The Carson’s are on a road trip they paid $62.70 for 16 1/2 gallons of gasoline
Part 1-Find the price of gasoline per gallon show your work
Part 2-Give an example of a cost and amount that would make the gasoline have a rate of $3.49 per gallon

Answer:

1. -6 ≤ x < -1, conjunction

2. x > 10   or   x ≤ 6, disjunction

3. 7 ≤ x ≤ 12, conjunction

4. x ≥ -3   or   x < -9, disjunction

Step-by-step explanation:

These inequalities are called "compound inequalities." Each compound inequality is made up of two simple inequalities.

A compound inequality of the type 5 < x < 8 means x > 5 and x < 8. Since the word between the simple inequalities is "and", it is a conjunction.

A compound inequality of the type "x < 3 or x > 12" uses the word "or" between the simple inequalities. It is called a disjunction.

1.

-4 ≤ x + 2 < 1

Conjunction

For this type of inequality, do what you need to do to get x alone in the middle section. Do the same to all three "sides" of the inequality.

The middle section has x + 2. We want x alone,s o w must subtract 2. We subtract 2 from all three sides.

-4 - 2 ≤ x + 2 - 2 < 1 - 2

-6 ≤ x < -1

2. 5x - 4 > 46 or 4x ≤ 3x + 6

Disjunction

In this type of compound inequality, solve each inequality by itself, and always keep the word "or" between the inequalities.

5x - 4 > 46 or 4x ≤ 3x + 6

5x - 4 + 4 > 46 + 4   or   4x - 3x ≤ 3x - 3x + 6

5x > 50   or   x ≤ 6

x > 10   or   x ≤ 6

3. Similar to problem 1.

Conjunction

10 ≤ 2x - 4 ≤ 20

Add 4 to all sections.

14 ≤ 2x ≤ 24

Divide all sections by 2.

7 ≤ x ≤ 12

4.

6 - 2x ≤ 12 or 7 + 2x < -11

Disjunction

-2x ≤ 6   or   2x < -18

x ≥ -3   or   x < -9

Answer:

1. -6≤x<-1

conjunction

2.x>10   or     x≤6

Disjunction

3.7≤x≤12

Conjunction    

4.x ≥-6                    or                           x < -6

Disjunction

5.2≤x≤5

Conjunction

6. x ≤ 54                                        or               x≥66

Disjunction

7.  39< x≤43

Conjunction

Step-by-step explanation:

conjunction is "and"  like a sandwich between 2 points

disjunction is " or"  like boat oars with a gap for the boat in the middle

1. -4≤x+2<1

Subtract 2 from all sides

-4-2≤x+2-2<1 -2

-6≤x<-1

conjunction

2. 5x-4>46"                                 or          " 4x≤3x+6

Add 4 to each side                                  Subtract 3x from each side

5x-4+4 > 46+4                                           4x-3x≤3x-3x+6

5x >50                                                           x≤6

Divide by 5                                                  

5x/5 >50/5

x>10   or     x≤6

Disjunction

3. 10≤2x-4≤20

Add 4 to all sides

10≤2x-4≤20

10+4 ≤2x-4+4≤20+4

14≤2x≤24

Divide by 2 on all sides

14/2≤2x/2≤24/2

7≤x≤12

Conjunction    

4. 6-2x≤12" or                             " 7+2x<-11

Subtract 6 from each side       Subtract 7 from each side

6-6-2x≤12                                or " 7-7+2x<-11-7

-2x≤12                                        2x<-18

Divide by -2                                Divide by 2

Flips the inequality

-2x/-2≥12/-2                             2x/2 <-18/2

x ≥-6                    or                           x < -6

Disjunction

5. 5≤2x+1≤11

Subtract 1 from all sides

5-1≤2x+1-1≤11-1

4≤2x≤10

Divide all sides by 2

4/2≤2x/2≤10/2

2≤x≤5

Conjunction

6. 2/3 x-20≤16"                            or " x/3+10≥32

Add 20 from each side                     Subtract 10 from each side

2/3 x-20+20 ≤16+20                     x/3 +10-10 ≥32 -10

2/3 x ≤36                                                x/3≥22

Multiply by 3/2 on each side            Multiply by 3 on each side

3/2 * 2/3x ≤ 36*3/2                      x/3*3 ≥22 *3

x ≤ 54                                        or               x≥66

Disjunction

7. 10<1/4 (x+1)≤11

Multiply all sides by 4

4*10<1/4*4 (x+1)≤11*4

40< (x+1)≤44

Subtract 1 from all sides

40-1< (x+1-1)≤44-1  

39< x≤43

Conjunction

Answer:

C. 12x + 6y = 30

Step-by-step explanation:

A. x  3 4 5  

   y   3    6     9

We need to make and equation

slope = (y2-y1)/(x2-x1)

    = (9-3)/(5-3)

    6/2

  3

The slope is 3

Using point slope form

y-y1 = m(x-x1)

y-3  = 3(x-3)

Distribute

y-3 = 3x-9

Add 3 to each side

y = 3x-9+3

y = 3x-6

Let x=0

y = 0-6

y = -6

B. y = 4x – 7

Let x = 0

y = 0-7

y = -7

C. 12x + 6y = 30

Let x = 0

12(0) + 6 y = 30

6y = 30

Divide by 6

6y/6 = 30/6

y =5

D. A linear function that goes through point 1, negative 1 and point 0, 4

The point ((0,4) says when x=0   y=4

y =4

y=5  is the max so the answer is C

Answer:

 [tex]x^3 + 8x^2 + 11x-20[/tex]

Step-by-step explanation:

f(x) = x^2 + 3x − 4

g(x) = x + 5

To find f(x) * g(x) we multiply f(x) with g(x)

[tex]f(x) * g(x) = (x^2 + 3x -4) * (x+5)[/tex]

First multiply each term in f(x) and multiply with x+5

x^2 times x+5 becomes [tex]x^3+5x^2[/tex]

3x times x+5 becomes [tex]3x^2 + 15x[/tex]

-4 times x+ 5 becomes -4x -20

so f(x) * g(x) = [tex]x^3 + 5x^2 +3x^2 + 15x -4x -20[/tex]

Combine like terms

f(x) * g(x) = [tex]x^3 + 8x^2 + 11x-20[/tex]

Answer:    [C]:    " x³ + 8x² + 11x − 20 " .

______________________________________________________

Step-by-step explanation:

______________________________________________________

Given:      "  f(x) =  x² + 3x − 4 " ;   and

                " g(x) =  x + 5  "  ;

Find:         "  f(x) ⋅ g(x) "  :

______________________________________________________

    f(x) ⋅ g(x) =

     " (x² + 3x − 4) (x + 5) " ;

     ↔  " (x + 5) (x² + 3x − 4) " ;

______________________________________________________

Note:  " (a + b) (c + d + e)  =  ac + ad + ae + bc + bd + ae " ;

______________________________________________________

 →  " (x + 5) (x² + 3x − 4)

             =  (x * x²) + (x * 3x) + (x*-4) + (5*x²) + (5*3x) + (5*-4) " ;

             =  (x³) + (3x²)  + (-4x) + (5x²) + (15x) + (-20) ;

             =   x³  + 3x² − 4x + 5x² + 15x − 20 ;

 →  Combine the "like terms" :

          + 3x² + 5x²  =  + 8x²  ;

           − 4x + 15x   = + 11 x ;

______________________________________________________

 → And rewrite:

______________________________________________________

        →   "  x³ +  8x²  +  11x  − 20 " ;

______________________________________________________

       →  which is:  Answer choice:  [C]:   " x³  +  8x²  +  11x  −  20 " .

______________________________________________________

     Hope this helps!

        Best wishes!

______________________________________________________

Answer:

Step-by-step explanation:

Given that two points (-5,-9) and (-5,13)

We have to find the differences between these points

Both the points have -5 as x coordinate.

But y coordinate is negative for first one while positive for second one.

Also dimension is 9 units down for I point while for ii point it is 13 units up.

The first point lies in the III quadrant while II point lies in the II quadrant.

Both the points are located with a distance of 5 units from x axis to the left of x axis.

But first point is 9 units down y axis and ii point is 13 units up the y axis.

Distance between them is 22 units.

Answer: The difference between the points (-5,-9) and (-5,13) is 22 units.

Explanation:

Since we have given that

(-5,-9) and (-5,13)

As we can see that the points are along the x-axis as the x-coordinate are same in both the points.

So, to find the difference between the points we just need to get the distance between the y- coordinates.

[tex]13-(-9)\\\\=13+9\\\\=22\ units[/tex]

Hence, the difference between the points (-5,-9) and (-5,13) is 22 units.

Answer:

m<1=134

m<2=46

x=13

Step-by-step explanation:

Angle 2 can be set equal to 180 since the angle is supplementary after transferring angle 2 to its alternate interior.

4x-6+10x+4=180

Combine like terms

14x-2=180

Solve for x

14x=182

x=13

Now plug x in for the two angles

10(13)+4

130+4

m<1=134

4(13)-6

52-6

m<2=46

134+46=180, verified

Answer:

14.32 inches to nearest thousandth.

Step-by-step explanation:

Circumference = π * d        where d = the diameter.

So 45 = π * d

d = 45 / π

=  14.32 inches

The diameter of the circle is 14.33 inches.

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The circumference of the circle as 45 inches

We know that Circumference is give by 45=2×3.14×r

                                                                   2r=14.33 inches

Hence, The diameter of the circle is 14.33 inches.

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Answer:

6300 = s * 3

s=2100

Step-by-step explanation:

s =steps per mile

steps = steps per miles * miles

6300 = s * 3

This is the equation.

Divide each side by 3.

6300/3 = s3/3

2100 /s

Answer:

6300/3=s

s=2100

Step-by-step explanation:

six thousand three hundred over 3 equals s

s equals two thousand one hundred

Answer:

The adults shadow is 4.8 ft

Step-by-step explanation:

We can use ratio's to solve this problem

12 ft hoop             6ft adult

--------------         = -----------------

9.6 ft shadow      x ft shadow

Using cross products

12 * x = 9.6 * 6

12x = 57.6

Divide each side by 12

12x/12 = 57.6 /12

x = 4.8 ft

Answer:

3x6=18

Step-by-step explanation:

3x6=18

6 times as old is the same as saying TIMES by 6 :)

Joe's age can be found using the equation 'Joe's Age = 6 * 3', as Joe is 6 times as old as Mike, and Mike is 3 years old.

The question presents a situation where Joe is 6 times as old as Mike. We know that Mike is 3 years old, so to find Joe's age, we need to multiply Mike's age by 6. This situation can be expressed by the following equation: Joe's Age = 6 * Mike's Age.

Replacing 'Mike's Age' with the given value (3 years), we get: Joe's Age = 6 * 3

Therefore, the equation to find Joe's age is Joe's Age = 6 * 3.

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Answer:

(B) [tex]477=6(1+0.20)^t[/tex]

Step-by-step explanation:

we can use formula

[tex]P(t)=P_0(1+r)^t[/tex]

where

Po is the initial population

r is the growth rate

t is the time in months

We are given

initial population of insects

so, Po=6

The scientists find that the insect population, x, is growing exponentially 20% per month

so, r=0.20

now, we can plug these values

[tex]P(t)=6(1+0.20)^t[/tex]

there to be a population of 477 insects

so, P(t)=477

now, we plug it

and we get

[tex]477=6(1+0.20)^t[/tex]

To factor the trinomial x²-4x-32, follow the steps to identify coefficients, find suitable numbers, split the middle term, and factor by grouping. The answer is (x+4)(x-8).

To factor the trinomial x²-4x-32, you can follow these steps:

Identify the coefficients of the quadratic terms: a = 1, b = -4, and c = -32.

Find two numbers that multiply to c (a*c = -32) and add up to b (-4).

Split the middle term using these numbers: x²-4x-32 becomes x²-8x+4x-32.

Factor by grouping: (x²-8x) + (4x-32) = x(x-8) + 4(x-8) = (x+4)(x-8).

a - side of the square

4a - the perimeter of a square

76 in - the perimeter of a square

The equation:

4a = 76     divide both sides by 4

a = 19 in.

(a) The length of each side is equal to 19 inches.

In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;

P = 4s

Where:

By substituting the given parameters into the formula for the perimeter of a square, we have the following;

Perimeter of a square, P = 4s

76 = 4s

s = 76/4

s = 19 inches.

Therefore, each side has a length 19 inches.

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Answer:

or else we can divide again

Answer:

2 decimal places

Step-by-step explanation:

When you multiply two decimals, the largest possible number of decimal places in the product is the sum of the number of the decimal places of the factors. Here, the product has 2 decimal places. One factor is an integer, so it has no decimal places. The other factor must have at least 2 decimal places.

Answer:

length =25 and width =4

Step-by-step explanation:

If the area of a rectangle is 100, then the length is 25 and the width is 4. The counterexample is length = 20, width = 5.

If the area of a rectangle is 100, and the length is 25, we can find the width by dividing the area by the length: 100 ÷ 25 = 4. So the width is 4. To find the counterexample, we need to find another pair of length and width that give a different area.

Let's try length = 20 and width = 5. The area of this rectangle would be 20 × 5 = 100, which is the same as the original rectangle.

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Answer:

The total surface area of the square pyramid is [tex]SA=400\ mm^2[/tex]

Step-by-step explanation:

we know that

The surface area of a square pyramid is equal to the area of the square base plus the area of four triangular faces

so

[tex]SA=10^{2} +4[\frac{1}{2}(10)(15)][/tex]

[tex]SA=400\ mm^2[/tex]

Answer:7

Step-by-step explanation: 14%=14/100. (14/100)*50=7

Answer:

7

Step-by-step explanation:

to find your answer multiply .14 (14 as a fraction)  by 50 to get 7

Answer:

-18  

Step-by-step explanation:

f(x) = x² - 3x -10

f(-10) = (-10)² – 3(-10) – 10

f(-10) = 100 + 30 - 10

f(-10) = 120

f(-5) = (-5)² – 3(-5) – 10

f(-5) = 25 + 15 - 10

f(-5) = 30

=====

The average rate of change is the slope m of the straight line joining the two points.

m = (y₂ - y₁)/(x₂ - x₁)

m = (30 - 120)/(-5 – (-10))

m = -90/(-5+10)

m = -90/5

m = -18

Answer:

15

Step-by-step explanation:

you have to divide 975/65=$15 per person

Answer: choice C, 18

==============================

Explanation:

We don't know how long each little horizontal piece is, but we do know that the smaller horizontal pieces combine to fully span 5 units across. The top and bottom sides effectively are both 5 units long. Think of a rectangle. Similarly, the same happens with the vertical pieces as well. They combine to get 4.

We have a figure with a perimeter similar to a rectangle that is 4 by 5, the perimeter being 4+5+4+5 = 9+9 = 18

Alternatively, you can use the formula

P = 2*L + 2*W or P = 2*(L+W)

Plug in L = 5 and W = 4 as the length and width to get P = 18 for the perimeter

Answer:

200

Step-by-step explanation:

8x2=16

12 1/2x16=200

Answer:

(x - 6)(x + 3)

Step-by-step explanation:

Consider the product of the factors of the constant term which sum to give the coefficient of the x-term

product = - 18 and sum = - 3

The factors are - 6 and + 3, hence

x² - 3x - 18 = (x - 6)(x + 3)

Answer:

2/10

Step-by-step explanation:

2/10

The probability that Mike would pick two prime numbers from the stack of 10 cards without replacement is 2/15.

The probability of picking two prime numbers from a stack of 10 cards without replacement can be calculated by finding the probability of picking a prime number on the first draw and a prime number on the second draw, given that the first draw was successful.

There are four prime numbers among the 10 cards (2, 3, 5, and 7). So, the probability of picking a prime number on the first draw is 4/10.

Since we do not replace the first card, there are now 9 cards left in the deck, with 3 prime numbers. So, the probability of picking a prime number on the second draw, given that the first draw was successful, is 3/9.

To find the overall probability, we multiply the probabilities of the individual events: (4/10) * (3/9) = 12/90 = 2/15.

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Answer:

It takes 2.5 seconds for the ball to reach its  highest point

Maximum height is 196 feet

Step-by-step explanation:

h(t) = -16t^2+80t +96

a=-16, b= 80, c=96

To find the maximum height , we need to find vertex

Let find x coordinate of vertex

[tex]t=\frac{-b}{2a}[/tex]

Plug in the values

[tex]t=\frac{-80}{2(-16)}= 2.5[/tex]

It takes 2.5 seconds for the ball to reach its  highest point

Now plug in 2.5 for t to find maximum height

[tex]h(t) = -16t^2+80t +96[/tex]

[tex]h(2.5) = -16(2.5)^2+80(2.5) +96=196[/tex]

Maximum height is 196 feet

The complete factor of the expression x⁴ + 8x² – 9 will be (x² + 9), (x - 1), and (x + 1). Then the correct option is B.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given as,

⇒ x⁴ + 8x² – 9

Factorize the expression, then we have

⇒ x⁴ + 8x² - 9

⇒ x⁴ + 9x² - x² - 9

⇒ x²(x² + 9) - 1(x² + 9)

⇒ (x² + 9)(x² - 1)

⇒ (x² + 9)(x - 1)(x + 1)

The complete factor of the expression x⁴ + 8x² – 9 will be (x² + 9), (x - 1), and (x + 1). Then the correct option is B.

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The complete question is attached below.

Answer:

z5

Step-by-step explanation:

Answer:

z is your answer! :)

Answer:

120

Step-by-step explanation:

Answer:

The equation of this line would be y = 3x - 1

Step-by-step explanation:

In order to find this equation we must first find the slope of the original line. The original slope (the coefficient of x) is 3, which means the new slope will also be 3 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.

y - y1 = m(x - x1)

y + 7 = 3(x + 2)

y + 7 = 3x + 6

y = 3x - 1