Rewrite the expression 24x - 12 using the distributive property? Find eight equivalent expressions.

The expression \((x^2 + 1)(y^2 + 4)\) can be rewritten using Two Squares as \((xy-2)^2+(x+2y)^2\). The correct option is D.

The Two Squares identity is a special case of the identity: \((a^2 + b^2) = (a + b)^2 - 2ab\).

This identity can be used to factorize certain expressions involving squares of variables.

By using the Two Squares identity, we can rewrite expressions in the form of a sum of two squares as a difference of squares, or vice versa. This can be useful in simplifying and solving equations in algebra.

We can use the Two Squares identity, which states that:

\((a^2 + b^2)(c^2 + d^2) = (ac - bd)^2 + (ad + bc)^2\)

Comparing with the given expression, we can see that a = x, b = 1, c = y, and d = 2. Substituting these values into the Two Squares identity, we get:

\((x^2 + 1)(y^2 + 4) = (xy - 2)^2 + (x + 2y)^2\)

Therefore, the answer is (D) \((xy-2)^2 + (x+2y)^2.\)

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Answerh

Step-by-step explanation:

huh

Answer:

\(v = u + at \\ v = 3 + (1.5 \times 7) \\ v = 3 +10.5 \\ \boxed{v = 13.5 \: m {s}^{ - 1}} \)

The range of the temperature on the surface of Mars is given by the compound inequality 28°C ≤ t ≤ 140°C or 82.4 ≤ F ≤ 284.

The given statements are:

The range of temperature, t, on the surface of Mars is from 28°C to 140°C.

The statement says that the temperature lies in between those two values. That is nothing but the word "and" separates the two values.

So, compound inequality for the given statement is

28°C ≤ t ≤ 140°C

To convert the temperature from Celcius to Fahrenheit, we need to substitute t = 5/9(F - 32)

28 ≤ 5/9(F - 32) ≤ 140

Multiplying both sides with 9/5, we get

28 × 9/5 ≤ 5/9(F - 32) × 9/5 ≤ 140 × 9/5

⇒ 50.4 ≤ F - 32 ≤ 252

Adding 32 on both sides, we get

50.4 +32 ≤ F - 32 + 32 ≤ 252 + 32

⇒ 82.4 ≤ F ≤ 284

Thus the compound inequality for the given statement is 28°C ≤ t ≤ 140°C or 82.4 ≤ F ≤ 284.

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Answer:

6y

Step-by-step explanation:

3(2y)

= 6y

So, the answer is 6y

Answer:

back 5 miles south west

Step-by-step explanation:

hope this help have a good day.

This problem is incomplete, but applying the relation between velocity, distance and time, LeBron could find the flight with the fastest average speed dividing distance by time.

Velocity is distance divided by time, that is:

v = d/t.

Hence, to find the fastest flight, he needs the highest speed, which is found  dividing distance by time.

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Answer:

Step-by-step explanation:

To solve the exercise, first, we are going to write in numerical form the equation shown in fraction models:

Now, you can solve the equation for x:

To subtract these fractions, you can amplify the fraction 4/10, that is, multiply by 10 in the numerator and denominator of the fraction:

Now that both fractions have the same denominator, it is easier to subtract them, since it is enough to subtract their numerators. So, you have:

Therefore, the fraction that makes the equation true is

and the correct answer is option C.

Answer:

a=\(\frac{-1}{2}\)x−4

Step-by-step explanation:

Step 1: Add -x to both sides.

2a+x+−x=−8+−x

2a=−x−8

Step 2: Divide both sides by 2.

\(\frac{2a}{2}\)=\(\frac{-x-8}{2}\)

Answer: 32.2 cubic inches

Step-by-step explanation:

 The volume of one coin can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.

Substituting the given values, we get:

V = π(1.4)^2(0.0625)

V ≈ 0.14 cubic inches (rounded to the nearest hundredth)

To find the total volume of all the coins, we can multiply the volume of one coin by the number of coins:

Total volume = 230 × 0.14

Total volume ≈ 32.2 cubic inches (rounded to the nearest hundredth)

Therefore, the coins take up approximately 32.2 cubic inches of the treasure chest.

Answer: 0.18 (18 cents) per ounce

Step-by-step explanation:

2.88/16 = 0.18

Answer:

An adult cheetah can run 103 feet per second!

Step-by-step explanation:

First we need to convert our miles to feet, there are 5,280 feet in one mile.

So 70 miles multiplied by 5,280 feet is 369,600 feet.

Now we need to convert an hour to seconds.

There are 60 seconds in one minute, so we multiply 60 seconds by 60 minutes, there are 3,600 seconds in one hour.

Now we need to divide the number of feet by the number of seconds.

369,600 ÷ 3,600 = 102.666667

102.666667 rounded to the nearest whole number is 103.

Answer:

151°

Step-by-step explanation:

The above shape is a quadrilateral.

The exterior angles are :

82°, 70°, 62°, and (x -5)°

Therefore,

82 + 70 + 62 + x - 5 = 360

214 -5 + x = 360

209 + x = 360

x = 360 - 209

x = 151°

Answer:

30.00

Step-by-step explanation:

The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:

\(V(x) = x(10-2x)(16-2x)\)
Taking the derivative with respect to x:
\(V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x\)
Setting V'(x) = 0 and solving for x:
\(10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0\)
Solving for x using the quadratic formula:
\(x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07\)
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.

Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106

Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.

Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

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a) The extreme values of V are:

Minimum value: V(0) = 0

Relative maximum value: V(3) = 216

Absolute maximum value: V(4) = 128

b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.

a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of V(x), we get:

\(V'(x) = 48x - 36x^2 - 4x^3\)

Setting this equal to zero and solving for x, we get:

\(48x - 36x^2 - 4x^3 = 0\)
4x(4-x)(3-x) = 0

So the critical points are x = 0, x = 4, and x = 3.

We now need to test these critical points to see which ones correspond to maximum or minimum values of V.

We can use the second derivative test to do this. Taking the derivative of V'(x), we get:

\(V''(x) = 48 - 72x - 12x^2\)

Plugging in the critical points, we get:

V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)

To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:

V(0) = 0
V(3) = 216
V(4) = 128

So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
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Answer:

$166.71

Step-by-step explanation:

210.19-43.48=166.71

1) Estimate value of the product of 2/3 and 0.55 is, 2/3.

2) The fraction part is, 55 / 100

3) The product of the two numbers is, 11/30

We have to given that,

Estimate the product of 2/3 and 0.55.

And, Convert the decimal 0.55 to a fraction.

And, The product of the two numbers.

Now,

Estimate the product of 2/3 and 0.55,

So, we can round 0.55 to the nearest whole number, which is 1.

Then, multiply 2/3 by 1 to get an estimate of the product.

so, The correct answer is 2/3.

Now, we can convert the decimal 0.55 to a fraction,

= 0.55

= 55/100

= 11/20

Thus,  The correct answer is, 55/100.

And,  the product of 2/3 and 0.55,

= 2/3 x 55/100

= 110/300

= 11/30.

Hence, The correct answer is, 110/300 or 11/30

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Answer:

x = 5

Step-by-step explanation:

Answer:

Amount of money she gets per day -> $1.50

Amount of money she gets after x days -> \(1.5x\)

Total amount of money = 3 + 1.5x

Total amount of money = y

\(1.5x+3=y\)

There are 130 shark cookies should they order this month.

We have to given that;

Last month, they sold 65 shark cookies and 85 clown fish cookies.

Hence, If they plan to order 170 clown fish cookies this month.

Then, Number of shark cookies should they order this month is, x

Hence, We get;

65 / 85 = x / 170

x = 130

Thus, There are 130 shark cookies should they order this month.

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Using the coefficient of variation, it is found that the correct statement is:

The coefficient of variation of a data-set is given by the division of the standard deviation of the data-set by the mean of the data-set. The higher the coefficient, the most dispersed the data-set is from the mean.

For the Stars, the mean is of 16 and the standard deviation is of 4.1, hence the coefficient is:

\(cv_S = \frac{4.1}{16} = 0.256\)

For the Dolphins, the mean is of 18 and the standard deviation is of 1.5, hence the coefficient is:

\(cv_D = \frac{1.5}{18} = 0.083\)

For the Giants, the mean is of 14 and the standard deviation is of 0.3, hence the coefficient is:

\(cv_G = \frac{0.3}{14} = 0.021\)

For the Mackerels, the mean is of 15 and the standard deviation is of 2.3, hence the coefficient is:

\(cv_M = \frac{2.3}{15} = 0.153\)

Due to the higher coefficient, the ages of the Stars are the most dispersed from the team's mean.

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Answer:

Statement 2 (The ages of the Stars are the most dispersed from the team’s mean).

Step-by-step explanation:

Edge

Given parameters:

Real area = 9000sq yards

Map area = 6sq yards

Unknown:

Scale of the map = ?

Solution:

A scale is the ratio of the map unit to the real world expression. Maps use scales to present the real world in a smaller sample space:

   For this problem;

              6sq yards on map = 9000sq yards on ground

              1sq yards on map = xsq yards on ground

                     6x  = 9000

                         x = \(\frac{9000}{6}\)  = 1500sq yards

So,

            1sq yards on map is 1500sq yards on ground

As a result of answering the given question, we may state that Rounding equation up to the nearest hundred dollars, the car's value 19 years later is around $2,500.

In mathematics, an equation is a statement stating the equality or two expressions. An equation consists of two sides split by an algebraic equation (=). For illustration, the argument "2x + 3 = 9" argues that the statement "2x + 3" is equal to the value "9". The goal of equation solving is to find the value or values of the variable(s) to make the equation true. Simple or complex equations, regular or nonlinear, and including one or more factors are all possible. For example, the equation "x2 + 2x - 3 = 0" has the variable x raised to the second power. Lines are used in many fields of mathematics, including algebra, calculus, or geometry.

Because the car depreciates by half every six years, the car's value after t years is provided by:

\(V(t) =18000*(1/2)^(t/6)\)

To determine the worth of the car 19 years after purchase, we must analyse V(19):

\(V(19) = 18000*(1/2)^(19/6) ≈ $2,480.32\)

Rounding up to the nearest hundred dollars, the car's value 19 years later is around $2,500.

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The height of the intersection of a line from the bottom of the first to the top of the second is a line from the top of the first to the bottom of the second, and it is 6 m.

In order to find the height of the point where a line from the top of the first to the bottom of the second intersects a line from the bottom of the first to the top of the second if two flagpoles are 10 m and 70 m tall and are 100 m apart, we can use similar triangles.

        The height can be found by calculating the length of the third side of a triangle whose other two sides are the height of the first flagpole and the length between the two flagpoles respectively.

        Let us now assume that a line is drawn from the top of the first flagpole to the bottom of the second flagpole. The point where it intersects with a line drawn from the bottom of the first flagpole to the top of the second flagpole is the point where we are to find the height. The flagpoles are 100 m apart, so the horizontal distance between these two lines is 100 m.

       The height of the first flagpole is 10 m, and the height of the second flagpole is 70 m, respectively.

       The height of the point where these two lines intersect can be found using similar triangles. Since these two lines intersect at right angles, we can use Pythagoras' theorem to find the distance between the two flagpoles.

        This distance is √(100² + 60²) = √10000 + 3600

                                                           = √13600

                                                           ≈ 116.62 m.

         Let x be the height that we are to find. Thus, we have a right triangle where one side is x, and another side is     116.62 - 100 = 16.62. The third side is the difference between the heights of the two flagpoles, which is 60.

       The similar triangles will be:

                          x/10 = (60 + x)/70x

                                  = 7x/6 + 1.7x

                                   = 10.2x

                                x = 6m

                  Therefore, the height of the point where a line from the top of the first to the bottom of the second intersects a line from the bottom of the first to the top of the second is 6 m.

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The probability that a student scored less than 55% on the exam is 0.134%.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of the sample = 70

Standard deviation = 5

= P(X<55%)

Z = (55-70)/5

Z = -3

P(X < -3)

From the Z table:

P(x<-3) = 0.0013499

or

P(x<-3) = 0.134%  

Thus, the probability that a student scored less than 55% on the exam is 0.134%.

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Answer:

1.2

Step-by-step explanation:

(I am not a good explainer)

Step-by-step explanation:

y = x² - 3x + 6

y = 2x + 6

y = y

x² - 3x + 6 = 2x + 6

x² - 5x = 0

x(x - 5) = 0

x = 0 and x = 5

y = 2x + 6 and y = 2x + 6

y = 2(0) + 6 and y = 2(5) + 6

y = 0 + 6 and y = 10 + 6

y = 6 and y = 16

(x1,y1) and (x2, y2) = (0,6) and (5,16)

Option → A