Modeling with Mathematics:

A square-shaped parking lot with 100-foot sides is reduced by x feet on one side and extended by x feet on an adjacent side.

a) The area of the new parking lot is represpresented by (100+ x)(100 – x).
Find this product.

b) Does this area of the parking lot increase, decrease, or stay the same? Explain your thinking. (You can use example values for x to help explain.)

1) For this question, all we need to do is to plug it in the value for x.

So,

2/3x -8 =0 Plugging into x the value x=12

2/3(12) -8 =0

8 -8 =0

0

So when x=12, then the equation is equal to zero. This leads us to conclude that 12 is the root or the solution of this equation.

The positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].

The given expression is [tex](4^{-2})^3[/tex].

A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.

The given expression can be simplified as follows

[tex](4^{-2})^3[/tex] = [tex]4^{-2\times3}=4^{-6}[/tex]

So, the positive exponent = [tex]\frac{1}{4^6}[/tex]

Therefore, the positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].

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Answer:

Step-by-step explanation:

Given Equation

3x^2 + x = - 2x - 7  

Solution

Add 2x + 7 to both sides

3x^2 +x + 2x + 7 = -2x - 7 + 2x + 7           Combine like terms

3x^2  + 3x + 7 = 0

Givens

x = (-b +/(√b^2 - 4ac))/2

x = (-3 +/- (√3^2 - 4(3 *7)) / 2*3

x = (- 3 +/- (9 - 84)) / 2 *3

x = (- 3 +/- √ (-75))/6

x = (- 3 +/-  8.660i ) / 6

x = -.5 +/-1.443i

Answer

x = -.5 + 1.443.i

x = -.5 - 1.443i

Answer:

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Explanation:

To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.

Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so

r² = 537/1986

r² = 0.2704

r = √0.2704

r = 0.52

Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so

For 1 hour

Amount left = 1986(0.52) = 1032.7 grams

In the same way, the amount left after 3 and 4 hours is

For 3 hours

Amount left = 537(0.52) = 279.2 grams

For 4 hours

Amount left = 279.2(0.52) = 145.2 grams

Therefore, the complete table is

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Answer:

BIDMAS is a math term that is used to describe these 6 terms.

Brackets

Indices, which is another word for exponents

Division

Multiplication

Addition

Subtraction

Answer:

It is the order of operation in order to know how to calculate an equation starting from which order.

Step-by-step explanation:

Brackets first

Indices second

Division and multipaction third. From left to right

Addition and subtraction last. From left to right

The equation for the cost when the bowling alley charges $14 for the first game $10 for the second game is 24 + 5x.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario

In this case, the bowling alley charges $14 for the first game $10 for the second game and $5 per game for every game after.

Let the number of games be illustrated as x.

Therefore, the equation will be:

14 + 10 + (5 × x)

= 24 + 5x

This illustrates the cost.

An overview was given as the information given is incomplete.

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Using proportions, it is found that:

42. x and y are not proportional.

43. The number 21 is 60% of 35.

44. The number 27 is 36% of the number 75.

Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.

From the table, the ratios are given as follows:

Different ratios, hence the variables x and y are not proportional.

To find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.

The decimal equivalent of a percentage of 60% is:

60/100 = 0.6.

Hence the percentage of 35 is calculated as follows:

0.6 x 35 = 21.

The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:

27/75 x 100% = 36%.

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Answer

Option D is correct.

Midpoint = (2, 1)

Explanation

The midpoint of two coordinates is obtained by respective x-coordinates together and dividing by 2 and then doing similarly for the y-coordinate.

(-4, -8) and (8, 10)

Midpoint = (x, y)

x = (-4 + 8)/2 = (4/2) = 2

y = (-8 + 10)/2 = (2/2) = 1

Hope this Helps!!!

Answer: do c to my very ecucated guess bc c is always right

Step-by-step explanation:

Step-by-step explanation:

Solution

We are given

Distance = 5/2 miles

Time = 1/4 hours

Answer:

The speed would [tex]10~\text{mph}[/tex].

Step-by-step explanation:

Step 1: State the formulas required

The formula for speed is:

[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]

Step 2: Substitute the values into the formula

The distance is [tex]\frac{5}{2}~\text{miles}[/tex] and the time is [tex]\frac{1}{4}~\text{hours}[/tex].

Substitute these values into the formula:

[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\[/tex]

Step 3: Calculate

[tex]\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\div {\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\times 4\\\\\text{Speed}={\frac{20}{2}}\\\\\text{Speed}=10[/tex]

So, the speed is  [tex]10~\text{miles per hour}[/tex]  or  [tex]10~\text{mph}[/tex].

The distance between the two cities on the map is 0.45 inches , the correct  option is (A) 0.45inches  .

In the question ,
it is given that

the scale factor of the  map is 25 miles = 0.1 inches

So, 1 mile = 0.1/25 inches

= 0.004 inches

So , on the map 1 mile is represented by 0.004 inches

Given that the real distance between the two cities is 112.5 miles

So , on the map  112.5 miles = 112.5*0.004 inches

= 0.45 inches

Therefore , the distance between the two cities on the map is 0.45 inches , the correct  option is (A)0.45inches  .

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Answer : x = 30 degrees

< JKL and < MKQ are complementary

Let < MKQ = x

Angle JKL is twice the measure of angle MKQ

JKL = 2 x MKQ

Sum of a complementary angles = 90 degrees

< JKL + < MKQ = 90

< JKL = 2MKQ

Substitute the value of < jkl

2(<2MKQ + Since, Therefore,

2x + x = 90

3x = 90

Divide both sides by 3

3x / 3 = 90/3

x = 30 degrees

The probability that they pick the same number is 1/8.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

As given two students each use a random number generator to pick an integer between 1 and 8 inclusive.

So, the possible choices are,

8 - 1 + 1 = 8  Possible choices: 1, 2, 3, 4, 5, 6, 7, 8.

So, the probability is, 1/8.

Therefore, the probability that they pick the same number is 1/8.

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[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.

Given:

[tex]f(x) = 1048 - 16x^{2}[/tex]

Since the function f(x) is the height (h), we can write the function as :

[tex]h = 1048 - 16x^{2}[/tex]

We will make x the subject:

[tex]16x^{2} = 1048 - h[/tex]

[tex]x^{2} = \frac{1048 - h}{16}[/tex]

[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]

[tex]x = \sqrt{65.5 - 0.0625h }[/tex]

Since:

[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]

Thus:

[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]

Therefore, the inverse function is  [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.

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Answer:

Explanation:

The volume of a gas in a container varies inversely with the pressure on the gas

Let V represent volume

Let P represent Pressure

Rewrting the statement above Mathematically:

when V = 230 in³

P = 8 lb/in³

Substitute the value of P and V in the equation in order to ger k:

Given:

Price of chair = $320

Price of lamp = $55

Total cost of furniture Greg purchased is = $320 + $55 = $375

Since the store charges a 7% sales tax, it means the amount Greg paid in tax is

7% of Total cost of furniture purchased.

Thus, the amount Greg paid in tax is:

The amount Greg paid in tax

Answer:

the value of 2/3 ^-2 is 18

Answer:

Step-by-step explanation:-32x³z³+48x∧4z

Using the concept of area, we got 165 bags is the smallest number of bags there groundskeeper must buy to cover the circular field.

The branch of mathematics which deals with measuring is known as Mensuration. It was basically first used for land surveys and other civic works in  Egypt. The father of mensuration is known as Archimedes. Mensuration is a discipline of mathematics which studies the measurements of various geometrical forms  possible and their areas, perimeters, and volumes, among other things.

Diameter of the field = 290 feet, radius = 145 feet

Area of the circular field =[tex]\pi r^{2}[/tex]

=>[tex]\pi[/tex]×145×145 =66018.5 square feet.

No of bags to be brought = 66018.5/400=165bags,

Hence, the smallest number of bags is 165 which groundskeeper must buy to cover the circular field.

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Answer: x = -4

Step-by-step explanation:

Multiply both sides by 2 to get:

-3x = 12

Then, divide both sides by -3 to get:

x = -4

Hope this helps!

Answer:

x = -4

Step-by-step explanation:

Triangles A, B, and C have a scale factor less than 1 in common

The figure that completes the question is added as an attachment

From the figure, we can see that triangles A, B, and C are smaller than the original triangle i.e. the triangle D

This means that triangle D is dilated by a scale factor less than 1 to form each of these triangles

This has just a slight difference to (a)

From the figure, we can see that triangles E, F, and G are bigger than the original triangle i.e. the triangle D

This means that triangle D is dilated by a scale factor greater than 1 to form each of these triangles

The conclusion about the scale factors is that

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There is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.

The equation of a perpendicular line to a line in point-slope form is expressed as:

Determine the slope:

Since there is no slope, hence the equation of the line will be in the form y = b.

Therefore, there is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.

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Correct question:

2) Choose the correct answer.

A given line passes through points (2, 3) and (2, 3). Determine the equation of thethe line that is perpendicular to the given line and passes through the point (1,5).

(A) y = 5

(B) x = -1

(C) x=5

(D) y= -1/2x + 13/3

(E) y = -1

The coat has a total cost of  $533.644

From the question, the given parameters are:

Cost of a coat = $74.95

Sales tax in the city = 612%

Using the sales tax, the total cost for the coat is calculated using

Total cost of coat = Cost of a coat + Cost of a coat * Sales tax in the city

Substitute the known values in the above equation

So, we have the following equation

Total cost of coat = 74.95 + 74.95 * 612%

Evaluate the products

Total cost of coat = 74.95 + 458.694

Evaluate the sum

Total cost of coat = 533.644

Hence, the total cost of the coat is $533.644

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The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional.

Occurrence to determine the conditional probability. P(A and B) = P(A) * P if A and B are two Independent events (B).

How can you calculate the likelihood of two occurrences, A and B, coming together?

The probability of their union, or the event that either A or B occurs, is equal to the total of their probabilities less the sum of their intersection if two occurrences A and B are not disjoint. P(A) + P(B) - P(A and B) (A and B).

The answer is then (0.28 + P(B) - (0.51 = 0.23).

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To calculate hte possible values of y you have to apply the Pythagoras theorem:

Where

c will be the distance between the given points, and the hypothenuse of a right triangle

a will be the base of a theoretical triangle below the hypothenuse, you calculate it as (x2-x1)

b= will be the heigth of said triangle, you calculate it using the y-coordinates (y2-y1)

So:

Replace the expression with the given measurements to calculate the y-coordinate of the first point:

The possible values for y, since its

The discount rate is 15% and the VAT rate is 13%

The following can be deduced:

MP = 2080

Discount = d%

VAT = (d-2)%

Cost = 1997.84

Apply discount:

2080 - d% = 2080*(1 - 0.01d)

Add VAT:

2080*(1 - 0.01d) + (d - 2)%

2080*(1 - 0.01d) * (1 + (d -2)/100)

2080*(1 - 0.01d) * (0.98 + 0.01d)

= 1997.84

(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080

0.98 + 0.01d - 0.0098d - 0.0001d²

= 0.9605

- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0

0.0001d²- 0.0002d - 0.0195 = 0

d² - 2d + 195 = 0

Solving the quadratic equation we get:

d = 15

Therefore discount is 15%

VAT rate = d - 2 = 15% - 2% = 13%

The concept shown above is the calculation for the discount and the amount of the value added tax.

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The image above represents a proof of the Pythagorean Theorem is image B.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship in Euclidean geometry between the three sides of a right triangle.

It states that the sum of the squares of the leg lengths equals the square of the hypotenuse length.

This is illustrated as:

a² = b² + c²

The values in image 2 will be used to ascertain this. Therefore,

5² + 12² = 13²

25 + 144 = 169

169 = 169

Therefore, B is correct as the value is gotten.

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Answer:

u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye

Step-by-step explanation:

The result of the expression given is 3x - 3

To solve this problem, we have to simplify the equation, and write the expression.

Given that

[tex]\sqrt{x^2}+ 2x -3[/tex]

In the square root, we can eliminate the square and square root using the square root rule.

Lets apply that in this expression

[tex]\sqrt{x^2} + 2x - 3\\x + 2x - 3[/tex]

Lets solve the expression

[tex]x + 2x - 3\\3x - 3[/tex]

The value of the expression given is 3x - 3

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SOLUTION:

Step 1:

In this question, we have the following:

Step 2:

Part A:

The function that models the population of Star, ID in years since 2000 is:

Part B :

Use your function to predict the population of Star, ID in 2050

The year 2050 means that t= 50, we have that:

Part C:

The function:

models the population of Eagle, ID in years (x) since 2000.

Which city is growing faster? How do you know?

Answer:

From this equation, we can see that the growth rate is 5.6% annually.

Comparing this, with the initial function:

We can see that the annual growth rate of f(x) is 9.9 %

CONCLUSION:

The population of Star ID, with the function, g (x) has a faster growth rate.