help me pls i’m gonna fail the class>3

Help Me Pls Im Gonna Fail The Class>3

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Answer 1
what’s the question ?

Related Questions

one fruit punch has fruit juice and another is fruit juice. how much of the punch should be mixed with of the punch to create fruit punch that is fruit juice?

Answers

The below calculation allows us to determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

To create a fruit punch that is entirely fruit juice, we must calculate the ratio of fruit juice to total punch. To do this, we will use the following formula:

Fruit Juice Ratio = (Fruit Juice / (Fruit Juice + Punch)) x 100

For example, if we have 10 ounces of fruit juice and 10 ounces of fruit punch, the ratio of fruit juice to total punch is 50%. Therefore, we need to mix 50% fruit juice with 50% punch to create a fruit punch that is entirely fruit juice.

To calculate this for any given amount of fruit juice and punch, we simply plug the numbers into the formula. For instance, if we have 20 ounces of fruit juice and 60 ounces of punch, the ratio of fruit juice to total punch is 25%. Therefore, we need to mix 25% fruit juice with 75% punch to create a fruit punch that is entirely fruit juice.

By using this formula, we can easily determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

We can use the formula Fruit Juice Ratio = (Fruit Juice / (Fruit Juice + Punch)) x 100 to calculate the ratio of fruit juice to total punch. This allows us to determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

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6. If f(x) = x2 - 1, which of the following is equal to g(x) = f(x - 3)?
A.g(x) = x/ +8
B.g(x) = x2 + 6x+8
C.g(x)= x2 - 6x + 8
D.g(x) = x2 + 6x- 10

Answers

( x - 2) ( x - 4 ) is function which is equal to g(x) .

In the simplest terms, what is a function?

As a set of inputs with one output for each, a function is defined as a relationship between them. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

f(x) = x² - 1

f( x - 3 ) = ( x - 3 )² - 1

             = x² + 9 - 6x -1

             = x² -6x + 8

             = x² -4x -2x + 8

             = x( x - 4 ) -2( x - 4)

             = ( x - 2) ( x - 4 )

g(x) = f(x - 3)

       = ( x - 2) ( x - 4 )

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The table below shows the approximate height of a ball thrown up in the air after x seconds. A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 1, 2, 3, 4. The second column is labeled height (feet) with entries 5, 90, 140, 160, 150. Which quadratic model best represents the data? f(x) = –16x2 + 99x + 6 f(x) = –36x2 + 37x + 5 f(x) = 36x2 + 37x + 5 f(x) = 16x2 + 99x + 6

Answers

Answer:

A) . f(x) = –16x2 + 99x + 6  

AAAAAAA is the answerrrrrr!!!!

Step-by-step explanation:

By analyzing the data and the situation modeled, we got the vertex of the quadratic function, and with that, we conclude that the correct option is:

f(x) = –16x^2 + 99x + 6

Which equation best represents the data?

Here we have the table:

x         y

0        5

1         90

2        140

3         160

4         150

First, we know that this represents the height of a ball that is thrown in the air, and we know that it must go up and then back, this means that the leading coefficient must be negative.

So there are two options:

f(x) = –16x^2 + 99x + 6

f(x) = –36x^2 + 37x + 5

Analyzing the data, we can see that the maximum value is at x = 3, so we can assume that the vertex is near x = 3.

Remember that for a quadratic:

y = a*x^2 + b*x + c

The x-value of the vertex is at:

x = -b/2a

Then for our functions the x-values of the vertex are:

f(x) = –16x^2 + 99x + 6

x = -99/(2*-16) = 3.1

f(x) = –36x^2 + 37x + 5

x = -37/(2*-36) = 0.5

The option that has a vertex near x = 3 is the first one, so that is the best fit.

f(x) = –16x^2 + 99x + 6

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The dashed triangle is a dilation image of the solid triangle. What is the scale factor? A. 1/4 B. 1/2 C. 2/3 D. 2

The dashed triangle is a dilation image of the solid triangle. What is the scale factor? A. 1/4 B. 1/2

Answers

Answer:

I am not good in maths but I think it is

A 1/4

A model's scale ratio is the ratio of linear dimensions. The scale factor of the triangle is (1/2).

What is the scale ratio?

A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.

The scale ratio of the triangle can be found by taking the ratio of any one side of the dashed triangle to the solid triangle. Therefore, the scale ratio will be,

\(\rm Scale\ ratio = \dfrac{\text{Length of the dashed line}}{\text{Length of the solid line}}\\\\ Scale\ ratio = \dfrac{2}{4} = \dfrac{1}{2}\)

Hence, the scale factor of the triangle is (1/2).

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CAN SOMEONE PLEASE HELP ME???

CAN SOMEONE PLEASE HELP ME???

Answers

Answer:

C

Step-by-step explanation:

The blue line is the one that that slants from lower right to upper left. It has a negative slope as in - 1/2. The line is solid so that means the values of the line are included in the expression.

The area covered is purple, so y is less than the y values of the line. C is the only value that shows the paragraph above.

But we have to check the other inequality just to make sure you are right.        y >  2/3 x - 4. The line is not included, so C is your answer.

Find EF. Please help!

Find EF. Please help!

Answers

Answer:

EF = 7 + 39 = 46

Step-by-step explanation:

EF = FG

x + 39 = 7x - 3

39 + 3 = 7x - x

42 = 6x

x = 42/6

x = 7

hope this helps :)

Can anyone help! Struggling on this question!!

Can anyone help! Struggling on this question!!

Answers

Answer:

\(\frac{1}{10}\)

Step-by-step explanation:

note that in terms of the given fraction

1 = \(\frac{10}{10}\) , then

\(\frac{9}{10}\) + \(\frac{1}{10}\) = \(\frac{10}{10}\) = 1

Answer:

\( \frac{9}{10} + x = 1 \\ x = 1 - \frac{9}{10} \\ x = \frac{(10 - 9)}{10} \\ \boxed{x = \frac{1}{10} } \: is \: the \: required \: number\)

If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 8 times x plus 6 end quantity which of the following could accurately represent f and g?

f of x is equal to the square root of the quantity 4 times x plus 3 end quantity and g of x is equal to the square root of the quantity 4 times x plus 3 end quantity
f of x is equal to the square root of the quantity 4 times x plus 3 end quantity and g of x is equal to the square root of 2
f (x) = 8x + 6 and g of x is equal to the square root of x
f of x is equal to the square root of x and g(x) = 8x + 6

Answers

The possible definitions of f(x) and g(x), considering the composition of the functions, are given as follows:

\(f(x) = \sqrt{x}\)g(x) = 8x + 6.

What is the composite function of f(x) and g(x)?

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The functions for this problem are defined as follows:

\(f(x) = \sqrt{x}\)g(x) = 8x + 6.

As the composition of the functions is then given as follows:

\(h(x) = f(g(x)) = f(8x + 6) = \sqrt{8x + 6}\)

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heyyyyyyyy
I need urgent help with this.
Please offer assistance.​

heyyyyyyyyI need urgent help with this. Please offer assistance.

Answers

Answer:

a) 20 m/s²

b) 0

Step-by-step explanation:

average acceleration is, Vₙ - vₓ / Δt

where, Vₙ stands for final velocity,

Vₓ stands for initial velocity, and

Δt stands for change in time

according to the question,

for t₂, s = 2³ - 2² - 2 - 2 = 8 - 4 - 4 = 0

for t₄, s = 4³ - 4² - 4 - 2 = 64 - 16 - 8 = 64 - 24 = 40

substituting the values in the formulae,

average acceleration = 40 - 0 / 4 - 2 = 40/2 = 20 m/s²

when the velocity is 0 it indicates that acceleration will also be 0

Answer:

A - The Average Acceleration Between:

T  =  2  and   T  =  4  is   16 m/s^2

B - The Acceleration When the Velocity is: Zero (0)   is  0 m/s^2  at  

      T = 1/3  and 4 m/s^2  at   T  = 1

Step-by-step explanation:Make A Plan:We need to find the Average Acceleration between  T = 2 and T = 4, and The Acceleration When the Velocity is Zero (0).  First, We need to find the velocity function and the acceleration function.

1) - Solve the Problem:Given Distance Function:

        s(t)  =  t^3  - t^2  - t  -  2

2) - Find the velocity function by taking the first derivative of the distance function with respect to (T):

        v(t) = d/dt(t^3  - t^2 - t - 2 )  = 3t^2  - 2t  -  1

3) - Find the acceleration function by taking the first derivative of the velocity function with respect to (T):

        a(t) = d/dt(3t^2  - 2t  -  1 )  =  6t - 2

A) - To find the average Acceleration Between  T = 2  and  T  = 4, We need to find the acceleration at  T  = 2  and  T  = 4, and then find the average of these two values.

        a(2)  =  6(2) - 2 = 10

        a(4) = 6(4) - 2 = 22

Average Acceleration

        =  a(2) + a(4)/2  

        =   10 + 22/2

        =   16

B) - To find the Acceleration When the Velocity is Zero (0), We need to find the Time (T)  When V(T)  =  0

        3t^2  -  2t  -  1   =  0

Solve the quadratic Equation for (T):

        t  =  1/3,  1

Now find the Acceleration at these times:

       a(1/3)  =  6(1/3)  -  2  =  0

       a(1)   =   6(1)     -  2   =  4  

Draw the conclusions:

A - The Average Acceleration Between T  =  2  and   T  =  4  is  16 m/s^2

B - The Acceleration When the Velocity is Zero (0)   is  0 m/s^2  at  

      T = 1/3  and 4 m/s^2  at   T  = 1

I hope this helps you!

5
3
2
The total area of the rectangular prism shown is

Answers

Answer:

30

Step-by-step explanation:

You multipy 5 by 3 by 2

I NEED THIS ASAP its geometry ( look at picture).

I NEED THIS ASAP its geometry ( look at picture).

Answers

Answer:

-1.118 is the required value of tan theta

The average cost of a pizza in 2022 is $18. Inflation has been averaging 3.25% for many years. In what year was the average cost of a pizza 9$ (half)? Approximate using rule of 72.

Answers

The year in which the approximate cost of a pizza was of $9 is given as follows:

2000.

What is the rule of 72?

The rule of 72 is a quick and simple mathematical formula that is used to estimate the number of years it takes for an investment or a debt to double, given a fixed annual interest rate. The rule states that if you divide 72 by the annual interest rate (expressed as a percentage), the result will give you an approximate number of years it takes for the investment or debt to double.

Hence the equation is given as follows:

Time to double = 72/Rate.

The rate for this problem is of 3.25%, hence the time to double is given as follows:

T = 72/3.25

T = 22 years.

Hence the pizza cost half of what it cost in 2022 in 22 years before, hence:

2022 - 22 = year of 2000.

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Determine if the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. Select true or false for each statement. This set is closed under scalar multiplications This set is a subspace This set is closed under vector addition The set contains the zero vector

Answers

If the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. The statement: This set is closed under scalar multiplications This set is a subspace .This set is closed under vector addition The set contains the zero vector is False.

Vector:

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.

Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a Scalar . Examples of scalars include speed, mass, electrical resistance, and hard-drive storage capacity.

Scalar Multiplication:

Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).

For quaternion scalars and matrices:

λ = 2     A = \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\)

2A = 2\(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\)

     = \(\left[\begin{array}{ccc}2a&2b\\2c&2d\\\end{array}\right]\)  = \(\left[\begin{array}{ccc}a.2&b.2\\c.2&d.2\\\end{array}\right]\)

     = \(\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]\) × 2 = A2

Subspace:

In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.

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95 % of the class is on santa's nice list if there are 20 students how many are naughty

Answers

Answer: 1 Student

Step-by-step explanation:

Hope this helps!

solving step
\(144x^{2} +36\)

Answers

You can’t “solve” an expression

A line passes through point (-8,-2) and has a slope of -3/2.write an equation in Ax+By=C from for this line.Use integers for A,B,C.

Answers

Answer

\(3x+2y=-28\)

Explanation

A linear equation can be written in the following form:

\(y=mx+b\)

where m is the slope and b the y-intercept.

As we are already given the slope, then we get the equation:

\(y=-\frac{3}{2}x+b\)

Replacing the point given we can calculate b:

\(-2=-\frac{3}{2}(-8)+b\)\(b=-2-12=-14\)

Then the equation is:

\(y=-\frac{3}{2}x-14\)

Then, we would have to get the form Ax+By=C , however, as we do not want fractions, we have to multiply the equation times two:

\(2y=-3x-28\)

Rearranging the function we get:

\(3x+2y=-28\)

HELP IM BEING TIMEDDDDDDDDDDDDDDDDDDDDDD

HELP IM BEING TIMEDDDDDDDDDDDDDDDDDDDDDD

Answers

Answer:11

Step-by-step explanation:

Answer:19

Step-by-step explanation:15+4=19

19-15=4

2. You are riding your bicycle. It takes you 20 minutes to go 5 miles.
a. Find your average speed per minute.
b.
How long would it take you to cycle 12 miles?

Answers

Answer:

a= one mile in 4 minutes

b =48 minutes

Step-by-step explanation:

A

t = 20 minutes

d = 5 miles

Average speed = distance ÷ time

5 miles÷ 20 minutes

= 1 mile in 4 minutes

= 0.25 miles in 1 minute

B

0.25 miles in 1 minute

12 miles in g minutes

12 miles in 48 minutes

we get this answer because 0.25 in one minute is 1 ÷4

12÷ 12 × 4

12÷ 48

= 12 miles In 48 minutes

The point D(-6, -5) is translated 3 units up. What are the coordinates of the resulting point, D′?
y
x
-6
6
-6
6
0
D

Answers

Answer:

D' (-6, -2)

Step-by-step explanation:

3 units up means y will increase by 3

y = -5 + 3 = -2

x will stay the same

x = -6

New coordinate

D' (-6, -2)

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)

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Answer: I hope it helps :)

x=6 , y=6√3x =23√3 , y=23u =12 , v= 6a =18√2 , b =18x = 13 , y= 13

Step-by-step explanation:

1.

\(Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}\)

2.

\(Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23\)

3.

\(Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6\)

4.

\(Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}\)

5.

\(Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y\)


5, x 10^ 5, is how many times as large as 1 x 10^5
?

Answers

Answer:

you should use a calculator

Step-by-step explanation:

simplify 3y-3(4x-1)-8y+5

Answers

Answer:

- 12x - 5y + 8

Step-by-step explanation:

Answer:

-5y - 12x + 8

Step-by-step explanation:

mark brainiest

Is the inequality true or false when t = -3: 33/t - 2 ≥ -8

Answers

False is the answer

Stepping from the embrace, she smoothly extracts the broom from my grip. Which type of phrase is the underlined portion of the sentence? A. prepositional phrase B. verb phrase C. noun phrase D. participle phrase

Answers

Answer:

A). Participle phrase.

Step-by-step explanation:

'Participle phrases' are defined as the phrases that consist of a participle(present or past) followed by modifiers and their object plus any/or complements. These phrases primarily function as adjectives by providing information about a noun or pronoun in the sentence.

In the given sentence, the underlined portion('stepping from the embrace') is a participle phrase as it begins with a participle('present as it ends with 'ing') followed by the modifier prepositional phrase 'from the embrace'(as an adverb). It is functioning as an adjective as it modifies the pronoun 'she' in the sentence. Thus, option A is the correct answer.

The underlined portion of the sentence is a participle phrase. the correct option is D.

What is a participle phrase?

"Participle phrases" are characterized as being composed of a participle (present or past), a modifier, the object of the modifier, and any/or complements. These expressions mainly serve as adjectives by describing a noun or pronoun in the sentence.

The part of the sentence that is emphasized in the example, "stepping from the hug," is a participle phrase because it starts with the participle "present" and finishes with the preposition "from" (as an adverb). As it changes the pronoun "she" in the sentence, it acts as an adjective.

Therefore, the underlined portion of the sentence is a participle phrase. the correct option is D.

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Which statement is true?

A.

The mean lies to the right of the median for a positively skewed distribution.

B.

The mean lies to the left of the median for a positively skewed distribution.

C.

The mean lies to the left of the median for a symmetric distribution.

D.

A distribution skewed to the right is said to be negatively skewed.

E.

A distribution skewed to the left is said to be positively skewed.


PLEASE ALSO EXPLAIN, AND ONLY PICK ONE OPTION

Answers

Statement (B) The mean lies to the left of the median for a positively skewed distribution because there will be fewer data on the right side is correct.

What is a histogram?

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

We know on the left side skewed histogram has more data on the right and on the left side, there are fewer data. It is also called a negatively skewed histogram.

On the right side skewed histogram, there is fewer data on the right side and more data on the left side. It is also called a positive histogram.

Thus, statement (B) The mean lies to the left of the median for a positively skewed distribution because there will be fewer data on the right side is correct.

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Each unit on the drawing is 0. 5 inch long. Using the scale given, find the actual length of the shortest side of the picnic area, in feet

Answers

The actual length of the shortest side of the picnic area = (x * 0.5) / 12 feet.

We can start by converting the units in the drawing to the actual length by multiplying each unit by 0.5 inches.

If the shortest side of the picnic area is represented by x units on the drawing, then the actual length in inches can be found by x * 0.5 inches.

Next, we can convert the length in inches to feet by dividing by 12 inches/foot. So, the actual length in feet is given by: x * 0.5 inches / 12 inches/foot = x * 0.5 / 12 feet.

Therefore, the actual length of the shortest side of the picnic area in feet is given by x * 0.5 / 12 feet.

The use of a scale on a drawing is a common method for representing actual sizes of objects on a smaller or larger scale. The scale tells us how many units on the drawing correspond to a certain length in the real world. In this case, each unit on the drawing represents 0.5 inches in the real world.

To find the actual length of the shortest side of the picnic area, we start by determining how many units represent this length on the drawing. Let's call this length x units.

Next, we use the scale given to convert the units on the drawing to inches. This is done by multiplying each unit by 0.5 inches, since each unit on the drawing represents 0.5 inches in the real world. So, the length in inches is given by x * 0.5 inches.

However, the question asks for the length in feet, not inches. To convert inches to feet, we divide the length in inches by 12, since there are 12 inches in a foot. So, the actual length of the shortest side of the picnic area in feet is given by: x * 0.5 inches / 12 inches/foot = x * 0.5 / 12 feet.

By knowing the scale and the length in units on the drawing, we can use these steps to find the actual length of any object represented on the drawing.

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The complete question is:

Each unit on the drawing is 0.5 inch long. Using the scale and if the shortest side of the picnic area is x given, find the actual length of the shortest side of the picnic area in feet.

The volume of calls, V( h), at a particular customer service center can be written as a function of the number of hours after opening each day, h. What would the ordered pair (6,8) represent for this function?

Answers

The ordered pair (6,8) represents the number of calls made after the customer service center opened for 6 hours.

Given that the volume of calls, V( h), at a particular customer service center can be written as a function of the number of hours after opening each day, h. So, (6,8) means that the center has been opened for 6 hours and that there have been 8 calls during this period. It represents the value of the volume of calls V(6) which is 8. Therefore, after opening the customer service center for 6 hours, 8 calls were made.

This function has a direct relationship between the number of hours after opening the center and the number of calls made. Therefore, the longer the center is open, the more calls are expected to be received, and vice versa.

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Pls help?!?!?! 10 points

Pls help?!?!?! 10 points

Answers

Answer:

I solved it for u!

Hope ot helps!!!

Pls help?!?!?! 10 points

a special window has the shape of a rectangle surmounted by an equilateral triangle. see the figure. if the perimeter of the window is 16 feet, what dimensions will admit the most light?

Answers

A triangle whose sides are all equal is called an equilateral triangle and its area is given by A=\(\frac{\sqrt{3} }{4}\) \(x^{2}\), where x is the side of the triangle.

The area of a rectangle is found by using the formula

A=lw, where l is the length and w is the width.

The given figure can be split into two shapes: a rectangle and an equilateral triangle as shown in the diagram. Let l be the length of the rectangle.

Add all of the sides of the window and equate their result to 16. Then solve for l.

x + x + l + x + l = 16

3x + 2l = 16

2l = 16 - 3x

l = \(\frac{16-3x}{2}\)

The total area of the window will be the sum of the area of the equilateral triangle ABE and the area of rectangle BCDE.

A = \(\frac{\sqrt{3} }{4}\)\(x^{2}\) + lx

Subsitute  \(\frac{16-3x}{2}\) for l into the obtained equation and simplify.

A =\(\frac{\sqrt{3} }{4}\)\(x^{2}\) + ( \(\frac{16-3x}{2}\))x

A = \(\frac{\sqrt{3} }{4} x^{2}\) + 8x - \(\frac{3}{2} x^{2}\)

Differentiate the obtained equation with respect to x and equate the first derivative to 0 to calculate the critical point x .

\(\frac{dA}{dx}\) = \(\frac{\sqrt{3} }{4}\) (2x) + 8 - \(\frac{3}{2}\) (2x)

0 = \(\frac{\sqrt{3} }{2}\) x - 3x + 8

x (3 - \(\frac{\sqrt{3} }{2}\)) = 8

x = \(\frac{16}{6-\sqrt{3} }\)≈3.74887

Again, differentiate the equation

\(\frac{dA}{dx}\) = \(\frac{\sqrt{3} }{2}\)x - 3x + 8  with respect to x.

\(\frac{d^{2}A }{dx^{2} }\) = \(\frac{\sqrt{3} }{2}\) - 3

The value of the second derivative is \(\frac{\sqrt{3} }{2}\)−3, which is negative. This implies that the area will be maximum at the critical point.

Subsitute x = 3.74887 into the equation

l = \(\frac{16-3x}{2}\) and simplify

l = \(\frac{16-(3)(.74887)}{2}\) ≈ 2.3767

The maximum light will enter through the window when the triangular portion will have the side length of 3.74887 feet and the dimensions of the rectangular portion will be 3.74887-ft-by-2.3767-ft.

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a special window has the shape of a rectangle surmounted by an equilateral triangle. see the figure.

what can you say conclusively about a star that lacks calcium lines?

Answers

The lack of calcium lines indicates that the star's outer atmosphere is not dense enough to produce observable absorption lines.

What are Calcium Lines?

Calcium lines are dark absorption lines in the spectrum of a star or other astronomical object that are produced by the absorption of specific wavelengths of light by calcium atoms in the object's outer atmosphere.

If a star lacks calcium lines in its spectrum, it is likely to be a relatively young and hot star, with a surface temperature above about 7,000 K. This is because the calcium lines that are typically observed in the spectra of cooler stars are formed in the star's outer atmosphere, which is cooler and more diffuse than the layers closer to the star's core.

The absence of calcium lines in the spectrum of a star suggests that its outer atmosphere is relatively thin or transparent, and that the star's light is not passing through enough calcium-rich material to produce observable absorption lines.

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