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blsea [12.9K]
3 years ago
6

The cities Cleveland, Ohio; Erie, Pennsylvania; and Rochester, New York, in respective order, lie approximately in a straight li

ne. The distance from Cleveland to Erie is 94 miles. The distance from Cleveland to Rochester is 239 miles. Find the distance from Erie to Rochester.
Mathematics
1 answer:
Ann [662]3 years ago
7 0

Answer:

  Erie to Rochester is 145 miles

Step-by-step explanation:

If we designate the points of interest as C, E, and R, we are told that ...

  CE + ER = CR . . . . . the various distances are segments of a straight line

For CE = 94 and CR = 239, we can fill in the given information and solve for ER.

  94 + ER = 239

  ER = 239 -94 . . . . . . subtract 94 from both sides of the equation

  ER = 145

The distance from Erie to Rochester is 145 miles.

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Solve each proportion. <br> 8/x+9=2/x-3<br> Please show work.
emmainna [20.7K]


8/x+9-(2/x-3)=0

Step by step solution :


Step 1 :

2
Simplify —
x
Equation at the end of step 1 :

8 2
(— + 9) - (— - 3) = 0
x x
Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using x as the denominator :

3 3 • x
3 = — = —————
1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 - (3 • x) 2 - 3x
——————————— = ——————
x x
Equation at the end of step 2 :

8 (2 - 3x)
(— + 9) - ———————— = 0
x x
Step 3 :

8
Simplify —
x
Equation at the end of step 3 :

8 (2 - 3x)
(— + 9) - ———————— = 0
x x
Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x as the denominator :

9 9 • x
9 = — = —————
1 x
Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

8 + 9 • x 9x + 8
————————— = ——————
x x
Equation at the end of step 4 :

(9x + 8) (2 - 3x)
———————— - ———————— = 0
x x
Step 5 :

Adding fractions which have a common denominator :

5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(9x+8) - ((2-3x)) 12x + 6
————————————————— = ———————
x x
Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

12x + 6 = 6 • (2x + 1)

Equation at the end of step 6 :

6 • (2x + 1)
———————————— = 0
x
Step 7 :

When a fraction equals zero :

7.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

6•(2x+1)
———————— • x = 0 • x
x
Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
6 • (2x+1) = 0

Equations which are never true :

7.2 Solve : 6 = 0

This equation has no solution.
A a non-zero constant never equals zero.
7 0
3 years ago
Read 2 more answers
I need help with this ​
gtnhenbr [62]
So what are we trying to find the reduced fraction or inverse operation
5 0
3 years ago
A pharmacist wants to make 36ml of a 65% hydrogen peroxide solution. how many pls of 75% hydrogen peroxide must he mix with 57%
faltersainse [42]

Answer:

16 mls of the 75% solution and 20 mls of the 0.57% solution.

Step-by-step explanation:

Set up a system of equations:

Let x = volume of 75% solution and y be volume of 57% solution

0.75x + 0.57y = 36*0.65

0.75x + 0.57y = 23.4.......(1)

x + y = 36.........(2)

From equation (2):

y = 36 - x

Substituting this into equation(1):

0.75x + (0.57(36 - x) = 23.4

0.75x + 20.52 - 0.57x = 23.4

0.18x = 23.40 - 20.52 = 2.88

x = 2.88/0.18

x = 16

so from equation (2): y = 36-16 = 20.

8 0
2 years ago
A pentigonal prism is cut by a plane perpendicular to the base. What is the shape of the cross section that is formed ?
Sholpan [36]

Answer:

In a right pentagonal prism, the bases are pentagons and the lateral faces are rectangles. If we take a cross-section perpendicular to the base, this same cross-section will be parallel to the lateral faces. This means it will be the same shape as the lateral faces, which is a rectangle.

Step-by-step explanation:

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3 years ago
Use the imaginary number i to rewrite the expression below as a complex number. Simplify
Zinaida [17]

Step-by-step explanation:

Revin imediat...... ✨.

8 0
2 years ago
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