Gas mileage is the number of miles you can drive on a a gallon of gasoline.
A test of a new car results in 580 miles on 10 gallons of gas. How far could
you drive on 55 gallons of gas? What is the car's gas mileage?

Answer:

3x + 10 y = -80

Step-by-step explanation:

We are given the equation y = −3/10x − 8  and we want to write it in standard form.

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot equal 0 and a cannot be negative.

The equation is currently is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.

As you can see, in standard form, x and y are on both sides, but in slope-intercept, the equation is solved for y.

So, to start, we can add 3/10x to both sides.

y = -3/10x - 8

+3/10x +3/10x

_______________

3/10x + y = - 8

Now, we have x and y on the same side, but remember that the the coefficients should be integers (non-fractions).

So, we need to clear the fraction.

Multiply both sides by 10.

10(3/10x + y) = 10(-8)
3x + 10y = -80

Answer:

you dont have 7 to 11

Step-by-step explanation:

13.a

15.a

12.i

14.h

Answer:

The graph shows no trend.

Step-by-step explanation:

See attachment for given graph

Required

What is true about the graph?

From the attached graph, the following points can be deduced:

Because of the highlighted points, it is safe to conclude that the graph shows no trend.

Answer:

D

Step-by-step explanation:

Answer:

y = 1/2x + 4

Step-by-step explanation:

9514 1404 393

Answer:

  1 scoop

Explanation:

There are 16 tablespoons in 1 cup, so Xander uses (1/8)·(16 tbsp) = 2 tbsp of topping for each scoop of ice cream.

For 1 scoop of ice cream, Pedro will use 1+1 = 2 tbsp of topping.

Hence, both use the same amount of topping (2 tbsp) for 1 scoop of ice cream.

A frequency distribution is a distribution in which the values of the variable are tabled or plotted against their frequency of occurrence and is often a first step of organizing the data into a logical order. .

As a general rule:

An example of a frequency table is

Commute time   Frequency

1 - 15                        10

16 - 30                      18

31 - 45                        11

46 - 60                        5

61 - 75                        0

76 - 90                        1

By comparing the above highlights to the given definitions, we have the correct options to be:

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The value of A from the given expression is 4288.5

Exponential equations are inverse of logarithmic equation and the standard form of the equation is given as:

y = ab^x

Given the expression below:

A = 3000(1+0.018/12)^(12*2)

Simplify for the value of A
A = 3000(1+0.015)^24

A = 3000 (1.015)^24

A = 3000 (1.4295)

A = 4288.5

Hence the value of A from the given expression is = 4288.5

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Answer: 1,3,60°

Step-by-step explanation:

The required probability would be 0.57, representing getting all three cubes are the same color.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Bag 1 contains 1 yellow and 2 green cubes.

Bag 2 contains 1 yellow and 3 green cubes.

Seven cubes total would be present.

You select one cube from Bag 2 and two cubes from Bag 1 without returning the first cube.

As per the condition,

So the probability of getting all three cubes are the same color would be

⇒ (³c₂ × ⁴c₁) / ⁷c₂

⇒ (3 × 4) / 21

⇒ 12 / 21

⇒ 0.57

Therefore, the probability would be 0.57, representing getting all three cubes are the same color.

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Answer: 1,176

Step-by-step explanation:

Answer:

The height of the tree would be 30 ft.

Step-by-step explanation:

This is because the smaller triangle would be 6/12 and the bigger triangle would be x/60. When you cross multiply these you find that x is 30.

Answer:

90 percent

Step-by-step explanation:

easy 36/40=0.9

that means 90 percent

just get big number divided by small

Answer:

90%

Step-by-step explanation:

I hope this helps!

Answer:

33. y = -x² - 2x + 3

34. y = x² + 4x + 3

Equation of a parabola is given by y = a(x - h)² + k

where:

33.

Looking at the graph find the vertex, vertex is at (-1, 4)

Take one point: (1, 0)

Substitute (h, k) = (-1, 4) and (x, y) = (1, 0) into equation to find value of a:

Now equation:

y = a(x - h)² + k

y = -1(x - (-1))² + 4

y = -(x + 1)² + 4

y = -(x² + 2x + 1) + 4

y = -x² - 2x - 1 + 4

y = -x² - 2x + 3

34.

The vertex is at (h, k) = (-2, -1) and the curve passes through (x, y) = (0, 3)

Find value of a:

Now equation:

y = a(x - h)² + k

y = 1(x - (-2))² - 1

y = 1(x + 2)² - 1

y = (x² + 4x + 4) - 1

y = x² + 4x + 3

Answer:

[tex]\textsf{33.} \quad y=-x^2-2x+3[/tex]

[tex]\textsf{34.} \quad y = x^2+4x+3[/tex]

Step-by-step explanation:

Factored form of a quadratic equation:

[tex]\boxed{y=a(x-r_1)(x-r_2)}[/tex]

where:

From inspection of the graph:

Substitute the roots and the vertex into the formula and solve for [tex]a[/tex]:

[tex]\begin{aligned}y & =a(x-r_1)(x-r_2)\\\implies 4 & = a(-1-(-3))(-1-1)\\4 & = a(2)(-2)\\4 & = -4a\\-4a & = 4\\\dfrac{-4a}{-4} & = \dfrac{4}{-4}\\a & = -1\end{aligned}[/tex]

Substitute the found value of [tex]a[/tex] and the roots into the formula and rewrite in standard form:

[tex]\begin{aligned}y & =a(x-r_1)(x-r_2)\\\implies y & = -1(x-(-3))(x-1)\\y & = -(x+3)(x-1)\\y & = -(x^2+2x-3)\\y & = -x^2-2x+3\end{aligned}[/tex]

Therefore, the equation of the parabola in standard form is:

[tex]y=-x^2-2x+3[/tex]

Vertex form of a quadratic equation:  

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

From inspection of the graph:

Substitute the vertex and y-intercept into the formula and solve for [tex]a[/tex]:

[tex]\begin{aligned}y & = a(x-h)^2+k\\\implies 3 & = a(0-(-2))^2+(-1)\\3 & = a(0+2)^2-1\\3 & = 4a-1\\3 +1& = 4a-1+1\\4 & = 4a\\4a & = 4\\\dfrac{4a}{4} & = \dfrac{4}{4}\\a & = 1\end{aligned}[/tex]

Substitute the found value of [tex]a[/tex] and the vertex into the formula and rewrite in standard form:

[tex]\begin{aligned}y & = a(x-h)^2+k\\\implies y & = 1(x-(-2))^2+(-1)\\y & = (x+2)^2-1\\y & = (x+2)(x+2)-1\\y & = x^2+4x+4-1\\y & = x^2+4x+3\end{aligned}[/tex]

Therefore, the equation of the parabola in standard form is:

[tex]y & = x^2+4x+3[/tex]

Answer:

Step-by-step explanation:

Let the number of games be x

Inequality:

Since there should be more than 0 left, another inequality for it:

So 13 < x < 15, which leaves us with 14

Answer:

The answer is 32.63

Step-by-step explanation:

Answer:

= −26.97

Step-by-step explanation:

Answer:

Step-by-step explanation:

Option C is the correct answer

Answer: 475 inches

Step-by-step explanation:

if we have 100 tiles and each is 4.75 inches wide

100*4.75=475 inches

Answer:

1/3

Step-by-step explanation:

4/5 + 3/15

We first find a common denominator which will be 15.

Multiplying the top and bottom of 4/5, we have 12/15

12/15 + 3/15 = 15/15 = 1

1 - 2/3 is 1/3

The length of the line segment PT is 72 / 7.  

In this problem we have the case of five colinear points, that is, points lying on a line, where the following conditions are fulfilled:

PT = 2 · PQ = 2 · QT        (Q is the midpoint of PT)              (1)

QT = 2 · PR = 2 · RT          (R is the midpoint of QT)            (2)

RT = 2 · RS = 2 · ST          (S is the midpoint RT)                  (3)

PS = 9                                                                                     (4)

PT = PS + ST                                                                          (5)

By (4) and (3) in (5):

PT = 9 + RT / 2                    (5b)

(1) in (5b):

2 · QT = 9 + RT / 2              (5c)

(2) in (5c):

4 · RT = 9 + RT / 2    

(7 / 2) · RT = 9

RT = 18 / 7

By (5b):

PT = 9 + 18 / 14

PT = 9 + 9 / 7

PT = 72 / 7

The length of the line segment PT is 72 / 7.    

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Answer:

fifty eight centimeters I believe

Answer:

58cm

Step-by-step explanation:

a rectangle has two of the same sides so 16×2=32

and

13×2=26

so

32+26=58

Answer:8(2g+1)(4g2-2g+1)

Step-by-step explanation:

Explanation:

You want a tutorial and a rationale for writing numbers and doing arithmetic in bases other than 10.

For integers, an easy way to write a number in a different base is to repeatedly divide by the desired base, and list the remainders right to left.

Example 1: convert 67 to base 3:

67₁₀ = 2111₃

Example 2: convert 44 to base 3:

44₁₀ = 1122₃

The usual rules of addition apply. A sum of two digits that equals or exceeds the value of the base causes a carry to the next digit to the left. (It can be convenient to write the carries on a separate line.)

In the first attachment, the sum of the two numbers above is developed in base 3. The relevant addition facts for base 3 are ...

Of course, zero (0) is still the additive identity element.

The usual rules of subtraction apply. When a larger digit is subtracted from a smaller one, a "borrow" is indicated from the digit immediately to the left. The relevant subtraction facts for base 3 are ...

Example: 67 -44 = 23, done in base 3

For subtraction of a smaller number from a larger one, it can work well to do the computation left to right:

  2111 -1122 = ...

4th digit: 2 - 1 = 1

3rd digit: 1 - 1 = 0

2nd digit: 1 - 2 = 2 (borrow 1 from 3rd digit: 0 - 1 = 2, borrow 1 from 4th digit: 1 - 1 = 0). The difference is now 0 2 2 x

1st digit: 1 - 2 = 2 (borrow 1 from 2nd digit: 2 - 1 = 1). The difference is now ...

  2111 -1122 = 0212, done in base 3

Consider the expanded forms of the sum and difference numbers in base 3:

  11010₃ = 1×3⁴ +1×3³ +0×3² +1×3¹ +0×3⁰ = 81 +27 +3 = 111₁₀   (67+44=111)

  212₃ = 2×3² +1×3¹ +2×3⁰ = 18 +3 +2 = 23₁₀   (67-44=23)

These forms clearly show the place value of a digit position is given by the corresponding power of the number base. You see this when you write base-10 numbers in expanded form. The point is driven home by working with numbers in other bases.

In short, working with numbers in other bases gives you a better understanding of place value.

__

Additional comment

Fractions can be converted to a different base by multiplying the fraction by the base, then using the integer digit as the next digit to the right.

Consider 5/9 in base 3:

Then 5/9 in base 3 is 0.12

As with base 10, any fraction that cannot be written using a power of the base as its denominator will have a repeating fractional part. For example, ...

  1/10 = 0.00220022...(4-digit repeat) in base 3

Answer:

x= [tex]\frac{12}{5}[/tex]-[tex]\frac{2y}{5}[/tex]

x=[tex]-\frac{10}{3}[/tex]-[tex]\frac{2y}{3}[/tex]

The wrench having the size as 5/8inch will accommodate the largest bolt.

When the denominator of all the fractions is same , then the fraction with largest numerator is the largest .

For Example : in 2/9 and 7/9   , the largest is 7/9.

In the given question  

the different sizes of wrenches are 1/2 inch, 7/16 inch, 5/8 inch and 15/32 inch.

For comparison , first make the denominator equal

To make the denominator equal , take LCM of denominator

LCM of 2,16,8,32 is 32.

so in 1/2  multiplying the denominator and numerator by 16 we get

1/2 inches as 16/32inches    ...(i)

In 7/16  multiplying the denominator and numerator by 2 we get

7/16 inches as 14/32 inches     ...(ii)

In 5/8  multiplying the denominator and numerator by 4 we get

5/8inches as 20/32 inches    ...(iii)

Writing all sizes of wrenches with same denominator

{16/32 , 14/32 , 20/32 , 15/32 }

Rearranging in descending order we get ,

{20/32 > 16/32 > 15/32 > 14/32}  

Which means {5/8 > 1/2 > 15/32 > 7/16}    ...(from (i),(ii)&(iii)  )

Therefore , the wrench having the size as 5/8 inch will accommodate the largest bolt. the correct option is (c)5/8inch .

The given question is incomplete , the complete question is

Workers use box end wrenches in sizes such as 1/2 inch, 7/16 inch, 5/8 inch and 15/32 inch. Which size of wrench accommodates the largest bolt?

(a)1/2 inch

(b)7/16 inch

(c)5/8 inch

(d)15/32 inch

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Answer:

The answer is that Alex wrote checks for 42.50 more than the amount he had.

Step-by-step explanation:

If he has -42.50 that means he owes the bank 42.50 the only way he would owe the bank that much is if he spent 42.50 that he didn't have.