PLEASE HELP, I NEED TO FACTOR THESE EQUESTIONS WITH STEP BY STEP SHOWN PLEASE !!!

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:

It will take him 11 hours to mow 12 lawns

Step-by-step explanation:

110/2=55   (meaning it takes him 55 minutes to mow 1 lawn)

55x12=660    (meaning it takes him 660 minutes to mow 12 lawns)

660/60=11   (meaning it takes him 11 hours to mow 12 lawns)

Why 660/60? Because there is 60 minutes in 1 hour.

Answer:

34.56 in

Step-by-step explanation:

2.4*2.4*6=34.56

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.

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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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

Answer:

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

Step-by-step explanation:

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:

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.

The set A.{x | x R, x < 5} would have a graph with an open circle on 5 and a ray pointing left on the number line.

What exactly is a set?

In mathematics, a set is a collection of distinct objects or elements, which are considered as a single entity. The objects or elements in a set can be anything, such as numbers, letters, people, animals, or other things, depending on the context.

Now,

The set  A.{x | x R, x < 5}  would have a graph with an open circle on 5 and a ray pointing left on the number line.

This is because the symbol "<" means "less than," so the set A includes all real numbers less than 5. The open circle on 5 indicates that 5 is not included in the set, so the graph will have an open circle on 5. The ray pointing left indicates that the set extends infinitely to the left of 5.

In contrast, set B.{x | x R, x > 5} would have an open circle on 5 and a ray pointing to the right, since it includes all real numbers greater than 5. Set C.{x | x R, x ≤ 5} would have a closed circle on 5 and a ray pointing to the left, since it includes all real numbers less than or equal to 5.

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Answer: You'll have to plug each function into a calculator and match the corresponding ones with each other.

for example Sin45° = B cos 45°

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: Its A

Ive took this test :3

The proportion of red gumballs in the random sample is 0.4, meaning 40% of the 200 gumballs are red. To estimate the number of red gumballs in the entire population of 200 gumballs, we multiply the proportion of red gumballs by the total number of gumballs, 0.4 x 200 = 80.

Proportion in mathematics refers to the equality of two ratios. It asserts that two ratios are comparable. A ratio is a fractional comparison of two numbers or quantities, such as a/b or c/d.

To estimate how many of the 200 gumballs are red, we can use the proportion of red gumballs in the random sample and apply it to the entire population of 200 gumballs.

The proportion of red gumballs in the random sample is:

10/25 = 0.4

This means that 40% of the gumballs in the random sample are red.

To estimate the number of red gumballs in the entire population of 200 gumballs, we can multiply the proportion of red gumballs by the total number of gumballs:

0.4 x 200 = 80

Therefore, we can estimate that there are approximately 80 red gumballs in the machine.

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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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Answer:

a. 4

b. -2

c. 0,5

Step-by-step explanation:

1. 4

2.2

3.0,5

IT IS SAYING TO WORK OUT WHAT THAT LINE REPRESENTS

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

The car has actually travelled 1745 miles, even though the odometer reads 2005. This is because the odometer skips the digit 4, so the number of valid readings must be counted and subtracted from the odometer reading.

We can approach this problem by counting the number of valid readings on the odometer between 3000 and 5000. We can then subtract the number of invalid readings (i.e., readings that contain the digit 4) to determine the actual number of miles the car has travelled.

The valid readings between 3000 and 5000 are: 3001, 3002, 3003, 3005, 3006, 3007, 3008, 3009, 3010, ..., 4997, 4998, 4999, 5000.

There are a total of 2001 valid readings in this range.

However, we need to subtract the number of invalid readings, which are the readings that contain the digit 4. Since the odometer skips the digit 4, we can think of each valid reading as having four possible digits (0, 1, 2, or 5) for each of its four places. Therefore, the number of invalid readings is 4 x 4 x 4 x 4 = 256.

So the actual number of miles the car has travelled is 2001 - 256 = 1745.

Therefore, the car has actually travelled 1745 miles.

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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:50%

Step-by-step explanation: Since there are 6 letters in orange, and there are 3 vowels in the word (o,a,e), that would mean there is a 3/6 chance (50%) of selecting a vowel.

Answer:

I think it is not ?

Step-by-step explanation:

You get a remainder at the end when you solve it and that's the opposite of what divisible means

"(of a number) capable of being divided by another number without a remainder."

Answer:

Not divisible

Step-by-step explanation:

5^7  is 78125

5^6 is 15625

15625 + 78125 = 93750

93750/60 = 1562.5

Therefore it is not fully divisible by 60.

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:

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]

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.

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...

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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