A rectangular garden has a perimeter of 172 feet. The length of the garden is 24 feet more than the width. What are the dimensions of the garden? (Recall the formula P = 2L + 2W.)

The perimeter of the polygon to the nearest tenth of a unit  [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.

Further explanation:

The distance between the two points can be calculated as follows,

[tex]\boxed{{\text{Distance}}=\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}}[/tex]

Given:

The coordinates of the vertices of the polygon are [tex]\left({ - 2, - 2}\right),\left( {3, - 3}\right),\left( {4, - 6}\right),\left( {1, - 6}\right)[/tex] and [tex]\left( { - 2, - 4}\right).[/tex]

Explanation:

Consider the points as A [tex]\left( { - 2, - 2} \right), B\left( {3, - 3} \right), C\left( {4, - 6} \right), D\left( {1, - 6} \right)[/tex] and  [tex]E\left({ - 2, - 4} \right).[/tex]

The distance between point A and point B can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {3 + 2} \right)}^2} + {{\left( { - 3 + 2}\right)}^2}}\\ &= \sqrt {25 + 1}\\&= \sqrt {26}\\&= 5.2\\\end{aligned}[/tex]

The distance between point B and point C can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {4 - 3} \right)}^2} + {{\left( { - 6 + 3} \right)}^2}}\\&= \sqrt {{1^2} + 9}\\&= \sqrt {10}\\&= 3.17\\\end{aligned}[/tex]

The distance between point C and point D can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left({1 - 4} \right)}^2} + {{\left( { - 6 + 6}\right)}^2}}  \\&=\sqrt {{3^2} + 0}\\&= \sqrt9\\&= 3\\\end{aligned}[/tex]

The distance between point D and point E can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 2 - 1}\right)}^2} + {{\left( { - 4 + 6}\right)}^2}}\\&= \sqrt{ - {3^2} + {2^2}}\\&= \sqrt {9 + 4}\\&= \sqrt {13}\\&= 3.61\\\end{aligned}[/tex]

The distance between point E and point A can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 + 2} \right)}^2} + {{\left( { - 4 + 2} \right)}^2}}\\ &= \sqrt {{0^2} + {2^2}}\\&=\sqrt4\\&= 2\\\end{aligned}[/tex]

The perimeter of the polygon can be calculated as follows,

[tex]\begin{aligned}{\text{Perimeter}}&= 5.12 + 3.17 + 3 + 3.61 + 2\\&= 16.9\\\end{aligned}[/tex]

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.

Answer:

here is the answer

Step-by-step explanation:

Answer:

[tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]

Step-by-step explanation:

The factorization is in the form (x-a)(x-b) where a,b are zeros of the equation [tex]x^{2} +50=0[/tex].

[tex]x^{2} =-50[/tex]

[tex]x =\sqrt{-50}[/tex]

[tex]x =\sqrt{50}i = 5\sqrt{2}i[/tex] and [tex]x =-\sqrt{50}i = -5\sqrt{2}i[/tex]

So, the factorization is [tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]

Complex numbers are numbers with real and imaginary part.

The factorized expression is [tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]

The expression is given as:

[tex]\mathbf{x^2 + 50}[/tex]

Set to 0

[tex]\mathbf{x^2 + 50 = 0}[/tex]

Subtract 50 from both sides

[tex]\mathbf{x^2 = -50}[/tex]

Take square roots

[tex]\mathbf{x = \sqrt{-50}}[/tex]

Expand

[tex]\mathbf{x = \sqrt{25 \times -2}}[/tex]

Take square roots of 25

[tex]\mathbf{x =\pm 5\sqrt{-2}}[/tex]

Expand

[tex]\mathbf{x = \pm5\sqrt{2 \times -1}}[/tex]

Split

[tex]\mathbf{x =\pm 5\sqrt{2} \times \sqrt{-1}}[/tex]

In complex numbers,

[tex]\mathbf{\sqrt{-1} = i}[/tex]

So, we have:

[tex]\mathbf{x = \pm5i\sqrt{2}}[/tex]

So, we have:

[tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]

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Answer:

69 and 11,  took me 1 hour to slove this

Step-by-step explanation:

The probability that John chooses exactly two green marbles is calculated using the binomial probability formula and is found to be 720/3125.

To solve this problem, we can use the binomial probability formula because John is performing independent trials of the same experiment and he is interested in the probability of exactly two successes (picking a green marble) in a specific number of trials (5).

The binomial probability formula is: [tex]P(X = k) = (n choose k) \times p^k \times (1-p)^{n-k[/tex]

For John's case:

n = 5 (since he is picking 5 marbles).

k = 2 (he wants exactly two green marbles).

p = 6/10 or 3/5 (because there are 6 green marbles out of a total of 10 marbles).

Using the formula, the probability that John picks exactly two green marbles is:

[tex]P(X = 2) = (5 choose 2) \times (3/5)^2 \times (2/5)^{5-2[/tex]

Calculating further:

[tex]P(X = 2) = 10 \times (3/5)^2 \times (2/5)^3 = 10 \times 9/25 \times 8/125 \\P(X = 2) = 720/3125[/tex]

The probability of heads on the fifth trial is still 0.5, just like any other coin flip.

The probability of heads on the fifth trial is still 0.5, just like any other coin flip. The outcome of each coin flip is independent of the previous flips, so each trial has the same probability of resulting in heads or tails.

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To find the dimensions of a cylinder with one open end that minimizes its surface area given a volume of 44 cm³, use calculus and the formulas for the cylinder's volume and surface area. The solution results in radius r ≈ 1.34 cm and height h ≈ 9.87 cm.

For a cylinder open at one end, the surface area is given by the formula A = πr² + πrh, where r is the radius and h is the height.
The volume of a cylinder is given by the formula V = πr²h. Given that V=44 cm³, we can write the volume equation as h = V / (πr²).
Substituting this into the surface area equation, we get A = πr² + πr(V / (πr²)) = πr² + V/r.
We want to minimize the surface area, so we take the derivative of A with respect to r, set it equal to zero and solve for r.
Doing this gives us: dA/dr = 2πr - V/r² = 0 => r = cuberoot(V/2π).
Substituting V=44 cm³ into this, we get r = cuberoot(22/π) ≈ 1.34 cm.
Substituting r back into h = V / (πr²), we derive that h = 44 / (π * (1.34)²) ≈ 9.87 cm.
Therefore, the dimensions that will minimize the surface area of the cylinder given that the volume is 44 cm³, are approximately r = 1.34 cm and h = 9.87 cm.
This is a classic problem of optimization in calculus.

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The simplified form of the expression 2(x+14)+(2x-14) is 4x + 14.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

An expression,

2(x+14)+(2x-14).

Simplifying,

2(x+14)+(2x-14),

= 2x + 28 + 2x - 14

= 4x + 28 - 14

= 4x + 14

Therefore, the solution is 4x + 14.

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Peter needs 33 whole days to be able to speak 75 words.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Peter begins his kindergarten year able to spell 10 words.

He is going to learn to spell 2 new words every day.

Assuming no. of days it will take him to be able to spell at least 75 words

is d.

∴ The inequality that represents this scenario is 2d + 10 ≥ 75.

2d ≥ 65.

d ≥ 32.5 but it will take him 33 whole days to learn 75 words.'

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For anyone who needs the measure itself, it's 70.

Final answer:

A 42.0-gallon barrel of oil is equivalent to 158.97 liters, calculated by multiplying the number of gallons by the conversion factor of 3.785 liters per gallon.

Explanation:

To discover out how numerous liters are in 42.0 gallons of oil, given that 1 gallon is proportionate to 3.785 liters, you'd perform the taking after calculation:

Multiply the number of gallons by the conversion factor from gallons to liters.

42.0 gallons × 3.785 liters/gallon = 158.97 liters.

Therefore, a barrel of oil, which contains 42.0 gallons, is equivalent to 158.97 liters.

Answer:

slope = -3

Step-by-step explanation:

To find the slope of the graphed line, we can use the slope formula:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope formula}}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\textsf{where:}\\\phantom{w}\bullet\;\;m\; \textsf{is the slope.}\\\phantom{w}\bullet\;\;(x_1,y_1)\;\textsf{and}\;(x_2,y_2)\;\textsf{are two points on the line.}\end{array}}[/tex]

First, identify two points on the line:

Substitute the coordinates into the slope formula:

[tex]m=\dfrac{0-3}{1-0}=\dfrac{-3}{1}=-3[/tex]

Therefore, the slope of the graphed line is:

[tex]\Large\boxed{\boxed{\textsf{slope}=-3}}[/tex]

Answer:

Commutative additive property.

Step-by-step explanation:

Given  : 3z+4=4+3z

To find : which property is illustrated the following statement.

Solution : We have given  

3z + 4 = 4 + 3z.

Commutative additive property : a + b = b + a .

Example :  2 + 3 = 3 +2 = 5.

Hence  this the commutative additive property 3z + 4 = 4 + 3z.

Therefore, Commutative additive property.

Answer:

Its 8:11 because theres eleven animals and 8 pigs

Step-by-step explanation:

The proof was completed by assuming that two supplementary angles could both be obtuse, which would mean that their sum is more than 180°. This contradicts the definition of supplementary angles, where their sum should always be exactly 180°, and hence proves that two supplementary angles cannot both be obtuse.

To complete the indirect proof, we start by assuming that two supplementary angles, let's call them angle1 and angle2, can indeed both be obtuse angles. An obtuse angle is defined as an angle which measures more than 90°. Therefore, if both angle1 and angle2 are obtuse, they would each measure more than 90°, meaning that their sum (angle1 + angle2) would measure more than 180°.

However, the definition of supplementary angles is such that their sum should always be exactly 180°. Therefore, we reach a contradiction in our assumed scenario: the sum of angle1 and angle2 cannot be both more than 180° (by our assumption that they are both obtuse) and exactly 180° (by the known definition of supplementary angles).

This contradiction means that our initial assumption was incorrect, thus completing the proof. In other words, two supplementary angles cannot both be obtuse, as it would contradict the definition of supplementary angles.

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