A company is replacing cables with fiber optic lines in rectangular casing BCDE. If line segment DE = 3 cm and line segment BE = 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth.



3.54 cm

3.91 cm

4.24 cm

4.95 cm

Answer:

(x - 3)(x - 1)

Step-by-step explanation:

Consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term.

The factors are - 3 and - 1, since

- 3 × - 1 = + 3 and - 3 - 1 = - 4, hence

x² - 4x + 3 = (x - 3)(x - 1) ← in factored form

Answer:

Factors are (x-1) (x-3)

Step-by-step explanation:

X^2-4x+3 = 0

x² - x - 3x + 3 =0

x(x - 1) -3(x - 1) = 0

        (x-1) (x-3) =0

Answer:

Amplitude = 1 foot; period = 12 hours; midline: y = 5

Step-by-step explanation:

The Chesapeake Bay tides vary between 4 feet and 6 feet.

This means the range is

[tex]4 \leqslant f(t) \leqslant 6[/tex]

The period is the length of the interval on which the function completes one full cycle.The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours.

The interval is [0,12] and its length is 12, hence the period is 12.

The midline

[tex]y = \frac{min + max}{2} [/tex]

[tex]y = \frac{4 + 6}{2} = 5[/tex]

The amplitude is the distance from the midline to the peak.

The amplitude is |5-4|=|5-6|=1

The first choice is correct.

The amplitude of the function modeling the Chesapeake Bay tides is 1 foot, the period is 12 hours, and the midline is at y = 5 feet.

The amplitude of a function that models a periodic phenomenon, like the tides in this case, is half of the total variation in height. Since the tides vary between 4 feet and 6 feet, the total variation is 2 feet (6 feet - 4 feet), and thus, the amplitude is 1 foot (2 feet / 2).

The period of the function is the time it takes for the tidal cycle to repeat itself. Given that the tide completes a full cycle in 12 hours, the period of the function is 12 hours.

The midline represents the average value around which the tide oscillates. It can be found by averaging the maximum and minimum tide levels. Therefore, the midline is (4 feet + 6 feet) / 2 = 5 feet.

Considering these calculations, the correct amplitude is 1 foot, the period is 12 hours, and the midline is y = 5 feet for the function that would model the periodic phenomenon of the Chesapeake Bay tides.

Answer:

3)5x-4y=-3

6x+4y=14

Step-by-step explanation:

The system of equations is given

5x-4y=-3

3x+2y=7

Multiplying both sides of the lower equation by 2, we get

6x + 4y = 14

That means your answer 3)

The system with the same solution as the given system of equations is the one where the second equation is a multiple of the original. In this case, option 2) 5x - 4y = -3 and 6x + 2y = 14 shows the same solution set, as it is the only one that is equivalent to the original system after multiplying the second equation by 2.

The student is trying to identify which system of equations has the same solution as the original system given by:

When comparing this system to the provided options, we look for a system that is equivalent after applying some algebraic operations, since the solutions of equivalent systems are the same. For the second equation in each system, it must be a multiple of the original (3x + 2y = 7), or it must be alterable to be equivalent through multiplicative or additive operations.

In case of options:

The only system that is equivalent to the original one is the second option because doubling the second equation of the original system (3x + 2y = 7) gives us 6x + 4y = 14, which has the same solution set as the original system.

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Let the balance = Y and the number of weeks = x

She takes out 15 per week, so multiply 15 by x ( the number of weeks) to get 15x.

You would then want to subtract that from the amount she started with in her account.

The equation becomes: Y = 150 - 15x

ANSWER

(10,100) is the correct answer

Answer:

The correct option is 3. The possible domain and range of the function is (10, 100).

Step-by-step explanation:

It is given that a bakery's production is modeled by function f(x), where

f(x) = The number of donuts made in a day

x = The number of bags of flour needed.

The number of donuts made in a day and the number of bags of flour needed can not be a fraction value of a negative number. So, the values of x and f(x) can not defined by negative or decimal numbers.

In ordered pair (-1,15), the value of x is negative, so option 1 is incorrect.

In ordered pair (5,92.75), the value of y is in decimal, so option 2 is incorrect.

In ordered pair (10,100), both coordinates are positive integers, so option 3 is correct.

In ordered pair (-5,110.5), the value of x is negative and the value of y is in decimal, so option 4 is incorrect.

The possible domain and range of the function is (10, 100). Therefore the correct option is 3.

Answer:

[-1,1]

Step-by-step explanation:

The question in English is

which of the following intervals contains the number 0?

case A) (0,1]

All real numbers greater than zero (the number 0 is not included) and less than or equal to 1 (the number 1 is included)

case B) [-1,1]

All real numbers greater than or equal to -1 (the number -1 is included) and less than or equal to 1 (the number 1 is included)

In this interval is included the number 0

case C) [-1,0)

All real numbers greater than or equal to -1 (the number -1 is included) and less than 0 (the number 0 is not included)

Answer: 61.1

Step-by-step explanation: The answer would be 61.1 because .062 is greater than .05, which means that it rounds up.

Answer:

x=7, y=-7

Step-by-step explanation:

3x – y = 28

3x + y = 14

Add the two equations together

3x – y = 28

3x + y = 14

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

6x = 42

Divide by 6

6x/6 = 42/6

x = 7

3x – y = 28

3x + y = 14

Multiply the second equation by -1, then add

3x – y = 28

-3x - y = -14

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

      -2y=14

Divide by -2

-2y/-2 = 14/-2

y = -7

recall your d = rt, distance = rate * time.

w = speed of the wind.

14 = speed of the bicycle without wind.

now, against the wind, the bicycle is not really going 14 mph fast, is really going "14 - w", since the wind is eroding speed from it, likewise, when the bicycle is going with the wind is not going 14 mph fast either, is really going "14 + w" due to the wind adding speed, let's say it took "t" hours against and also "t" hours with it.

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&10&14-w&t\\ \textit{with the wind}&20&14+w&t \end{array}~\hfill \begin{cases} 10=(14-w)t\\ \frac{10}{14-w}=\boxed{t}\\ \cline{1-1} 20=(14+w)t \end{cases}[/tex]

[tex]\bf 20=(14+w)t\implies \cfrac{20}{14+w}=t\implies \stackrel{\textit{substituting in the 2nd equation}}{\cfrac{20}{14+w}=\boxed{\cfrac{10}{14-w}}} \\\\\\ 280-20w=140+10w\implies 280=140+30w\implies 140=30w \\\\\\ \cfrac{140}{30}=w\implies \cfrac{14}{3}=w\implies 4\frac{2}{3}=w[/tex]

Answer:

(x - 2)² + (y + 5)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (2, - 5) and r = 4, hence

(x - 2)² + (y - (- 5))² = 4², that is

(x - 2)² + (y + 5)² = 16 ← is the equation of the circle

Answer:

B.612 units2

Step-by-step explanation:

To solve surface area you multiply the area of each of the faces then you add the areas together. So the equation you need to solve is 13×6+13×6+12×13+12×13+12×6+12×6

After you solve that equation the answer you should get is 612.

Answer:

612

Step-by-step explanation:

Answer:

The houses surveyed had between 1 and 10 rooms ..

Step-by-step explanation:

We can see from the histogram that the minimum number of rooms any house had was 1 and the maximum number of rooms were 10.

Range is the difference between highest and lowest value of a data set.

Hence, the range from the given histogram can be determined as:

The houses surveyed had between 1 and 10 rooms ..

Answer:  The houses surveyed had between 1 and 10 rooms.

Step-by-step explanation:

From the histogram, the minimum number of rooms = 1

The maximum number of rooms = 10

Hence, the range of rooms in Henry's histogram is between 1 and 10 rooms.

Answer:

Option B x=6 units

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and DEF are similar

therefore

∠A≅∠D

∠B≅∠E

∠C≅∠F

and

AB/DE=BC/EF=AC/DF

Find the value of x

AB/DE=BC/EF

substitute the given values

x/3=16/8

x=3*16/8

x=6 units

[tex]\huge{\boxed{66}}[/tex]

Start by substituting in the values. [tex]3(2)+6(8+2)[/tex]

Add. [tex]3(2)+6(10)[/tex]

Multiply. [tex]6+60[/tex]

Add. [tex]\boxed{66}[/tex]

Answer:

Step-by-step explanation:

3a+6(b+2)

=3(2)+6(8+2)

=6+6(10)

=6+60

=66

Answer:

a) 50

Step-by-step explanation:

The angle formed by two chords is the average of the arc angles.

7x = (5x + 90) / 2

14x = 5x + 90

9x = 90

x = 10

So the measure of arc EC is 5x = 50°.

The measure of arc EC is  a) 50

The angle of a complete circle is 360°

The angle formed by two chords angle= arc/radius

  ⇒7x = (5x + 90) / 2

  ⇒14x = 5x + 90

  ⇒ 9x = 90

  ⇒x = 10

So the arc EC is 5x = 50°.

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First you must solve system of equations.

Multiply the first equation by 4 and second one by 3.

You result with,

[tex]

16x-12y=4 \\

15x+12y=27

[/tex]

Add the equations so y terms cancel out.

[tex]31x=31\Longrightarrow x=1[/tex]

Insert x that was found in either one of the equations. I'll pick first one.

[tex]4\cdot1-3y=1[/tex]

Solve for y.

[tex]

-3y=-3 \\

y=1

[/tex]

The solutions to the system of equations are,

[tex]\boxed{x=1},\boxed{y=1}[/tex]

Therefore the number missing is 1.

Hope this helps.

r3t40

Answer:

(1,1)

Step-by-step explanation:

Answer:

1) Cubic

2) 2

3) -3

4) [tex]\frac{1}{9}x^{3}[/tex]

5) [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

The given polynomial is:

[tex]\frac{1}{9}x^{3}-3[/tex]

The degree i.e. the highest exponent of the variable involved is 3. So the polynomial is a Cubic polynomial.

The terms in a polynomial can be distinguished by addition and subtraction symbols. So, for the given polynomial there are 2 terms.

The constant term is the term without any variable. So the constant term in given polynomial is -3.

Leading term is the term with variable having highest exponet which defines the degree of the polynomial. So leading term of the given polynomial is [tex]\frac{1}{9}x^{3}[/tex]

Leading coefficient is the coefficient of the leading term. So for given polynomial the leading coefficient would be [tex]\frac{1}{9}[/tex]

Answer:

f(x)=(7(x-2)(x+5))/((x-1)(x+1))

Step-by-step explanation:

The vertical asymptotes should be in the denominator. The x-interceps should be in the numerator. Because the horizontal asymptote is y=7, you have to put 7 in the numerator because the horizontal asymptote is the coefficient of the numerator ÷ the coefficient of the denominator, when we have the same degree of the numerator and the denominator.

You could multiply 19.45 by 0.2 to solve for it, but if you're not using a calculator, then 19.45/5 would be much more convenient and easier.

0.2 is 1/5 in fraction form, which is why we can do that.

19.45/5 = 3.89

Dino should leave $3.89 as a tip.

Answer:

$3.89

Step-by-step explanation:

X = 20

19.45 = 100

19.45*20=389

389/100=$3.89

Final answer:

In converting 7.5 pounds to ounces, the unit placed in the denominator of the ratio is pounds. To do the conversion, multiply the number of pounds by 16, since there are 16 ounces in one pound. Therefore, 7.5 pounds is equal to 120 ounces.

Explanation:

When converting 7.5 pounds to ounces, we start by identifying the conversion factor between these two units of weight. The unit you would place in the denominator of your ratio is pounds, since the relationship is that 1 pound is equivalent to 16 ounces. So, the conversion from pounds to ounces requires multiplying the number of pounds by 16.

Here's how you would set up your conversion:

First, write down the amount of pounds you want to convert (7.5 pounds).

Multiply this amount by 16, the number of ounces in one pound (7.5 x 16).

The product will give you the amount in ounces (7.5 x 16 = 120 ounces).

The unit in the denominator for the ratio used in this conversion is pounds, as you are starting with pounds and converting to ounces.

Ans:

24 chairs in 9th row and 144 chairs in ist 9th rows

Step-by-step explanation:

ist row= 8

2nd = 10

3rd =  12

.

.

.

9th row = 24

and if we add all chairs = 8+10+12+14+16+18+20+22+24= 144

The requried, there are 24 chairs in the 9th row and there are 144 chairs in total in the first 9 rows.

Arithmetic progression is the series of numbers that have common differences between adjacent values

The first row has 8 chairs, and each subsequent row has 2 more chairs than the previous row. So the number of chairs in each row can be given by the equation:

number of chairs = 8 + 2(row - 1)

To find the number of chairs in the 9th row, we substitute row = 9 into the equation:
number of chairs = 8 + 2(9 - 1) = 8 + 2(8) = 24

So there are 24 chairs in the 9th row.

To find the total number of chairs in the first 9 rows, we need to add up the number of chairs in each row from 1 to 9. This can be done using the formula for the sum of an arithmetic series:

sum = (n/2)(first term + last term)
where "n" is the number of terms in the series.

In this case, the first term is 8, the last term is 24, and there are 9 terms (i.e. the first 9 rows). Substituting these values into the formula, we get:

sum = (9/2)(8 + 24) = 9(16) = 144

So there are 144 chairs in total in the first 9 rows.

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Answer:

I will assume

h = 82.5 sin (3 pi (t+0.5) )+97.5 , (you had no equation and no h)

so when t = 6

h = 82.5 sin (3π(6.5)) + 97.5

= 82.5(-1) + 97.5 = 15

check: period = 2π/(3π) = 2/3 minutes (that is a fast ride considering how huge it is)

So 6 ÷(2/3) = 9 , at the 6 minute mark, the last passenger has just completed 9 rotations.

the min height of the basket is -82.5 + 97.5 = 15

( the min value of 82.5 sin(anything) = 82.5(-1) )

so the last passenger must be at the platform level.

how did you get 79 ???

Step-by-step explanation:

Answer:

5r^3 + 4r^2 - 8r + 16

Step-by-step explanation:

(8 + 5r^3 - 2r^2) - (8r - 8 - 6r^2) =

The first set of parentheses is there just to show you that what is inside is a polynomial. The second set of parentheses has a second polynomial inside. The subtraction sign just to the left of the second set of parentheses shows that you are subtracting the second polynomial from the first one.

The first set of parentheses is not needed and can be dropped.

You are subtracting the second polynomial fromt he first one, so you can think of the the subtraction sign as a -1, and you need to distribute the -1 by the second polynomial, That will result in all signs inside the second set of parentheses changing.

Below, just the first set of parentheses is removed.

= 8 + 5r^3 - 2r^2 - (8r - 8 - 6r^2)

Now, we change every sign inside the second set of parentheses by distributing -1.

= 8 + 5r^3 - 2r^2 - 8r + 8 + 6r^2

Now we need to combine like terms. Like terms have the same variable part. We can rearrange the terms grouping like terms together before combining them. Also, it is customary to list the terms in descending order of degree.

= 5r^3 - 2r^2 + 6r^2 - 8r + 8 + 8

Now we combine like terms.

= 5r^3 + 4r^2 - 8r + 16

Answer:

B

Step-by-step explanation:

you add the like terms together and find the value of x multiple by 4

Answer:

x=1 and x=0

Step-by-step explanation:

We need to find the points at which the graphs y = x^2 + x – 2 and y = 2x – 2 intercept.

We know that:

x^2 + x – 2 =  2x – 2

x^2 - x = 0

Factorizing:

x(x-1) = 0

Therefore, the solution to the system of equation is x=1 and x=0.

Answer:

24

Step-by-step explanation:

2/10=3/x-9

2(x-9)=30

2x-18=30

2x=30+18

2x=48

x=24

Answer:

The value of x in the given phrase is 24.

Step-by-step explanation:

Given phrase,

2 over 10 equals 3 over quantity x minus 9

[tex]\frac{2}{10}=\frac{3}{x-9}[/tex]

By cross multiplication,

[tex]2x-18=30[/tex]

Adding 18 on both sides,

[tex]2x=48[/tex]

Divide both sides by 2,

[tex]x=24[/tex]

Hence, the value of x is 24.

Answer:

Step-by-step explanation:

The y-intercept is exist for x = 0.

We have the equation of the function: f(x) = x² + 3x + 5 → y = x² + 3x + 5.

Put x = 0:

y = 0² + 3(0) + 5 = 0 + 0 + 5 = 5

The correct option is option D: The y-intercept of the graph of the function will be (0,5).

The y-intercept of the function is determined by the point where the graph intercepts the y-axis.

At the point where the graph meets the y-axis, the x coordinate will be 0.

So by putting the x value =0 in the graph function, we can determine the y-intercept of the graph function. i.e. y=f(0)

Here, the function is given by f(x)=x²+3x+5

At the y-intercept point the x coordinate=0

So putting x=0, we can determine the y-intercept of the graph.

f(0)=0²+0+5=5

The y-coordinate of the y-intercept is 5.

The x-coordinate of the y-intercept is 0.

So the coordinate of the y-intercept is (0,5).

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Steps for the box plot are given below.

Since they are already in the order you know the 22 and the 61 are the upper and lower extremes.

To find the median you find the number that is in the middle which is 42.

We have to find the lower quartile find the middle number starting from the first number and the number to the left of the median (22 and 36 in this case). The lower quartile is 25.

a quartile is a type of quantile that divides the number of data points into four parts, or quarters, of more or less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic

To find the upper quartile, fine the middle number between the number to the right of the median and the last number (44 and 61 in this case.) If the upper quartile is 57 you then just plot it and graph it.

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Step-by-step explanation:

[tex]1a.\\ 8-y=2\qquad\text{subtract 8 from both sides}\\-y=-6\qquad\text{change the signs}\\\boxed{y=6}\\\\1b.\\11-9=2-b\\2=2-b\qquad\text{subtract 2 from both sides}\\0=-b\to \boxed{b=0}\\\\2a.\\5=\dfrac{c}{3}\qquad\text{multiply both sides by 3}\\15=c\to \boxed{c=15}\\\\2b.\\2=5-t\qquad\text{subtract 5 from both sides}\\-3=-t\qquad\text{change the signs}\\3=t\to\boxed{t=3}\\\\3a.\\5n=10\qquad\text{divide both sides by 5}\\\boxed{n=2}\\\\3b.\\a+6=12\qquad\text{subtract 6 from both sides}\\\boxed{a=6}[/tex]

[tex]4a.\\v-10=7\qquad\text{add 10 to both sides}\\\boxed{v=17}\\\\4b.\\7=7n+7n\\7=14n\qquad\text{divide both sides by 14}\\\dfrac{7}{14}=n\\\boxed{n=\dfrac{1}{2}}\\\\5a.\\m+11=12\cdot4\\m+11=48\qquad\text{subtract 11 from both sides}\\\boxed{m=37}\\\\5b.\\6y=7+5\\6y=12\qquad\text{divide both sides by 6}\\\boxed{y=2}\\\\6a.\\b-8=3\qquad\text{add 8 to both sides}\\\boxed{b=11}\\\\6b.\\1+c=8\qquad\text{subtract 1 from both sides}\\\boxed{c=7}[/tex]