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3 years ago

Caroline's car used 16 gallons to travel 544 miles. How far can she travel on 9 gallons?

Mathematics

1 answer:

kicyunya [14]3 years ago

8 0

Answer:

306 gallons

Step-by-step explanation:

Caroline traveled 544 miles on 16 gallons. We do some simple math and divide 544/16 and receive 34 miles/gallon. All we do now is multiply 34 * 9 and we receive 306 gallons.

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What is the solution to the system? 1. x-y + 2 z = -7<br> 2. y + z =1<br> 3. x-2 y - 3 z = 0

kvv77 [185]

You'd find this problem easier to understand and do if you'd please list the defining equations vertically and line up variables:

1. x - 1y + 2 z = -7

2. y + 1z = 1

3. x - 2 y - 3 z = 0 Now eliminate the line numbers:

x - 1y + 2 z = -7

1y + 1 z = 1

x - 2 y - 3 z = 0

Let's use the elimination method to eliminate variable z: Seeing that z = 1 - y, we transform the first equation into 1x - 1y + 2(1-y) = -7

and the third into x - 2y - 3(1-y) = 0.

Simplifying 1x - 1y + 2(1-y) = -7

and x - 2y - 3(1-y) = 0,

we get

1x - 2y - 3 + 3y) = 0 and 1x - 1y + 2 - 2y = -7

which in turn simplify to

1x + y = 3 and 1x - 3y = -9

Having eliminated the variable z, we now focus on eliminating x. Mult. the 1st equation by -1, obtaining -1x - 1y = -3. Add this result to 1x - 3y = -9:

0 - 4y = -12, which tells us that y = 3. Subbing 3 for y in 1x + 1y = 3 tells us that x = 0.

All we have left to determine is the vaue of z.

Borrowing Equation 3, from above, we get x - 2 y - 3 z = 0, and into this equation we substitute x = 0 and y = 3: 0 -2(3) - 3z = 0.

Thus, -3z = 6, and z = -2.

The solution set is (0, 3, -2). You should check this by substitution.

3 0

3 years ago

Translate each of these statements into logical expressions by using quatifiers and predicates with one or two variables. (a) A

nikdorinn [45]

Answer:

a) $A = \{\exists x \in M, \exist y \in U\,|\,xGy \}$ , b) $B = \{\exists x \in M,\,\exists y \in H\,|\,xMy \}$ , c) $C = \{\forall x \in M\,|\,xI \}$ , d) $D = \{\exists x \in M,\,\forall y \in U\,|\,xJy \}$ , e) $E = \{\exists x \in M, \forall y \in V, V \subseteq U\,|\,xJy \}$

Step-by-step explanation:

a) x - A student, M - Set of students of discrete math class, G - has lived in, y - Florida, U - Set of states of the United States of America.

$A = \{\exists x \in M, \exist y \in U\,|\,xGy \}$

b) x - A student, M - Set of students of discrete math class, y - A perfect grade, H - Midterm I.

$B = \{\exists x \in M,\,\exists y \in H\,|\,xMy \}$

c) x - A student, M - Set of students of discrete math class, I - loves discrete math.

$C = \{\forall x \in M\,|\,xI \}$

d) x - A student, M - Set of students of discrete math class, J - has been in, y - a state, U - Set of states of the United States of America.

$D = \{\exists x \in M,\,\forall y \in U\,|\,xJy \}$

e) x - A student, M - Set of students of discrete math class, J - has been in, y - a city, V - At least one state of the United States of America, U - Set of states of the United States of America.

$E = \{\exists x \in M, \forall y \in V, V \subseteq U\,|\,xJy \}$

5 0

3 years ago

Kenji earned the test scores below in English class.

lutik1710 [3]

Answer:

mean=87

median=87

Step-by-step explanation:

mean=sum of test score/number of subject

mean=79+91+93+85+86+88/6

mean=522/6

mean=87

Literal meaning of median is medium.

To find the number which lies in the medium, we must rearrange the number in ascending.

79, 91, 93, 85, 86, 88

79, 85, 86, 88, 91, 93

86+88/2=87

Hope this helps ;) ❤❤❤

Let me know if there is an error in my answer.

7 0

3 years ago

I need help and im dumb

Dahasolnce [82]

D he doesn't care about his family well being

6 0

3 years ago

If Mrs. Ramsey divides 5 pounds of flour equally into three bowls, what is the weight of flour in one bowl? A) 3 5 pound Elimina

Mariulka [41]

Hi there!

The key in the question is "divide". Therefore, we divide 5 by 3

5/3=1.6 pounds

I don't think any of these are right.

3 0

3 years ago

Read 2 more answers

Caroline's car used 16 gallons to travel 544 miles. How far can she travel on 9 gallons? ​

Caroline's car used 16 gallons to travel 544 miles. How far can she travel on 9 gallons?