Segment addition and how to do this ?

0 is correct, though...

\(\dfrac{\frac1x - \frac13}{x + 3}\)

is continuous at \(x=3\), so

\(\displaystyle \lim_{x\to3} \frac{\frac1x - \frac13}{x + 3} = \frac{\frac13 - \frac13}{\frac13 + 3} = \frac0{\frac{10}3} = 0\)

What was probably intended was the limit

\(\displaystyle \lim_{x\to3} \frac{\frac1x - \frac13}{x - 3}\)

which requires a little more finesse because the function is not continuous at \(x=3\).

Rewrite it as

\(\dfrac{\frac1x - \frac13}{x - 3} = \dfrac{3 - x}{3x(x-3)} = -\dfrac{x-3}{3x(x-3)}\)

When \(x\neq3\), we can cancel \(x-3\) so that

\(\displaystyle \lim_{x\to3} \frac{\frac1x-\frac13}{x-3} = \lim_{x\to3} -\frac1{3x} = -\frac1{3\times3} = -\frac19\)

The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² =  (a + ib)²(a - ib)²

From the question, we have the following parameters that can be used in our computation:

✓(x + iy) = a + ib

Changing the signs, we have

✓(x - iy) = a - ib

Multiply both expressions

This gives

✓(x + iy) * ✓(x - iy) =  (a + ib)(a - ib)

Square both sides

So, we have

(x + iy) * (x - iy) =  (a + ib)²(a - ib)²

This gives

x² + y² =  (a + ib)²(a - ib)²

Hence, the values of ✓(x - iy) is a - ib and x² + y² is  (a + ib)²(a - ib)²

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Answer:

4500

Step-by-step explanation:

250 x 18 = 4500

Answer:

4 1/10 when u have a inproper fraction like that every 10 is one whole number

Answer:

SOHCAHTOA

Step-by-step explanation:

Usually, in American schools, the term "SOHCAHTOA" is used to remember them. "SOH" is sine opposite hypotenuse, "CAH" is cosine adjacent hypotenuse, and "TOA" is tangent opposite adjacent. There is also Csc which is hypotenuse/opposite, Sec which is hypotenuse/adjacent, and Cot is adjacent/opposite.

Answer: SOHCAHTOA

Step-by-step explanation:

The pneumonic I learned is SOH-CAH-TOA.  it says that Sin = opposite/hypotenuse.  Cos = adjacent/hypotenuse.  Tan = opposite/adjacent.

Hope it helps <3

Step-by-step explanation:

the answer is regular octagon

i think

Answer:

Step-by-step explanation:

No explanation is needed because there is no question.

Answer:

you got it

Step-by-step explanation:

no explanation needed

\(x^2-12x+36=0\\(x-6)^2=0\\x-6=0\\x=6\)

Answer:

C. (5x + 6) (5x - 6)

Step-by-step explanation:

25 is a perfect square, meaning its two factors are identical (5), and 36 is also a perfect square with two identical factors (6). With this information, we can split the expression below like this:

\(25x^2 - 36\\(5x ) (5x )\)

Since 36 is negative, we have to have a positive 6 and a negative 6:

(5x - 6) (5x + 6)

Answer:

0.00000305564

Step-by-step explanation:

hope this helps lol!

The surface area of given triangular prism = 24 ft².

For the given triangular prism

Base = 2 ft

height = 3 ft

side = 3ft

We know that,

Surface area of triangular prism

= side x base + 3x base x height

=  3 x 2  + 3x2x3

= 6 + 18

= 24 ft²

Thus,

Surface area = 24 ft²

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The answer is x=-4

I’ve attached my work explaining why below :)

x≤-4 is the inequality represents all the solutions of -2(3x + 6) = 4(x + 7)

Two or more expressions with an Equal sign is called as Equation.

The given equation is -2(3x + 6) = 4(x + 7

We need to find the inequality which represents the solutions of the equation.

Let us solve for x

-2(3x + 6) = 4(x + 7)

Apply distributive property

-6x-12=4x+28

Take the variable terms on one side.

-6x-4x=28+12

-10x=40

Divide both sides by 10

x=-4

Hence, x≤-4 is the inequality represents all the solutions of -2(3x + 6) = 4(x + 7)

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Answer: \(y=(x-6)^2\)

Step-by-step explanation:

If the original equation is \(y=f(x)\), then the equation after the shift is \(y=f(x-6)\).

True. The length of AB can be gotten by 3^2 + b^2 = 4^2.

True.  The perimeter of the trapezoid shown is not 22 units.

The length of AB can be gotten by 3^2 + b^2 = 4^2.

9 + b^2 = 16

b^2 = 16 + 9

b = 5

Then we have to count the boxes to get the length of the other sides

CD = 4

AD = 8

BC = 5

AB = 5

Then the perimeter would be be 5 + 5 + 8 + 4

= 22

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Answer:

C

Step-by-step explanation:

all points on the line of the equation y = 1 will have the number 1 as the y-value in each ordered pair

y = 1 is a horizontal line which intersects the y-axis at (0, 1)

Given:

The function for the total lodging cost c (in dollars) for a stay at a vacation destination of n nights is

\(c=180n+250\)

Budget = $900

To find:

The number of nights you can stay at you vacation destination.

Solution:

Since, budget is $900, therefore, the cost must be less than or equal to $900.

\(c\leq 900\)

\(180n+250\leq 900\)

\(180n\leq 900-250\)

\(180n\leq 650\)

Divide both sides by 180.

\(n\leq \dfrac{650}{180}\)

\(n\leq 3.611\)

Number of nights must be a whole number. So, greatest whole value of n is 3.

Therefore, you can stay 3 nights, i.e., n=3.

Number of nights he stay is 3.6

Given that;

Cost function

C = 180n + 250

Total cost = $900

Number of nights

Cost function

C = 180n + 250

Total cost = $900

So,

900 = 180n +250

180n = 650

n = 3.6 nights (Approx.)

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Answer:

IQR = Q3-Q1

=30-10

=20

Interquartile range = Quartile3-Q1

= 30 - 10

= 20

Being a girl and playing a sport are C. No, they are not independent events, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62.

Let's consider the probabilities:

P(girl) = (number of girls) / (total number of students) = 135 / 275 ≈ 0.49

P(girl plays a sport) = (number of girls playing a sport) / (total number of students) = 76 / 275 ≈ 0.276

If being a girl and playing a sport were independent events, the joint probability would be the product of the individual probabilities:

P(girl) × P(girl plays a sport) ≈ 0.49 × 0.276 ≈ 0.13524

However, the actual joint probability is different from the expected value:

P(girl, plays a sport) ≈ 76 / 275 ≈ 0.276

Since the joint probability does not match the product of the individual probabilities, we can conclude that being a girl and playing a sport are not independent events based on the given data.

Therefore, option C. No, they are not independent, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62. is the correct answer.

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Answer:

x = 30

Step-by-step explanation:

Look at triangle LMN.

m<NLM + m<M + m<MNL = 180

90 + m<M + 45 = 180

m<M = 45

Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

<ONM is an exterior angle of triangle KMN.

The remote interior angles are <K and <M.

m<K + m<M = m<ONM

2x + 45 = 105

2x = 60

x = 30

Answer: x = 30

Answer:

118.2

Step-by-step explanation:

1.1m is 100%

2.4m×100=240

240/1.1= 218.(18)

218.(18)%-100%=118.(18)=118.2

The weight would the hedgehog lose during 115 day in hibernation is 3.45 ounces.

Using proportions, it exits found that the hedgehog loses 3.45 ounces after 115 days of hibernation.

A proportional relationship exists modeled by: y = kx

In which k exists the constant of proportionality.

In this problem, the ratio between the weight loss after x days in hibernation is given by:

k = 0.24/8 = 0.84/24 = 2.25/75 = 2.79/93 = 0.03

Since this ratio exists constant, the relationship is proportional, modeled by:

y = 0.03 x

The weight lost after 115 days of hibernation is y(115), hence:

y = 0.03(115) = 3.45

The hedgehog loses 3.45 ounces after 115 days of hibernation.

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Answer:

that truck must be straight fire

The true statement for the function p(x) is p(-2) and p(0) cannot be compared as p(0) is undefined. Option D is correct.

The given function is a logarithmic function and it is undefined at x = 0.

First, let us understand the logarithmic function:

A logarithmic function is a function of the form which is read as “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1.

We are given:

p(x) = log 5x

substitute x = 0 in the above equation, we will get;

p(0) = log 5 × 0

p(0) = log 0

p(0) = undefined

Thus, the true statement for the function p(x) is p(-2) and p(0) cannot be compared because p(0) is undefined. Option D is correct.

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Using the equation of the function p(x) below, determine which of the statements below is true. Show your work.

Captionless Image

p(-2) > p(0)

p(-2) < p(0)

p(-2) and p(0) cannot be compared because p(-2) is undefined.

p(-2) and p(0) cannot be compared because p(0) is undefined.

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Approximately 7 employees took a break longer than 49 minutes.

We have,

In a box-and-whisker plot, the box represents the interquartile range (IQR), which includes the middle 50% of the data.

The line within the box represents the median.

The "whiskers" extend to the minimum and maximum values, excluding any outliers.

Given the information provided:

Median = 41

Q1 = 37

Q3 = 49

Largest = 55

Smallest = 35

Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.

Now,

The number of employees who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:

25% of 27 employees

= (25/100) x 27

= 6.75

Since we cannot have a fractional number of employees, we round up to the nearest whole number.

Therefore,

Approximately 7 employees took a break longer than 49 minutes.

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Answer:

$7.35

Step-by-step explanation:

To find the answer to this question, you would need to multiply 15 times .49 which would equal 7.35