100 POINTS HELP EXPERTS PLEAASE!
The graph shows the functions f(x), p(x), and g(x):

Graph of function g of x is y is equal to 2 multiplied by 0.85 to the power of x. The straight line f of x joins ordered pairs minus 7, 3 and minus 3, minus 2 and is extended on both sides. The straight line p of x joins the ordered pairs 4, 1 and minus 3, minus 2 and is extended on both sides.

Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (4 points)

Part B: Write any two solutions for f(x). (4 points)

Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (6 points)

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.

The measure of the angle ∠PQR is 90 degrees

The equation of the line PQ is given as:

3x - y - 2 = 0

The coordinates of the QR are given as:

(0, -2) and (6, -4)

Make y the subject in 3x - y - 2 = 0

y = 3x - 2

The slope of the above line is

m1 = 3

Next, we calculate the slope (m2) of points Q and R.

So, we have:

m2 = (y2- y1)/(x2 - x1)

This gives

m2 = (-4 + 2)/(6 - 0)

Evaluate

m2 = -1/3

The slopes of perpendicular lines are opposite reciprocals.

m1 = 3 and m2 = -1/3 are opposite reciprocals.

This means the lines PQ and QR are perpendicular lines.

The angle at the point of perpendicularity is 90 degrees

Hence, the measure of the angle ∠PQR is 90 degrees

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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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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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Answer:

11. 333... which can also be written as 11 1/3.

Step-by-step explanation:

Sure.

√(6c - 4) = 8

Squaring both sides:

6c - 4 = 64

6c = 64 + 4 = 68

c = 68/6

  = 11. 333...

Answer:

[tex]c=\dfrac{34}{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt{6c-4}=8[/tex]

Square both sides:

[tex]\implies (\sqrt{6c-4})^2=8^2[/tex]

[tex]\implies 6c-4=64[/tex]

Add 4 to both sides:

[tex]\implies 6c-4+4=64+4[/tex]

[tex]\implies 6c=68[/tex]

Divide both sides by 6:

[tex]\implies \dfrac{6c}{6}=\dfrac{68}{6}[/tex]

[tex]\implies c=\dfrac{34}{3}[/tex]

Verify the solution by inputting the found value of c back into the equation:

[tex]\implies \sqrt{6\left(\dfrac{34}{3}\right)-4}[/tex]

[tex]\implies \sqrt{\dfrac{204}{3}-4}[/tex]

[tex]\implies \sqrt{68-4}[/tex]

[tex]\implies \sqrt{64}[/tex]

[tex]\implies \pm 8[/tex]

Therefore, the solution of the found value of c is verified.

The answer is 112 centimeters.

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

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 number of days christen’s book is overdue is 22.

The number of days christen’s book is overdue:

According to the graph, the fine levied stops rising after 20 overdue days and then stays at 10 for the remaining days.

Additionally, if Christen's fine was the same as yesterday, her late dates must be longer than 21 days (because the fine on day 20 will be the same).

22 might therefore be the number of days past due based on the options provided.

The number of days christen’s book is overdue is 22.

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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 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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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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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 :

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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[tex]\\ \tt{:}\dashrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180\ell}{\pi r}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180(13)}{5\pi}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149^{\circ}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149(60)[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=8940'[/tex]

The angle subtended at the center of a circle of radius 5 cm by a length of 13 cm is 149.1°.

Given that,

The angle is subtended at the center of a circle of radius 5 cm by a length of 13 cm.

Here, Lenght of an arc = 13 cm

The radius of an arc = 5 cm

Used the formula for the angles (θ);

Length of an arc = 2πrθ / 360°

Substitute all the values, we get;

13 = 2 × 3.14 × 5 × θ / 360°

Solve for θ;

13 × 360° = 31.4 × θ

4,680° = 31.4 × θ

θ = 4,680°/31.4

θ = 149.1°

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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

The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.

According to the given statement

we have given data set and we have to find the five number summary.

So, For this purpose,

the given data set is:

48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80

Firstly we have to find the upper quartile means median for it.

So, Median = n /2

median = 12/2

median = 6th term.

So, Upper quartile range for this data set is 63.

And

Lower quartile for data set is the lower value of the data set.

So, That's why

Lower quartile range for this data set is 48.

And now, we have to find the Interquartile range

so, Interquartile range means maximum value of data.

So, That's why

Interquartile range of this data is 80.

So, The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.

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La altura del triangulo está dada por el polinomio:

p(x) = a + 4

Recordar que para un triangulo de base B y altura H, el area es

A = B*H/2

En este caso, sabemos que la base es B = (4*a^2 + 6)

Y el area es A = 2a^3 + 8a^2 +3a +12

Entoces la altura será un polinomio tal que:

P(a)*(4*a^2 + 6)/2 = 2a^3 + 8a^2 +3a +12

P(a)*(4*a^2 + 6) = 2*(2a^3 + 8a^2 +3a +12) = 4a^3 + 16a^2 + 6a + 24

Podemos ver que p(a) va a ser un polinomio de grado 1, entonces:

p(a) = (c*a + b)

Reemplazando eso:

(c*a + b)*(4*a^2 + 6) = 4a^3 + 16a^2 + 6a + 24

Expandiendo:

(4c)*a^3 + (6c)*a + (4b)*a^2 + 6*b = 4a^3 + 16a^2 + 6a + 24

Comparando terminos del mismo exponente, podemos ver que:

(4c) = 4

6c = 6

4b = 16

6b = 24

Resolviendo esas ecuaciones para c y b, podemos ver que:

b = 16/4 = 4

c = 4/4 = 1

Entonces la altura del triangulo está dada por el polinomio:

p(x) = a + 4

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The probability of pulling a black or red card  = 3/10

Probability that a white card will be drawn, P(white) = 1/25

Probability that a blue card will be dealt, P(black)  = 1/5

Probability that a black card will be dealt, P(red) = 1/10

Probability that a pink card will be revealed, P(pink)  = 1/15

All of these occurrences are distinct from one another and do not relate to one another.

The likelihood that any one of any two events, A and B, with probability P(A) and P(B), will occur is:

                                        P( A ∪ B ) = P(A) + P(B)

Here, event A can be compared to getting a black card, and

incident B is comparable to receiving a red card.

So, P(black or red) = P(black) + P (red)

= (1/5) + (1/10)

= ( 2 + 1 )/10

= 3/10

So, the likelihood that a black or red card will be pulled from the hat:

= 3/10

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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.

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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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:

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

Answer:

perimeter = 24

Step-by-step explanation:

formula:

In an equilateral triangle with sides of lengths ‘a’

The height of the triangle is equal to :

[tex]= \frac{\sqrt{3} }{2} a[/tex]

……………………………………………

Calculating ‘a’ :

We have to solve the equation:

[tex]4\sqrt{3} =\frac{\sqrt{3} }{2} a[/tex]

[tex]\Longleftrightarrow 4=\frac{1 }{2} a[/tex]

[tex]\Longleftrightarrow a = 8[/tex]

Calculating the perimeter:

= 3a

= 3 × 8

= 24

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:

A, D, E

Step-by-step explanation:

I got it right.

the total volume of the chimney is:

V =456 in^3

Remember that the volume of a rectangular prism of dimensions L, W, and H is:

V = L*W*H

If you look at the image of the chimney (bottom right image) you can see that the figure can be viewed as 2 rectangular prisms, one smaller of dimensions:

4in x 12in x 9 in

Then the volume of the larger part is:

V = (4in)*(12in)*(9in) = 432 in^3

The smaller prism has dimensions:

of (6in - 4in) = 2in x 3in x 4in

Then the volume is:

V = (2in)*(3in)*(4in) = 24 in^3

Then the total volume of the chimney is:

V = 432 in^3 +  24 in^3 = 456 in^3

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It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

According to the question

Gregory can mow the family's lawn in 3 hours, she mows at a rate of 1/3 of the lawn per hour(1/3 lawn/hour)

Jennifer can mow it in 4 hours, which means her rate is 1/4 lawn/hour.

Together , their rates are 1/3 + 1/4.

This equals 7/12 lawns/hr.

We want to know how many hours they have to mow in order to mow 1 lawn.

This can be represented by the equation : [tex]\frac{7}{12} \times x = 1[/tex]

To solve for x, we would divide both sides by 7/12.

This leaves us with x = 12/7 which is 1.714.

Convert 1.714 to minutes by multiplying 60.

This gives you a final answer of about 1 hour 43 minutes.

Hence, It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

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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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