Help me please!!!!!!!!

The answer is 112 centimeters.

As this problem represents a right triangle, here we need to apply the Pythagorean Theorem.

3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.

What is diameter?

we know that

The diameter of the circle is equal to BD

Applying the Pythagoras Theorem

BD² = BE² + DE²

substitute the given values

BD² = (3)² + (2.5)²

BD² = 9 + 6.25

BD² = 15.25

BD = √15.25

BD = 3.9 cm

Therefore , 3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.

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the correct inequality is"any rational number less than 9"

x < 9

Remember that when we have a number line, an open circle means that we can use the symbols > or <.

While a closed circle uses the symbols ≤ or ≥.

Here we know that we have an open circle at 9, ant everything to the left of the circle is shaded.

To the left of 9 there are the numbers smaller than 9, then the inequality would be:

x < 9

Then the correct option is "any rational number less than 9"

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Answer: x<9

any rational number less than 9"

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

The slope is the change in y over the change in x.  

Your y's from the point given is -2, and 2.

Your x's from the point given is -1, and 2.  Since we want to know how much they have changed, we subtract these numbers to find the change.

Change in y's?  -2 - 2 or -4

Change in x's  -1 - 2 or -3

This gives me a slope of -4/-3  and a negative divided by a positive is a positive.

I could have found the change by going the opposite direction

Change in y's ? 2 - (-2) or 4

Change in x's? 2 - (-1) or 3

This gives me the same slope 4/3

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step

What does this problem want to find:

 ⇒ domain and range

Let's find domain

 ⇒ distance covered by graph horizontally

     ⇒ [-5, 1)  

Let's find range

  ⇒ distance covered by graph vertically

      ⇒ [-4, 7)

*note

            ⇒ those points are not included in domain and range

             ⇒ those points are included in domain and range

Answer:

Hope that helps!

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Domain of the function are the real values at which the function is defined, or has a unique value. generally domain is represented by the values that x - coordinate can take according to graph.

So, domain of given function is :

here,

Similarly, range represents all the values that the function can have, and it is represented by the values that y - coordinate can have.

So, range of given function is :

Answer:

Step-by-step explanation:

Remember the midpoint formula:

[tex](\frac{x2+x1}{2},\frac{y2+y1}{2} )\\[/tex]

Substitute in your values

 [tex](\frac{7.6+21.8}{2},\frac{1.7+9.3}{2} )\\[/tex]

Solve

[tex](\frac{29.4}{2},\frac{11}{2} )\\(14.7,5.5)\\[/tex]

Answer: (14.7,5.5)

Step-by-step explanation: I got it right on the test...

Answer:

A, D, E

Step-by-step explanation:

I got it right.

The expression that represents the volume of the cone is 6aπ.

What is called cone?

Given the data in the question;

Radius r = 3

Height h = 2a

Volume of the cone V = ?

We substitute our given values into the expression above.

V = (1/3) × π × r² × h

V = (1/3) × π × (3)² × 2a

V = (1/3) × π × 9 × 2a

V = 18aπ / 3

V = 6aπ

Therefore, the expression that represents the volume of the cone is 6aπ.

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Answer:

slope = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 5x - 2 ← is in slope- intercept form

with slope m = - 5

The volume of the similar triangular prism is:  1,280 cm³.

Volume of a right triangular prism = 0.5 × b × h × altitude, where:

b is the base length of the triangular base

h is the height of the triangular base

Find the of the first triangular prism

Base length of the triangular base (b) = 4 cm

Height of the triangular base (h) = 4 cm

Altitude of the prism = 20 cm

Volume of the first triangular prism = 0.5 × 4 × 4 × 20 = 160 cm³.

Volume of the first prism/Volume of the second prism = (leg of first prism)³/(leg of second prism)³

160/Volume of the second prism = (4)³/(8)³

160/Volume of the second prism = 64/512

160/Volume of the second prism = 0.125

Volume of the second prism = 1,280 cm³.

Thus, applying the volume formula for a right triangular prism, the volume of the given similar prism is calculated as: 1,280 cm³.

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The qualities of the set {(x,y): x>0,y>0} is as under:

Given a set {(x,y),x>0,y>0}.

We are required to determine the qualities of the set.

We know that a set is a collection of things,numbers, fractions, etc.

In any set the values of x represents the domain of the function and the values of y represents the value of codomain of the function with which the set belongs to.

Set={(x,y): x>0,y>0}

From the above set we can find the qualities stated below:

Hence the qualities of the set {(x,y): x>0,y>0} are that all values should be in first quadrant and all the values are positive.

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Answer:

True

Step-by-step explanation:

You are taking away sand from the ground and adding sand to the bucket. There is less sand on the ground and more in the bucket making it inverse.

2/3  is the slope of a line that is perpendicular to the line whose equation is 3x 2y=6.

What is slope?

we can find the slope from the equation that is given buy solving the equation for y

3x+2y = 6

2y = 6-3x

y = 3-3/2x

y = -3/2x+3

now that the equation is in slope-intercept form, we can easily see that the slope of the given line is -3/2

perpendicular lines have slopes that are negative reciprocals, so we can just take the negative reciprocal of the slope we have

-3/2 → 3/2 → 2/3

Therefore, the slope of the perpendicular line is 2/3.

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Based on the fact that the identical darts were thrown at four identical dartboards and Ben took a list, the number of different lists possible is 5 lists.

If all the darts hit on dartboard then the list would be:

= 0004

If one dart hit a dartboard and three hit one dartboard the list would be:

= 0031

If two darts hit two boards:

= 0022

If two darts hit one board, 1 dart two others:
= 0211

If all darts hit separate boards;

= 1111

This means that 5 lists are possible to Ben.

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Answer:

[tex]4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

[tex]\displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x[/tex]

Rewrite 9 as 3²:

[tex]\implies \displaystyle \int \dfrac{4}{x\sqrt{3^2+(\ln(x))^2}}\:\:\text{d}x[/tex]

Integration by substitution

[tex]\boxed{\textsf{For }\sqrt{a^2+x^2} \textsf{ use the substitution }x=a \tan\theta}[/tex]

[tex]\textsf{Let } \ln x=3 \tan \theta[/tex]

[tex]\begin{aligned}\implies \sqrt{3^2+(\ln x)^2} & =\sqrt{3^2+(3 \tan\theta)^2}\\ & = \sqrt{9+9\tan^2 \theta}\\ & = \sqrt{9(1+\tan^2 \theta)}\\ & = \sqrt{9\sec^2 \theta}\\ & = 3 \sec\theta\end{aligned}[/tex]

Find the derivative of ln x and rewrite it so that dx is on its own:

[tex]\implies \ln x=3 \tan \theta[/tex]

[tex]\implies \dfrac{1}{x}\dfrac{\text{d}x}{\text{d}\theta}=3 \sec^2\theta[/tex]

[tex]\implies \text{d}x=3x \sec^2\theta\:\:\text{d}\theta[/tex]

Substitute everything into the original integral:

[tex]\begin{aligned} \implies \displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x & = \int \dfrac{4}{3x \sec \theta} \cdot 3x \sec^2\theta\:\:\text{d}\theta\\\\ & = \int 4 \sec \theta \:\: \text{d}\theta\end{aligned}[/tex]

Take out the constant:

[tex]\implies \displaystyle 4 \int \sec \theta\:\:\text{d}\theta[/tex]

[tex]\boxed{\begin{minipage}{7 cm}\underline{Integrating $\sec kx$}\\\\$\displaystyle \int \sec kx\:\text{d}x=\dfrac{1}{k} \ln \left| \sec kx + \tan kx \right|\:\:(+\text{C})$\end{minipage}}[/tex]

[tex]\implies 4\ln \left| \sec \theta + \tan \theta \right|+\text{C}[/tex]

[tex]\textsf{Substitute back in } \tan\theta=\dfrac{1}{3}\ln x :[/tex]

[tex]\implies 4\ln \left| \sec \theta + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]

[tex]\textsf{Substitute back in } \sec\theta=\dfrac{1}{3}\sqrt{9+(\ln x)^2}:[/tex]

[tex]\implies 4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}[/tex]

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The total height of the pole from the ground to the top is 3.2 added to the height of the person

The given parameters are:

The question is an illustration of elevation

Where the height of the building is the sum of the height of the person and the height from the person's sight to the top of the building (h)

Start by calculating the value of h using the following sine function

[tex]\sin(\theta) = \frac{h}{L}[/tex]

Substitute the values of L and ∅ in the above equation

sin(32) = h/6

Multiply both sides by 6

h = 6 * sin(32)

Evaluate sin(32)

h = 6 * 0.5299

Evaluate the product

h = 3.1794

Approximate

h = 3.2

Hence, the total height of the pole from the ground to the top is 3.2 added to the height of the person

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Answer:

3:10

10:1

8:1

100:7

Step-by-step explanation:

900:3000

300:1000

3:10

80:8

10:1

2000:750

8:1

100:7

The cost for 10 people equals to $ 140.

What is cost simple word?

Cost of renting bowling alley = $ 100

Additional cost of renting bowling alley per person = $ 4

⇒ Total Cost for n no. of people = 100 + 4 × n

So, Cost for 10 people = Fix $100 for bowling alley  + $4 for each 10

people

                                         = 100 + 4 × 10

                                          = 100 + 40

                                           = 140

Therefore, The cost for 10 people equals to $ 140.

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Correct option is A. The value of f(3) is -11

The value of x = 3 corresponds to the following function on the piece wise

[tex]f(x) = -3x -2[/tex]

Substitute 3 for x

[tex]f(3) = -3(3) -2[/tex]

Expand

[tex]f(3) = -9 -2[/tex]

Evaluate -9 -2

[tex]f(3) = -11[/tex]

Hence, the value of f(3) is (a) -11

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Answer: A.) -11

Step-by-step explanation: i hope this helps :)

Coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.

From the question, we have the following statements:

As a general rule, circles that have the above features are referred to as concentric circles.

This is so because concentric circles have the same center, and they do not intersect

Hence, coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.

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Using the arrangements formula, it is found that:

a) There are 1365 possible outcomes that contain exactly four tails.

b) There are 1,307,674,399,889 possible outcomes that contain at least three heads.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repetitions, the number of ways is given as follows:

[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

In which [tex]n_1, n_2, \cdots, n_n[/tex] are the numbers of repetitions.

Item a:

11 heads and 4 tails, hence:

[tex]A_{15}^{11,4} = \frac{15!}{11!4!} = 1365[/tex]

There are 1365 possible outcomes that contain exactly four tails.

Item b:

The total number is:

[tex]A_{15} = 15! = 1,307,674,400,000[/tex]

With no heads:

[tex]A_{15}^{15,0} = \frac{15!}{15!0!} = 1[/tex]

With one head:

[tex]A_{15}^{14,1} = \frac{15!}{14!1!} = 15[/tex]

With two heads:

[tex]A_{15}^{13,2} = \frac{15!}{13!2!} = 95[/tex]

Hence the number of outcomes with less than three heads is:

1 + 15 + 95 = 111

With at least three heads, the number of outcomes is:

[tex]1,307,674,400,000 - 111 = 1,307,674,399,889[/tex]

There are 1,307,674,399,889 possible outcomes that contain at least three heads.

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Answer: (x) = x^3 − x^2 − 4x + 4End behavior- Falls to the left rises to the righty intercept-(0, 4)Zeros- (1,-2,2)g(x) = x^3 + 2x^2 − 9x − 18

Step-by-step explanation:

The equation of the line is b = am + c

Linear equations are equations that have a constant slope, average rate of change or gradients

The point is given as

(x, y) = (a, b)

The slope is given as

Slope = m

A linear equation is represented as

y = mx + c

Where me represents the slope

Substitute (x, y) = (a, b)

b = am + c

Hence, the equation of the line is b = am + c

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Answer:

the answers are -243 and 729

Step-by-step explanation:

you multiply each by -3. 1x-3 gives you -3. -3x-3 gives you 9. -3x9 gives you -27. -27x-3 gives you 81. 81x-3 gives you -243 and -243x-3 gives you 729. i hope this helps.

Explanation: The 4th one is the distributive property because it shows an     equal sign and the 5th one is the inverse property of addition because it uses more than addition.

Answer: 4th one is distributive property 5th one is inverse property of addition

P.S. I am sure 95% sure that I am correct.

The system of inequalities represented on the graph is:

A linear function is modeled by:

y = mx + b

In which:

The linear function in this problem has y-intercept of b = 3, and also goes through the point (1,5), hence the slope is of 2. The line is dashed, hence it is not included in the solution, hence only the part greater than the line is, hence:

y > 2x + 3

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this graph, the vertex of the parabola is of (-1,-4), hence h = -1, k = -4, and the equation is:

y = a(x + 1)² - 4

When x = 0, y = -3, hence the leading coefficient is found as follows:

-3 = a - 4

a = 1.

Hence:

y = (x + 1)² - 4.

And the inequality is:

y > (x + 1)² - 4.

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The correct option B.

The value of the zeros of function g is -6 and 7

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

The factors are  (x − 7) and (x + 6)

On simplifying the we get:

x²+ 6x -7x -42 = 0

x² - x - 42 = 0

The factorizing these equation we get.

So the zeros are -6 and 7 , so option b is correct.

[tex]x_{1,2}=\frac{-(-1) \pm \sqrt{(-1)^{2}-4 \cdot 1 \cdot(-42)}}{2 \cdot 1}[/tex]

[tex]$$x_{1,2}=\frac{-(-1) \pm 13}{2 \cdot 1}\\[/tex]

[tex]x_1,_2[/tex] = ((1) ± 13)/2.1

[tex]x_1[/tex]    = (1+13)/2.1

[tex]x_2[/tex]     = (1 - 13)/2.1

[tex]X_1\\[/tex] = 7 , [tex]X_2[/tex] = -6

The Zeros of the function are: (7 , -6)

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The type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)

In this problem we must check the characteristics of an expression and conclude what kind of function is. First, we need to find if any trascendent operator, it not, then the function may be either polynomial or rational. If the function has a trascendent operator, then we must check if it is logarithmic or exponential.

At first glance, we see that the function includes only one trascendent operator, a "log" operator that creates a function of the form f(x) = A · ㏒ₙ (B · x). Therefore, the type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)

The statement is poorly formatted, correct form is shown below:

What type of function is f(x) = 2 · ㏒₅ (3 · x)? a) Exponential, b) Logarithmic, c) Polynomial, d) Rational.

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Answer: Logarithmic

Step-by-step explanation: Got the question right on test.

If Mary measures the angle of elevation from a point A, to be 10°. She then walks 100m directly towards the tower, and finds the angle of elevation from the new point B to be 20°, the height of the tower comes out to be 37 meters.

Given Information and Formula Used:

The angle of elevation of the tower from point A (a in figure) = 10°

The angle of elevation of the tower from point B (b in figure) = 20°

The distance AB (ab n figure) = 100m

In right triangle adc, tan 10° = cd / ad ....... (1)

In right triangle bdc, tan 20° = cd / bd ......... (2)

Here, cd is the height of the tower.

Let the distance bd be x, then the ad = x + 100

Substituting this value of of ad in equation (1), we get,

tan 10° = cd / (x+100)

x+100 = cd / tan 10°

x+100 = cd / 0.18

x+100 = 5.6 cd ....... (3)

From equation (2),

tan 20° = cd / x

x = cd / tan 20°

x = cd / 0.34

x = 2.9 cd

Putting this value of x in equation (3), we obtain the height cd (or CD) as,

2.9 cd + 100 = 5.6 cd

(5.6 - 2.9)cd = 100

2.7cd = 100

cd = 100/2.7

cd ≈ 37m (To the nearest tenth of a meter)

Therefore, the height of the tower is calculated to be 37 meters.

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