If 4a² + 9b² = 25 and ab = 8, find the value of (2a + 3b)²​

Answer:

Commutative property of addition.

Step-by-step explanation:

The given expression is:

x + y + z = z + y + x

To match the example with the corresponding property, we need to simplify the expression using the commutative property of addition.

According to the commutative property of addition, the order of the terms in an addition expression does not affect its value. That is:

a + b = b + a

Using this property, we can rewrite the given expression as:

x + y + z = x + y + z

we see that both sides of the equation are identical. This means that the expression is true, regardless of the values of x, y, and z.

Therefore, the example "x + y + z = z + y + x" matches with the commutative property of addition.

For given expression e will be 7/3.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a single value.

Expressions can be simple or complex, and they can involve arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, logarithms, and trigonometric functions.

Now,

We can solve for e by setting the given value of f equal to 49 and then solving for e.

f = 9e²

When f = 49, we have:

49 = 9e²

Dividing both sides by 9, we get:

49/9 = e²

Taking the square root of both sides, we get:

±√(49/9) = ±(7/3) = e

So the solutions for e are e = 7/3 or e = -7/3. However, since e is a measure of distance and cannot be negative, the only valid solution is e = 7/3.

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Correct Question:-

Function f=9e² ,  If f=49 then solve for e.

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

The given equation is 4x+2 = 12.

To solve for x using the change of base formula, we need to isolate x on one side of the equation. We start subtracting 2 from LHS and RHS:

4x+2-2 = 12-2

4x = 10

Next, we use the change of base formula, which states log base a of b is equal to log base c of b divided by log base c of a. In this case, we want to find x, which is the exponent that 4 is raised to in order to get 10.

Rewrite equation:

x = log base 4 of 10

Use the change of base formula, we can present this as:

x = [tex]log base 10 of 10 / log base 10 of 4[/tex]

Simplifying:

x = 1.442114

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

In conclusion, using the change of base formula, the answer to the equation 4x+2 = 12 is roughly 1.442114. This method can be used to solve a variety of problems in the sciences, engineering, and financial sectors, as well as exponential and logarithmic equations.

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Answer:

Step-by-step explanation:

If the perimeter of a shape is 21 centimeters and one side is 7 centimeters, then we can find the total number of sides by dividing the perimeter by the length of one side:

Number of sides = Perimeter / Length of one side

Number of sides = 21 cm / 7 cm

Number of sides = 3

This means that the shape has 3 sides, which makes it a triangle.

Since all sides of the triangle have the same length, we can call it an equilateral triangle. In an equilateral triangle, all sides have the same length, and all angles are 60 degrees.

After answering the presented question, we can conclude that equation Therefore, the original price of the motorcycle is Rs 125700.

In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.

Let the original price of the motorcycle be P.

Depreciation per year = 4% of P = 0.04P

Cost of motorcycle after 3 years = P - 3(0.04P) = P - 0.12P = 0.88P

[tex]0.88P = Rs 110592\\P = Rs (110592/0.88)\\P = Rs 125700[/tex]

Therefore, the original price of the motorcycle is Rs 125700.

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Answer:

Median = 4.5

Step-by-step explanation:

4 and 5 are central numbers.

then:

(4+5)/2 = 4.5

Answer:

4.5

Step-by-step explanation:

if you add the two middle number 4+5=9

then i. you divide 9by2 you'll get the median

Answer:

Step-by-step explanation:

that would be 5 miles bc 3+2 is 5

The distance between Mary's and Roger's houses is approximately 3.6 miles.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

We can use the Pythagorean theorem to find the distance between Mary's and Roger's houses since they form a right triangle with the school at the vertex:

Let A be the school (0, 0), B be Mary's house (0, 2), and C be Roger's house (-3, 0).

Then the length of AB is 2 miles and the length of AC is 3 miles.

The distance between Mary's and Roger's houses is the length of the hypotenuse BC.

Using the Pythagorean theorem, we have[tex]BC^2 = AB^2 + AC^2 = 2^2 + 3^2 = 13.[/tex]

Taking the square root of both sides, we get[tex]BC = \sqrt{(13)} = 3.6[/tex] miles.

Therefore, Between Mary and Roger's homes, there are roughly 3.6 miles.

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Step-by-step explanation:

Triangle a) is half of an equilateral triangle therefore the height divides the base into two equal parts, same thing for triangle b), triangle c) instead is half square, therefore congruent catheti.

a)

n = 6 : 2

n = 3

m = √(6²+3²)

m = √45

b)

x = 10 x 2 = 20

y = √(20²-10²)

y = √300

c)

a = √(5²+5²)

a = √50

Answer:

34.56 in

Step-by-step explanation:

2.4*2.4*6=34.56

Answer:

C- 80 degrees Celsius

Step-by-step explanation:

If you followed the formula by subtracting 176 by 32 you would get 144 multiplied by 5/9 = 80 degrees

If three cards are drawn randomly for a standard card deck, then the probability that all three are different suits is 0.3976.

We know that the total number of cards in a standard deck is = 52 cards;

So, the probability of drawing 3 cards from a standard deck is =

⇒ ⁵²C₃ = 22100 ,

We know that each suit in a standard deck has 13 cards,

So, the probability of selecting 3 cards from a standard deck is :

⇒ 4(¹³C₁ × ¹³C₁ × ¹³C₁);

The probability that all three are different suits;

⇒ 4(¹³C₁ × ¹³C₁ × ¹³C₁)/22100,

⇒ 169/425,

⇒ 0.3976.

Therefore, the required probability is 0.3976.

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Answer:

B. y = f(x + 3) – 2

Step-by-step explanation:

We need move point (0,0) to point (-3,-2).

(-3,-2)=(a,b)

y=f(x-a)+b

y=f(x-(-3))-2

y=f(x+3)-2

Answer:

f(x) = (x+3)^3

I think this is the right answer...

Answer:

To find the maximum gas mileage, we need to find the vertex of the parabola representing the gas mileage function.

The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c is given by -b/2a.

In this case, the gas mileage function is m(x) = -0.026x^2 + 2.593x - 35.023, so a = -0.026 and b = 2.593.

The x-coordinate of the vertex is therefore:

x = -b/2a = -2.593/(2*(-0.026)) = 49.9 (rounded to one decimal place)

This means that the maximum gas mileage occurs at a speed of 49.9 mph.

To find the maximum gas mileage, we can substitute x = 49.9 into the gas mileage function:

m(49.9) = -0.026(49.9)^2 + 2.593(49.9) - 35.023 ≈ 36.1 mpg

Therefore, the maximum gas mileage is approximately 36.1 mpg.

Step-by-step explanation:

Answer:

The value of the vehicle would be $7,242

Step-by-step explanation:

Given,

The original value of the vehicle, P = $29,800,

Rate of depreciation, r = 9% = 0.09

Time, t = 15 years,

Thus, the value of the car after 15 years,

[tex]A=P(1-r)^t[/tex]

[tex]=29800(1-0.09)^{15}[/tex]

[tex]=29800(0.91)^{15}[/tex]

[tex]=7241.64363066[/tex]

[tex]\thickapprox \bold{\$ 7,242}[/tex]

The probability that the first white ball drawn in powerball will not be an 18 is 0.985.

Concept used:

Probability of an event = number of favorable outcomes / total number of outcomes.

We have 69 balls, out of which 1 is an 18. Thus, there are 68 balls that are not 18.

Therefore, the probability of the first white ball drawn in powerball will not be an 18 is given by,

P(event)= number of favorable outcomes / total number of outcomes= 68/69 = 0.985 (approx)

Thus, the required probability that the first white ball drawn in powerball will not be an 18 is 0.985, rounded to three decimal places.

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The correct population parameter for shop at this dealership that will purchase a Peterbilt truck is p that is option C.

In statistics, a population parameter characterises an individual or population. A population parameter describes the distribution of all values within a group and is a fixed but unknowable property. The parameters used in other sorts of maths should not be confused with this. These are the parameters of a mathematical function that never change. An indicator of the population is not a statistic. This information only applies to a portion of a certain demographic. You can determine the genuine population value with the aid of a well-designed research.

Statistics and parameters share many similarities. Both express a characteristic of the group, such as the fact that 20% of M&Ms are red. Yet, the fundamental distinction is in who and what they are describing. The entire population is referred to by parameters. The part or sample that was examined in a study is referred to as the statistic.

You might count the quantity of red M&Ms in the aforementioned example's various packs. Your statistic will be provided by this. If your study was well-designed, the statistic you obtain should precisely reflect the population parameter.

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Complete question:

A recent flyer claimed that 2 out of every 9 trucks sold at a local dealership are manufactured by Peterbilt. Find a 95% confidence interval for those who shop at this dealership that will purchase a Peterbilt truck. Identify the correct population parameter.

μ

х

р

p^

[tex]\mu_1 - \mu_2[/tex]

Xi – X2

î

Pi – P2

The volume of the cylinder is 785.40 cm³.

What is the formula for the volume of a cylinder?

[tex]V = π {r}^{2} h[/tex]

Where r is the radius of the cylinder and h is the height of the cylinder.

Since d is the diameter of the cylinder, we can find the radius by dividing d by 2.

Now, radius [tex]r = \frac{d}{2} = \frac{10}{2} = 5[/tex]

So, the volume of the cylinder is

[tex]V = π {r}^{2} h \\ = π {5}^{2} \times 10\\ = π×25×20 = 250π[/tex]

We know π = 3.14

So, V = 250×3.14

Using a calculator, we can approximate this to the nearest hundredth of a unit:

V ≈ 785.40

Therefore, the exact volume of the cylinder is 250π and its approximate value to the nearest hundredth of a unit is 785.40 cm³.

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The half-life of the radioactive substance is 7.5 days. This means that, after 7.5 days, half of the radioactive atoms will have decayed and the count per minute will be reduced by half

The half-life of a radioactive substance is the amount of time it takes for half of its radioactive atoms to decay. In this case, you are given the initial count per minute of 2800 and the count per minute after 15 days of 700. We can use this information to calculate the half-life of the radioactive substance. First, divide the initial count per minute (2800) by two. This gives us the count per minute that we need to find, which is 1400.

We then subtract the count per minute after 15 days (700) from the count per minute we need to find (1400). This gives us the difference in count per minute, which is 700. Now, we need to determine how much time it would take for the count per minute to decrease by 700. To do this, we divide the difference in count per minute (700) by the initial count per minute (2800). This gives us a decimal, which we then multiply by the number of days (15). The result is the half-life of the radioactive substance in days, which is 7.5 days.

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Answer: 10sec 660 feet, 20sec = 1320 feet, 30 sec = 1980 feet.

Step-by-step explanation:

It states that a car moves 660 feet in 10sec.

10sec = 660 feet

20sec: 660+660=1320f

30sec: 660+660+660=1980f

Answer:it’s wrong if so then 5 would’ve been in c’s place

Step-by-step explanation:

The volume of a sphere with a radius of 3cm is 113.04 cm³, which is approximately equal to 36π cm³. So, the correct option is D).

The formula for calculating the volume of a sphere, V = 4/3πr³, is used to find the amount of space enclosed by a sphere with a given radius. In this case, the sphere has a radius of 3cm. By substituting this value into the formula, we can solve for the volume of the sphere.

V = 4/3πr³

V = 4/3 × 3.14 × 3³ = 113.04 cm³

= approximately 36π cm³

The result is 113.04 cm³, which is approximately equal to 36π cm³. This calculation is important in many applications, such as engineering, physics, and mathematics. The correct answer is D).

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_____The given question is incomplete, the complete question is given below:

What is the volume of sphere r = 3cm? responses A 8π cm³ 8 pi, cm³  B 16π cm³ 16 pi, cm³ C 27π cm³ 27 pi, cm³ D 36π cm³

Answer: 86

Step-by-step explanation:

let x be the unknown

(84+92+88+ x)

-----------------------   =  87.5

          4

then cross multiply

(84+92+88+ x )= 87.5 times 4

84+ 92+ 88 + x= 350

add the left side

264+ x=350

subtract 264 from both sides

264 - 264 + x= 350 - 264

therefore x= 86.

Answer:

Step-by-step explanation:

Answer:

(-2,4) is quadrant 2, (8,4) is quadrant 1, (6,-2) is quadrant 4

Step-by-step explanation:

To prove that the sum of the exterior angles of any polygon is equal to 360 degrees, the Sum of interior angles = (n - 2) x 180 degrees.

we can use the following steps:

Draw any polygon and mark a point outside the polygon for each vertex.

Draw a line segment connecting each vertex to the point outside the polygon that corresponds to it, creating an exterior angle at each vertex.

Measure each exterior angle using a protractor and record the measurements.

Sum all the exterior angles together and observe the result.

We can see that the sum of all the exterior angles is always equal to 360 degrees, regardless of the number of sides or the shape of the polygon. This can be written as:

The sum of exterior angles = 360 degrees

To prove this algebraically, we can use the fact that the sum of the interior angles of any polygon is given by the formula:

Sum of interior angles = (n - 2) x 180 degrees

where n is the number of sides of the polygon. Each exterior angle is supplementary to the corresponding interior angle, so we can write:

The sum of exterior angles = Sum of interior angles (supplementary angles)

Substituting the formula for the sum of interior angles, we get:

Sum of exterior angles = (n - 2) x 180 degrees (supplementary angles)

= 180n - 360 degrees

= 360 degrees - 360 degrees + 180n

= 360 degrees - Sum of interior angles

= 360 degrees - (n - 2) x 180 degrees

= 360 degrees - 180n + 360 degrees

= 720 degrees - 180n

Since the sum of the exterior angles must be a positive value, we can take the absolute value and simplify:

|Sum of exterior angles| = |720 degrees - 180n|

= 180|4 - n|

Since n is always a positive integer greater than or equal to 3 (since a polygon must have at least three sides), we know that 4 - n is always a negative integer between -1 and -n+1. Therefore, |4 - n| is equal to n - 4. Substituting this into the equation above, we get:

|Sum of exterior angles| = 180|n - 4|

= 180(n - 4)

= 180n - 720 degrees

= 360 degrees - 360 degrees + 180n - 720 degrees

= 360 degrees - Sum of interior angles

Therefore, we have shown that the sum of the exterior angles of any polygon is equal to 360 degrees.

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We can conclude after answering the provided question that In order to slope make at least $225.00 in sales, we must solve for m:

[tex]s = 75m + 1500 225 = 75m + 1500\s75m = -1275\sm = -17[/tex]

Slope is the downward movement of a near - constant basis in mathematics. It is a test of how much the y-value of an activity appears to vary when the x-value changes. The curve of a line is ordinarily indicated by the letter m and can be determined using the equation: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) are any 2 things on the line. A line's slope can be positive, negative, zero, or unknown. A positive slope indicates that the line moves up from left to right, whereas a decreasing trend indicates that the line descends from left to right.

a. Because the relationship between the two variables is proportional, the function that connects the sales (s) and the number of muffins (m) is a linear function. The slope of the line can be calculated by dividing the change in sales by the change in the number of muffins:

slope = (2400 - 1800) / (12 - 4) = 600 / 8 = 75

The equation line is as follows:

s = 75m + b

To find the y-intercept (b), we can substitute one of the data points:

[tex]1800 = 75(4) + b\sb = 1800 - 300\sb = 1500[/tex]

As a result, the function that connects sales and the number of muffins is:

s = 75m + 1500

b. In order to make at least $225.00 in sales, we must solve for m:

[tex]s = 75m + 1500 225 = 75m + 1500\s75m = -1275\sm = -17[/tex]

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In the given figure of Rhombus, Angle ∠BAD is 0°. In summary: angle ∠ABC = 135°

angle ∠ADC = 135°

angle ∠BAD = 0°

What is rhombus?

A rhombus is a quadrilateral (four-sided) geometric shape with equal-length sides. Since it has two sets of opposite equal acute angles and opposite equal obtuse angles, it is also known as a diamond form. In other words, the opposite angles and the neighbouring sides of a rhombus are congruent. A rhombus has two equal-length diagonals that are right angles to one another. A rhombus's area is equal to the product of its diagonal lengths.

by the question.

In a rhombus, opposite angles are equal, so we know that:

angle ∠ABC = angle ∠ADC (opposite angles of rhombus)

angle ∠BCD = angle ∠BAD (opposite angles of rhombus)

We are given that angle ∠ADC is 135°. Therefore, angle ∠ABC is also 135°.

To find angle ∠BAD, we can use the fact that the angles of a quadrilateral sum to 360°. Since we know three of the angles (∠ABC, ∠BCD, and ∠ADC), we can find the fourth angle (∠BAD) by subtracting their sum from 360°:

∠BAD = 360° - (∠ABC + ∠BCD + ∠ADC)

= 360° - (135° + 90° + 135°)

= 360° - 360°

= 0°

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The volume of the pyramid is approximately 2.4 cubic centimeters.

The formula for the volume of a pyramid is given by

V = (1/3) × base area × height

Since the base of the pyramid is a square and the perimeter is 4.7 cm, each side of the square has a length of

s = perimeter/4 = 4.7/4 = 1.175 cm

The base area of the pyramid is

A = s² = 1.175² = 1.3806 cm²

Therefore, the volume of the pyramid is

V = (1/3) × 1.3806 × 4.7 = 2.4457 cm³

Rounding this to the nearest tenth of a cubic centimeter, we get

V ≈ 2.4 cm³

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The equation has no solution that satisfies the inequality.

This equation doesn't have a unique solution because it's contradictory. It should be noted that to see why, we can simplify the equation by subtracting 9 from both sides:

3x = 18 - 9

which simplifies to:

3x = 9

Now we can solve for x by dividing both sides by 3:

x = 3

However, if we substitute x = 3 back into the original equation, we get:

9 < 3(3) = 9

This isn't true. Therefore, the equation has no solution that satisfies the inequality.

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