My three cars can travel the same distance on a tank of gas. My second car gets 6 kilometers per liter more than
my first, but its tank holds 3 fewer liters than my first. My third car gets 6 kilometers per liter less than my first, but its tank holds 6 more liters
than my first. How many kilometers can each car travel on a tank of gas?

Step-by-step explanation:

20−5y+2x

20-5(-2)+2(5)

20+10+10=40

Answer:

20 − ( 5 ) ( −2 ) + ( 2 ) ( 5 )

= 20 − ( −10 ) + ( 2 ) ( 5 )

= 30 + ( 2 ) ( 5 )

= 30 + 10

= 40

Hope it helps

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9514 1404 393

Answer:

  4.  1.3 cm³

  5.  621.2 mm³

  6.  116.5 m³

Step-by-step explanation:

The height to the peak of the pyramid is one side of the right triangle that has its hypotenuse equal to the slant height, and one leg equal to half the base side length. The Pythagorean theorem is used to find the height from the slant height (s) and the base length (b):

  h = √(s² -(b/2)²)

The volume is found from the formula ...

  V = (1/3)b²h

where b is the base length and h is the height found using the previous formula.

The tedious arithmetic is nicely done using a spreadsheet. Results are attached.

Answer:

Subtract 5x from both sides of the equation.

7y=1−5x

x+4y=−5

Divide each term by 7 and simplify.

y=17−5x/7

x+4y=−5

Subtract x from both sides of the equation.

y=1/7−5x/7

4y=−5−x

y=1/7−5x/7

Divide each term by 4 and simplify.

y=1/7−5x/7

y=−5/4−x/4

y=1/7−5x/7

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution. (3,−2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

write a rule for the n th term of the geometric sequence for which a_1=11 and a_4=88

Answer:

∠ A = 48°

Step-by-step explanation:

Supplementary angles are those angles that measure up to 180 degrees.

∠A and ∠B are supplementary angles. If m ∠ A = ( 4 x − 16 ) ∘ and m ∠ B = ( 8 x + 4 ) ∘,then find the measure of ∠ A

Step 1

∠A + ∠B = 180°

(4x−16)° + (8x+4)° = 180

4x - 16 + 8x + 4 = 180

12x -12 = 180

12x = 180 + 12

12x = 192

x = 192/12

x = 16

Step 2

To find the measure of ∠ A

∠ A = 4x - 16

= 4 × 16 - 16

= 64 - 16

= 48°

Therefore,

∠ A = 48°

Answer:

20, 21, 29

Step-by-step explanation:

h²= p²+b²

29² = 20²+ 21²

[tex]5\frac{1}{3} =\frac{16}{3}[/tex]

[tex]\frac{16}{3} -\frac{2}{3} \\=\frac{14}{3}[/tex]

Hope this helped!!!!!!!

Answer:

21.5

Step-by-step explanation:

square is 10x10 = 100

circle is A=πr2=π·5²≈78.54

100-78.54 = 21.46 = 21.5

Answer:

21.5 sq cm

Step-by-step explanation:

Area of Square:

A= LXW= 10x10= 100 sq cm

Area of Circle=

A=πr²

Radius= D/2= 10/2= 5 cm

A=3.14(5²)

A=3.14(25)= 78.5 sq cm

Shaded Region= 100-78.5= 21.5

The area of the shaded region is 21.5 sq cm.

Half of R is shown as 20 degrees, so the other half of r is also 20 degrees.

A tangent line forms a right angle, so the tangent at P is 90 degrees.

X would be 180 - 90 - 20 = 70 degrees.

X = 70 degrees.

Answer:

B wpuld be your answer

Step-by-step explanation:

Its the nearest ft from 70.

Answer:

the probability of getting exactly 2 fours is 0.16

Step-by-step explanation:

The probability of obtaining a number that is four = ¹/₆

The probability of obtaining a non 4 number = 1 - ¹/₆ = ⁵/₆

The number of ways 2 fours can be arrange in five numbers = ⁵C₂ = 10 ways

If the die is tossed five times, the probability of the events is calculated as;

P = 10 x (¹/₆)² x (⁵/₆)³

P = 10 x (¹/₃₆) x  (¹²⁵/₂₁₆)

P = 10 x 0.02778 x 0.5787

P = 0.16

Therefore, the probability of getting exactly 2 fours is 0.16

The probability of exactly [tex]2[/tex] four's in [tex]5[/tex] tosses is [tex]0.1608[/tex].

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.

Let [tex]X[/tex] be the number of fours in [tex]5[/tex] coin tosses.

We have no. of tosses [tex]n=5[/tex].

Probability of a success i.e., getting four [tex](p)=\frac{1}{6}[/tex] and probability of not getting a four [tex](q)=\frac{5}{6}[/tex].

[tex]X[/tex] follows a binomial distribution. So,

[tex]P(X=x)=\binom{n}{x}p^{x}q^{n-x}[/tex]

[tex]\therefore[/tex] the probability of exactly [tex]2[/tex] four's in [tex]5[/tex] tosses is given by,

[tex]P(X=2)=\binom{5}{2}\left ( \frac{1}{6}^{2} \right )\left ( \frac{5}{6} \right )^{3}[/tex]

               [tex]=0.1608[/tex]

Learn more about the topic of Probability: https://brainly.com/question/26959834

Answer:

volume of cylinder : πr²×h = π × 5² × 15 = 375π ≈ 1177.5 cm³

Answer:

The new coordinates of E are (-3,-15/2).

Step-by-step explanation:

Here we just need to multiply each element of this point by r.

So we have:

[tex]E_{new}(-2*(\frac{3}{2}),-5*(\frac{3}{2}))[/tex]

[tex]E_{new}(-3,-\frac{15}{2})[/tex]

Therefore, the new coordinates of E are (-3,-15/2).

I hope it helps you!

Answer:

√6 × √6 × √6 = 6√6

Step-by-step explanation:

[tex] \rm \sqrt{6} \times \sqrt{6} \times \sqrt{6} [/tex]

[tex] \rm = \sqrt{36} \times \sqrt{6} [/tex]

[tex] \blue{\boxed{\rm = 6 \sqrt{6} }}[/tex]

Answer:

8.06 units  = AD

(just write sq rt 65 = 8.062 ) then write or try sq rt of 65  to 3 sf = nearest tenth 8.06 tenth units rounded.

Step-by-step explanation:

AE = 7

ED = 4

We use Pythagoras Theorem as it is a right angle as AE^2 + ED^2 = AD^2

7^2 + 4^2 = AD^2

49 + 16 = 65 sq rt

sq rt  65 = AD^2 = 8.062^2

AD = 8.062 units

Answer:

Area = 220.8 units²

Step-by-step explanation:

Since, given regular hexagon is made up of 6 congruent triangles joined together.

Area of the given regular hexagon = 6(Area of ΔAOB)

Area of ΔAOB = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                        = [tex]\frac{1}{2}(AB)(OC)[/tex]

                        = [tex]\frac{1}{2}(9.2)(8)[/tex]

                        = 36.8 unit²

Therefore, area of regular hexagon = 6(36.8)

                                                 = 220.8 units²

Answer:

1 1/2 cakes

Step-by-step explanation:

3/8 ÷ 1/4

3/8 * 4/1

12/8

3/2

1 1/2

Answer:

3/10

Step-by-step explanation:

Probability will be the number of goats, since goats is what you're looking for, over the number of total animals. So that gives 3/10.

To get that as a decimal, divide 3 by 10. Then take your decimal and multiply it by 100 to give the percent.

Answer:

Step-by-step explanation:

slope=-2

y-intercept=(0,2)

Answer:

10 15 75

Step-by-step explanation:

− 7 = 3

− 7 + 7 = 3 + 7

 =  10

Answer:

∠ AOB = 139°

Step-by-step explanation:

Since AOC is a straight line then

∠ AOB + ∠BOC = 180° , that is

8x + 51 + 6x - 25 = 180

14x + 26 = 180 ( subtract 26 from both sides )

14x = 154 ( divide both sides by 14 )

x = 11

Then

∠ AOB = 8x + 51 = 8(11) + 51 = 88 + 51 = 139°

Answer:

x = 3 and y = 6

Step-by-step explanation:

Hope this helps :)

Answer:

x = 3, y = 30

Step-by-step explanation:

Since the 3 sides are congruent then the triangle is equilateral.

The 3 angles are congruent and equal tp 60°

Evaluate each of the angles to 60 and solve for x and y , that is

25x - 15 = 60 ( add 15 to both sides )

25x = 75 ( divide both sides by 25 )

x = 3

and

2y = 60 ( divide both sides by 2 )

y = 30

Answer: 14



Step-by-step explanation: To get this answer you would first of all 6 more means we're adding.

Quotient means division. What we're dividing is an unknown quantity -- x -- and 3.

The final total says 14. That gives us the following:

6 + x/3 = 14