MATHEMATICS HIGH SCHOOL

A rectangular garden is 5 feet longer than twice its width. It has a sidewalk 3 feet wide on two of its sides. The area of the sidewalk is 213 square feet. Find the dimensions of the garden.

Answers

Answer 1

Answer:

The length and width of the garden are 47 ft and 21 ft respectively.

Explanation

Suppose, the width of the garden is $x$ feet.

As the garden is 5 feet longer than twice its width, so the length will be: $(2x+5) feet$

So, the area of the garden $= length*width=x(2x+5)ft^2$

Now, the garden has a sidewalk 3 feet wide on two of its sides. That means, the length of the garden including the sidewalk $=(2x+5+3)ft =(2x+8)ft$ and the width including the sidewalk $=(x+3)ft$

Given that, the area of the sidewalk is 213 ft². So the equation will be.....

$(2x+8)(x+3)-x(2x+5)=213\n \n 2x^2+14x+24-2x^2-5x=213\n \n 9x+24=213\n \n 9x=189\n \n x=(189)/(9)=21$

So, the width of the garden is 21 feet and the length is $(2*21+5)ft= 47 ft$

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Which quadratic function has a leading coefficient of 2 and a constant term of –3? f(x) = 2x3 – 3 f(x) = –3x2 – 3x 2 f(x) = –3x3 2 f(x) = 2x2 3x – 3

Answers

The standard form of quadratic function is:
f(x) = a x² + b x + c
where: a - a leading coefficient, c- constant term:
a = 2, c = -3
Answer: D) f( x ) = 2 x² + 3 x - 3

Answer:

tHE ANSWER IS d

Step-by-step explanation:

Which of the following represents the factored form of f(x) = x3 − 81x?f(x) = x(x − 9)2
f(x) = (x + 9)(x − 9)
f(x) = x(x + 9)(x − 9)
f(x) = x(x2 − 9)

Answers

Factored form of $f(x) = x^(3) -81x$ is equal to $x(x+9)(x -9)$ .

What is factored form?

" Factored form is defined as for the given polynomial product of the constant along with linear expressions."

Formula used

$a^(2) -b^(2) =(a+ b)(a- b)$

According to the question,

Given polynomial,

$f(x) = x^(3) -81x$

Simplify the given polynomial to get its factored form using formula,

$x^(3) -81x\n\n= x(x^(2) -81)\n\n= x(x^(2) -9^(2) )\n\n= x(x+ 9)(x-9)$

Hence, Option(C) is the correct answer.

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You're original equation has a -81, so the factored form will have to have a positive and negative multiplying one another to achieve that...

f(x) = x(x + 9)(x - 9)

Consider the graph of f(x) = 2x 3 – 3x 2 – 14x. On a coordinate plane, a graph increases through (negative 2, 0) to (negative 1, 10), decreases through (0, 0) to (2, negative 24), and then increases through (3.5, 0) through (4, 20). Based on the graph, what is the solution to 2x 3 – 3x 2 ≥ 14x?

Answers

Answer:

Answer D

Step-by-step explanation:

Final answer:

The solution to the inequality 2x³ – 3x² – 14x ≥ 0, as indicated by the graph provided, is given by the intervals of x where the function is increasing. Therefore, the solution is comprised of the intervals [-2, -1] and [3.5, ∞].

Explanation:

The solution to 2x³ – 3x² ≥ 14x can be found by solving the inequality. First, let's rearrange the inequality to: 2x³ – 3x² – 14x ≥ 0. This equation represents where the function is positive (above the x-axis) on the graph. Therefore, we must identify the intervals of x where the function increases or decreases.

Based on the description of the graph, the function increases in the intervals (-2, -1) and (3.5, ∞) and decreases in the interval (-1, 3.5). So, the solution to the inequality would be the union of the intervals where the function increases: [-2, -1] U [3.5, ∞].

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Which of the following is the function representing the graph below? graph begins in the third quadrant near the line y equals negative 3 and increases slowly while crossing the ordered pair 0, negative 2. When the graph enters the first quadrant, it begins to increase quickly throughout the graph.f(x) = 4x
f(x) = 4x − 3
f(x) = 4x + 3
f(x) = 4(x + 3)

Answers

Answer:

f(x) = 4^x -3

Step-by-step explanation:

All of the listed functions are linear functions with a constant slope of 4. None of them goes through the point (0, -2).

So, we assume that there is a missing exponentiation operator, and that these are supposed to be exponential functions. If the horizontal asymptote is -3, then there is only one answer choice that makes any sense:

f(x) = 4^x -3

_____

The minimum value of 4^z for any z will be near zero. In order to make it be near -3, 3 must be subtracted from the exponential term.

In a train yard, there are 6 flatcars, 7 boxcars, and 3 livestock cars. A train is made up of 9 cars.Which would you use to find the number of ways the train could be made up?

Answers

The number of ways the train could be made up are 4,151,347,200.

What is permutation?

A permutation of a set is an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

Now the given cars are 6 flatcars, 7 boxcars, and 3 livestock cars.

So the total number of cars, n = 6 + 7 + 3

= 16

Now, a train is made up of 9 cars,

Therefore, r = 9

Hence the required number of ways the train could be made is nPr

nPr = n!/(n-r)!

nPr = 16!/(16-9)!

nPr = 16!/7!

nPr = 16*15*14*13*12*11*10*9*8

nPr = 4,151,347,200

Hence,the number of ways the train could be made up are 4,151,347,200.

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Answer:

The answer is A on edge

Step-by-step explanation:

The gravitational force exerted on a baseball is 2.24 N down. A pitcher throws the ball horizontally with velocity 17.0 m/s by uniformly accelerating it along a straight horizontal line for a time interval of 183 ms. The ball starts from rest. Through what distance does it move before its release? What are the magnitude and direction of the force the pitcher exerts on the ball?

Answers

To have a weight of 2.21N., the ball's mass is (2.21/9.8) = .226kg.
a) d = 1/2 (vt), = 1/2 (18 x .17), = 1.53m.
b) Acceleration of the ball = (v/t), = 18/.17, = 105.88m/sec^2.
f = (ma), = .226 x 105.88, = 23.92N.

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