How many of these equations have the solution
x
=
12
x
=
12
?

x
−
2
=
10
x
−
2
=
10
x
2
=
24
x
2
=
24
10
−
x
=
2
10
−
x
=
2
2x1=25
2x−1=25

Answer:

1.2kg

Step-by-step explanation:

6 identical toys weigh 1.8kg.

1 toy would weigh:

1.8/6 = 0.3

0.3 kg.

Multiply 0.3 with 4 to find how much 4 identical toys would weigh.

0.3 × 4 = 1.2

4 identical toys would weigh 1.2kg

Answer:

[tex]1.2kg[/tex]

Step-by-step explanation:

6 identical toys weigh = 1.8kg

Let's find the weight of 1 toy ,

[tex]1.8 \div 6 = 0.3[/tex]

Now, lets find the weigh of 6 toys,

[tex]0.3 \times 4 = 1.2kg[/tex]

Answer:

0.495 probability that Jim and Molly take counters of different colours

Step-by-step explanation:

For each trial, there are only two possible outcomes. Either a blue counter is picked, or a red counter is picked. The counter is put back in the bag after it is taken, which means that we can use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that the counter is red is 0.45

This means that [tex]p = 0.45[/tex]

Jim taken a counter, then Molly:

Two trials, so [tex]n = 2[/tex]

What is the probability that Jim and Molly take counters of different colours?

One red and one blue. So this is P(X = 1).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{2,1}.(0.45)^{1}.(0.55)^{1} = 0.495[/tex]

0.495 probability that Jim and Molly take counters of different colours

Answer:

6x(x - 6y +2)

Step-by-step explanation:

Step 1: Write out expression

6x² - 36xy + 12x

Step 2: Factor out x

x(6x - 36y + 12)

Step 3: Factor out 6

6x(x - 6y + 2)

That is the most we can do. We can only take GCF to factor. Since we don't have an y² term we do not have binomial factors.

Answer:

C

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

There is the same amount of teachers in each department of the school.

He asks 7 different departments of the school and collects the data he wants to.

I think it is not bias

Answer:

no

Step-by-step explanation:

This sample of teachers in the school is not likely to be biased.

Answer:

a. The distribution is bell-shaped and symmetric: True.

b. The distribution is bell-shaped and symmetric: True.

c. The probability to the left of the mean is 0: False.

d. The standard deviation of the distribution is 1: True.

Step-by-step explanation:

The Standard Normal distribution is a normal distribution with mean, [tex] \\ \mu = 0[/tex], and standard deviation, [tex] \\ \sigma = 1[/tex].

It is important to recall that the parameters of the Normal distributions, namely, [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] characterized them.

We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where [tex] \\ x[/tex] is the raw score that we want to standardize.

Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:

(a) True or False: The distribution is bell-shaped and symmetric

Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.

(b) True or False: The mean of the distribution is 0.

Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

If [tex] \\ x = \mu[/tex]

[tex] \\ z = \frac{\mu - \mu}{\sigma}[/tex]

[tex] \\ z = \frac{0}{\sigma}[/tex]

[tex] \\ z = 0[/tex]

Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.

(c) True or False: The probability to the left of the mean is 0.

Answer: False. The probability to the left of the mean is not 0. The cumulative probability from [tex] \\ -\infty[/tex] until the mean is 0.5000 or [tex] \\ P(-\infty < z < 0) = 0.5[/tex].

(d) True or False: The standard deviation of the distribution is 1.

Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.

In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, [tex] \\ x - \mu[/tex], by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, [tex] \\ \sigma[/tex].

In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.

Answer:

A: true

B: true

C: false

D: true

Answer:

Minimum = 25

First quartile = 58

Second quartile = 72

Third quartile = 80

Maximum = 98

Step-by-step explanation:

Answer: z = 55.

Step-by-step explanation:

we want to find values of k that make this inconsistent.

x - 2y + 4z = 3

4x + 5y + kz = 9

y + 3z = 2

First, can you can see that k never can make some of the equations linearly dependent because of how constructed is the set. Now, let's see if there are values of k that give problems to our system.

To see it, let's solve the system.

from the third equation we can write y = 2 - 3z, and we can replace it into the first two equations:

x - 2(2 - 3z) + 4z  = 3

4x + 5(2 - 3z) + kz = 9

simplify both equations and get

x  + 10z = 7

4x  + ( k - 15)*z = - 1

from the first equation, we have that:

x = 7 - 10z

we can replace it into the other equation:

4*(7 - 10z) + (k - 15)*z = -1

28 - 40z + (k -15)*z = -1

(k - 55)*z = -29

z = -29/(k - 55)

here you can see that the only value of z that has problems is z = 55, because we never can have a 0 in the denominator.

Answer:

a) Critical value = -1.4052

Since we are checking if the mean time is less than 10 minutes, the rejection area would be

z < -1.4052

b) Option C is correct.

Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.

That is, the mean time is significantly less than 10 minutes.

Step-by-Step Explanation:

a) Using z-distribution, the critical value is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction (checking if the claim is less than 10 minutes significantly)

P(z < Critical value) = 0.08

From the z-tables, critical value = -1.4052

Since we are checking if the mean time is less than 10 minutes, the rejection area would be

z < -1.4052

b) We first give the null and alternative hypothesis

The null hypothesis is that there isn't significant evidence to suggest that the mean time is less than 10 minutes.

And the alternative hypothesis is is that there is significant evidence to suggest that the mean time is less than 10 minutes.

To now perform this hypothesis test, we need to obtain the test statistic

Test statistic = (x - μ)/σₓ

x = sample mean = (Σx/N)

The data is

1.2, 2.8, 1.5, 19.3, 2.4, 0.7, 2.2, 0.7, 18.8, 6.1, 6, 1.7, 29.1, 2.6, 0.2, 10.2, 5.1, 0.9, 8.2

Σx = 119.7

N = Sample size = 19

x = sample mean = (119.7/19) = 6.3

μ = standard to be compared against = 10 minutes

σₓ = standard error = (σ/√N)

where N = Sample size = 19

σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean = 6.3

N = Sample size = 19

Σ(x - xbar)² = 1122.74

σ = (√1122.74/19) = 7.687

σₓ = (7.687/√19) = 1.7635

Test statistic = (x - μ)/σₓ

Test statistic = (6.3 - 10)/1.7635

= -2.098 = -2.10

z = -2.10 and is in the rejection region, (z < -1.4052), hence, we reject the null hypothesis and the claim and say that the mean time is significantly less than 10 minutes.

The test statistic is less than the critical point, hence, we reject the null hypothesis and the claim and conclude that the mean time is less than 10 minutes.

Hope this Helps!!!

The critical value for the test based on the sampling distribution is -1.4052 and one needs to reject the claim.

From the complete information given, the descriptive statistics from the sample information has been given. The sample mean and variance are given. Therefore, the value of the test statistics from the information is -1.4052.

Also, the conclusion is to reject the claim since the test statistic is smaller than the critical point.

Therefore, the correct option is to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.

Learn more about sampling on:

https://brainly.com/question/17831271

Answer and Step-by-step explanation: Congruent triangles are triangles with the same three sides and same three angles.

There many ways to determine if 2 triangles are congruent.

One of them is ASA or Angle, Side, Angle and it means that if two angles and the included side of one triangle are equal to the corresponding angles and side on the other triangle, they are congruent.

In this case, angle MRQ and angle NQR are equal. The included side of both triangles are the same QR, so it can be concluded that triangle QNR is congruent to triangle RMQ.

The image in the attachment shows the angles and their included side, which are colored.

Answer:

4

Step-by-step explanation:

Answer:

a) 13% of people did not experience problems with an online transaction.

b) 36.54% of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website

c) 46.11% of people experienced problems with an online transaction and contacted customer-service representatives.

Step-by-step explanation:

a. What percentage of people did not experience problems with an online transaction?

87% of people have experienced problems with an online transaction. So 100 - 87 = 13% of people did not experience problems with an online transaction.

b. What percentage of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website?

87% of people have experienced problems with an online transaction. Forty-two percent of people who experienced a problem abandoned the transaction or switched to a competitor′s website.

Then:

0.87*0.42 = 0.3654

36.54% of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website.

c. What percentage of people experienced problems with an online transaction and contacted customer-service representatives?

87% of people have experienced problems with an online transaction. Fifty-three percent of people who experienced problems contacted customer-service representatives.

Then:

0.87*0.53 = 0.4611

46.11% of people experienced problems with an online transaction and contacted customer-service representatives.

Answer:

The value of 7.9-4.36 is 3.54

The value of 5.27 + 3.5 is 8.77

Step-by-step explanation:

Answer:

y= 2x +7

Step-by-step explanation:

Slope-intercept form:

y= mx +c, where m is the slope and c is the y-intercept.

Given that the slope is 2, m=2.

y= 2x +c

Given that the y-intercept is -7, c = -7.

y= 2x +7

Answer:

You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. but you're worried that only 100 students will show up to vote. how often will the underdog (the one with 45% support) win? to find out, you set up a simulation.

a. describe-how-you-will-simulate a component.

b. describe-how-you-will-simulate a trial.

c. describe-the-response-variable

Step-by-step explanation:

Part A:

A component is one voter's voting. An outcome is a vote in favor of our candidate.

Since there are 100 voters, we can stimulate the component by using two random digits from 00 - 99, where the digits 00 - 64 represents a vote for our candidate and the digits 65 - 99 represents a vote for the under dog.

Part B:

A trial is 100 votes. We can stimulate the trial by randomly picking 100 two-digits numbers from 00 - 99.

And counted how many people voted for each candidate.  Whoever gets the majority of the votes wins the trial.

Part C:

The response variable is whether the underdog  wins or not.

To calculate the experimental probability, divide the number of trials in which the simulated underdog wins by the total number of trials.

Answer:

[tex]z=-1.49[/tex]

Step-by-step explanation:

[tex]\text{Standard Score, z} =\dfrac{X-\mu}{\sigma} $ where:\\\\Mean Pulse rate, \mu =67.3$ beats per minute\\Standard Deviation, \sigma = 10.3$ beats per minute.\\[/tex]

For a male student who has a measured pulse rate of 52 beats per  minute.

Raw Score, X =52 beats per  minute.

Therefore:

[tex]\text{Standard Score, z} =\dfrac{52-67.3}{10.3}\\z=-1.49[/tex]

Since the usual pulse rates are within 2 standard deviations of the mean, a z-score of -1.49 tells us that the selected student's pulse rate is within the usual pulse rates.

Answer:

D.

Step-by-step explanation:

One slope is positive and one negative, so one line should go up and one down. B or D.

y = 1/2 x - 1 line goes up and y-int. = - 1.  Answer D.

y = - 1/2 x + 3 line goes up and y-int. = 3.  Answer D.

Answer:

[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]

Time for bacteria count reaching 8019: t = 2.543 hours

Step-by-step explanation:

To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:

[tex]N(T(t)) = 22 * (8t + 1.7)^2 - 123 * (8t + 1.7) + 40[/tex]

[tex]N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40[/tex]

[tex]N(T(t)) = 1408t^2 + 598.4t + 63.58 - 984t - 169.1[/tex]

[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]

Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:

[tex]8019 = 1408t^2 - 385.6t - 105.52[/tex]

[tex]1408t^2 - 385.6t - 8124.52 = 0[/tex]

Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.

Answer:

i found the question mark ;)

Step-by-step explanation:

Answer:

6%

Step-by-step explanation:

We have to calculate the interest rate in the note, we must follow the following steps, calculate the amount of time remaining from the year 2021, as follows:

interest is for 5 months i.e. from Aug 01 to Dec 31 for year 2021 , so it means it would be 5/12 months.

We have to calculate the interest as follows:

I = P * R * T

We replace:

200 = 8000 * R * 5/12

we solve for R

200 * 12/5 = 8000 * R

R * 8000 = 480

R = 480/8000

R = 0.06

Which means that the interest rate on the note is 6%

Answer:

Sugar:

Honey:

Sugar substitute:

Step-by-step explanation:

35 + 14 + 21 = 70

35 out of 70 = 50%

14 out of 70 = 20%

21 out of 70 = 30%

Hope this helps!

Answer:

<XWZ is a right angle

Step-by-step explanation:

Since <YWZ and <XWY both equal 45 degrees, So, <XWZ is a right angle.

Given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,

Triangles that are similar possess equal corresponding angles.

We are given that:

ΔYWZ ~ ΔYXW

∠YWZ = ∠XWY = 45 degrees

∠YWZ + ∠XWY = ∠XWZ

45 + 45 = ∠XWZ

∠XWZ = 90 degrees (right angle).

Therefore, given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,

Learn more about similar triangles on:

https://brainly.com/question/2644832

Answer:

[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]

So the answer for this case would be n=183 rounded up to the nearest integer

Step-by-step explanation:

Information provided

[tex]\bar X[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma = 0.143[/tex] represent the population standard deviation

n represent the sample size  

[tex] ME = 0.023[/tex] the margin of error desired

Solution to the problem

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.023 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The confidence level is 97% or 0.97 and the significance would be [tex]\alpha=1-0.97=0.03[/tex] and [tex]\alpha/2 = 0.015[/tex] then the critical value would be: [tex]z_{\alpha/2}=2.17[/tex], replacing into formula (5) we got:

[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]

So the answer for this case would be n=183 rounded up to the nearest integer

Answer:

a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 18, \sigma = 5.2, n = 35, s = \frac{5.2}{\sqrt{35}} = 0.879[/tex]

95% of the sample means:

From the: 50 - (95/2) = 2.5th percentile.

To the: 50 + (95/2) = 97.5th percentile.

2.5th percentile:

X when Z has a pvalue of 0.025. So X when Z = -1.96.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-1.96 = \frac{X - 18}{0.879}[/tex]

[tex]X - 18 = -1.96*0.879[/tex]

[tex]X = 16.3[/tex]

97.5th percentile:

X when Z has a pvalue of 0.975. So X when Z = 1.96.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]1.96 = \frac{X - 18}{0.879}[/tex]

[tex]X - 18 = 1.96*0.879[/tex]

[tex]X = 19.7[/tex]

95% of the sample means are between 16.3 and 19.7 hours. This interval contains the sample mean of 16.8 hours, which supports the study.

So the correct answer is:

a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.

Answer:

[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]

And we can find this probability using the normal standard table with this difference:

[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(1539,1580)[/tex]  

Where [tex]\mu=1400[/tex] and [tex]\sigma=\sqrt{10000}= 100[/tex]

We are interested on this probability

[tex]P(1539<X<1580)[/tex]

And we can solve the problem using the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]

And we can find this probability using the normal standard table with this difference:

[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]

Answer:

0.0164 probability that exactly 11 black balls are drawn

Step-by-step explanation:

The balls are drawn without replacement, so we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Total of 88 + 88 = 176 balls, so [tex]N = 176[/tex]

33 balls are drawn, so [tex]n = 33[/tex]

We want 11 black balls(sucesses), so [tex]n = 11[/tex]

There are 88 black balls, so [tex]k = 88[/tex]

Then

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 11) = h(11,176,88,33) = \frac{C_{88,11}*C_{88,22}}{C_{176,33}} = 0.0164[/tex]

0.0164 probability that exactly 11 black balls are drawn

Answer:

if the sequence is:

12, 13, 13, 14, 14 etc, and each term keeps growing up, the sequence obviusly diverges.

Now, if the sequence is

1/2, 1/3, 1/3, 1/4, 1/4, 1/5 , 1/5

so the terms after the first one repeat, we could group the terms with the same denominator and get:

1/2, 2/3, 2/4, 2/5..... etc.

So the terms after the first one are aₙ = 2/n.

Now, a criteria to see if a sequence converges if seing if:

[tex]\lim_{n \to \infty} a_n = 0[/tex]

and here we have;

[tex]\lim_{n \to \infty} 2/n[/tex]

that obviusly tends to zero, so we can conclude that this sequence converges.

then the limit is:

There exist a n' such that for any n > n' then IL -aₙI < ε

where L is the limit

I2/n - 0I = I2/nI < ε

then this is true if n > 2/ε = n'

Answer:

8

Step-by-step explanation:

2,3,5,11,13,14

Mean= 8

Standard deviation= 4.830

Answer:

  x = -1

Step-by-step explanation:

The usual approach to these is to square the radicals until they are gone.

  [tex]\displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}[/tex]

Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.

The solution is x = -1.

_____

Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.

Answer:

(h, k) is the point that represents the vertex of this absolute value function

Step-by-step explanation:

Recall that the vertex of an absolute value function occurs when the expression within the absolute value symbol becomes "zero", because it is at this point that the results in sign differ for x-values to the left and x-values to the right of this boundary point.

Therefore, in your case, the vertex occurs at  x = h, and when x = h, then you can find the y-value of the vertex by looking at what f(h) renders:

f(h) = a | h - h | + k = 0 + k = k

Then the point of the vertex is: (h, k)

Answer:

D on edg2020

Step-by-step explanation:

Took the test