1. If a truck tire holds 25.0 liters of air at 25.0°C, what will be the volume of air in the tire if the temperature
increases to 30.0 C

A variable can be any number or alphabet that may constantly vary and the equation to represent the given situation for Kira is (3x+y) and for Hector is (3x+z) where x is the time for solos and y and z are times for piano. The value of x and y is 3.5 minutes and that of z is 7 minutes.

According to the question,

We have the following information:

Each person performed for the same amount of time. Kira sang three solos and played a piano piece. Hector sang 2 solos and played a piano piece that lasted twice as long as Kira's. Each of the solos Kira and Hector sang was 3.5 minutes long.

Now, let's take time for solos to be x min and time for Kira's piano to be y min and that for Hector is z min.

So, we have the following equations:

Kira:

3x+y

Hector:

2x+z

Now, z = 2y

x = 3.5 minutes

Time is equal:

3x+y = 2x+z

3x+y = 2x+2y

3x-2x = 2y-y

x = y

y = 3.5 min

z = 2*3.5

z = 7 min

Hence, a variable can be any number or alphabet that may constantly vary and the equation to represent the given situation for Kira is (3x+y) and for Hector is (3x+z) where x is the time for solos and y and z are times for piano. The value of x and y is 3.5 minutes and that of z is 7 minutes.

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The equation that represents the relationship between m and n is written as: n = 7m.

A proportional relationship between two variables have a slope of constant of proportionality, k, which is y/x.

The equation that represents a proportional relationship is expressed in slope-intercept form as y = kx.

In this situation m = x, and n = y.

The constant of proportionality, k = n/m.

Find the constant of proportionality, k, using a pair of values from the given table, say (3, 21):

k = 21/3

k = 7

To write the equation, substitute k = 7 into n = km:

n = 7m.

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Answer:

The coordinates of B are (4, 2)

Step-by-step explanation:

The coordinates of B can be calculated as follows ?

The midpoint of line AB is M(3,-3)  is derived from the formula

[tex]M=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]

Where [tex]x_1[/tex] and [tex]y_1[/tex] are the coordinates of A and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the coordinates of B

Since the coordinates of A are (2, -8), then the value of [tex]x_1[/tex] is 2 and the value of [tex]y_{1}[/tex] is -8.

Since the [tex]x[/tex]-coordinate of M is 3, then the equation to follow is

[tex]\frac{x_{1}+x_{2}}{2}=3[/tex]

Substitute 2 for [tex]x_{1}[/tex], then it follows that

[tex]\frac{2+x_{2}}{2}=3[/tex]

Multiply both sides of the equation by 2

[tex]\frac{2+x_{2}}{2}\times 2=3\times 2[/tex]

Simplify both sides of the equation

[tex]2+x_{2}=6[/tex]

Substract 2 from both sides of the equation

[tex]2-2+x_{2}=6-2[/tex]

Simplify the equation

[tex]x_{2}=4[/tex]

Since the [tex]y[/tex]-coordinate of M is -3, then the equation to follow is

[tex]\frac{y_{1}+y_{2}}{2}=-3[/tex]

Substitute -8 for [tex]y_{1}[/tex], then it follows that

[tex]\frac{-8+y_{2}}{2}=3[/tex]

Multiply both sides of the equation by 2

[tex]\frac{-8+y_{2}}{2}\times 2=-3\times 2[/tex]

Simplify both sides of the equation

[tex]-8+y_{2}=-6[/tex]

Add 8 to both sides

[tex]-8+8+y_{2}=-6+8[/tex]

Simplify the equation

[tex]y_{2}=2[/tex]

Since the value of [tex]x_{2}[/tex] is 4 and the value of [tex]y_{2}[/tex] is 2, then the coordinates of B are (4,2).

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The division equation is x * 3/8 = 5/4 and there are (10/3) times 3/8s there in 5/4.

Let's assume that x times 3/8 are in 5/4.

So, calculating a division equation for the value of x.

x * 3/8 = 5/4

=> x = 5/4 * 8/3

=> x = 40/12

Dividing the numerator and denominator by 4.

We get, the value of x equal to

=> x = 10/3

Division equation: A division equation is a mathematical expression containing a division operator. Division equations are useful not only in math class but also in everyday life.

For example, if we want to share a bundle of papers equally with our friends, we can use this solution to find the given question. 100 papers and we have 10 friends. To find out how many papers each person gets, divide 100 by 10. The solution is 10. This means that each friend receives 10 papers.

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Step-by-step explanation:

we know, the area of a rectangle is

length × width

so, we have here

length × (x - 5) = x² - 7x + 10

therefore,

length = (x² - 7x + 10) / (x - 5)

so, just by looking at it (with experience) I see that length is (x - 2).

but let's do the actual polynomial division, which seems to be the desired exercise here.

x² - 7x + 10 ÷ x - 5 =

it is very similar to actual number divisions.

we go from left to right.

we start with the first term (x²) and see how many times (x - 5) would fit into it. for that we look only at the first term in x - 5 (that is x).

x² / x = x

that is already our first term of the result (quotient) :

x² - 7x + 10 ÷ x - 5 = x

now, we multiply that result with the divisor (x - 5) and subtract that from the dividend.

x² - 7x + 10 ÷ x - 5 = x

- x² - 5x

--------------

0 - 2x

and now we pull down the next term from the dividend :

x² - 7x + 10 ÷ x - 5 = x

- x² - 5x

--------------

0 - 2x + 10

and we repeat the process with that new dividend :

-2x / x = -2

that is our next term of the quotient.

x² - 7x + 10 ÷ x - 5 = x - 2

- x² - 5x

--------------

0 - 2x + 10

we repeat the process of multiplying that term (-2) with the divisor (x - 5) and subtracting that result from the dividend :

x² - 7x + 10 ÷ x - 5 = x - 2

- x² - 5x

--------------

0 - 2x + 10

- -2x + 10

-------------

0 0

there is no remainder, and there is no more term to pull down. we are finished.

the result of the division is (as expected) : x - 2

the expression to describe the length is therefore

x - 2

Answer:

Original equation

distributive property

subtract 5x from both sides

add 12 to both sides

Divide both sides by 14

Step-by-step explanation:

The value of n is 22.

In this question, we have been given the parallel lines HE and AD are

cut by transversal BF at points G and C, respectively.

Consider the following diagram.

If m∠HGF = 5n and m∠BCD = 2n +66, we need to find n.

∠HGF and ∠BCD are alternate exterior angles.

We know that  alternate exterior angles are congruent.

So, m∠HGF = m∠BCD

5n = 2n +66

5n - 2n = 66

3n = 66

n = 66/3

n = 22

Therefore, the value of n is 22.

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Answer:6978

Step-by-step explanation:304585

The maximum height of the diver as calculated from the function is   14.54 feet.

The function that represents the position of the diver is

h(t) = -16t² + vt + 10

The diver is at a height of 10 feet.

So at t=0 , h=10

Now we will find the rest of the solutions from the graph which follows the path of a parabola .

at t=1.42 , h(t)=0

Therefore 0 = -16(1.42)² + 1.42t + 10

or, V =15.68 ft/s

Again:

For h(t) to be maximum we have to find t for which h'(t)=0 , so we diff

h'(t) = -32t +15.68

or, t = -15.68 / 32

or, t = 0.49 seconds

Now h(0.49) =  16(0.49)² + 1.42 × 0.49 + 10 = 14.54 feet

Hence the maximum height of function is 14.54 feet

Therefore the diver has an initial velocity of 15.68 ft/sec and the diver reached a height of 14.54 feet at the maximum point.

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The area of trapezoid ABCD is 37.5 units^2.

Trapezoid is a type of quadrilateral with at least one pair of parallel sides. The area of trapezoid is given by:

Area = ½(a + b)*h

Where a and b are the length of two parallel sides and h is the perpendicular length between the length of two parallel sides.

In the given trapezoid ABCD, which is defined by coordinates of A, B, C, and D, the distance of each side is given by: √((x2 – x1)^2 + (y2 – y1)^2)

The length of a (DA) = √((x2 – x1)^2 + (y2 – y1)^2) = √((-3 – 0)^2 + (2 – (-2))^2) = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5 units

The length of b (BC) = √((x2 – x1)^2 + (y2 – y1)^2) = √((7 – 1)^2 + (-3 – 5)^2) = √((6)^2 + (-8)^2) = √(36 + 64) = √(36 + 64) = √(100) = 10 units

The length of h (AB) = √((x2 – x1)^2 + (y2 – y1)^2) = √((1 – (-3))^2 + (5 – 2)^2) = √((4)^2 + (3)^2) = √(16 + 9) = √(25) = 5 units

Hence, the area of trapezoid:

Area = ½ (5 + 10) * 5 = 7.5 * 5 = 37.5 units^2

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Answer: [-1, ∞)

Step-by-step explanation:

     First, we will simplify the equation.

     Given:

t - 1/3 ≥ -12/9

     Add 1/3 to both sides of the equation:

t ≥ -1

     Next, we know that a bracket is used when representing greater than or equal to and less than or equal to. Here, it's greater than or equal to so we will use a bracket on the left side.

     Then, t can be any value to infinity above -1, so we will use ∞) on the right side.

[-1, ∞)

The equation in terms of log(x) and log(z) is, [tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].

What is logarithmic expression?

A logarithmic equation is one in which a variable-containing expression's logarithm is used as a solution. If you can write both sides of the equation as powers of the same number, that will help you answer exponential equations.

Consider, the given logarithmic expression,

[tex]logx\sqrt{z}[/tex]

By using the logarithmic rule: log(ab) = log(a) + log(b)

So,

[tex]logx\sqrt{z} = log(x) + log\sqrt{z}[/tex]           ..(1)

Replace [tex]\sqrt{z}[/tex] by [tex]z^\frac{1}{2}[/tex].

So,

[tex]log\sqrt{z} = logz^\frac{1}{2}[/tex]

Apply the rule: [tex]loga^b = b log(a)[/tex]

Therefore, [tex]log(\sqrt{z}) = \frac{1}{2}log(z)[/tex]

Substitute this value in equation (1).

[tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].

Hence, the expression in terms of x and z is, [tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].

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Based on heads and feet of chicken and rabbits, there are 12 rabbits in the cage.

Let us represent chicken by x and rabbit by y. So, we all know that chicken and rabbit have 1 head each. We also know that chicken has 2 feet and rabbit has 4 legs. Now forming the equation accordingly.

Equation for head -

x + y = 35 : Equation 1

Equation for feet -

2x + 4y = 94 : Equation 2

Rewriting equation 1 according to x

x = 35 - y : Equation 3

Keep the value of x from equation 3 in equation 2

2(35 - y) + 4y = 94

Preforming multiplication on Left Hand Side

70 - 2y + 4y = 94

Performing subtraction

2y = 94 - 70

2y = 24

y = 24 ÷ 2

Performing division

y = 12

Thus, there are 12 rabbits in the cage.

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The expression represents the time she spent driving is       [tex]\frac{228.95}{x}[/tex]

The expression represent the time she spent driving can be calculated as follows:

We know that

Time = [tex]\frac{distance}{ speed}[/tex]

Let x be her speed on the first half of the trip.

Then for first half , the tiime she takes is

T1= [tex]\frac{150}{x}[/tex]

while in a second half the time taken by her is

T2= [tex]\frac{150}{1.9x}[/tex]

T2= [tex]\frac{78.95}{x}[/tex]

the total time she spent on driving is

T1 + T2 =    [tex]\frac{150}{x}[/tex] + [tex]\frac{78.95}{x}[/tex] =    [tex]\frac{228.95}{x}[/tex]

Hence, the expression represents the time she spent driving is       [tex]\frac{228.95}{x}[/tex]

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The expression that could represent the amount of sodium per serving, in milligrams, in the new soup recipe is y = 0.67x

From the information, the new soup recipe contains 33% less sodium per serving than the old soup recipe.

Let's say Sodium in an old soup recipe per serving = x mg

Let's say Sodium in a new soup recipe per serving = y mg

The new soup recipe contains 33% less sodium per serving than the old soup recipe

y = x  - (33/100)x

100y = 100x  - 33x

100y = 67x

Divide through by 100

y = 0.67x

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The amount owed by the debtor is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Using the range idea, the following scenario is represented by the inequality 0 ≤ y ≤ 2000. Here option D is the correct answer.

A function's range is the set that contains all of the output values that the function can take. In the context of this problem, the following input and output are provided:

Input the number of crates that have been loaded into the vehicle. Total weight of the crates loaded into the vehicle as output.

Because the weight of an amount can never be negative, and the greatest weight is 2,000 pounds, as stated in the issue, the range in this context is reflected by the following inequality: 0 ≤ y ≤ 2000.

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x = 1.53347526

Take the log of both sides of the equation.

[tex]ln(2^{3x-1} ) = ln(3^{x-2} )[/tex]

Expand [tex]ln(2^{3x-1} )[/tex] by moving 3x-1 outside the logarithm

[tex](3x-1)ln(2)= ln(3^{x-2} )[/tex]

Move x-2 outside the logarithm      [tex]ln(3^{x-2} )[/tex]

[tex](3x-1)ln(2) = (x-2)ln(3)[/tex]  

Solve the equation for x

[tex]x = -[\frac{{2ln(3)-ln(2)}}{3ln(2)-ln(3)} ][/tex]

The value of x is 1.53347526(After applying the log values)

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Answer:

∴ x = 90

Step-by-step explanation:

(180 - x)° = x° (vertically opposite angles)

  180 - x = x

        -2x = -180

         2x = 180

        ∴ x = 90

Nathan can drive 83 miles without exceeding the budget.

Let us assume the number of miles Nathan can go in $75 budget be x. Now forming the equation based on the mentioned information -

The total budget = daily rental charge + number of miles × cost per mile

Keep the values in formula -

75 = 29.50 + 0.55x

Rewriting the equation according to variable x

0.55x = 75 - 29.50

Performing subtraction on Right Hand Side of the equation

0.55x = 45.5

x = 45.5 ÷ 0.55

Performing division on Right Hand Side of the equation

x = 82.7

As 0.7 will be counted a mile, thus, Nathan can drive 83 miles.

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The numeric value of the expression 8n at n = 6 is different of 56, hence n = 6 is not a solution to the expression 8n = 56.

A number a is a solution to an expression if the numeric value of the expression at input a generates an identity with the expression.

In this problem, the expression is given as follows:

8n = 56.

We want to verify if the number six is a solution to the presented expression.

The numeric value of the expression at n = 6 is found replacing the lone instance of n by 6, hence it is obtained as follows:

8n = 8 x 6 = 48.

(the product of 8 and 6 is 48).

Then the equality would be of:

48 = 56.

Which is a contradiction, hence n = 6 is not a solution to the expression 8n = 56.

The problem is:

Explain how to determine if the number is a solution to the equation. 56 = 8n for n = 6

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Answer:

Step-by-step explanation:

In the given triangle AED, segments GB and FC are parallel to base ED. Points G and F are on segment AE in that order. Lengths AG=2, GF=5, FE=3, GB=6, and CD=7 are given. You want the lengths of AB, BC, FC, and ED.

Segments of transversals crossed by parallel lines are proportional:

  AG : GF : FE = AB : BC : CD

  2 : 5 : 3 = AB : BC : 7

Multiplying the first ratios by 2 1/3 will give the second ratios:

  2 : 5 : 3 = 4 2/3 : 11 2/3 : 7

This lets us conclude ...

  AB = 4 2/3

  BC = 11 2/3

Corresponding segments of similar triangles are proportional:

  AG : GB = FA : FC = AE : ED

  2 : 6 = (5+2) : FC = (5+2+3) : ED

We notice the second number in the first ratio is 3 times the first number. That means these ratios are ...

  2 : 6 = 7 : 21 = 10 : 30

This lets us conclude ...

  FC = 21

  ED = 30

The lengths of the missing sides are calculated to be

The parallel lines in the figure created similarity between the dimensions, this makes the ratio of the dimensions equal

The given dimensions that is used to find the missing sides

Solving for AB

AB / CD = AG / FE

AB / 7 = 2 / 3

cross multiplying

3 * AB = 7 * 2

AB = 14/3 = 4.667

Using AB, GF is calculated

AB / BC = AG / GF

14/3 / BC = 2 / 5

cross multiplying

BC = (5 * 14/3) / 2

BC = 35/3 = 11.667

Solving for FC

GB / FC = AG / A'F

6 / FC = 2 / (2 + 5)

cross multiplying

2 * FC = 6 * 7

FC = 42/2 = 21

Solving for ED

GB / ED = AG / AE

6 / ED = 2 / (2 + 5 + 3)

cross multiplying

2 * ED = 6 * 10

ED = 60/2 = 30

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Answer:

320 pounds sterling

Step-by-step explanation:

All you have to do is $380.80 divided by $1.19 which is equal to one pound sterling. Hope this helps!

The system that models the equation is m = 2.5 lb.

This is a mixed-up issue.  The combination of

80% almonds and 20% peanuts make up combination A.

Completely peanuts in mixture B

both the

As a combination, use 60% peanuts and 40% almonds.

Since mixture C is created by combining mixtures A and B, we may calculate its combined weight in pounds to be 5 pounds.

Hence, we

Let m be the weight in pounds of mixture A (20% peanuts, 80 % almonds).

and

50-m is the quantity of mixture B in pounds.

Consequently, the set of equations that models this circumstance is:

0.20m + 1(50-m) = 0.60(5) (5)

0.80m + 0(50-m) = 0.40(5)

Equation 2's solution for m gives us

m = 2.5 lb.

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Answer:

1.35⁷ = 8.1722 (to 5sf)

By using the distance formula, The distance between the points (−6, −3) and (0, 5) is 10 units.

In geometry, we use the distance formula to evaluate the distance between two points whose coordinates are given,

The coordinates of the points are given as [tex](x_{1} ,y_{1})( x_{2} ,y_{2} )[/tex]

Then, the distance (D) between them is given by :

[tex]D = \sqrt{(x_{1} -x_{2} )^{2} -(y_{1} -y_{2} )^{2} }[/tex]

Now, the given points are  (−6, −3) and (0, 5).

Putting these values in the distance formula, we have

[tex]D = \sqrt{(-6-0)^{2}+ (-3 -5)^{2} }\\ \\D = \sqrt{36 +64 \\\\ \\D = 10[/tex]

Hence, the distance between the points (−6, −3) and (0, 5) is 10 units.

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Answer: 10 units

Step-by-step explanation: i took the test and got it right

From the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.

As given in the question,

Let x represents the number of nickels

And y represents the number of quarters

Total number of nickels and quarters are 35

Total value of given coins = $2.50

Required equation for the given condition is:

x + y = 35   ___(1)

1 nickel = 0.05 dollars

1 quarter = 0.25 dollars

0.05x + 0.25y <2.50 ___(2)

Substitute x = 35 - y in (2) we get,

0.05 ( 35 - y ) + 0.25y < 2.50

⇒1.75 - 0.05y + 0.25y < 2.50

⇒ 0.2y < 2.50 - 1.75

⇒ 0.2y < 0.75

⇒ y < 3.75

Maximum number of quarters for the given condition is equal to 3.

Therefore, for the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.

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The graph that represents the solutions of the given system of equations is attached below.

We are given a system of equations. The first equation is a quadratic polynomial. The second equation is linear in nature. The equations are given below.

x² - y = -2

4y - 8 = x

We need to find the solution to the equations using a graph. The graph of the equations is attached below. The graph of the first equation is represented by an upward parabola. The graph of the second equation is represented by a straight line. The intersection points of the two curves are the solutions to the given system of equations.

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Answer:10 blocks

Step-by-step explanation: East And West are in a straight line

Answer: -1

Step-by-step explanation:

Answer:

By counting, to go from one point to another, we go down 4, over 4. This means the slope is -4/4. This can then be simplified.

-4/4 = -1

So, the slope is -1