Triangles and Their Side Lengths

Writing Reflections: Careers and Geometry

Write a short essay researching different fields and how they use geometry or trigonometry. Discuss the field that you have chosen does (50 points) and how that field uses geometry or trigonometry (50 points). Use complete sentences and at least 3 paragraphs.

Answer:

yes because its closer to not being negitibve

Step-by-step explanation:

Answer:

Greater!

Step-by-step explanation:

-3 is closer to 0 than -5 is.

Answer:

(x, y) = (57/4, 31/4)

Step-by-step explanation:

-2x + 6y = 18

-2x = 18 - 6y

x = -9 + 3y

3(-9 + 3y) - 5y = 4

-27 + 9y - 5y = 4

4y = 31

y = 31/4

x = -9 + 3(31/4) = 57/4

Answer:

Step-by-step explanation:

-5y=4-3x

y=(4/-5)-(3/-5x)

2x+6y=18

6y=18-2x

y=18/6-(2/6x)

y=y

(4/-5)-(3/-5x)=18/6-(2/6x)

0.93x=3.8

x=3.8/0.93

x=4.09

sub 4.09 for the 3x-5y=4

which will give you y=1.65

sub 4.09 for -2x+6y=18

which will give you y=4.36

Answer:

each bottle of juice costs $2.04

Step-by-step explanation:

we first need to minus the cost of chips so we can focus on just the price of the juice bottles.

51.23-2.27

=48.96

this gives the total cost of all 24 bottles but we need the cost of just one, so we divide 48.96 by 24.

which gives us our answer of $2.04 per bottle.

The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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Answer:

416/3, or about 138.6666... miles

Step-by-step explanation:

8mi/3wks = x mi/52wks gives

52*8 = 3x

x = 416/3, or about 138.6666...

Answer:

416 miles

Step-by-step explanation:

8 (miles per week) x 52 (total weeks jogged)

= 416 total miles jogged in 52 weeks

Answer:

4.4 < x < 18.8

Step-by-step explanation:

11.6 - 7.2 = 4.4

11.6 + 7.2 =18.8

Answer:

a)   Length of the parking lot: 98 m

b)   Width of the pool: 89 m

Step-by-step explanation:

a)   The formula for the area of a rectangle is \(A=lw\).

We need to evaluate the length. Lets solve for \(l.\)

\(A=lw\)

Divide both sides of the equation by \(w\).

\(\frac{A}{w} =l\)

We are given

\(A=8428\\w=86\)

Lets evaluate \(l\).

\(\frac{8428}{86}=l\)

\(l=98\)

b)   The formula for the perimeter of a rectangle is \(P=2l+2w\).

We need to evaluate the width. Lets solve for \(w\).

\(P=2l+2w\)

Subtract \(2l\) from both sides of the equation.

\(P-2l=2w\)

Divide each term by 2.

\(\frac{P}{2} -\frac{2l}{2} =\frac{2w}{2}\)

Simplify.

\(w=\frac{P}{2}-l\)

We are given

\(P=376\\l=99\)

Lets evaluate \(w\).

\(w=\frac{376}{2}-99\)

\(w=188-99\)

\(w=89\)

Answer:

a) 98m , b) 89m

Step-by-step explanation:

(a) Given,

To Find : Length of the Parking lot

Length of a rectangle shape can be derived by the formula,

\(l = \frac{A}{w}\)

\(l = \frac{8428}{86}\)

\(l = 98m\)

Hence , the length of a rectangular parking lot is 98m

(b) Given ,

To Find : The width of the rectangular pool

We take the width as variable 'x'

Now we plug it into the perimeter of a rectangle equation

\(376 = 2(99 + x)\)

Using distributive property we,

\(376 = 198 + 2x\)

We now flip the equation

\(2x + 198 = 376\)

\(2x = 376 - 198\) ( Transposing into the right hand side)

\(2x = 178\)

\(x = \frac{178}{2}\)

\(x = 89\)\(m\)

Hence , the width of the rectangular swimming pool is 89m

Answer:

Below

Step-by-step explanation:

First we can find the volume of the box

v = lwh

v = (20)(16)(16)

v = 5120 in^3

Find the volume of the cylinder using this formula

   V = πr^2h

   V = π(5)^2(20)

   V = 1570.79633 (plug this into the final equation, not the rounded one in case it screws up the final value)

   V = 1570.8 in^3

Now we can find the volume of the shaded region by subtraction

5120 - 1570.7963= 3549.2037

Rounding to the nearest 10th and you get....

V = 3549.2

Hope this helps!

Answer: 1.3

Step-by-step explanation:

581.59 cubic inches juice  can Ramon pour into 6 cups

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that Ramon is filling cups with juice.

The shape of the cup is like cylinder.

The cup has a diameter of 4.2 inches and height of 7 inches.

We need to find the amount of  juice can Ramon pour into 6 cups

Volume of one glass=πr²h

=3.14×(2.1)²×7

=3.14×4.41×7

=96.9318

Now for 6 glasses we have to calculate

=6×96.932

=581.59 cubic inches

Hence, 581.59 cubic inches juice can Ramon pour into 6 cups

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Answer:581.59 cubic inches

The first person to answer was correct.

Step-by-step explanation:

I took the quiz so you don't have to!

Answer:

45

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 cm × 1000 = 4000 cm = 40 meters

3 cm × 1000 = 3000 cm = 30 meters

A 4 cm by 3 cm  section on the map represents 40 m by 30 m.

area = 40 m × 30 m = 1200 m²

To determine the vertices of image U′V′W′ after a 180° counterclockwise rotation, we can apply the following transformation rules:

Using these rules, we can find the vertices of image U′V′W′ as follows:

Therefore, the vertices of image U′V′W′ after a 180° counterclockwise rotation are U′(0, -2), V′(1, -3), and W′(3, -3).

So, the answer is option (b) U′(0, −2), V′(1, −3), W′(3, −3).

Formula: 1/2(πr²)

radius: 14/2=7

1/2(π x 7²)

So the Surface Area is: 76.96902001. Round it to the decimal point u want

If Nathan orders a large pizza (14-inch diameter), the surface area of the remaining pizza is 24.5π square inches.

To find the surface area of the remaining pizza, we first need to determine the surface area of the whole pizza and then calculate half of that.

The surface area of a pizza can be calculated using the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. In this case, the diameter is given as 14 inches, so the radius would be half of that, which is 7 inches.

Plugging the radius value into the formula, we have A = π(7)². Simplifying, we get A = 49π square inches.

Since Nathan eats half of the pizza, we need to calculate half of the surface area. Half of 49π is (49π)/2, which simplifies to 24.5π square inches.

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Answer:

l = 5 + 2w

_______

Answer: If you are asking for percentage, 18/400 bulbs were defective. In other words, 4.5% of bulbs were defective. This also means that 95.5% of bulbs were not defective.

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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If three cards are drawn from a standard deck of 52 cards , then the probability that all the cards are of same rank is  1/425  .

The number of cards in the standard deck is = 52 cards ;

thee cards are drawn from the deck ,

we have to find the probability that they all are of the same rank , that means ( e.g. all 3 are queens ) ;

we have to draw 3 cards from 4 suits. which means 1 card is taken from the 13 numbers.

the number of favorable outcomes (all from same rank) = ⁴C₃×13

= 52  ;

total number of outcomes is = ⁵²C₃ = 22100 ;

the required probability is = 52/22100  ;

= 1/425 .

Therefore , the probability that all 3 cards are of same rank is 1/425  .

The given question is incomplete , the complete question is

The three cards were randomly drawn from a standard deck of 52 cards.

What is the probability they are all the same rank ?

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9514 1404 393

Answer:

 f^-1(x) = 2x/(x -1)

Step-by-step explanation:

You can find the inverse function by solving for y:

  \(f(y)=x\\\\\dfrac{y}{y-2}=x\\\\x(y-2)=y \qquad\text{multiply by $y-2$}\\\\xy-2x=y \qquad\text{eliminate parentheses}\\\\xy-y=2x \qquad\text{add $2x-y$}\\\\y(x-1)=2x \qquad\text{factor}\\\\y=\dfrac{2x}{x-1} \qquad\text{divide by the coefficient of $y$}\\\\\boxed{f^{-1}(x)=\dfrac{2x}{x-1}} \qquad\text{in functional form}\)

If 4.2712 moles of Fe(OH)3 are produced, 12.8136 moles of NH4Cl will be produced as well.

An equation is a mathematical statement that expresses two expressions as equal. It is typically written using an equals sign (=) and consists of two expressions separated by an equals sign. The expressions in the equation represent a relationship between the two terms, and the equation can be used to solve for an unknown value. Equations can involve numbers, variables, and constants.

To determine the number of moles of NH4Cl that will be produced, we can use the mole ratio from the balanced chemical equation. According to the equation, for every 1 mole of Fe(OH)3 that is produced, 3 moles of NH4Cl will also be produced. Therefore, if 4.2712 moles of Fe(OH)3 are produced, 12.8136 moles of NH4Cl will be produced as well.

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For every 4 moles of Fe(OH)3 produced, 3 moles of NH4Cl are also produced. Since 4.2712 moles of Fe(OH)3 are produced, then 3 x 4.2712 = 12.8136 moles of NH4Cl will also be produced

An equation is a mathematical statement that expresses two expressions as equal. It is typically written using an equals sign (=) and consists of two expressions separated by an equals sign. The expressions in the equation represent a relationship between the two terms, and the equation can be used to solve for an unknown value. Equations can involve numbers, variables, and constants.


The reaction of FeCl3 with 3 moles of NH4OH produces 4.2712 moles of Fe(OH)3 and 3 moles of NH4Cl. This can be determined by using the balanced chemical equation for the reaction:

FeCl3 + 3 NH4OH → Fe(OH)3 + 3 NH4Cl

Since the reaction produces 4.2712 moles of Fe(OH)3, then the amount of NH4Cl produced can be calculated using the mole ratio. The mole ratio of NH4Cl to Fe(OH)3 is 3:4.2712, which can be simplified to 3:4. Therefore, for every 4 moles of Fe(OH)3 produced, 3 moles of NH4Cl are also produced. Since 4.2712 moles of Fe(OH)3 are produced, then 3 x 4.2712 = 12.8136 moles of NH4Cl will also be produced.

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Answer:

C. Multiply the bottom equation by 2

Step-by-step explanation:

-2x+ 4y= 10

3x- 2y =-7

We want to multiply the second equation by 2

-2x+ 4y= 10

6x- 4y =-14

------------------

4x +0y = -4

Answer:

C. Multiply the bottom equation by 2

x = - 1

y = 2

Step-by-step explanation:

Multiplying 3x - 2y = - 7 by 2, we get:  

- 2x + 4y = 10

6x - 4y = - 14

____________

4x = - 4

x = - 1

Putting x = - 1 in 3x - 2y = - 7, we get:

3 * (- 1) - 2y = - 7

= - 3 - 2y = - 7

= - 2y = - 7 + 3

= - 2y = - 4

= y = 2

Hope this helps!

The cat population in Catonsville in 2007 was 200. The answer is option B.

Population refers to the total number of people, animals, or objects in a particular group or area. It is the entire group or collection of individuals, things, or events that we are interested in studying or describing.

We can use the given equation to find the cat population at any given time in years since the beginning of 2010. However, to find the population in 2007, we need to make a conversion from years since the beginning of 2010 to years since the beginning of 2007.

From the beginning of 2007 to the beginning of 2010, there are 3 years, so if we subtract 3 from the number of years since the beginning of 2010, we will get the number of years since the beginning of 2007. Therefore, we need to substitute t = -3 into the given equation and solve for p:

\(p = 1600(2)^t\\p = 1600(2)^(-3)\\p = 1600(1/8)\\p = 200\)

Therefore, the cat population in Catonsville in 2007 was 200. The answer is option B.

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The polyhedron has:

6 Faces, 8 vertices and 12 edges in total.

But

3 Faces, 7 vertices and 7 edges are visible.

The polyhedron has 6 faces, 8 vertices and 12 edges.

a polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.

A polyhedron is a three-dimensional solid with faces that are all flat

To count the number of faces in a polyhedron, count the number of flat polygonal faces.

The number of faces are 6 in number.

Counting the vertices of a polyhedron is generally a little easier than counting the edges.

The rectangular box above has four vertices on the top and four on the bottom, which gives a total of eight vertices in all.

The number of vertices are 8 in number.

The rectangular box above has four edges along the top, four along the bottom, and four in the middle, for a total of 12 edges in all.

Hence, the polyhedron has 6 faces, 8 vertices and 12 edges.

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To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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Cost price refers to the original purchase or production cost of a product, while selling price is the price at which the product is sold to customers. The difference between the selling price and the cost price determines the profit or loss incurred in the transaction.

To find the cost of 54 ft of the crown molding, we need to determine the cost per foot and then multiply it by the desired length.

Given that 7 ft of the crown molding costs $13.50, we can calculate the cost per foot by dividing the total cost by the length: $13.50 ÷ 7 ft = $1.93 per foot.

Now, to find the cost of 54 ft, we multiply the cost per foot by the desired length: $1.93 per foot × 54 ft = $104.22.

Therefore, it would cost $104.22 for 54 ft of the 3-inch crown molding.

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A histogram is a column chart that displays the frequency of occurrence on the vertical axis.

In a histogram, the horizontal axis represents the range or categories of data, and the vertical axis represents the frequency or count of data falling within each range or category. The height of each column in the histogram corresponds to the frequency or count of data in that particular range or category.

Histograms are commonly used to visualize the distribution of numerical data and provide insights into the shape, center, and spread of the data. They are particularly useful in identifying patterns, outliers, and understanding the overall distributional characteristics of a dataset.

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Since the discriminant is negative, the equation has no real roots and therefore the function does not have any x-intercepts.

Why it is?

To analyze the function f(x) = 2x² + 12x + 2001:

   Axis of Symmetry: The axis of symmetry of a parabola is given by the equation x = -b/2a. In this case, a = 2 and b = 12, so the axis of symmetry is x = -12/(2*2) = -3.

   Vertex: The vertex of a parabola is located on the axis of symmetry. Using x = -3 as the axis of symmetry, we can find the y-coordinate of the vertex by plugging it into the function: f(-3) = 2(-3)² + 12(-3) + 2001 = 1983. Therefore, the vertex is (-3, 1983).

   Max or Min: Since the coefficient of the x² term is positive, the parabola opens upwards, so the vertex is a minimum point. Therefore, the function has a minimum value at x = -3.

   Y-Intercept: To find the y-intercept, we set x = 0: f(0) = 2(0)² + 12(0) + 2001 = 2001. Therefore, the y-intercept is (0, 2001).

   X-intercepts: To find the x-intercepts, we set f(x) = 0 and solve for x: 2x² + 12x + 2001 = 0. This quadratic equation does not factor, so we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. Plugging in the values, we get:

x = (-12 ± √(12² - 4(2)(2001))) / (2*2) = (-12 ± √(144 - 16008)) / 4

x = (-12 ± √(-15864)) / 4

Since the discriminant is negative, the equation has no real roots and therefore the function does not have any x-intercepts.

   Increasing Interval: The function is increasing to the left of the vertex and decreasing to the right of the vertex. Therefore, the increasing interval is (-∞, -3).

   Decreasing Interval: The decreasing interval is (-3, ∞).

   End Behavior: As x approaches positive or negative infinity, the dominant term of the function becomes 2x², which grows without bound. Therefore, the end behavior of the function is that it approaches positive infinity as x approaches either positive or negative infinity.

   Positive Interval: The function is positive everywhere since the coefficient of the x² term is positive.

   Negative Intervals: The function does not have any negative intervals since it is positive everywhere.

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Answer:

(6x-7y)(6x-7y).

Step-by-step explanation:

.

Answer:  

36x² - 84xy + 49y² =

6²x² - 2 (6x) (7y) + 7²y² =

(6x - 7y) ²

Answer.

(6x - 7y) ²

Answer:

Increase?

Step-by-step explanation:

Because think about it let's use 1/2 as an example.

1/2 equals .5 now lets add 2 to both the numerator and denominator

3/4 is the result and it also equals .75 which is larger than .5 so that's why the answer is increase.

and u can keep on going on with the method

4/5=.8

If equal amounts are added to the numerator and the denominator of the current ratio, the ratio will always decrease.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Let m be the positive number.

And the ratio is p:q = p/q.

If equal amounts are added to the numerator and the denominator of the current ratio is,

(p+m)/(q+m).

The ratio will always decrease.

Therefore, the ratio will always decrease.

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