Pls Help! Geometry
How much will the molding cost?

By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.

Herein we must simplify an expression that uses logarithms by applying any of the following three laws:

[tex]\log_{a} (b \cdot c) = \log_{a} b + \log_{a} c[/tex]      (1)

[tex]\log_{a} \left(\frac{b}{c} \right) = \log_{a} b - \log_{a} c[/tex]     (2)

[tex]\log_{a}{b^{c}} = c \cdot \log_{a} b[/tex]     (3)

Now we proceed to simplify the expression:

[tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex]

[tex]\log_{2} 2\cdot y = \log_{2} 8\cdot x^{3} - \log_{2} \frac{8\cdot x^{3}}{2}[/tex]

[tex]\log_{2} 2 \cdot y = \log_{2} \frac{\frac{8\cdot x^{3}}{1} }{\frac{8\cdot x^{3}}{2} }[/tex]

[tex]\log_{2} 2\cdot y = \log_{2} 2[/tex]

By the relationship between logarithms and powers of same base:

2 · y = 2

y = 1

By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.

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The center of mass is mathematically given as

[tex]\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

[tex]\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end[/tex]

We calculate the total mass of the system.

[tex]\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}[/tex]

Step 03: Calculate the moment of the system.

[tex]\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}[/tex]

we calculate the center of mass.

[tex]\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]

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Answer:

See below

Step-by-step explanation:

Start by subtracting 5.2 from both sides of the equation

  so  "subtraction property of equality "    I suppose ......

then the next step would be divide both sides by 2.5  

  which would be division property of equality  

Answer: Subtraction Property of Equality

Step-by-step explanation:

- the subtraction property of equality is the rule that when you subtract the same number to or from both sides of an equation and get an equivalent equation

__________________________________________________________

- for this equation you would subtract 5.2 from the left-side of the equation and subtract it from 35.2 on the right side of the equation

      - this is to isolate n

- basically 2.5n = 30 since n is a variable and that number multiplied by 2.5 will equal 30

- so the new equation would be 2.5n = 30

- so then:  [tex]\frac{n}{2.5}[/tex] = [tex]\frac{30}{2.5}[/tex]  so n = 12

hope this helps :)

Rewriting the equation of the given line in slope-intercept form,

[tex]3x+6y=18\\\\x+2y=6\\\\2y=-x+6\\\\y=-\frac{1}{2}x+3[/tex]

This means the slope of the given line is -1/2.

As perpendicular lines have slopes that are negative reciprocals, the answer is 2.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Determine the slope of the line perpendicular to 3x+6y=18

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}[/tex] | dividing the ENTIRE equation by 6, to make it easier to write in y=mx+b form

[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x

[tex]\bf{y=-\dfrac{1}{2}x+3[/tex].

[tex]\cline{1-2}[/tex]

Now, perpendicular lines' slopes are opposite inverses of each other.

The opposite inverse of -1/2 is

                  = 2

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                 [tex]\bf{=2}[/tex]

[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]

Answer:

B

Step-by-step explanation:

y² - 12y + 32

consider the product of  factors of the constant term (+ 32) which sum to give the coefficient of the y- term (- 12)

the factors are - 4 and - 8 , since

- 4 × - 8 = + 32 and - 4 - 8 = - 12 , then

y² - 12y + 32 = (y - 4)(y - 8)

Answer:

B. (y-4)(y-8)

Step-by-step explanation:

Given equation: y² - 12y + 32. Essentially, we are going to find two numbers that multiply to 32 and add up to -12.

1) Pull out the factors of 32 and find the pair that multiply to 32 and add up -12.

They are: -8 and -4.

2) Rewrite the b of the original quadratic equation as a sum, then factorise by grouping.

y² - 8y - 4y +32

y(y - 8) - 4(y - 8)

(y - 4)(y -8)

Answer:

The value of g(-2) and g(4) cannot be compared because they are two different functions with two completely different values.

Step-by-step explanation:

So, you plug in -2 in the function of the x in g(x) = 8x - 2

Then, you multiply 8 by -2 in g(-2) = 8x - 2

8 × -2 would be -16

Afterwards you subtract -16 by 2 in g(-2) = -16 - 2

The function of g(-2) is -14 in g (x) = -14

You plug in 4 in the function of x in g(4) = 8x - 2

g(4) = 8 (4) - 2

Then, You multiply 8 by 4 which will give you 32 in

g(4) = 32 - 2

Lastly, you subtract the 32 by 2 and the function of the answer would be 30 in g(x) = 30

If one finalist is randomly selected for a prize then the probability that person will be selected is 6.25%.

Given A person is one of 16 finalists and one finalist is randomly selected for a prize.

Probability is the likeliness of happening an event among all the events possible. The formula of calculating probability is number of events possible/total outcomes.

The value of probability lies between 0 and 1. It cannot be negative because there might be chances of something and sometimes not so the value be 0.

Total finalists=16

Probability=1/16

When we convert it in percentage it will be 1*100/16

=6.25%

Hence the probability that person  will be selected is 6.25%.

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Answer: 18 feet

Step-by-step explanation:

The area of a rectangle is given by [tex]A=lw[/tex], which means that the length of the unknown side is [tex]\frac{216}{12}=18[/tex] feet.

By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.

Unit circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and trigonometric functions related to them. If we use rectangular coordinate system and the definition of the tangent function, we find that the angle OA is equal to:

[tex]\tan \theta = \frac{\sqrt{1 - x^{2}}}{x}[/tex]

[tex]\tan \theta = \frac{\sqrt{1-0.222^{2}}}{0.222}[/tex]

tan θ ≈ 77.173°

By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.

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Answer and Explanation:

First, solve for x in both inequalities:

4x − 1 > 7                         5x − 1 < −6

4x > 8                             5x < −5

x > 2                               x < −1

Because this is an OR problem, determine if there is any overlap. (See the attached image for details.) There is not, so the answer is no solution or Ø.

The additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ

The six basic properties of parallelograms are primarily;

Now, looking at the parallelogram properties above and comparing with the given image of the quadrilateral attached, we can say that the additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ

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The length of a square with diagonal of 10 cm is 5√2 cm.

Each angle in a square is 90 degrees.

Therefore, the diagonal form a right triangle with the length of the square.

The length of the square are equal.

Hence, using Pythagoras theorem,

let

x = length of square

x² + x² = 10²

2x² = 100

x² = 50

x = √50

x = 5√2

Therefore, the length of a square with diagonal of 10 cm is 5√2 cm.

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The given expression is equivalent to the number 147.

We have given that,

[tex](3\times4)^2+\frac{6}{2}[/tex]

We have to determine the value of the given expression.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

[tex]=(12)^2+\frac{6}{2} \\=144+3\\=147[/tex]

Therefore the given expression is equivalent to the number 147.

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A is zero

B) D

C) x= - 1 & x= 4

Hope this helps!

Answer:

Vertex form: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]

Standard Form: [tex]y=0.50x^2-2x-1[/tex]

Step-by-step explanation:

Well the vertex form of an equation is given in the form: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex, and by looking at the graph, you'll see the vertex is at (2, -3). So plugging this into the equation gives you: [tex]y=a(x-2)^2-3[/tex]. Now to find a which will determine the stretch/compression, you can substitute any point in (besides the vertex, because that'll result in (x-2) being 0). So I'll use the point (0, -1) which is the only point I think I can accurately determine by looking at the graph (besides (4, -1) since it's symmetric). Anyways I'll plug this in

Plug in (0, -1) as (x, y)

[tex]-1 = a(0-2)^2-3[/tex]

calculate inside the parenthesis

[tex]-1 = a(-2)^2-3[/tex]

square the -2

[tex]-1 = 4a-3[/tex]

Add 3 to both 3 to both sides

[tex]2 = 4a[/tex]

divide both sides by 4

[tex]a=\frac{1}{2}[/tex]

This gives you the equation: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]

To convert this into standard form you simply expand the square binomial, you can use the foil method to achieve this, but it generally expands to: [tex](a+b)^2=a^2+2ab+b^2[/tex].

Original equation:

[tex]y=\frac{1}{2}(x-2)^2-3[/tex]

expand square binomial:

[tex]y=\frac{1}{2}(x^2-4x+4)^2-3[/tex]

Distribute the 1/2

[tex]y=0.50x^2-2x+2-3[/tex]

Combine like terms:

[tex]y=0.50x^2-2x-1[/tex]

Answer:

the distance between both points is 10

Step-by-step explanation:

Distance (d) = √(-14 - -8)2 + (-16 - -8)2

= √(-6)2 + (-8)2

= √100

= 10

The distance between the two points (-8, -8) and (-14, -16) is 10 units.

We have,

To find the distance between two points in a coordinate plane, you can use the distance formula:

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

In this case, the two points are (-8, -8) and (-14, -16).

Let's plug the values into the distance formula:

Distance = √[(-14 - (-8))² + (-16 - (-8))²]

Distance = √[(-14 + 8)² + (-16 + 8)²]

Distance = √[(-6)² + (-8)²]

Distance = √[36 + 64]

Distance = √100

Distance = 10

Thus,

The distance between the two points (-8, -8) and (-14, -16) is 10 units.

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Using proportions, the ratios are given as follows:

a) 9:196.

b) 27:2744.

c) 3:14.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the standard ratio of 3:14 units, we have that:

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Answer:

?=3

Step-by-step explanation:

3=3/1

Flip 3/1 and you get

1/3

Answer:

$3820 total, $32 per alumnus.

Step-by-step explanation:

The total cost will be [tex]12\times120+650+730+1000=3820[/tex]

Each alumnus pays [tex]\frac{3820}{120} =31\frac{5}{6}[/tex]

Rounding to nearest whole number = $32 per alumnus.

Answer: 44.2

Step-by-step explanation:

108.29*2/4.9=44.2

Based on the given parameters about old cone, the height of the new cone is 12 inches

Old cone:

New cone:

equate ratio of radius to height in old and new cone

2 : 6 = 4 : h

2/6 = 4/h

cross product

2 × h = 6 × 4

2h = 24

h = 24/2

h = 12 inches

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The amount paid in tax based on the information is Rs 13500.

From the information given, the monthly salary is 45000. Therefore, the yearly salary will be:

= 45000 × 12

= 540000

Also, it's stated that the tax rate for first 450000 is 1% and next 100000 is 10%. Therefore, the amount that will be paid in tax will be:

= (450000 × 1%) + (90000 × 10%)

= 4500 + 9000

= 13500

Therefore, the amount paid in tax will be Rs 13500.

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The brackets or error bars shown at the top of each bar extend one standard error above and below each of the group means. For group 1, the error bar extends 3.9 units above and below the mean for group 1.

A researcher is investigating whether a reading intervention program improves reading comprehension for second graders. He collects a random sample of second graders
Group 1 consists of n₁ = 52 second graders who did not participate in the program. Their mean reading comprehension score is M₁ = 36.8.
Group 2 consists of n₂ = 56 second graders who did participate in the program. Their mean reading comprehension score is M₂ = 52.4.

Error bar, are the line through a point on a graph,axes, which emphasizes  the uncertainty or variation of the corresponding coordinate of the point.

We have the data,
σ = 25.24, n₁ = 52 M₁ = 36.8.

n₂ = 56  M₂ = 52.4.

Error bar  = M2-M1/n2-n1
      =  (52.4-36.8)/(56-52)
      =  3.9

Thus, the required value that will be put in black space is 3.9

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Answer:

1) 150 mph

2) 90 mph

3) 3 mph

Explanation:

1) The trains move at a constant speed, and after 5 hours they are 750 miles apart. 750/5=150

2) The faster train is 1.5 faster than the slower train, and we know their combined speed is 150 mph. 150/5=30, and 30x3=90.

3) We know that both trains combined travel 150 mph. 450/150=3.

Based on the data given, the speeds and time taken are as follows:

Speed is the ratio of distance covered and time taken.

1)The distance covered by the two trains in 5 hours = 750 miles.

The trains move at a constant speed and their combined speed will be:

Combined speed = 750/5

Combined speed = 150 mph

2) The train heading south has a speed 1.5 times faster than the other train heading north.

Ratio of speeds = 3 : 2

Speed of faster train 150 x 3/5 = 90 mph

3) The combined speed of the trains = 150 mph

Distance to be covered = 450 miles

Time taken = 450/150

Time taken = 3 hours

In conclusion, the speed of the two trains are determined from the distance travelled and time taken.

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Answer:

Distance on the map (in centimeters) represents an actual distance of 4 kilometers is 3,2 cm.

Step-by-step explanation:

The scale of a map = 4 cm : 5 km

The scale of a map = 4 : 500.000

So, 0,000008 times the actual distance is the distance on the map.

0,000008 × 400.000 = 3,2 cm

Answer: A

Step-by-step explanation:

[tex]C=2\pi r=2(\pi)(17) \approx 106.8[/tex]

The input and output table that works for both rules is input = 20 and output = 10.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the output and x represent the input.

From the first rule:

y = x/2

From the second rule:

y = x - 10

To work for both rules:

x/2 = x - 10

x = 2x - 20

x = 20

y = 20 - 10 = 10

The input and output table that works for both rules is input = 20 and output = 10.

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Answer: 10

Step-by-step explanation:

The first term is 3 and the common ratio is 1/2.

Using the sum of a geometric series formula,

[tex]\frac{3069}{512}=\frac{3(1-(1/2)^{n}}{1-(1/2)}\\\\\frac{3069}{1024}=3(1-(1/2)^{n})\\\\\frac{1023}{1024}=1-(1/2)^{n}\\\\-(1/2)^{n}=-\frac{1}{1024}\\\\(1/2)^n=\frac{1}[1024}\\\\2^{-n}=2^{-10}\\\\n=10[/tex]

Answer:

-100/3,0

Step-by-step explanation:

substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

if that makes sense Hope this helps pls brainliest have a nice day :>

Answer:

100- 3X

Step-by-step explanation:

SLAY

The area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)

From the information about the polygon MNOPQR, side MN is parallel to side RQ and also the side MR is parallel to side PQ

With a perpendicular line drawn from point O on the side RQ, which intersects with line  RQ at point S.

We can then  divide the  polygon into two different rectangles

MNSR  with A₁ as its area

OPQS  with A₂ as its area

For rectangle MNSR, line MN is 5 units and line MR is 3 units

The formula for area of a rectangle is given as;

A₁ = (length)×(width)

Substitute the values

A₁ = 5 × 3

A₁ = 15 square units

For rectangle MNSR, line MN= line RS and line MR = line NS,

We have RS= 5 units and NS= 3 units

So, line SQ= RQ- RS = 7-5 = 2 units

Also,  OS= NS - NO = 3- 2 = 1 unit

Let's substitute the values

A₂ = 2 × 1

A₂ = 2 square units

Therefore, the area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)

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