A toll collector on a highway receives ​$4 for cars and ​$9 for buses. At the end of a 2​-hour ​period, she collected ​$188. How many cars and buses passed through the toll booth during that​ period? List all possible solutions.

Final answer:

To find the actual distance from Rose Lake to the hiking trail, a proportion is used based on the given information of the map scale, resulting in an actual distance of 7 miles.

Explanation:

The question involves solving for an actual distance on a map scale, which is a proportional relationship problem in mathematics. To find the actual distance between Rose Lake and the hiking trail, we can set up a proportion using the given distances: if 2 inches on the map equal 3.5 miles in reality, then 4 inches would represent the distance from Rose Lake to the hiking trail (since the relationship between inches on the map and actual miles should be consistent).

Set up the proportion as follows:

2 inches (map) / 3.5 miles (real) = 4 inches (map) / X miles (real)

Now, solve for X, which represents the unknown actual distance in miles. By cross-multiplying and solving for X, we get:

X = (4 inches * 3.5 miles) / 2 inches

Therefore, the actual distance between Rose Lake and the hiking trail is 7 miles.

a total of $9500 is invested, part at 10% simple interest and part at 9%

if the total annual return from the two investments is $914.00

Amount invested = 9500

Total amount return means total yield = $914

Let x amount  is invested at 10% simple interest

Interest for first part =  10 % times x = 0.10x

Remaining part invested is 9500 -x

Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)

Total interest yield is 914. Now we frame an equation

0.10x + 0.09(9500-x) = 914

0.10x +855 - 0.09x = 914 (combine like terms)

0.01 x + 855 = 914 (subtract 855)

0.01x = 59 ( divide both sides by 0.01)

So x = 5900

$5900 is invested in 10% simple interest

9500 - 5900 = $3600 is invested in 9% simple interest

Final answer:

To solve the problem, we set up a system of equations based on the provided information. After simplifying and solving the system, we find that $5900 is invested at 10% and $3600 is invested at 9%.

Explanation:

Investment Allocation Problem

Let's denote the amount of money invested at 10% as $x and the amount of money invested at 9% as $y. Since the total amount invested is $9500, we can write the first equation as:

x + y = 9500

The total annual return from the investments is $914. We know that the interest from the first investment is 0.10x and from the second investment is 0.09y. Thus, our second equation, based on the total interest earned is:

0.10x + 0.09y = 914

Now we can solve the system of equations:

x + y = 9500 (Equation 1)

0.10x + 0.09y = 914 (Equation 2)

Multiplying Equation 1 by 0.10 gives us a new equation:

0.10x + 0.10y = 950 (Equation 3)

Now, we subtract Equation 2 from Equation 3:

(0.10x + 0.10y) - (0.10x + 0.09y) = 950 - 914

0.10y - 0.09y = 36

0.01y = 36

y = 3600

Substitute y = 3600 into Equation 1 to find x:

x + 3600 = 9500

x = 5900

Therefore, $5900 is invested at 10% and $3600 is invested at 9%.

First the two angles are equal to one another so take note of that.

Now setup the equation which will be

x+90=4x

Now get rid of alike terms

So subtract x from both sides

90=3x

Now divide 90 by 3

x=30

Answer:  The correct option is

(C) x = 30.

Step-by-step explanation:  We are given to find the value of x from the figure shown.

From the figure, we note that the angles with measures (x+90)° and 4x° are vertically opposite angles.

Since the measures of two vertically opposite angles are equal, so we must have

[tex](x+90)^\circ=4x^\circ\\\\\Rightarrow x+90=4x\\\\\Rightarrow 4x-x=90\\\\\Rightarrow 3x=90\\\\\Rightarrow x=\dfrac{90}{3}\\\\\Rightarrow x=30.[/tex]

Thus, the required value of x is 30.

Option (C) is CORRECT.

These are the polygons

The transformation of Polygon A to Polygon B could involve translation, rotation, or reflection. Observe differences in position and orientation between the two polygons to identify the type of transformation.

The transformation of a polygon to another can involve a series of moves such as translation (sliding), rotation (turning around a point), or reflection (flipping over a line). By closely comparing the two polyhgons A and B, you can determine which type of transformation has taken place.

For instance, if every point on polygon A has moved in the same direction and distance to form polygon B, a translation has taken place. If polygon B can be obtained by turning polygon A around a point, then a rotation has occurred. If polygon B is a mirror image of polygon A, then it has been reflected.

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B.) Any temperature change is the original temperature plus the numerical value of the change. (temp + change) If it is an increase, the number will be positive. If it is a decrease, the number will be negative. 

Since there is a decrease of 11, c would be replaced with -11. When you plug this into your expression (85 + c: 85 + -11), the answer to this would be 74.

                                                 hope it helps

Final answer:

Explaining how to define a variable, write an expression, and evaluate the temperature after a decrease in Fahrenheit degrees.

Explanation:

Variable: Let c represent the temperature change.

Expression: To find the new temperature after a decrease of 11°F, the expression is 85 - c.

Evaluation: By substituting c with -11 (decrease of 11°F), 85 - (-11) equals 96°F.

CE is equal to 58 units.

To find the length of CE, we'll use the fact that D is the midpoint of CE. The midpoint of a line segment divides it into two equal parts.

If CD is one part and DE is the other, then we can set up an equation:

CD=DE

9X−7=3X+17

Now, solve for X:

6X=24

X=4

Now that we have the value of X, substitute it back into either CD or DE to find the length of each part:

CD=9X−7=9(4) −7=36−7=29

DE=3X+17=3(4) +17=12+17=29

Now, since D is the midpoint, CD and DE are equal.

CD=DE=29

Finally, CE, the total length, is the sum of CD and DE:

CE=CD+DE=29+29=58

So, CE is indeed 58

what do you mean ¨ what is the distance between¨ what is the rest of the question?

Answer:

 [tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]

 [tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]

Explanation:

Ratio between [tex]4*10^{15}[/tex] and [tex]8*10^9[/tex] = [tex]\frac{4*10^{15}}{8*10^9} =5*10^5[/tex]

 So [tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]

Ratio between [tex]2*10^{-5}[/tex] and [tex]4*10^{-12}[/tex] = [tex]\frac{2*10^{-5}}{4*10^{-12}} =5*10^6[/tex]

 So [tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]

The cube of the product of 3 and a number is expressed as (3x)³ or 27x³, which involves cubing the numeric part and multiplying the exponent of the variable by 3.

The question is asking about the volume of a cube with sides of length a and also about the process of cubing the product of a number and three. When we cube a product, such as 3 times an unknown number, we are calculating the result of multiplying that product by itself three times.

For example, if our number is x, we would express this as (3x)³ or 27x³. This is because when we cube a product, we cube the numeric part as usual, obtaining 3³ which is 27, and we multiply the exponent of the exponential term by 3, thus x becomes x³.

[tex]\displaystyle\\4^2+7^2+\ldots+(3n+1)^2=\\\\\sum_{k=1}^n(3k+1)^2=\\\\\sum_{k=1}^n(9k^2+6k+1)=\\\\\sum_{k=1}^n9k^2+\sum_{k=1}^n 6k+\sum_{k=1}^n1=\\\\9\sum_{k=1}^nk^2+6\sum_{k=1}^n k+n=\\\\9\left(\dfrac{n(n+1)(2n+1)}{6}\right)+6\left(\dfrac{n(n+1)}{2}\right)+n=\\\\\dfrac{3n(n+1)(2n+1)}{2}+3n(n+1)+n=\\\\\dfrac{3n(2n^2+n+2n+1)}{2}+3n^2+3n+n=\\\\\dfrac{3n(2n^2+3n+1)}{2}+3n^2+4n=\\\\\dfrac{6n^3+9n^2+3n}{2}+\dfrac{6n^2+8n}{2}=\\\\\dfrac{6n^3+15n^2+11n}{2}[/tex]

8^14 is the answer.

This is because since they both have the same base, the exponents could be added together if the numbers are multiplied together

Hello Tim!

[tex]8^1^0*8^4[/tex]

First you had to used apply exponent rule.

[tex]8^1^0*8^4=8^1^0^+^4=8^1^4[/tex]

[tex]=8^1^4[/tex]

Answer⇒⇒⇒8¹⁴

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

2) angles are vertical so they are congruent- 7x-27= 4x+12 --> subtract 4x from both sides so 3x-27=12 --> add 12 to both sides so 3x=39 (divide both sides by 3) so then x= 13

3) again, vertical angles so 8x-120= 4x+16 --> subtract 4x so that 4x-120=16 --> add 120 to both sides and then 4x=136, divide both by 4 and x= 34

hope this helps:))

Answer:

1. The fixed costs is $40 and the cost per mile is [tex]\$\frac{3}{2}[/tex].

2.Therefore, the coffees did they sell is, 85 coffees

Step-by-step explanation:

1. To find the fixed cost and Cost per mile.

Since, a shipping company charges a fixed amount for their services and a certain amount per mile , they must travel.

Let the number of fixed amount be x and the certain amount per mile be y

then, the general linear equation for this we have:

[tex]x+y=C[/tex] where C is the charges cost by the shipping company.

It is given that for a 50 mile trip company costs $115 and an 80 mile trip costs $157.

we have an equation in linear form from the above data:

[tex]x+50y=\$115[/tex]            .....(1)

[tex]x+80y=\$157[/tex]           ....(2)

Now, solving these equation simultaneously we get,

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

Substitute the value of y in equation (1),

[tex]x+50\times\frac{3}{2}=\$115[/tex]

[tex]x+75=\$ 115[/tex]

⇒[tex]x=\$40[/tex]

Therefore, the fixed costs is $40 and the cost per mile is [tex]\$\frac{3}{2}[/tex].

2.

Let the hot chocolate sells be x and that of coffee be y.

At one game they sold, $200 worth of drinks and used 295 cups. if hot chocolate sells for $0.75 and coffee sell for $0.50.

An equation from the given condition are given by:

[tex]x+y=295[/tex]

[tex]0.75x+0.50y=200[/tex]

Solving these equation simultaneously we get the value of y=85

Therefore, the coffees did they sell is, 85 coffees

(64+36)x50= 5,000

Brainliest Please

50(64 + 36) = 5000

Hope this helps

-AaronWiseIsBae

3s+6 <=  -5(s+2)

3s+6 <=  -5s - 10

8s + 6 <= -10

8s <= -16

  s <= -2

Hello...

Tony and his three friends live in Albuquerque, New Mexico, but they all attend college in Boston, Massachusetts. Because they want to have a car at school this year, they are planning to drive Tony's car from Albuquerque to Boston at the beginning of the school year. Although they'll each pay for their own food during the road trip, the friends plan to split the costs for gas and hotels evenly between the four of them.

Estimate the total cost that each friend will have to pay for gas and hotels. Explain how you got your answer. Here are some figures that may help you out:

•Tony's car can travel 28 miles for each gallon of gas.

•The average fuel cost at the time of their trip is $3 per gallon.

•They plan to drive about 650 miles each day.

•They estimate the average cost of a hotel each night is $85.

•They will drive approximately 2,240 miles to get from Albuquerque to Boston.

Solution:

Cost of Gas:

2240 / 28 x 3 = $240

Cost of Lodging:

85 x floor2240 / 650 = $255

Cost of both: $240 +255 = $495.

The cost for a 1/4 share is $495/4 = $123.75.

A) N +2 = Q which equals

A) N -Q = -2

B) .05N +.25Q = 3.50  multiplying A) by .25

A) .25N -.25Q = -.5  then adding A) and B)

.30N = 3

Nickels = 10 Quarters = 12

*************DOUBLE CHECK ***************

.05 nickels = $0.50  .25 Quarters = $3.00

Melinda has 12 quarters and 10 nickels in her bank, totaling $3.50. By setting up and solving equations based on the values of the coins, we were able to determine the exact number of each type of coin.

Little Melinda has nickels and quarters in her bank, with two fewer nickels than quarters. The total amount of money she has is $3.50. To determine how many coins of each type she has, we need to set up equations based on the values of the coins and the given conditions.

Let's define:
Q = number of quarters
N = number of nickels
Since each quarter is worth 25 cents and each nickel is worth 5 cents, we have the following equations:

1. N = Q - 2 (since she has two fewer nickels than quarters)
2. (5 × N) + (25 × Q) = 350 cents (because the total amount is $3.50)

Substitute the first equation into the second to find the number of each coin:
5(Q - 2) + 25Q = 350
5Q - 10 + 25Q = 350
30Q - 10 = 350
30Q = 360
Q = 12

Then, substitute Q = 12 into the first equation to find N:
N = 12 - 2
N = 10

Therefore, Melinda has 12 quarters and 10 nickels.

Answer:

-29, -30, -31, -32, -33

Step-by-step explanation:

add them together

Answer: 4:1

Step-by-step explanation:

Given:- Number of tables in the classroom=6

Number of students on each table = 4

thus number of students in the classroom =6×4=24 students

Now ratio of numbers of students to the tables in the classroom= numbers of students/tables in the classroom=24/6=4/1=4:1

Ratio of numbers of students to the tables in the classroom= 4:1

Answer: -4x + 2y

Step-by-step explanation:

6x - 3y + 5y - 10 x

Group like terms:

= 6x - 10x  - 3y + 5y

Add similar elements :

6x - 10 x = - 4x

- 3y + 5y = +2y

Therefore:

-4x + 2y

Hope that helps!

The simplified form of the equation [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].

Further explanation:

A binomial is an algebraic expression which consists of two terms having operations of addition and subtraction.

Procedure:

The following steps are involved to simplify the algebraic expression.

1) First we collect the like terms from the given algebraic expression.

2) Second we add or subtract the like terms in the algebraic expression.

Given:

The algebraic expression is [tex]6x-3y+5y-10x[/tex].

Calculation:

Step 1:

First we collect the like terms from the given algebraic expression.

The given algebraic expression consists two variables [tex]x[/tex] and [tex]y[/tex].

Clearly, we can see that the given algebraic expression is in the form of binomial.

So, collect the terms of [tex]x[/tex] aside and the [tex]y[/tex] term on other side as follows:

[tex]\boxed{(6x-10x)+(5y-3y)}[/tex]

Step 2:

Now, add the given algebraic expression to simplify it.

[tex]\boxed{(6x-10x)+(5y-3y)=-4x+2y}[/tex]  

The above algebraic expression can be written as,

[tex]\boxed{2y-4x}[/tex]  

The simplified form of the algebraic expression [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].

Thus,  the simplified form of the algebraic expression [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].

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Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Simplification

Keywords: Addition, subtraction, operation, terms, like terms, unlike terms, variables, binomial, monomial, simplification, collecting the terms, coefficient, constant, value, algebraic expressions.

3 pens  per 1 seconds it is so easy

2/3 x 12 = 8

8 jelly beans were eaten

You would have to multiply 2/3 and 12 to find out how many jelly beans were eaten. 2/3*12=8

Follow below steps:

The question is asking to identify how many days will pass before Heather will have both a jelly sandwich and milk again, given that she eats a jelly sandwich every 5th day and drinks milk every 4th day. To find out when Heather will have both on the same day again, we need to find the Least Common Multiple (LCM) of the two numbers, 5 and 4.

The multiples of 5 are 5, 10, 15, 20, 25, and so on. The multiples of 4 are 4, 8, 12, 16, 20, and so on. The first common multiple of both 5 and 4 is 20. Therefore, Heather will have both a jelly sandwich and milk together on every 20th day after today.

So, after today, Heather will wait 19 more days before having both a jelly sandwich and milk on the same day again.

1 place to the right of a decimal point is the tenths, so you would multiply 7 by 1/10.

2 places to the right of the decimal point is the hundredths place, so you would multiply 23 by 1/100

The correct answer is D.

The answer is  B. 525 square units.

The polygon pictured is a composite figure made up of several rectangles. To find the total area, we can find the area of each of the rectangles and sum them together.

From the image we can find the following areas:

Top left rectangle: 9 square units

Top right rectangle: 14 x 3 = 42 square units

Bottom left rectangle: 7 x 14 = 98 square units

Bottom right rectangle: 27 square units

Summing the areas of each rectangle together gives us a total area of  9 + 42 + 98 + 27 = 176 square units.

However the prompt specifies that this is not the total area. There is a small square removed from the bottom left rectangle.  We can find the area of this square by subtracting the length of the small rectangle’s missing side (3 units) from the length of the whole rectangle’s side (14 units) and squaring the result. Subtracting 3 from 14 gives us 11 and squaring 11 gives us 121.

So the final area of the polygon is 176 - 121 = 55 square units.

Of the answer choices provided, only  55 square units matches our calculation. So the answer is  B. 525 square units.

helppppppp with???????

Answer:

y = 3x^2+15x-18

Step-by-step explanation:

Parabola has an equation with one variable in degree 2 and other in degree 1.

Given that y=3(x-1)(x+6) is the function.

y is of degree 1 and x of degree 2

Standard form of these types of parabolas would be

y =ax^2+bx+c.

To make the given equation in standard form, we multiply all factors on  the right side

y = 3(x-1)(x+6) = 3(x^2+5x-6)

= 3x^2+15x-18

a=3 b = 15 and c =-18

y = 3x^2+15x-18 is the standard form of the parabola

Answer:

y = 3x^2 + 15x - 18

Step-by-step explanation:

To represent the function y = 3 (x - 1) (x + 6), start by by expanding the equation by multiplying the common factor with each term inside the brackets to get:

y = 3 (x - 1) (x + 6)

y = (3x - 3) (x + 6)

Now multiply both the terms with each other to get:

y = 3x^2 + 18x - 3x - 18

Arrange the like terms together and add them:

y = 3x^2 + 15x  - 18

Hence, y = 3x^2 + 15x - 18 is the standard form of the given function.