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3 years ago

50 POINTS! :D

Mathematics

1 answer:

Alexxandr [17]3 years ago

8 0

Answer:

The speed of the first car is 60 mph

Step-by-step explanation:

speed = distance/time

Solve the above equation for distance to get

distance = speed * time

or simply

d = st

Now we use this formula for distance to write an equation for each car.

Let s = speed of second car

Then since the speed of the first car is 10 mph faster, the first car's speed is s + 10.

The time the two cars traveled is equal but unknown, so let the time = t.

First car: speed = s + 10; time = t; distance = 120 miles

d = st

120 = (s + 10)t

(s + 10)t = 120 Equation 1

Second car: speed = s; time = t; 100 miles

d = st

100 = st

st = 100 Equation 2

Equations 1 and 2 form a system of 2 equations in 2 unknowns.

(s + 10)t = 120

st = 100

Distribute t in the first equation.

st + 10t = 120

From the second equation we know st = 100, so substitute 100 for st.

100 + 10t = 120

10t = 120

t = 2

The time traveled was 2 hours.

Equation 2:

st = 100

Substitute t with 2.

s * 2 = 100

s = 50

The speed of the second car was 50 mph.

The speed of the first car is s + 10.

s + 10 = 50 + 10 = 60

Answer: The speed of the first car is 60 mph

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The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.

Ratling [72]

The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x

The equation to represent the perimeter of the triangle would be:
y = 3x - 6

The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).

Explanation
The area of a triangle is found using the formula
A = 1/2bh

For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x

We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x

The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)

Combining like terms we get:
P = 3x - 6

We will replace P with y, so we have:
y = 3x - 6

Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:

3x - 6 = 1/2(x²) - (7/2)x

It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x

We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x

When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12

This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)

Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.

Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)

We cannot have a negative perimeter, so the only viable solution is (12, 30).

8 0

3 years ago

Apr 17, 1:48:02 AM

galben [10]

Answer:

y = 9.54

and, x = 0.08

Step-by-step explanation:

Given that

x - 2y = -19 .......................(1)

3x + 5y = 48 ...............(2)

Based on the above information

Multiply by 3 in equation 1

So,

3x - 6y = -57

3x + 5y = 48

- - -

-11y = -105

y = 9.54

So, the x would be

x - 2(9.54) = -19

x - 19.08 = -19

x = -19 + 19.08

x = 0.08

5 0

3 years ago

The product of two consecutive even integers is 360360. find the integers.

professor190 [17]

There are no 2 consecutive integers which give a product 360360

5 0

3 years ago

A rectangular swimming pool measures 40 ft by 60 ft and is surrounded by a path of uniform width around the four edges. The peri

Alex_Xolod [135]

Answer:

6ft

Step-by-step explanation:

Lets x = the width of the path the surrounding path will add 2x to the pool dimension,therefore over all dimesion: (2x+40) by (2x+60) the overall perimeter (2x + 40) + 2(2x+60) = 248 Simplify divide by 2, result (2x+40) +(2x+60) = 124

 Combine like terms 2x + 2x +40 +60 =124 

4x + 100 = 124 

4x=124 = 100

4x=24

x=24/4

x= 6ft is the width of the path

check this by finding the perimeter with these values; 2x = 12 ft 

2 ( 12 + 40 ) + 2( 12 +60 ) 

2( 52 + 2(72)

104 + 144 = 248; confirms our solution of x= 6 ft

5 0

3 years ago

8=1/3(a+5) What does a equal?

IrinaK [193]

Answer: a=19

Step-by-step explanation: In order to solve this question, we must first take out the parenthesis, we can do this by taking 1/3 and multiply it by a and 5. This will give us 8=1/3a+5/3, with this we can subtract 5/3 on both sides of the equation, which will then give us, 19/3=1/3a. Last, we can divide 19/3 by 1/3 giving us 19 as our final anwser. a=19

6 0

3 years ago

Read 2 more answers