=
For the function f(x) = x2 – 6, find the equation of the tangent line at
X = -1.

Answer:

86.60254

Step-by-step explanation:

30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.

The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.

An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.

However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.

In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.

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Answer:

Yes

Step-by-step explanation:

     c+5

×        7

--------------

7c+35

=  7c+35-7

=7c+28

Answer:

pretty sure it b

Step-by-step explanation:

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Let the normal speed = x mph

The way to his grandmothers they drove 2x miles

Return trip was 2.25(x-5)

Set those equal and solve for x:

2x = 2.25(x-5)

Simplify:

2x = 2.25x -11.25

Subtract 2.25x from both sides:

-0.25x = -11.25

Divide both sides by-0.25:

X = 45

The usual speed is 45 mph.

So now 2 hours at 45 mph = 90 miles to his grandmothers house

Answer:

90 miles

Step-by-step explanation:

We did this in class when we were going over the hw and decided to help. Sorry if I'm too late.

Answer:

19a + 11b

Step-by-step explanation:

first (3 • (5a + b)) +  4 • (a + 2b) then you do this 3 • (5a + b) +  4 • (a + 2b) then you get this answer 19a + 11b.

Answer:

502.65

Step-by-step explanation:

\(\pi(8)(12) + \pi(8) ^{2} = 160\pi\)

So if you converted in to decimal, it would be 502.65

Step-by-step explanation:

The correct answer is:

There is a 5% chance we will conclude μ=60, but is in fact μ>60.

This is because we are using a significance level of α=0.05, which means that we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true). In this case, the null hypothesis is that the average warranty length is 60 days or less, and the alternative hypothesis is that it is longer than 60 days. Therefore, if we reject the null hypothesis, we would conclude that the average warranty length is longer than 60 days, but there is a possibility that we are wrong and the true mean is actually equal to 60 days.

Answer:

Let's assume that 225 is 3/4.

225/3 = 75

75 x 4 = 300

Step-by-step explanation:

Hope this helped! Have a great day!

Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

Answer:

This answer is correct.

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

2 x 3 = 6

1 x 7 = 7

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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Neglecting the fractional points and taking the whole number values for volume, the probability of getting equivalence point at 100 ml is 1/10. The probability of getting less than 100 ml is 1/2.

The probability is the measurement of the chance of an event to happen. It is determined based on the total possibilities and criteria.

Given that the experiment trials got the values from 95 to 104. From 95 to 104, there are 10 numbers. Thus, the volume of the acid can be any of these 10.

Thus, total possibility = 10.

probability of getting 100 = 1/10

There are 5 volumes which are  less than 100 here,  [95, 99]. Thus, the probability = 5/10 = 1/2.

There are 5 values between 98 and 102 including these two values.

Hence, probability of getting these range  = 5/10 = 1/2.

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The distance between points P and Q is √73

First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:

distance = √( (a - c)² + (b - d)²)

Here we can see that the coordinates of the two shown points are:

P = (-3, 2)

Q = (5, -1)

Replacing that in the distance formula we will get:

distance = √( (-3 - 5)² + (2 + 1)²)

distance = √( (-8)² + (3)²)

distance = √73

So the correct option is the third one.

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Answer:

55

Step-by-step explanation:

Remark

This is a really good question to know the answer to. <PRQ = 1/2 POQ (the central angle. )

The central angle for this question is 110o. So any angle that has its vertex on the circumference is 1/2 110 = 55. The central angle and the angle on the circumference must be related as they are as this question is. (Both are on the same side of PQ which is not drawn but you can draw it).

Answer:

the answer is C, NOT B

Step-by-step explanation:

The system of inequalities will have more solutions than the system of equations , Option C is the corrrect answer.

Inequality is the relation between two unequal numbers or algebraic expression.

The inequality symbols are less than , greater than , less than equal to, greater than equal to.

It is given in the question that

the system of equations y= -1/2x + 1 and y = x - 5.

the system of inequalities y > -1/2x + 1 and y < x - 5.

x-5 = -1/2 x +1

2x+x=6*2

3x = 12

x = 4

x-5 >-1/2 x +1

x>4

The system of inequalities generally have more solutions and in this case definitely have more solutions than the system of equations.

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Step-by-step explanation:

3x × 8x- 3x×16

24x -48x

-24x

Note that the doubling equation can be written as: y = 1000 * 2⁽ˣ/⁷*⁹⁵⁾

The doubling equation for the information given in question 4 can be written as:

y = 1000 * 2⁽ˣ⁺k⁾


To solve for k, we will use the fasts that:

on 240 days after the 100,000- death mark, there will be 2 million deaths.

2000,000 = 100 * x ^(240/k)

Takin the log of both sides we have:

Log 2 (2,000) =log2 (2^240/k))

⇒ Log 2 (2,000) =240/k * log 2(2)

⇒ log 2 (2000) = 240/k
Making k subjet of the formula, we have

k = 240/log2 2000)

k \(\approx\) 7.95

Thus, the doubling equation is y = 1000 * 2⁽ˣ/⁷*⁹⁵⁾

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Full Question:

Although part of your question is missing, you might be referring to this full question:

- We know that the number of deaths is growing exponentially, so we can use the exponential function y = a * bnx to model it. - We also know that on day O, there were 1,000 deaths, and on day 240 after the 100,000-death mark, there will be 2,000,000 deaths. - We can use these two points to solve for a and b.

Write a doubling equation for the information in question 4 that will find the number of Covid 19 related deaths for any given day. Then calculate the number of deaths expected 240 days from the 100,000-death mark.

Answer:

D.payment history

Step-by-step explanation:

Answer:

Step-by-step explanation:

250 divided by 50 = 5

50 goes into 250 5 times

Answer:

You want to set up an equation that will match the word problem. Let's call the amount of the first brand, F, and the amount of the second brand, S.

We want the total mixture to be 310mL so: F + S = 310

Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)

Now, we can solve the system of equations using substitution.

F + S = 310

.06F + .11S = .08(310)

F = 310 - S      [solve 1st equation for F]

.06(310 - S) + .11S = .08(310)     [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

F + 124 = 310     [substitute answer for S back into original equation]

F = 186

Answer: To make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.

Answer:

ST = 8 m

Step-by-step explanation:

Since both triangles are congruent to each other, therefore their corresponding angles and corresponding side lengths would be equal to each other accordingly.

Side ST in ∆STU corresponds to side PQ in ∆PQR. ST = PQ.

Side PQ = 8 m

Therefore, side ST = PQ = 8 m

Answer:

1. (-9,-2)

2. (2, -9)

what the first one just swap the coordinates first then change the x coordinate sign .

for the second question while rotating the coordinates along hundred eighty degrees clockwise just change the signs of X and Y coordinates

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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The pairs of triangles can be proven similar through SSS similarity is given by Third pair.

We know that the SSS similarity criteria will have the ratio of three corresponding sides of both triangles congruent.

1. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

2. KL / EG = HL / DG = HK / DE

3/10 ≠ 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

3. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 = 5/10

Thus, SSS similarity follow.

4. All three angles are congruent.

Thus, SSS similarity does not follow.

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