OD 2x - 4
Let f(x) = 6x + 5 and g(x) = -4x - 7. Find f(x) + g(x).
An answer to this question is required
A 10x + 12
2x - 2
C 10x - 2
OD 2x + 12
OB

Answer:

Below

Step-by-step explanation:

Find unit rate (since it starts at 0,0)

at 45 seconds  it is 900 bottles

             900 bottles / 45 seconds = 20 bottle / sec

20 bottles / sec * 80 sec = 1600 bottles

The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

How to find  x-intercepts?

To find the x-intercepts, we set y = 0 and solve for x:

(x⁴/4) - x² + 1 = 0

This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.

To find the y-intercept, we set x = 0:

y = (0/4) - 0² + 1 = 1

So the y-intercept is (0, 1).

To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.

To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.

To find the critical points, we take the derivative of the function and set it equal to zero:

y' = x³- 2x

x(x² - 2) = 0

x = 0 or x = sqrt(2) or x = -sqrt(2)

These are the critical points.

To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.

Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).

We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:

Interval (-infinity, -sqrt(2)):

Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.

Interval (-sqrt(2), 0):

Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.

Interval (0, sqrt(2)):

Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.

Interval (sqrt(2), infinity):

Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.

Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).

To find the inflection points, we take the second derivative of the function and set it equal to zero:

y'' = 3x² - 2

3x² - 2 = 0

x² = 2/3

x = sqrt(2/3) or x = -sqrt(2/3)

These are the inflection points.

To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.

Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).

We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:

Interval (-infinity, -sqrt(2/3)):

Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Interval (-sqrt(2/3), sqrt(2/3)):

Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.

Interval (sqrt(2/3), infinity):

Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).

To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:

y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509

Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

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Answer:

-31.4

Step-by-step explanation:

\(2.7(3+5)-11-42\\=2.7*8-11-42\\=21.6-53\\=-31.4\)

Answer:

C.

Step-by-step explanation:

because x value cannot be repeated in an ordered pair

1. The scale between Nick's true height and his new height is 1:384.

2A. The scale is 1/ 105,600.

2B. The scale from #1 and the scale from #2 are not consistent. The scale.

2C. The scale from #1 seems more reasonable, as it suggests that Nick is now about the size of a child.

A. It's difficult to estimate Nick's height without additional information. However, based on average heights in the US, we can assume Nick is around 5-6 feet tall.

B. If we assume Nick's original height was 6 feet, and he is now 1/4 inch tall, we can set up a proportion:

6 feet / x = 1/4 inch / (1/12 feet)

Solving for x, we get:

x = (6 feet * 1/4 inch) / (1/12 feet) = 18 inches

So, the scale between Nick's true height and his new height is 1:18.

2A. If the backyard is 64 feet long, and Nick estimates they need to travel 3.2 miles to reach the house, we can set up a proportion to find the scale:

64 feet / x = 3.2 miles / (5280 feet/mile)

Solving for x, we get:

x = (64 feet x 5280 feet/mile) / 3.2 miles = 105,600 feet

B. The scale from #1 suggests that Nick is now 1/18 of his original height, while the scale from #2 suggests that he is now 1/105,600 of his original height.

C. The scale from #1 seems more reasonable, as it suggests that Nick is now about the size of a child, which seems more plausible given the context of the story. The scale from #2 suggests that Nick is now much smaller than a single cell, which seems unlikely.

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Answer:d = 69c+63/79, c=79n+30

Step-by-step explanation:

79d=63+69c

divide both sides by 79,

d = 69c+63/79

c=79n+30, n can be any real number

Answer:

Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.

Now, let's find the new vertices of the dilated image:

Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).

Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).

Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).

Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).

Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).

Step-by-step explanation:

Hope this helps you!! Have a good day/night!!

Two lines \(y_1,y_2\) are perpendicular if their slopes are in a relation \(m_1=-\frac{1}{m_2}\).

So we need to find slopes and if the above relation holds then we can claim the lines are perpendicular.

To find slopes, use slope formula

\(m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}\)

The first slope of a line passing through \(PQ\) is

\(m_1=\frac{-13-(-9)}{6-2}=\frac{-4}{4}=-1\)

The second slope of a line passing through \(RS\) is

\(m_2=\frac{-1-(-5)}{5-1}=\frac{4}{4}=1\)

Now check if \(m_1=-\frac{1}{m_2}\) is true

\(-1=-\frac{1}{1}\implies -1=-1\)

This means the two lines are perpendicular.

Hope this helps.

It's asking  would not be a solution soo

(-10, -9) as you can see

You're welcome thank me later

Answer:

y = -x + 9

Step-by-step explanation:

Since the line is going down, you can safely assume that it is a negative slope function.  The y-intercept is at (0, 9), so your final slope function should be y = -x + 9.

The factor of the equation 4x² + 12x + 9 is 2x+3. Then the correct option is A.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

The factor of the polynomial is calculated as:-

4x² + 12x + 9 = 4x² + 6x + 6x + 9

                     = 2x ( 2x + 3 ) + 3 ( 2x + 3 )

                     = (2x + 3)(2x + 3)

The factor is (2x + 3). Hence, the correct option is A.

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The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

b) $120 , $ 80

Step-by-step explanation:

Ratio = 3 :2

Total = 3 + 2 = 5

3/5 of 200 = \(\frac{3}{5}*200\)

                  = 3 * 40

                  = $ 120

2/5 of 200 = \(\frac{2}{5}*200\)

                 = 2 * 40

                  = $ 80

Answer:

x+6<20

x<14

Step-by-step explanation:

Answer:

20-6+x

Step-by-step explanation:

you would add six and x and then subtract it from twenty becouse less than means to subract

Answer -3/8, -2/3 1/2

Step-by-step explanation:

Thats least to greatest

Answer:

3/8, 2/3, 1/2

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

First off, 1/5 is equal to 20%. If you're diving something into 5ths, you can do 100 / 5, which is 20. So you know that Raul scored at least 20% of the points. His friend Jake ALSO scores 20% of the teams points, making 20 + 20 = 40%. Therefore, 40% of the teams points were scored by Raul and Jake.

The required quadratic equation is s² - 25 = 0 and length of sides  be 5 cm.

Given that

Number of square pieces of wood = 8

Length of side of each piece = s cm

Area of 8 pieces of wood = 200 cm²

We know the equation A = s²,

Where s is the side length, determines the area of a square.

Then total area of all the pieces can be written as:

 8s² = 200

⇒ s² = 25

⇒ s² - 25 = 0

or s = 5 cm

Hence quadratic equation ⇒ s² - 25 = 0 and side = 5 cm

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Answer:

Yes  dog owners in the country spend more time walking their dogs than do dog owners in the city

Step-by-step explanation:

From the question we are told that

    The sample size from country is \(n_1 = 21\)

     The  sample  size from city is  \(n_2 = 23\)

     The  sample  mean for  country is   \(\= x_1 =  15 \)

      The  Sample  mean for  city is  \(\= x_2 =  10\)

       The  standard deviation for country  is \(\sigma _1 =  4\)

        The standard deviation for  city is  \(\sigma _2 =  3\)

Let the level of significance is  \(\alpha = 0.05\)

The null hypothesis is  \(H_o : \mu_1 = \mu_2\)

The  alternative hypothesis is  \(H_a : \mu_1 > \mu_2\)

 The  pooled standard deviation is  mathematically represented as

       \(s =  \sqrt{ \frac{s_1 ^2  *  (n_1 - 1 ) + s_2 ^2 *  (n_2 - 1 )}{ df} }\)

Here  df is the degree of freedom which is mathematically represented as

          \(df =  n_1 + n_2  - 2\)

         \(df =  21 + 23 -2 \)

        \(df =  42\)

So

    \(s =  \sqrt{ \frac{4 ^2  *  (15.0 - 1 ) + 3 ^2 *  (10 - 1 )}{ 42} }\)  

    \(s =  3.5\)

Generally the test statistics is mathematically represented

        \(t =  \frac{\= x_1 - \= x_2 }{ s *  \sqrt{\frac{1}{n_1} +\frac{1}{n_2}  } }\)

          \(t =  \frac{ 15 -10 }{ 3.5 * \sqrt{\frac{1}{ 21 } + \frac{1}{23} } }\)

\(t =  4.733\)

Generally the p-value  is obtained from the student t-distribution table   table , the value  is  

         \(P(T >   4.733)=  t_{4.733,  42 } = 0.000013  \)

From the calculation we see that

         \(p-value  < \alpha\)

So we reject the null hypothesis

Hence we can conclude that there is  sufficient evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city

Step-by-step explanation:

a= c-b pls let me know if it is correct or not

Answer:

\( 24 \sqrt{3} \)

Step-by-step explanation:

\(3(5 \sqrt{3} + 3 \sqrt{3} ) \\ \\ = 3(5 + 3 ) \sqrt{3} \\ \\ = 3(8) \sqrt{3} \\ \\ = 24 \sqrt{3} \)

The two figures show equivalent graphs because:

A. The graphs have several edges that match the number of vertices.

B. The graphs have the same number of edges.

C. The vertices are connected in the same way.

D. The graphs have the same number of vertices.

The third equivalent graph is at option D.

The graphs that have the same number of vertices connected in the same way are called equivalent graphs. If they are connected in the same way then their count of edges will be the same for both graphs. They are also said to be isomorphic graphs.

The given graphs have
Graph1: vertices BCJK

Graph2: vertices BCJK

So, there is the same number of vertices for both graphs.

The connection between the vertices:

Graph1: J - B - C - K - B

Graph2: J - B - C - K - B

So, they are connected in the same way.

The edges formed by these vertices:

Graph1: JB; BC; CK; KB

Graph2: JB; BC; CK; KB

So, there is the same number of edges for both graphs.

Here the number of edges = the number of vertices i.e., (4 = 4)

From all these comparisons, the given graphs are equivalent.

The third equivalent graph made from these graphs is at option D in the diagram attached below.

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Disclaimer: The given question is incomplete. There is no image attached in the given question. Here the image is attached.

Answer:

\((x-6)^2=8\)

Step-by-step explanation:

\(x^2-12x+32=4\)

\(x^2-12x+32+4=4+4\)

\(x^2-12x+36=8\)

\((x-6)^2=8\)

Basically, you need to add a number to both sides so that you can reduce the left side to a square. In this case, you add 4.

Answer:

a) Cancellations are independent and similar to arrivals.

b) 22.31% probability that no cancellations will occur on a particular Wednesday

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given time interval.

Mean rate of 1.5 per day on a typical Wednesday.

This means that \(\mu = 1.5\)

(a) Justify the use of the Poisson model.

Each wednesday is independent of each other, and each wednesday has the same mean number of cancellations.

So the answer is:

Cancellations are independent and similar to arrivals.

(b) What is the probability that no cancellations will occur on a particular Wednesday

This is P(X = 0).

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-1.5}*(1.5)^{0}}{(0)!} = 0.2231\)

22.31% probability that no cancellations will occur on a particular Wednesday

Answer:500m

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

The ship started at the Position 0.14 units.

To determine the starting position of the ship, we can consider the distance sailed to the left and the distance to the treasure.

Given that you sailed 0.055 units to the left and found the treasure at 0.085 units, we can represent this situation mathematically as follows:

Starting position + Distance sailed to the left = Distance to the treasure

Let's assign a variable, "x," to represent the starting position of the ship.

The equation becomes:

x - 0.055 = 0.085

To find the value of x, we can solve this equation by isolating x on one side:

x = 0.085 + 0.055

x = 0.14

Therefore, the ship started at the position 0.14 units.

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Given Information:

Mean clear height = μ = 22 feet

Standard deviation of clear height = σ = 4 feet

Required Information:

a) P(X > 16) = ?

b) P(X < 14) = ?

c) P(25 < X < 30) = ?

Answer:

a) P(X > 16) = 93.12%

b) P(X < 14) = 2.27%

c) P(25 < X < 30) = 20.39%

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

a) We want to find out the probability that the clear height is greater than 16 feet.

\(P(X > 16) = 1 - P(X < 16)\\\\P(X > 16) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 16) = 1 - P(Z < \frac{16 - 22}{4} )\\\\P(X > 16) = 1 - P(Z < \frac{-6}{4} )\\\\P(X > 16) = 1 - P(Z < -1.5)\\\\\)

The z-score corresponding to -1.5 is 0.0668

\(P(X > 16) = 1 - 0.0668\\\\P(X > 16) = 0.9312\\\\P(X > 16) = 93.12 \%\)

Therefore, the probability that the clear height is greater than 16 feet is 93.12%

b) We want to find out the probability that the clear height is less than 14 feet

\(P(X < 14) = P(Z < \frac{x - \mu}{\sigma} )\\\\P(X < 14) = P(Z < \frac{14 - 22}{4} )\\\\P(X < 14) = P(Z < \frac{-8}{4} )\\\\P(X < 14) = P(Z < -2)\\\\\)

The z-score corresponding to -2 is 0.02275

\(P(X < 14) = 0.02275\\\\P(X < 14) = 2.27 \%\)

Therefore, the probability that the clear height is less than 14 feet is 2.27%

c) We want to find out the probability that the clear height is between 25 and 30 feet.  

\(P(25 < X < 30) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(25 < X < 30) = P( \frac{25 - 22}{4} < Z < \frac{30 - 22}{4} )\\\\P(25 < X < 30) = P( \frac{3}{4} < Z < \frac{8}{4} )\\\\P(25 < X < 30) = P( 0.75 < Z < 2 )\\\\\)

The z-score corresponding to 0.75 is 0.7734 and 2 is 0.9773

\(P(25 < X < 30) = P( Z < 2 ) - P( Z < 0.75 ) \\\\P(25 < X < 30) = 0.9773 - 0.7734 \\\\P(25 < X < 30) = 0.2039\\\\P(25 < X < 30) = 20.39 \%\)

Therefore, the probability that a child spends more than 4 hours and less than 8 hours per day unsupervised is 20.39%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.5, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.50 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

Answer:

There is not sufficient evidence to support a claim of linear correlation between the two variables.

Step-by-step explanation:

(a)

The scatter plot for the provided data is attached below.

(b)

The hypothesis to test significance of linear correlation between the two variables is:

H₀: There is no linear correlation between the two variables, i.e. ρ = 0.

Hₐ: There is a significant linear correlation between the two variables, i.e. ρ ≠ 0.

(c)

Use the Excel function: =CORREL(array1, array2) to compute the correlation coefficient, r.

The correlation coefficient between the number of internet users and the award winners is,

r = 0.786.

The test statistic value is:

\(t=r\sqrt{\frac{n-2}{1-r^{2}}}\)

  \(=0.786\times\sqrt{\frac{6-2}{1-(0.786)^{2}}}\\\\=2.5427\\\\\approx 2.54\)

Thus, the test statistic is 2.54.

(d)

The degrees of freedom is,

df = n - 2  

  = 6 - 2

  = 4

Compute the p-value as follows:

\(p-value=2\cdot P(t_{n-2}<2.54)=2\times 0.032=0.064\)

*Use a t-table.

p-value = 0.064 > α = 0.05

The null hypothesis will not be rejected.

Thus, it can be concluded that there is not sufficient evidence to support a claim of linear correlation between the two variables.

Answer: Equilateral

Step-by-step explanation:

It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.

Hope you understood.