Question 3 (4 MARKS) Find the equation of the tangents to the curve of the function with rule y = x^2 at the points where x = a and x =-a and find the coordinates of the point of intersection of these two tangents.​

Answer:

B.  ABCD =EFGH

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Answer:

The answer is B

Step-by-step explanation:

Hard to explain but i will try. So in order to find the correct concurrency statement you have to find corresponding parts in order to find these you have to find "the same spot" on both figures then all you do is match the letters in the statement. For example A is to E and B is to F as they are in the same spot. Hope this helps

Answer:

The number is 27

Step-by-step explanation:

Attached is the solution step by step

Answer:

See below ↓

Step-by-step explanation:

Measures of the angles are equal 360° (total degree measure) - [∠G + ∠E]

10 miles per hour is the average journey speed.

Given that,

Some pupils choose to ride bikes. They move at a 15 mph average speed for the first two hours, and then they stop for lunch for an hour. The pupils ride at a 10 mph speed for an additional hour.

Average speed is ( total distance ) / ( total time )

During the 1st 2 hrs:

distance = speed * time

distance = 15 *2 = 30 miles

During the last hour:

distance = speed * time

distance = 10 *1 = 10 miles

Average speed = 30+10 / 2+1+1 = 40/4 = 10 mil/hr

Therefore, their average speed for the trip is 10 mil/hr

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The solution to the equation 16 = 4^x-6 is x ≈ 2.23.

To solve the equation 16 = 4^x-6, we can start by adding 6 to both sides:

16 + 6 = 4^x

Simplifying the left side:

22 = 4^x

Next, we can take the logarithm of both sides of the equation, using any base we like. Let's use the natural logarithm (ln):

ln(22) = ln(4^x)

Using the rule that ln(a^b) = b ln(a):

ln(22) = x ln(4)

Finally, we can solve for x by dividing both sides by ln(4):

x = ln(22) / ln(4)

Using a calculator, we can find:

x ≈ 2.23

Therefore, the solution to the equation 16 = 4^x-6 is x ≈ 2.23.

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The equation representing this function is y = tan(x)

The equation which represents a tangent function with a domain of all real numbers such that x is not equal to pi over 4 plus pi over 2 times n comma where n is an integer is:y = tan(x)The tangent function is one of the six trigonometric functions, which is abbreviated as tan. The inverse of the cotangent function is the tangent function. It is also referred to as the inverse tangent, arctan, or tan^-1.

It is defined by the ratio of the opposite side to the adjacent side of a right triangle. The tangent function is a periodic function with a period of π radians or 180°. Its value alternates between negative and positive infinity over each period.The tangent function is not defined at odd multiples of π/2, that is, (2n+1)π/2 for all integers n. This is because the denominator in the tangent function becomes zero, causing a vertical asymptote.
For example, the values of the tangent function for π/2, 3π/2, 5π/2, etc. are undefined. Therefore, the domain of the tangent function is all real numbers except for odd multiples of π/2. The notation for the domain is (-∞, -π/2) U (-π/2, π/2) U (π/2, 3π/2) U (3π/2, ∞).However, in this case, the domain is all real numbers except π/4 + nπ/2, where n is any integer.

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To find the line segment C connecting the points (0, 0, 0) and (1, 2, 3), you can use the parametric equations for a line in 3D space. The general form of these equations is:

x = x0 + at
y = y0 + bt
z = z0 + ct

where (x0, y0, z0) is the initial point, (a, b, c) is the direction vector from the initial point to the final point, and t is the parameter that varies from 0 to 1.

For the given points (0, 0, 0) and (1, 2, 3), the direction vector is (1-0, 2-0, 3-0) = (1, 2, 3). So, the parametric equations for the line segment C are: x = 0 + 1t, y = 0 + 2t, z = 0 + 3t
or simply: x = t
y = 2t
z = 3t
with t ranging from 0 to 1.

Source: Stewart, James. Multivariable Calculus (p. 1124). Cengage Learning. Kindle Edition.

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Alessandra's statement corresponds to the alternative hypothesis (c) in a hypothesis test, suggesting a change or effect of the independent variable on the dependent variable.

The statement made by Alessandra regarding a hypothesis test suggests the use of an alternative hypothesis (c). In hypothesis testing, the alternative hypothesis represents the claim or belief that there will be a change or effect on the dependent variable due to the independent variable. It opposes the null hypothesis, which assumes no change or effect. In this case, Alessandra is proposing that there will be a difference or relationship between the independent and dependent variables.

To further elaborate, a hypothesis test is a statistical method used to make inferences about a population based on sample data. It involves formulating a null hypothesis (b), which assumes no significant difference or relationship between variables, and an alternative hypothesis (c), which asserts that there is a significant difference or relationship. The independent-measures t-test and repeated-measures t-test (d) are specific types of statistical tests used to compare means or differences between groups, but they are not directly related to the hypothesis statement provided by Alessandra.

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The equation about the two angles must be true is  

D) cos 36 = sin 54.

What is complementary angles?

We know that when sum of two angles is add upto 90° then that is called as complementary angles and the equation must be cos A = sin B.

Then, \(\angle A+\angle B=90\textdegree\)

Now solving the options then,

A) 54°+54°=108°≠90°

Then the equation is false.

B) Here sin 36=sin 54 is not correct equation.

C) 36°+36°=72°≠90°

Then the equation is false.

D) 36°+54° = 90°=90°

Then the equation is true.

Hence the equation about the two angles must be true is  

D) cos 36 = sin 54.

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Answer:

2/3

Step-by-step explanation:

There is a 2 in 3 chance the pointer will not land on c or d.

Answer:

x + 37 = 90

Step-by-step explanation:

Since complementary angles add up to 90 degrees, we would need to add 37 and x to equal 90 degrees. Therefore, x + 37 equals 90 degrees. As for solving, subtract 37 from both sides and you are left with x = 53.

Answer:

r = 1/6

Step-by-step explanation:

\(\dfrac{3}{4}r=\dfrac{1}{8}\\\\\\\)

Multiply both sides by 4

\(4*\dfrac{3}{4}r=4*\dfrac{1}{8}\\\\3r = \dfrac{1}{2}\)

Divide both sides by 3

\(\dfrac{3}{3}r=\dfrac{1}{2*3}\\\\r = \dfrac{1}{6}\)

Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

It will take 5.625 hours for both Darryl and Valerie to paint the room if they work together .

In the question ,

it is given that ,

Darryl can paint the room in 9 hours .

So , in 1 hour Darryl can paint 1/9 of the room .

Valerie can paint the room in 15 hours .

So , in 1 hour Valerie can paint 1/15 of the room .

So , the time taken to paint the room together can be calculated using ,

1/t = 1/9 + 1/15

1/t = 5/45 + 3/45

1/t = 8/45

Simplifying further ,

we get ,

t = 45/8

t = 5.625

Therefore , the time taken will be 5.625 hours .

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Answer:

More cows

Step-by-step explanation:

more cows because:

8*1/4=2

12*1/4=3

\([25.318\ ,\ 31.121]\) is a 95% confidence interval for the population variance.

A confidence interval in statistics denotes the probability/likelihood that a population parameter will fall between a set of values for a given proportion of the time. Analysts often use confidence intervals that include 95% or 99% of the expected observations.

Given,

Sample = 21 23 25 27 28 35 30 32 33.

confidence level = 95%

sample size =9

To determine confidence interval use formula,

\(C.I=mean \pm z(\frac{S}{\sqrt{n}})\)

where,

S=standard deviation

n=sample size

z-value for 95% =1.96

At first,

\(Mean=\frac{sum\ of\ numbers}{total\ numbers}\\\\Mean=\frac{21+23+25+27+28+35+30+32+33}{9}\\\\Mean=28.22\)

Now calculate standard deviation,

\(S=\sqrt{\frac{1}{n}\sum(x_i-mean)^2}\\\\S=\sqrt{\frac{1}{9}((21-28.22)^2+(21-28.22)^2+(23-28.22)^2+...+(33-28.22)^2}\\\\\\S=4.441\)

Now, calculate confidence interval,

\(C.I=28.22 \pm 1.96(\frac{4.441}{\sqrt{9}})\\\\C=28.22 \pm 2.901\\\\C=25.318\ ,\ 31.121\)

Thus, the confidence level is  \(C=[25.318\ ,\ 31.121]\)

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Your question is incomplete, here is the complete question.

The values taken from a normally distributed population are 21 23 25 27 28 35 30 32 33. Which of the following is a 95% confidence interval for the population variance.

[2.03, 16.30]

[10.12, 81.43]

[9.00, 72.41]

[11.39, 91.64]

[25.31, 31.12]

Lo corregí es 127.50 .u.

El precio total por 3 1/2 kg de jitomate que compró Juana es 127.75

Para saber el precio total de los 3 1/2 kg de jitomate que compró Juana debemos hacer el siguiente procedimiento.

Necesitamos saber cuánto vale medio kg de jitomate, para ello dividimos 36.50 en 2.

36.50/2 = 18.25

Luego multiplicamos 36.50 por 3, para saber cuánto valen 3 kg de jitomate.

36.50 X 3 = 109.5

Por último, sumamos el precio de medio kilo con el precio de tres kilos para tener el total que pagó Juana.

109.5 + 18.25 = 127,75

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Answer:

x= 16.6ft

Step-by-step explanation:

We have solved the equation AB=BC for A, assuming that A, B, and C are square matrices and B is invertible, then the solution is A=C B⁻¹.

First, let's take a look at the equation AB=BC. This is an equation that involves matrices, which are essentially rectangular arrays of numbers. In this case, we have three matrices: A, B, and C. The equation tells us that the product of A and B is equal to the product of B and C.

Now, we want to solve this equation for A. This means that we want to isolate A on one side of the equation and have everything else on the other side. To do this, we can use matrix algebra.

One property of matrices is that we can multiply both sides of an equation by the inverse of a matrix without changing the solution. Since we know that B is invertible, we can multiply both sides of the equation by B⁻¹, the inverse of B:

AB B⁻¹ = BC B⁻¹

Now, we can simplify the left side of the equation, because B times its inverse gives us the identity matrix I:

A I = C B⁻¹

Again, we can simplify the left side of the equation, because anything multiplied by the identity matrix stays the same:

A = C B⁻¹

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Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

Answer:

Step-by-step explanation:

2-(-1\8)±-7\4 then

2 plus 1\8 plus -7\4

2 plus 1\8 plus -14\8

2 -13\8

2= 16/8

3\8?

Answer:

3/8

Step-by-step explanation:

Substitute given information into given equation

b=2, c=-7/4

2-(-1/8) + - 7/4

Make 2 into 16/8 (by multiplying it by 8/8 To make denominator the same)

16/8 -(-1/8) + -7/4

17/8 (Because when negative and negative will make positive)

17/8+ -7/4

Make -7/4 into -14/8 (by multiplying it by 2/2 To make denominator the same)

17/8 -14/8 (Because negative and positive will make negative)

3/8 is the final answer

I hope this helps, dont hesitate to ask for any question.

Mark me as brainliest is appreciated.Tq!!

Answer:

x=10

Step-by-step explanation:

If we subtract 2 from 52 we get 50 and ten mutiplys into 50.

The margin of error for the 99% confidence interval used to estimate the population proportion is approximately 0.00992 or 0.992%.

To find the margin of error for a 99% confidence interval for a population proportion, we need to follow these steps:

Step 1: Determine the sample proportion (p-hat)
In this case, 1860 out of 9300 subjects showed improvement. So, the sample proportion is:
p-hat = 1860/9300 ≈ 0.2

Step 2: Find the critical value (z-score) for the 99% confidence interval
For a 99% confidence interval, the critical value (z-score) is approximately 2.576. This can be found using a z-table or statistical calculator.

Step 3: Calculate the standard error
The standard error can be found using the formula:
SE = sqrt((p-hat * (1 - p-hat))/n)
Where n is the number of subjects. In this case:
SE = sqrt((0.2 * (1 - 0.2))/9300) ≈ 0.00385

Step 4: Calculate the margin of error
Finally, the margin of error can be found by multiplying the critical value and the standard error:
Margin of Error = z-score * SE
Margin of Error = 2.576 * 0.00385 ≈ 0.00992

So, the margin of error for the 99% confidence interval used to estimate the population proportion is approximately 0.00992 or 0.992%.

In summary, the margin of error for this clinical test is 0.992%, which represents the uncertainty around the estimated population proportion of subjects who show improvement after treatment. This means that we can be 99% confident that the true population proportion lies within 0.2 ± 0.00992.

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ANSWER :

Yes

EXPLANATION :

An arithmetic sequence has a common difference.

Let's check if the given sequence has a common dfference.

We have :

Get the difference of succeeding terms.

4 - 2 = 2

6 - 4 = 2

8 - 6 = 2

10 - 8 = 2

Since there is a common difference of 2. The sequence is arithmetic.

Answer:

Step-by-step explanation:

so we know 3w = L + 5

and then we know that 2w + 2L = 194

so those are our two equations

since we have L by itself in the first equation, we are going to move the 5

L = 3w - 5

so now we can plug that in as L in the second equation

2w + 2(3w - 5) = 194

so now we distribute that 2

2w + 6w - 10 = 194

then simplify

8w - 10 = 194

then add the 10 to the other side

8w = 204

then we divide the 8

we get w = 25.5

so now we take that and go all the way back and plug that into the othr equation (ik this is a lot)

L = 3w - 5

so we plug in what we got for w

L = 3(25.5) -5

then multiply

L = 76.5 - 5

L = 71.5

so we end up with

w = 25.5 and L = 71.5

have a great day!! <3

To find the score that separates the bottom 82% from the top 18% in a normal distribution with a mean of 80.1 and a standard deviation of 46, we need to find the corresponding z-score and then convert it back to the original score using the formula x = μ + zσ. Therefore, the score that separates the bottom 82% from the top 18% is approximately 123.24.

In a normal distribution, the area under the curve represents the probability of obtaining a value below a certain point. To find the score that separates the bottom 82% from the top 18%, we need to find the z-score that corresponds to the 82nd percentile.

The z-score represents the number of standard deviations an observation is from the mean. To find the z-score, we can use a standard normal distribution table or a statistical calculator.

For the 82nd percentile, the area under the curve to the left of the z-score is 0.82. Using the standard normal distribution table, we can find the z-score corresponding to this area, which is approximately 0.94.

To convert the z-score back to the original score, we use the formula x = μ + zσ, where x is the score, μ is the mean, z is the z-score, and σ is the standard deviation.

Using the given values, we can calculate the score separating the bottom 82% from the top 18%:

x = 80.1 + 0.94 * 46

x ≈ 123.24

Therefore, the score that separates the bottom 82% from the top 18% is approximately 123.24.

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Answer:

I don't know ask your parents

Step-by-step explanation:

Answer: $146,410

Step-by-step explanation: