Ayden filled up his car with gas before embarking on a road trip across the country. The car uses 2 gallons of gas for every hour driven, and after driving for 4 hours, there were 4 gallons of gas left in the tank. Write an equation for
�
,
G, in terms of
�
,
t, representing the number of gallons of gas remaining in Ayden's gas tank after
�
t hours of driving.

the hands do form a right angle during Mario's math class, at 2:35:17.5 p.m. (rounded to the nearest half-second).

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

During the class from 2:00 p.m. to 2:50 p.m.,

the hour hand will move from the 2 to the 3 and will be halfway between the 2 and 3 at 2:30 p.m. The minute hand will make one full revolution around the clock face, from the 12 to the 12, during this time.

Let's calculate the positions of the hour and minute hands at 2:30 p.m.:

The hour hand moves 1/12 of the way around the clock face for each hour or 30 degrees for each hour. At 2:30 p.m.,

it will have moved 2.5 hours, so it will be 2.5 * 30 = 75 degrees past the 2 o'clock mark.

The minute hand moves 360 degrees in 60 minutes or 6 degrees per minute. At 2:30 p.m.,

it will have moved 30 minutes, so it will be 30 * 6 = 180 degrees past the 12 o'clock mark.

To determine if the hands form a right angle, we need to calculate the angle between them. Let's call this angle "A".

The angle between the hour and minute hands is the absolute difference between their positions, which is 105 degrees in this case (180 degrees - 75 degrees).

If the minute hand is ahead of the hour hand by exactly a quarter of a revolution or 90 degrees, then the hands will form a right angle.

So, we need to check whether angle A is equal to 90 degrees. If A = 90 degrees, then the hands form a right angle, and we can calculate the time when this happens by finding the time at which the minute hand is exactly 90 degrees ahead of the hour hand.

Let's set up an equation to solve for the time t:

A = 90 = 180 - 75 - 6t

Solving for t, we get:

t = 17.5

Therefore, the hands do form a right angle during Mario's math class, at 2:35:17.5 p.m. (rounded to the nearest half-second).

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Answer:

Step-by-step explanation:

a. 4x + 8

b. 14x

c. 8x + 12

d. 6x + 6y + 6z

Answer:

Step-by-step explanation:

1]4(x+2)

using distributive property ,

Multiply 4 to x and 2

4x + 8

2]4(2x+3)

using distributive property ,

Multiply 4 to 2x and 3

= 4 x 2x + 4 x 3

= 8x +12

3](6 + 8).x

= (14).x

14x

4] 6(x + y + z)

using distributive property ,

multiply 6 to x and y and z

6.x + 6.y + 6.z

6x + 6y +6z

The number of ways that this can be done is given as follows:

272,160.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The number of ways for each department is given as follows:

Hence the total number of ways is given as follows:

9 x 8 x 7 x 6 x 10 x 9 = 272,160.

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Answer: 32 Ounces

Step-by-step explanation:

The container holds 32 ounces because if there are 2 pounds of peanuts, and 1 pound = 16 ounces, then you multiply 16 by 2.

16 x 2 = 32

The one making the most money in one week is by sales manager which is an amount of $1006.25.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

Given that,

Hourly rate of a head mechanic = $37.52 per hour

Number of hours worked in a week = 25 hours

Money made = 25 × 37.52 = $938

Hourly rate of a assistant mechanic = $30.42 per hour

Number of hours worked in a week = 30 hours

Money made = 30 × 30.42 = $912.6

Hourly rate of a sales manager = $28.75 per hour

Number of hours worked in a week = 35 hours

Money made = 35 × 28.75 = $1006.25

Hourly rate of a front desk clerk = $15.09 per hour

Number of hours worked in a week = 40 hours

Money made = 40 × 15.09 = $603.6

Money most made is by sales manager.

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Your question is incomplete. The complete question is given as,

Who would make the most money in one week? a head mechanic working 25 hours with an hourly rate $37.52 per hour, an assistant mechanic working 30 hours with an hourly rate $30.42 per hour, a sales manager working 35 hours with an hourly rate $28.75 per hour, a front desk clerk working 40 hours with an hourly rate $15.09 per hour?

The expression "eight more than the sum of a number and 7 is 90" can be written as: 8 + (x + 7) = 90

From the question, we have the following parameters that can be used in our computation:

eight more than the sum of a number and 7 is 90

Express the numbers properly

So, we have

8 more than the sum of a number and 7 is 90

Express the operators properly

8 + (x + 7) = 90

hence, the expression is 8 + (x + 7) = 90

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Therefore , the solution of the given problem of square comes out to be the square's perimeter is higher than the number of square units for the square's surface.

A square, according to Euclidean mathematics, is a quadrilateral with four equal sides and four equal angles. Another term for a rectangle is a shape with two neighboring sides that are the same length. A quadrilateral is said to be equilateral if one of its 4 triangular edges and four equal corners is a square. A cubical angle refers to one that's 90 ° or straight. The square's diagonals are evenly spaced and split in half at a 90-degree angle.

Here,

We can use the formulas for area and perimeter of a square to decide which is greater: its area or perimeter with sides that are 10 units long.

A = s², where s is the extent of one edge, calculates the area of a square. The square's size in this instance is

=> 102 = 100 square units.

P = 4s, where s is the length of one edge, calculates the perimeter of a square. In this instance, the square's circumference is

=> 4(10)

=> 40 units.

We can see that the perimeter is larger than the area by comparing the two values.

Consequently, we can draw the conclusion that the number of units for the square's perimeter is higher than the number of square units for the square's surface.

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Answer:

a and b

Step-by-step ex

Answer:

8.407

Step-by-step explanation:

8.767−0.36

= 8.767−0.36

=8.767+(−0.36)

= 8.407

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Solution:-

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Hope it helps! :)

To find the area of the given circle we have to use the formula πr², where π=22/7 and r is radius of the circle. The area of the circle is 1519.76 square feet.

A circle is a closed two-dimensional figure in which all sets of points in the plane are equidistant from a specific point called the "center". A line passing through the circle forms a line of specular symmetry. It is also rotationally symmetrical about the center at any angle. 

Solution for the area of the circle:

Given, radius = 22 feet

∴Area of the circle = πr²

                               = (22/7)×22²

                               = 3.14 × 484

                               = 1519.76 square feet

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Answer: 7 batches

Step-by-step explanation:

If Eduardo makes 4 batches, he will need 2/3 x 4 = 8/3 cups of flour.

To add 3 more batches, he will need 3 x 8/3 = 8 cups of flour.

In total, Eduardo will need 8/3 + 8 = 32/3 + 8 = 32/3 + 24/3 = 56/3 cups of flour for 7 batches. Therefore, Eduardo will need 8 cups of flour if he makes 3 more batches, and he will need 56/3 cups of flour in total if he makes 7 batches.

Answer:

Step-by-step explanation:

A.  h = -2(1)² + 7(1) + 4 = 9 ft

B.  use the quadratic formula to find the 2 solutions to t when

y = f(t) = -2t² + 7t + 4 = 0         a=-2, b=7, c=4

the 2 solutions for t are:  -1/2, 4

halfway between t=-1/2 and t=4 is:  (-1/2 + 4) /2 = 1.75   (vertex of the parabola)

so, at t = 1.75 s, the toy is at its max. height:

h = -2(1.75)² + 7(1.75) + 4 = 10.125 ft

C.  Toy is in the air for 4 sec

The answer is 4 s because f(4) = 0, meaning the toy hits the ground after 4 sec

Mary can bake 8 cakes the with 7 cups of flour she possesses because we are unable to create a quarter of a cake.

Starch, a polymer, is one of the ingredients in all-purpose flour, which has the chemical formula (C6H5O10)n (C 6 H 5 O 10) n.

We need to divide Mary's total flour supply by the quantity of flour required for creating one cake in order to determine how many cakes she can produce.

First, we must divide 5 by 6 to get the fraction 5/6 in decimal form:

5 ÷ 6 = 0.8333...

Hence, 0.8333 cups of flour are required to produce one cake.

We're able to divide Mary's entire flour supply by the quantity of flour needed to produce one cake:

7 cups of flour ÷ 0.8333 cups of flour per cake = 8.4 cakes

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The estimated area of the field enclosed by the fence is approximately 220.5 square meters.

A basic geometry theorem that explains the relationship between a right triangle's three sides is known as the Pythagorean theorem.

We can employ the following strategy to determine how much of the field the fence is enclosing:

Include the lengths of the fence sections in a rough sketch of the field.

Make a straightforward polygon that resembles the field's shape using the fence sections.

To calculate the area of the triangle-shaped portion of the field, use the triangle's area formula ([tex]A = 1/2 \times base \times height[/tex]). We must identify the triangle's base and height in order to accomplish this.

The Pythagorean theorem can be used to calculate the triangle's height: [tex]a^2 + b^2 = c^2[/tex]where a and b are the triangle's two shorter sides (9 meters and 12 meters, respectively), and c is the longest side (15 meters). When we solve for (a), we see that it is equal to

(a)

[tex]= \sqrt{(c^2 - b^2)} \\= \sqrt{(15 2 - 12 2}) \\= \sqrt{(81)} \\= 9 meters.\\[/tex]

The triangle is therefore 9 meters tall. The 9-meter fence portion serves as the triangle's base.

When we apply the triangle's area formula, we obtain:

A is equal to half of the base plus the height, or 9 meters plus 9 meters, or 40.5 square meters.

The area of the remaining field must be increased by the area of the triangle. This estimate may not be very exact because we have just estimated the field's form, but it should at least give us a general notion of the field's size.

If the remaining area of the field has a roughly rectangular form, we can calculate its area by multiplying the rectangle's length and width. The 12-meter and 15-meter fence sections can be used as a guide to determine the rectangle's size.

By dividing the width by the length, we obtain:

180 square meters is the size of the remaining part (12 meters times 15 meters).

To determine the approximate total size of the field, add the areas of the rectangle and triangle portions:

Total area estimated: 40.5 square meters plus 180 square meters, which equals 220.5 square meters.

As a result, the field's approximate area inside the barrier is 220.5 square meters.

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Answer:

8.52

Step-by-step explanation:

add the two 3.99 making 7.98 then add 3.50 making 11.48 then substract that from 20.00 making the final answer 8.52

Answer:

[tex]\frac{1}{256}[/tex]

Step-by-step explanation:

Given

[tex]\left(4^4\right)^{-1}[/tex]

We can use the power rule to multiply the exponents.

The power rule for exponents states

[tex]\left(a^b\right)^{c}=a^{bc}[/tex]

[tex]4^{4*-1}[/tex]

Multiply 4 by −1.

[tex]4^{-4}[/tex]

Rewrite the expression using the negative exponent rule.

The negative exponent rule states

[tex]a^{-b}=\frac{1}{a^b}[/tex]

[tex]\frac{1}{4^4}[/tex]

Raise 4 to the power of 4.

[tex]\frac{1}{256}[/tex]

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Check the picture below.

so we really have six 5.5x5.5 squares

[tex]\stackrel{ \textit{Area for 6 squares} }{(6)(5.5)(5.5)}\implies \text{\LARGE 181.5}[/tex]

Answer:

it 39 ×90 for sure it 3510

So, the simplified form of the given expression is cosxsinx(3cosx - sinx).

A statement, at least two parameters or integers, and one or more calculations make up a mathematical expression. It is possible to multiply, divide, add, or subtract quantities using this mathematical operation. The following is the expression's structure: An expression is (total count, numerical operator, number, or variable).

We can simplify the given expression using the product-to-sum identities:

sin2x × cosx + cos2x × sinx

= 2sinx × cosx × cosx + (cos²x - sin² x) × sinx [using the identity sin2x

= 2sinx × cosx and cos²x = cos² x - sin² x]

= 2sinx × cos² x + cos²x × sinx - sin² x × sinx [expanding the brackets]

= cosx × sinx(2cosx + cosx - sinx)

= cosx × sinx(3cosx - sinx)

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The future value earning need to save $527.13.

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

Here  $50,000 now at 3% inflation will become 50000*1.03^250 after 20 years.

i.e.  $121,363 is required in retirement years (for 20 years)

Calculate the PV of these payments 7% is calculated as below.

FV = 0; 1/y = 7%; n=20; PMT = 121363; calculate PV = $1,191,560

Now we want to get $1,191,560 at the start of retirement by saving per year  to get the per month amount.

FV = 1191560; PV = 0; n= 12*35; 1/y = 7%/12; calculate PMT  = $527.13

Hence you have to save $527.13 dollar per month.

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In response to the supplied query, we may state that Margo will thus interest have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The principle balance divided by the interest rate is the most typical approach to compute interest.

Margo will be required to repay the $2000 she borrowed plus an additional 8% of that sum as interest each year if she borrows the money at an 8% annual interest rate.

principle multiplied by the interest rate equals interest.

where "principal" refers to the initial loan amount and "rate" is the interest rate in decimal form. The interest rate in this situation is 8%, or 0.08 in decimal form.

Margo will so be required to pay the following interest each year:

interest: $160 x ($2,000 x 0.08)

Margo will thus have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.

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Step-by-step explanation:

20/28 = (20 ÷ 2) / (28 ÷ 2) = 10/14 = 5/7

15/21 = (15 ÷ 5) / (21 ÷ 5) = 5/7

25/35 = (25 ÷ 5) / (35 ÷ 5) = 5/7

So, 20/28, 15/21, and 25/35 are equivalent to 10/14.

This expression divides 360 by -1 to get -360.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.

Here are two possible multiplication/division expressions that equal -360:

18 x (-20) = -360

This expression multiplies 18 by -20 to get -360.

360 ÷ (-1) = -360

Therefore, This expression divides 360 by -1 to get -360.

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &708000\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A = 708000(1 - 0.16)^{10} \implies A=708000(0.84)^{10}\implies A \approx 123830.07[/tex]

Answer: the length is 6

Step-by-step explanation:

3+3+6+6=18

3x6=18

Answer:

105 or 40500

Step-by-step explanation:

you have too add or mutilple

Answer:

3. x = 3, y = 1 --> = (3,1)

4. x = 2, y = 1 --> = (2,1)

Step-by-step explanation:

3.

x+5y =8

x = 8-5y

-x+2y=-1

-8+5y+2y=-1

7y-8=-1

7y=-1+8

7y=7

Divide 7 from both sides

y = 1

x=8-5y

x=8-5(1)

x = 3

4.

y=x-1

y=-2x+5

-2x+5=x-1

5=x-1+2x

5=3x-1

5+1=3x

6=3x

Divide 3 from both sides

2=x

x=2

Answer: 9 and 3

Step-by-step explanation: Depends the signs +/- and the problem.

The slope of the lines are given as

a) m₁ = -2

b) m₂ = 4/3

c) m₃ = 5/2

d) The equation of line is y = ( 1/2 )x + 9/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

a)

Let the first point be P ( 3 , 5 )

Let the second point be Q ( 7 , -3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = ( -3 - 5 ) / ( 7 - 3 )

Slope m₁ = -8/4

Slope m₁ = -2

b)

Let the first point be P ( 4 , 2 )

Let the second point be Q ( 10 , 10 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₂ = ( 10 - 2 ) / ( 10 - 4 )

Slope m₂ = 8/6

Slope m₂ = 4/3

c)

Let the first point be P ( -1 , -2 )

Let the second point be Q ( -3 , -7 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₃ = ( -7 - ( -2 ) ) / ( -3 - ( -1 ) )

Slope m₃ = -5/-2

Slope m₃ = 5/2

d)

Let the first point be P ( 5 , 7 )

The slope of the line is y = 1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 7 = ( 1/2 ) ( x - 5 )

y - 7 = ( 1/2 )x - 5/2

Adding 7 on both sides , we get

y = ( 1/2 )x + 9/2

e)

The slope of the line is y = 5/2 and the points are linear

Hence , the equation of line is y = ( 1/2 )x + 9/2

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The complete question is :

Determine the slopes between the points in lowest terms

a) ( 3 , 5 ) and ( 7 , -3 )

b) ( 4 , 2 ) and ( 10 , 10 )

c) ( -1 , -2 ) and ( -3 , -7 )

d) Draw and accurate graph of the line with the slope of ( 1/2 ) that passes through the point ( 5 , 7 )