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yawa3891 [41]
3 years ago
10

Lindsay fills up the gas tank before beginning a long trip. When the gas gauge shows that she has used three-eights of a tank of

gas, she has drive. 165 miles. How far could she expect to drive in a full tank.
Mathematics
1 answer:
Ksju [112]3 years ago
4 0

Answer:

440miles

Step-by-step explanation:

We are told that mileage of 165 = 3/8 of a tank of gas

as inverse 5/8 would be left and the product we seek to add to 165.

We find a ratio to distribute 165 as 3/8

First we double and find 6/8 is an even number and = 330 miles.

= 3/4 ratio and that is 6:8 so 2 extra we seek to make a full tank before we add is 1/3 of 330 miles as 1/3 = 2/8 to make this balance only in this question is this possible as we call it distribution like percentage 10% added to 100 would always be 10 just like it is added, but finding 10% of 110 is different.

Therefore so would 1/3 afterwards once we find 1/3 = 2/8 is not the same as finding 1/3 after we find the full tank.

1/3 of 330 = 110

110 +330 = 440miles

I hope that helps you see how to work out close range distribution.

As now not that it's asking you to see 1/3 of 440miles but in same principal as explained about the 10% theory, you see 1/3 of 440 miles is now more than 110. it is 1/3 x 440 = 146.66 = 1/3. and so we can prove distribution is possible and say 2/8 = 1/3 even though in relation to 1 as a whole number its not true. It's only true in distribution.

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How many distinct positive integer-valued solutions exist to the equation (x2 - 7x + 11)(x2 - 13x + 42) = 1
Anna35 [415]

Answer:

The given equation has TWO positive integer valued solutions, {6, 7}

Step-by-step explanation:

Here we are given two trinomial factors, each of which needs to be set equal to zero and in each case the resulting quadratic equation solved.

(x^2 - 7x + 11) has the coefficients {1, -7, 11}, and so the discriminant of this quadratic is b^2 - 4(a)(c), or 49 - 4(11), or 5.

Because this discriminant is positive, we know immediately that this quadratic has two real, unequal roots involving √5 (NO integer roots).

Next we focus on (x^2 - 13x + 42).  The discriminant is b^2 - 4(a)(c), or

169 - 168, or 1.  Again we see that there are two real, unequal roots:

      +13 ± √1                  +13 ± 1

x = ---------------  or  x = -------------

             2                            2

OR x = 14/2 = 7 (integer) or x = 12/2 = 6 (integer).

The given equation has TWO positive integer valued solutions, {6, 7}

5 0
3 years ago
What is the y-intercept of this quadratic function?<br> f(x)=-x2+10x-22
IrinaK [193]

Answer:

The y intercept is (0,-22)

Step-by-step explanation:

To find the y intercept, set x =0 and solve for y

f(0)=-0^2+10*0-22

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7 0
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AfilCa [17]

Answer:

f(1)=0; f(0)= -2; f(-1)=(-4); f(2)=2

Step-by-step explanation:

For the first four questions, f(1) means that x= 1, so you need to look at the graph, find the point where x= 1, and find the corresponding y value which is 0. You do this same process for each of the rest.

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8 0
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Solve number 3 please, with explanation
Andreyy89

Answer:

97,655

Step-by-step explanation:

5(5)^(n-1) = 78,125

5^n = 78,125

n = 7

=> S7 = 5(5^7 -1) / (5-1)

= 5/4 (78, 125 -1)

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