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Marat540 [252]
3 years ago
10

Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 630 miles on 15 gallons

of gas. How far could you drive on 50 gallons of gas?
Mathematics
1 answer:
Ne4ueva [31]3 years ago
7 0

Answer:

2,100 miles

Step-by-step explanation:

<u>Step 1-</u> Find the miles the car can travel per gallon

630 miles/ 15 gallons=42 miles per gallon

<u>Step 2-</u> Multiply the miles per gallon by the number of gallons being used

42x50=2,100 miles

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Which of the following sets are subspaces of R3 ?
Ratling [72]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

for point A:

\to A={(x,y,z)|3x+8y-5z=2} \\\\\to  for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)

                                        =3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)

The set A is not part of the subspace R^3

for point B:

\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon  B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)

                                             =-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0

\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon  B

The set B is part of the subspace R^3

for point C: \to C={(x,y,z)|x

In this, the scalar multiplication can't behold

\to for (-2,-1,2) \varepsilon  C

\to -1(-2,-1,2)= (2,1,-1) ∉ C

this inequality is not hold

The set C is not a part of the subspace R^3

for point D:

\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)

The scalar multiplication s is not to hold

\to for (-4, 1,2)\varepsilon  D\\\\\to  -1(-4,1,2) = (4,-1,-2) ∉ D

this is an inequality, which is not hold

The set D is not part of the subspace R^3

For point E:

\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to  a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\

The  x_1, x_2 is the arbitrary, in which ax_1+bx_2is arbitrary  

\to a(x_1,0,0)+b(x_2,0,0) \varepsilon  E

The set E is the part of the subspace R^3

For point F:

\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon  F \\\\\to  a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))

The x_1, x_2 arbitrary so, they have ax_1+bx_2 as the arbitrary \to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F

The set F is the subspace of R^3

5 0
3 years ago
What is the sum of 2 1/3, 3 5/6 and 6 2/3
Andreas93 [3]
2 1/3+ 3 5/6+ 6 2/3
= 7/3+ 23/6+ 20/3
= 14/6+ 23/6+ 40/6
= 77/6
= 12 5/6

The final answer is 12 5/6~
5 0
3 years ago
Can someone please help me on this. Identify the terms, coefficients, and constants in the expression.
Makovka662 [10]

Answer:

45

Step-by-step explanation:

8 0
3 years ago
The pass marks pf a mathematics test is 75% what percentage is the fail marks?
photoshop1234 [79]

Answer:Marks below 75%

Step-by-step explanation:

Since the pass marks is 75%,the fail marks should be Marks below 75%

7 0
4 years ago
Think about all of the ways in which a line and a
Vikentia [17]

Answer:

Infinitely many

Step-by-step explanation:

4 0
3 years ago
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