what function is equivalent to y = 3x(x+2)^2+7?

The Perimeter of the pentagon ABCDE is 17 units.

If two points in coordinates plane P(a, b) and Q(c, d) then the distance between these points are

PQ = √(c-a)² + (d-b)²

Given:

The coordinates of Pentagon are  A (4, 3), B (7, 3), C (8, 0), and D (2, -3) and E(0, 1).

Using Distance formula

AB = √(7-4)² + (3-3)²

AB = √9

AB = 3

BC = √(8-7)² + (0-3)²

BC = √1 + 9

BC = √10

CD = √(2-8)² + (-3-0)²

CD = √36  + 9

CD = √45

CD = 3√5

DE = √(0-2)² + (-3-1)²

DE = √4 + 16

DE = √20

DE = 2√5

So, Perimeter of the pentagon ABCDE = AB+BC+CD+DE+EA

                                                                 = 3 + √10 + 3√5 + 2√5

                                                                 = 3 + √10 + 5√5

                                                                 = 17.342 unit

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Answer: 22

Step-by-step explanation:

Just because it is right yk.

Based on the ratio of the​ office's area to the area of the home, the deductible amount is $760.

The ratio refers to the relative quantity of one value contained in another.

Generally, ratios are depicted as fractions, decimals, or percentages.

Total home area = 2400 ft²

Office area =380 ft² (20 x 19)

The ratio of office to home area = 380/2400

The percentage of office use of the home-related expense = 15.83% (380/2400 x 100)

The Electricity bill for the year = $4,800

The deductible amount for office use = $760 ($4,800 x 380/2400) or ($4,800 x 15.83%)

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The solution of the equation is (3, 0).

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b. Basically, there are infinitely many solutions to a linear equation with two variables.

Given:

-x+y=-3....................(1)

3x+3y=9...................(2)

Solving Equation (1) and (2) we get

3x + 3(-3 + x) = 9

3x - 9 + 3x= 9

6x = 18

x= 18/ 6

x= 3

and, y= -3+ x

y= -3 + 3

y= 0

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Answer:

Step-by-step explanation:

The rate of deflation of the hot-air balloon is 0.25 feet per minute. Let's represent the diameter of the balloon at any time t in minutes as D(t).

We know that D(0) = 14 feet (initial diameter) and we want to find x when D(x) = 8 feet.

Using the fact that the rate of change of D with respect to time is -0.25 (negative because the diameter is decreasing), we can set up a differential equation:

dD/dt = -0.25

Separating variables and integrating, we get:

∫(1/D) dD = ∫(-0.25) dt

ln|D| = -0.25t + C

where C is the constant of integration.

Using the initial condition D(0) = 14, we get:

ln|14| = C

C = ln(14)

Substituting this value of C into the equation, we get:

ln|D| = -0.25t + ln(14)

Taking the exponential of both sides, we get:

|D| = e^(-0.25t + ln(14)) = e^ln(14) e^(-0.25t) = 14 e^(-0.25t)

Since we are only interested in the positive value of D, we can drop the absolute value sign:

D = 14 e^(-0.25t)

Now we can solve for x by setting D = 8:

8 = 14 e^(-0.25x)

Dividing both sides by 14, we get:

e^(-0.25x) = 8/14 = 4/7

Taking the natural logarithm of both sides, we get:

ln(e^(-0.25x)) = ln(4/7)

-0.25x = ln(4/7)

x = -4 ln(4/7) / 0.25

x ≈ 6.21

Therefore, it will take about 6.21 minutes for the balloon to shrink to a diameter of 8 feet.

If Malcolm trains on his kayak every weekend. The speed is 12km/h and the distance is 31.5km.

Let's call Malcolm's paddling speed in still water "v".

When paddling upstream, Malcolm is fighting the current, so his effective speed is v - 3 km/h. And when paddling downstream, his effective speed is v + 3 km/h.

The time it takes for him to paddle upstream= 3.5 hours

Distance he covers in this time =  (v - 3) * 3.5.

The time it takes for him to paddle downstream = 2.1 hours

Distance he covers in this time = (v + 3) * 2.1.

Let  set the sum of these two distances equal to each other and solve for v:

(v - 3) * 3.5 = (v + 3) * 2.1

Expanding both sides:

3.5v - 10.5 = 2.1v + 6.3

Subtracting 2.1v from both sides:

1.4v - 10.5 = 6.3

Adding 10.5 to both sides:

1.4v = 16.8

Dividing both sides by 1.4:

v = 12 km/h

So Malcolm's paddling speed in still water is 12 km/h. To find the distance he paddles upstream, we can use the formula (v - 3) * 3.5, which gives us:

(12 - 3) * 3.5 = 9 * 3.5 = 31.5 km

Therefore  the distance Malcolm paddles upstream is 31.5 km.

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One gallon is a unit of volume that is equivalent to 3.785 liters. This means that one gallon is equal to 3.785 liters.

The gallon is an imperial unit of measurement, which means that it is not used in most countries outside of the United States and the United Kingdom. In the US customary system, the gallon is divided into four quarts, each of which is equal to two pints. One US gallon is equivalent to approximately 0.83 imperial gallons, which are used in the UK.The gallon originated in medieval England as a measure for ale and other alcoholic beverages. It was adopted by the Romans during their invasion of Britain, and the term "gallon" is derived from the Latin term "galleta," which means "a pailful." The gallon was standardized in the 18th century by the British Imperial System.In the United States, the gallon is used in both the customary and imperial systems. In the customary system, the gallon is equal to 128 fluid ounces, while in the imperial system, it is equal to 160 fluid ounces. The US liquid gallon is divided into four quarts, which is equivalent to eight pints. One US dry gallon is equal to 4.4 liters.

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Answer:

279.987

Step-by-step explanation:

Answer:

279.987073 lbs

Step-by-step explanation:

1 kg = 2.20462262 lbs

2.20462262 * 127 = 279.987073

The required amount of sauce in each bottle is given by fraction 5/7. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Sum the total amount of sauce in the 7 bottles present at each booth,
Total sauce = 0 × 2 + 1/2×1 + 1×3 + 1 1/2 × 1
                 = 1/2 + 3 + 3/2
                 = 2 + 3 = 5

Now, the ratio of the total sauce to the total number of bottles will give the amount of sauce in each bottle.

So,
= 5/7

Thus, the required amount of sauce in each bottle is given by fraction 5/7.

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The number of centimeters in 9 meters is 900.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

Given that, the measure is 9 meters.

We know that, 1 meter = 100 centimeters

Now, 9 meters

= 9×100

= 900 centimeters

Therefore, the number of centimeters in 9 meters is 900.

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The end behavior of this the end behavior of this polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity.

The end behavior of a polynomial can be determined by looking at the degree (highest exponent) and the leading coefficient (coefficient of the highest degree term). If the degree is even and the leading coefficient is positive, the end behavior of the polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity. Similarly, if the degree is even and the leading coefficient is negative, the end behavior of the polynomial is negative, meaning that as x approaches positive and negative infinity, the y values approach negative infinity. If the degree is odd and the leading coefficient is positive, the end behavior of the polynomial is positive, and if the degree is odd and the leading coefficient is negative, the end behavior of the polynomial is negative.For example, consider a polynomial of degree 5, f(x) = 3x5 + 2x4 - 3x2 + 4. The leading coefficient is 3, which is positive, and the degree is 5, which is odd. Therefore, the end behavior of this polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity. This can be verified by using the formula: End Behavior = Leading Coefficient x ∞limitx→±∞ End Behavior = 3 x ∞limitx→±∞  End Behavior = +∞.

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Answer:

2

Step-by-step explanation:

sqrt 16/4 is 4/2

4/2 is 2

Answer:

  540x⁴

Step-by-step explanation:

You want the 3rd term of the expansion of (x +6)⁶.

The k-th term of (a +b)^n is ...

   C(n, k)a^(n-k)b^k

where terms are numbered 0 to n.

The third term of (x+6)⁶ is the above expression with k=2:

  C(6, 2)a⁴b²

Where a=x and b=6, this is ...

  15x⁴6² = 540x⁴

__

Additional comment

C(n, k) is the function that represents the number of combinations of n things taken k at a time:

  C(n, k) = n!/(k!(n-k)!)

  C(6, 2) = 6!/(2!·4!) = 6·5/(2·1) = 15

Answer:

Step-by-step explanation

It seems like you are to use trig functions to find the missing sides.

soh - cah - toa

Sin(what degree angle you have) = opposite of the angle over the hypotenuse

cosine (what degree angle you have) = adjacent (side that is next to angle that isn't hypotenuse) over hypotenuse

tangent (what degree angle you have) = opposite side from angle over adjacent side to angle

for number 1:

sine59 = d/ 37

cross multiply

sin59 multiplied by 37 which equals 31.7

so this means d is 31.7

use the trig functions to find the rest. it is just a pattern and SOH-CAH-TOA will help.

lmk if you have questions

The area of given trapezoid is 92 square yards.

The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (a+b)×h.

where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b).

Given that, a right-angled trapezoid with length of two parallel sides measuring 10 yards and 13 yards.

The height of the trapezoid is 8 yards.

Here, area = 1/2 (10+13)×8

= 23×4

= 92

Therefore, the area is 92 square yards.

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Each interior angles of a rectangle is equal to 90° so m∠MON and m∠LOM are complementary as they add up to 90°. The value of x = 9. Angles m∠MON = 72° and m∠LOM = 18°. The angle m∠POQ = 18° because m∠LOM and m∠POQ are vertical angles.

The angles m∠MON and m∠LOM form one of the interior angles of a rectangle, hence they are complementary as they add up to 90°.

we shall solve for x as follows:

2x + 7x + 9 = 90

9x + 9 = 90

9x = 90 - 9 {subtract 9 from both sides}

9x = 81

x = 81/9 {divide through by 9}

x = 9

m∠MON = 7(9) + 9 = 72°

m∠LOM = 2(9) = 18°

The angles m∠LOM and m∠POQ are vertical angles formed by the two straight lines MA and LP, hence;

m∠LOM = m∠POQ = 18°

In conclusion, each interior angles of a rectangle is equal to 90° so m∠MON and m∠LOM are complementary as they add up to 90°. The value of x = 9. Angles m∠MON = 72° and m∠LOM = 18°. The angle m∠POQ = 18° because m∠LOM and m∠POQ are vertical angles.

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The area of the sector is evaluated to be equal to 15π ft². B) is the correct option.

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

the angle of the sector = 150°

the radius = 6 ft

hence the area of the sector is calculated as follows:

(150°/360°) × π × 6 ft × 6 ft

we simplify by division and multiplication

5/12 × π × 6 ft × 6 ft

5/12 × π × 36 ft²

5π × 3 ft²

15π ft²

Therefore, the area of the sector is evaluated to be equal to 15π ft² square meters.

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Answer:

please give the complete question..

Step-by-step explanation:

please give the complete question..

Answer

Step-by-step explanation:

The cubic equation is given by A = x³ - 7x² + 14x - 8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The coordinates of the points are A ( 1 , 0 ) , B ( 2 , 0 ) , C ( 0 , -8 ) , D ( 4 , 0 )

Now , the equation will be

f ( x ) = a ( x - 1 ) ( x - 2 ) ( x - 4 )

So , when x = 0 , the value of y = -8

-8 = a ( -1 ) ( -2 ) ( -4 )

-8 = a ( -8 )

8a = 8

Divide by 8 on both sides of the equation , we get

a = 1

Substitute the value of a in the equation , we get

f ( x ) = ( x - 1 ) ( x - 2 ) ( x - 4 )

f ( x ) = x³ - 7x² + 14x - 8

Hence , the equation is f ( x ) = x³ - 7x² + 14x - 8

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Answer: 36.2

Step-by-step explanation:

To find the mean, you add up all the values then divide by the number of values present. So, 45+35+35+30+36= 181. 181 divided by 5 is 36.2

A quarter pound hamburger is counted as one servings which is four ounces.

A pound is usually a unit which is used to measure the weight of a body.  It is known as one pound is approximately equal to 454 grams. One kilogram is roughly the same as equal to 2.2 lbs. There are 16 ounces in one pound which is mentioned.

This question can be solved due to the rule of proportions.

A pound is an imperial unit of mass or weight measure, it is abbreviated as lb, lbm and one pound is considered to be equal to 0.4535 kilograms.

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The solution to the system of equations is given as follows:

x = 2.31, y = 0.93.

The system of equations for this problem is defined as follows:

To solve by elimination, we first multiply the first equation by 4, and then add the first equation with the second, hence:

Hence the solution for x is given as follows:

13x = 30

x = 30/13

x = 2.31.

Then the solution for y is of:

y = 3x - 6

y = 3(2.31) - 6

y = 0.93.

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(C) 48 = V2 -2 -2 -2 - 3 = 4√3 correctly uses prime factorization to write V48 in simplest form.

In number theory, the breakdown of a composite number into a sum of smaller integers is known as integer factorization.

The procedure is known as prime factorization if these factors are further limited to prime numbers.

The technique of expressing all numbers as the product of primes is known as prime factorization.

So, let's take something like the number 20 as an example.

It can be divided into two components.

"Well, that's 4 times 5," we can respond.

Observe that 5 is a prime number. The number 4 is not a prime.

So, it is necessary to write 48 as the product of its prime elements:

2 * 3 * 2 * 2 * 2

Then,

√48 = √(2 * 2 * 2 * 2 * 2)

Lower radical form: √48

Hence, (C) could be the correct option.

Therefore, (C) 48 = V2 -2 -2 -2 - 3 = 4√3 correctly uses prime factorization to write V48 in simplest form.

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Correct question:

Which calculation correctly uses prime factorization to write V48 in simplest form?

A. 48 = V2 -2 -2 -2 - 3 = 2V12

B. 48 = 14 - 12 = 2/12

C. 48 = V2 -2 -2 -2 - 3 = 4V3

D. V48 = 16 - 3 = 4V3​

Answer:

here u go

Step-by-step explanation:

Sounds like you're very young but here I go!

since 1 inch = 2.5 cm

and 24 inches = 2 feet

multiply inches and cm by 24

answer is 60 cm

i hope it helped it may be wrong tho :(

The number of styrofoam is 11.

It is a polygon having six faces.

The volume of a cube is a side³

We have,

The area of the box = 44 square inches

Styrofoam is considered a square shape.

The side length of the styrofoam = 2 in

The area of the foam = 2² = 4 square inches

Now,

The number of styrofoam.

= 44 / 4

= 11

Thus,

11 styrofoam.

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Complete question:

Jason packs a box full of styrofoam pieces in a rectangular shape surface with an area of 44 square inches.

Each styrofoam is a square shape with a side length of 2 inches.

How many square inches of styrofoam can the box fold ?

The triangle with side lengths of  48 in., 56 in., and 83 in.  is obtuse, because 832> 48² +56²

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

The side lengths of the triangles are 48 in., 56 in., and 83 in

The smallest side lengths are: 48 in., 56 in

The sum of the squares of these side lengths is

48^2+ 56^2

For the triangle to be obtuse, then the following must be true

83^2> 48² +56²

Evaluate the exponents

6889> 5440

The above inequality is true.

Hence, the triangle is obtuse, because 83^2> 48² +56²

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Answer:

Quadrant I is located on the top right of the graph (Positive x, Positive y)

Quadrant II is located on the top left of the graph (Negative x , Positive y)

Quadrant III is located on the bottom left of the graph (Negative x, Negative y)

Quadrant IIII is located on the bottom right of the graph (Positive x, Negative y)

The origin is at the center of the graph with (0,0) as its x and y components

Step-by-step explanation: ^^ Please give 5 star and thanks.

The function represented by the graph is y = |x + 1|

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The equation of the graph is an absolute value graph

An absolute value graph is represented as

y = |x|

The function is shifted left by 1 units

So, we have

y = |x + 1|

Hence, the function is y = |x + 1|

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The average with two digits after the decimal point followed by a newline is 7.4

An integer is a whole number, either positive or negative, that does not have any decimal points. Non-negative integers are those that are greater than or equal to zero.

To write such a program, we can use a loop to continuously read in integers from the user until a negative integer is entered. We then ignore the negative integer and calculate the maximum and average of the non-negative integers that were entered.

The maximum is simply the largest integer in the set. We can use a variable to keep track of the largest integer as we read in the input. At the end of the loop, the variable will hold the maximum value.

The average is the sum of all the integers divided by the total number of integers.

We add each non-negative integer to the sum and increment the count. At the end of the loop, we divide the sum by the count to get the average.

To output the average with two digits after the decimal point, we can use the printf method, which allows us to format our output. The format string "%.2f\n" specifies that we want to output a floating-point number with two decimal places followed by a newline character.

=> (15 + 20 + 0 + 3 - 1) / 5 = 7.4

In summary, a program that takes any number of non-negative integers as input, and outputs the max and average can be written using a loop, variables to keep track of the maximum, sum, and count, and the printf method to format the output. Understanding the basics of integers and how to perform calculations with them is essential for programming and statistical analysis.

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