x = 1 hour

Cross multiply;

3 * x = 3/24 * 1

3x = 3/24

Cross multiply;

3x * 24 = 3

72x = 3

x = 3/72

x = 1/24

Hence the distance travelled each hour is 1/24 miles

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Use the quadratic formula to solve the equation: 8x(x - 2) - 20 = 5x(x - 4)​
FromTheMoon [43]

Answer: x = 2, -\frac{10}{3}

Write the equation in standard form: ax^{2} + bx + c = 0.

8x(x - 2) - 20 = 5x(x - 4)\\\\8x^{2} - 16x - 20 = 5x^{2} - 20x\\\\3x^{2} - 16x - 20 = -20x\\\\3x^{2} + 4x -20 = 0

Use the quadratic formula. <em>(+-) = </em>±

\frac{-b (+-) \sqrt{b^{2} - 4ac } }{2a}

Substitute in the values, where a = 3, b = 4, and c = -20, and simplify.

\frac{-4(+-)\sqrt{(4)^{2} - 4(3)(-20)} }{2(3)} \\\\\frac{-4(+-)\sqrt{16 + 240} }{6}} \\\\\frac{-4(+-)\sqrt{256} }{6} \\\\\frac{-4(+-)16}{6} \\\\\frac{-4 + 16}{6}, \frac{-4 - 16}{6} \\\\\frac{12}{6}, \frac{-20}{6} \\\\2, -\frac{10}{3}

x = 2, -\frac{10}{3}  

3 0
4 years ago
The system of equations above is graphed below. Find the solution to the system.
Oksana_A [137]

Option D: x=3,y=-2 is the solution to the system of equations.

Explanation:

Given that the equations are 4x+y=10 and 2x+y=4

We need to determine the solution of the system of equations.

The solution can be determined by solving the two equations.

Let us solve the system of equations using substitution method.

Consider the equation 4x+y=10 , the value of y is given by

y=10-4x

Substituting the value of y=10-4x in the equation 2x+y=4 , we get,

2x+(10-4x)=4

Simplifying, we get,

2x+10-4x=4

     -2x+10=4

             -2x=-6

                 x=3

Substituting the value of x=3 in 4x+y=10 , we get,

4(3)+y=10

  12+y=10

         y=-2

Thus, the solution to the system of equations is x=3,y=-2

Hence, Option D is the correct answer.

7 0
3 years ago
On his first three tests, Hiram got scores of 89, 95, and 90. His final test score brought his median score to 91.5. What was I
Elena-2011 [213]
The median is the middle score, it is also the average of the two middle scores when total number is even.

original 3 scores:  89, 90, 95  ----> median = 90

with final score:  89,90,X,95  ----> median = 91.5

(90+x)/2 = 91.5
90+x = 183
x = 93

Final score was a 93.
6 0
3 years ago
7 less than a number n
Alex_Xolod [135]

Answer:

n>7

Step-by-step explanation:

5 0
3 years ago
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The ratio of Isabellas money to Shane's money is 3:11. If Isabellas money is $33, how much money do Shane and Isabella have toge
Ksenya-84 [330]
They have 155 dollars together.
4 0
4 years ago
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