At a certain gas station, gas costs $2.85 a gallon. Jason paid $25.50 to fill his tank. Write and solve an equation to
find how many gallons of gas he bought?

The value of angle A and B are 60° and 120° respectively.

It is important to note that in isosceles trapezoid, the angles adjacent to the bases are congruent.

Therefore A = D

B = C

When in the right angle, the hypothenuse is twice the leg, the angle opposite it will be:

ABK = 30°

Also, KBC = 90°

Therefore, B = 30° + 90° = 120°

A = D = 180° - 120° = 60°

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Complete question:

Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4

Find: mA and mB.

Answer: n=1/27=0.037

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*n-(1/9)=0

Simplify 1/9

3n -  1/9  = 0

Rewrite the whole as a fraction using  9  as the denominator :

          3n     3n • 9

    3n =  ——  =  ——————

          1        9  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3n • 9 - (1)     27n - 1

————————————  =  ———————

     9              9  

End of step 2  

27n - 1

 ———————  = 0

    9  

Start of step 3

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 27n-1

 ————— • 9 = 0 • 9

   9  

Now, on the left hand side, the  9  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  27n-1  = 0

Solving a Single Variable Equation:

3.2      Solve:    27n-1 = 0

Add  1  to both sides of the equation :

                     27n = 1

Divide both sides of the equation by 27:

                    n = 1/27 = 0.037

If Lisa sells 50 watch bands, she gets a profit of $262.50.

A unitary method is defined.

Mathematicians use the unitary method to solve problems by first determining the value of a single unit, or 1, (by dividing), and then determining the necessary value by multiplying the value of the single unit.

We must first ascertain the cost of one watch band.

To determine this, we simply divide $105 by 20, which equals $5.25.

We can divide $5.25 by 50 because she sells all 50 watchbands.

50 multiplied by $5.25 equals $262.50.

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Answer:

x=0.75

Step-by-step explanation:

5x=3.75

/5.  /5

x=0.75

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The hawk is closer to the ground after 8 minutes

It is 130 feet closer

We have the equation as;

Also, x represents the descending time in minutes

Now, let's substitute the value of x as 8 minutes in the equations

If x = 8

For equation (1)

y = - 20(8) + 350

expand the bracket

y = - 160 + 350

y = 190 feet

For equation (2)

y = -10(8) + 400

expand the bracket

y = -80 + 400

y = 320 feet

The hawk is closer after 8 minutes

The distance from the ground(eagle) - The distance from the ground(hawk)

320 - 190

130 feet

Hence, the hawk is closer to the ground

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The current price of the clarinet and the various discounts and markups illustrate that the amount the store paid was $90.

First find out the selling price of the clarinet:

= Discounted price / ( 1 - discount rate)

= 93.60 / ( 1 - 20%)

= $117

This selling price is 30% more than what the store paid so the price the store paid was:

= Selling price / ( 1 + rate of increase)

= 117 / ( 1 + 30%)

= $90

In conclusion, the amount the store paid was $90.

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Complete question

A music store buys instruments and then sells them for 30% more than they paid. During a 20% off sale, the store offers a clarinet for $93.60.

How much did the store pay for the clarinet?

Answer:

its A.

Step-by-step explanation:

There were 58 cars sold with exactly two of the given options.

1. There were 90 cars sold with air conditioning.

2. There were 102 cars sold with automatic transmission.

3. There were 72 cars sold with power steering.

4. There were 7 cars sold with all three options.

5. There were 22 cars sold with none of the options.

6. There were 25 cars sold with only air conditioning.

7. There were 61 cars sold with only automatic transmission.

8. There were 33 cars sold with only power steering.

9. There were 11 cars sold with both automatic transmission and power steering.

Let's just count the number of cars that have exactly two of the given options:

Air Conditioning & Automatic Transmission: 25

Air Conditioning & Power Steering: 22

Automatic Transmission & Power Steering: 11

So there are 25 + 22 + 11 = 58 cars that have exactly two of the given options.

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Answer:

negative

Step-by-step explanation:

Answer:

x= 40° y= 66° z=106° ....

The value of angles are x = 40° , y = 66°, z = 106°

Since there are two parallel lines and two intersecting lines forming a triangle we will use the properties of lines and triangles to find out the value of x,y,z. First of all y = 66° because of the vertical angle theorem, which means that adjacent angles formed by the intersection of two lines are supplementary or equal to 180° degrees. The third angle of the triangle formed is 74°. Using the sum of all angles of the triangle is equal to 180° we can find the third angle of triangle x which is equal to 40°. Now z can be found using the property sum of two opposite interior angles which will come out to be 106°. Hence by this, we can find all the angles.

I hope this answer helps.

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The solution of given system of linear equations is x = 3.6 and y = 2.5.

A "system" of equations is a collection of equations that you answer all at once. Ax + By + C = 0, where A and B are the coefficients and C is the constant, can be used to describe a linear equation. Non-linear equations are more difficult to comprehend than linear equations.

Solving the equations,

5x +4y = 8

10x − 4y = 46

Adding the above equations, we get

5x + 10x + 4y - 4y = 8 + 46

15x=54

Dividing by 15,

x = 3.6

Now, putting the value of x in second equation,

10(3.6) - 4y = 46

36 - 4y = 46

4y = -10

Dividing by 4, we get

y = -2.5

Therefore, the solution of given system of linear equations is x = 3.6 and y = 2.5.

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Answer:

the answer is 350

Step-by-step explanation:

if it increased by 200% that means it doubled

so when x is doubled we get 700

so: 2x=700

       x=700/2

       x=350

No. of par-3 holes be represented by = 5

No. of par-4 holes be represented by = 8

No. of par-5 holes are represented by = 5

Total number of courses in the club= 18 (given in the question)

Total shot taken by golfer=72 (given in the question)

Let par-3 holes be represented by t

Let par-4 holes be represented by f

Let par-5 holes be represented by v

forming equations:

f+2=2v

t=v

f + v + t = 18

f+2=2v

f=2v-2 -(i)

t=v -(ii)

f + t + v=18

putting values from (i) and (ii)

(2v-2) + v + v=18

2v-2+2v=18

4v=18+2

4v=20

v=20/4

v=5

Number of par-5 holes=5

from (i)

f=2v-2

putting value

f=2(5)-2

f=10-2

f=8

Number of par-4 holes=8

from (i)

t=v-

putting value

t=5

t=5

Number of par-3 holes=5

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For the given equation, the slope is 3 and the y-intercept is -5. From the graph, it is possible to see that the point (0,0) does not satisfy the equation.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=x+19. A line equation also can be represented by the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex].

m= the slope.

[tex](x_1,y_1)[/tex]= the coordinate of a point.

For the given example: m=1 and b=19.

The question gives: y + 2 = 3(x - 1). Therefore,

y + 2 = 3(x - 1)

y=3x-3-2

y=3x-5

If y=3x-5 . Here, you have a standard form of a linear equation y=mx+b. Where:

m= the slope. It can be calculated for Δy/Δx.

b= the constant term that represents the y-intercept

Thus, the slope is 3 and the y-intercept is -5.

For this, you should do a table with points

x     y= 3x-5

-2   y=3*(-2)-5=-6-5= -11

-1    y=3*(-1)-5=-3-5= -8

0   y=3*(0)-5=0-5= -5

1    y=3*(1)-5=3-5= -2

2    y=3*(2)-5=6-5= 1

Draw a graph from these points, see the attached image.

The point (0,0) does not satisfy the equation because when x=0 because y is different than zero (0). See below.

y= 3x-5, for x=0

y=3*0-5

y=0-5

y=-5

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Answer: the i8 49

Step-by-step explanation:98493

Translation of the given sentence with variable y into inequality is given by 3y + 23 > 25.

As given in the question,

Given sentence is :

Let the number be represented by y.

The sum of y times of 3 and 23 is greater than 25.

Translation of the given sentence into inequality is given by :

y times 3 is represented by 3y

Sum of y times 3 and 23 is given by 3y + 23

Sum is greater than 25

3y + 23 > 25

Simplify the inequality we get,

3y > 25 -23

⇒3y > 2

⇒y > 2/3

Therefore, translation of the given sentence with variable y into inequality is given by 3y + 23 > 25.

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There is a 1/3 chance that random variable will have a value higher than 5.

For the variable t, which follows uniform probability distribution.

0 ≤ t ≤ 8

Total variables = 9.

For the probability of value greater than 5 for the random variable.

P(t > 5) = P(t = 6) + P(t = 7) + P(t = 8)

P(t > 5) = 1/9 + 1/9 + 1/9

P(t > 5) = 3/9

P(t > 5) = 1/3

Thus, there is a 1/3 chance that random variable will have a value higher than 5.

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There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.

Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes. Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how likely it is that a coin will land heads up after being tossed into the air.

Given,

On a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.

Either the wait is over 25 minutes or it is less than 25 minutes. Decimal 1 represents the total of these events' probabilities. So,

P( X ≤ 25) + P(X > 25) = 1

For P(X > 25):

1 -P(X ≤ 25)

1 - e ⁻⁰⁶⁶⁶⁽²⁵⁾

0.1892

There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.

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Answer:

x=17/14 y=5/21

it's a easy question I think you can solve it

Answer:

In order to complete the equation we need to use this method :      

Future Amount = I(1+r)^t

I=Initial Amount

R=Growth rate

T=Time periods

Now that we know that....

Letsss seee:

You started with 55 so

Future Amount = 55(1+r)^t

The growth rate is 73% so we have to convert to decimal so

Future Amount=55(1+.73)^t

Time period is 73% every 2 days and you want to see how large the colony would be after 10 days so you do 10/2:

Future Amount=55(1+.73)^5

Future Amount therefore equals 852.301407 BUT You have to round to the nearest whole number Sooo

Step-by-step explanation:

Hope this helpss you Tony!

Answer:

How large would the colony be after 10 days?

852 is the answer.

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

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Answer:

-1

Step-by-step explanation:

Replace the variable x with 1 in the expression .

f(1)= 2(1) - 3

Remove the parenthasis

2(1) - 3

Multiply 2 by 1

2 - 3

subtract 2 from 3

-1

The solutions of the quadratic equation using the quadratic formula is x = 3 + 2√2 and x = 3 - 2√2

From the question, we are to solve the given quadratic equation using the quadratic formula

The given quadratic equation is

x² - 6x + 1 = 0

Using the quadratic formula,

x = [-b±√(b² - 4ac)] / 2a

a = 1, b = -6, and c = 1

Thus,

x = [-(-6) ±√((-6)² - 4(1)(1))] / 2(1)

x = [6 ±√(36 - 4)] / 2

x = [6 ±√(32)] / 2

x = [6 ± 4√2] / 2

x = [2(3 ± 2√2)] / 2

x = 2(3 ± 2√2) / 2

x = (3 ± 2√2)

x = 3 + 2√2 and 3 - 2√2

Hence, the roots are 3 + 2√2 and 3 - 2√2

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The required value of ∠ABC in the given triangle is 50°

The relation between interior and exterior angles of the triangle are related as, the sum two interior angles of triangle is equal to the opposite exterior angle of that triangle.

As we see in the given question, the sum of angle ∠A and ∠B is equal to the exterior angle which is 145°

⇒ 2x° + 95° = 145°

⇒ 2x° = 145° - 95°

⇒ 2x = 50°

Thus, required answer of angle ∠ABC is 50°

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Now we have to,

→ find the required value of b.

Formula we use,

→ (AC)² = (BC)² + (AB)²

Then the value of a will be,

→ (10.5)² = b² + (3)²

→ 110.25 = b² + 9

→ b² = 110.25 - 9

→ b = √101.25

→ [ b = 10.06 in ]

Hence, value of b is 10.06 in.

The price of gasoline when Ryan's mother started driving is $0. 45

A fraction can be defined as the part of a whole set, data or element.

The different types of fractions include;

Example of mixed fractions; 2 1/ 3

Example of simple fractions; 1/ 2

Example of proper fractions; 2/5

From the information given, we have;

Price of a gallon of gasoline is $2. 25

1/ 5 of $2.25

This is represented as;

1/ 5 × $2.25

Multiply the values

$0. 45

Hence, the value is $0. 45

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Answer:

Step-by-step explanation:

There are 15 circles and 6 squares.

Total shapes:

Ratio of squares to total shapes:

Answer:

the answer is 2:7

Step-by-step explanation:

6÷3 : 21÷3

=2:7

Step-by-step explanation:

the angles between 2 intersecting lines must be the same on both sides of either line, they are just left-right mirrored.

so,

123 = 2v + 1

2v = 122

v = 61

The total spots moved, after the 3 plays is 15 spots to the left.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that the football team lost 5 yards on each 3 plays.

Assume that a number line to be able to see how far in the field did they lost in 3 games.

Therefore,

1 : 5  (1 game is to 5 yards)

3 : 15 (3 games is to 15 yards )

After the first play, we would move to the left on the line 5 spots (to simulate 5 yards lost) and then make a dot to show your new position.

The total spots moved, after the 3 plays is 15 spots to the left.

Hence, All they lost 15 yards in 3 games.

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