Answers
The solution of the system of equation 2x + 4y = 16, 2x - 4y = 0 is (4, 2). The correct option is A.
How to solve the system of equation?System of equations can be solved using different method such as substitution method, elimination method and graphical method. The system of equation can be solved with the elimination method as follows:
2x + 4y = 162x - 4y = 0
add equation(ii) to equation(i)
2x + 2x = 16 + 04x = 16
divide both sides by 4x = 16
x = 4
Let's find y
2x - 4y = 0-4
y = -2x-4y = -2(4)
-4y = -8
divide both sides by -4y = -8 / -4y = 2
Therefore, the solution is (4, 2)
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Related Questions
Name Yala. Al Write down each of the following expressions in the form of a power of one number a) 5³x5⁴ b) (-7)² ×(-7)³ c) 3⁶x3³ d) 27⁰x27² e) (-2)² ×(-2)³ × (-2)⁴ f) 3⁴x9²x(-3)⁶ g) (-4)⁶ × (-4)⁵ (-4)³ h) (-8)x(-8)x2² i) (0.25)×(0.25)⁴ × (0.25)⁰ J) 7³x7²x7
Answers
Answer:
A. [tex] {5}^{7} [/tex]
B. [tex] ( { - 7})^{5} [/tex]
C. [tex] {3}^{9} [/tex]
D. [tex] {27}^{2} [/tex]
E. [tex] ({ - 2})^{9} [/tex]
F. [tex] {3}^{14} [/tex]
G. [tex] {( - 4)}^{14} [/tex]
H. [tex] {2}^{8} [/tex]
I. [tex] {(0.25)}^{5} [/tex]
J. [tex] {7}^{6} [/tex]
Step-by-step explanation:
A.
[tex] {5}^{3} \times {5}^{4} \\ = {5}^{3 + 4} \\ = {5}^{7} [/tex]
B.
[tex]( { - 7})^{2} \times ( { - 7})^{3} \\ = ( { - 7})^{2 + 3} \\ = ( { - 7})^{5} [/tex]
C.
[tex] {3}^{6} \times {3}^{3} \\ = {3}^{6 + 3} \\ = {3}^{9} [/tex]
D.
[tex] {27}^{0} \times {27}^{2} \\ = {27}^{0 + 2} \\ = {27}^{2} [/tex]
E.
[tex]( { - 2})^{2} \times ( { - 2})^{3} \times ( { - 2})^{4} \\ = ( { - 2})^{2 + 3 + 4} \\ = ({ - 2})^{9} [/tex]
F.
[tex] {3}^{4} \times {9}^{2} \times ( { - 3})^{6} \\ = {3}^{4} \times {3}^{2 \times 2} \times {3}^{6} \\ = {3}^{4} \times {3}^{4} \times {3}^{6} \\ = {3}^{4 + 4 + 6} \\ = {3}^{14} [/tex]
G.
[tex] {( - 4)}^{6} \times {( - 4)}^{5} \times {( - 4)}^{3} \\ = {( - 4)}^{6 + 5 + 3} \\ = {( - 4)}^{14} [/tex]
H.
[tex] ( - 8) \times ( - 8) \times {2}^{2} \\ = 8 \times 8 \times {2}^{2} \\ = {2}^{3} \times {2}^{3} \times {2}^{2} \\ = {2}^{3 + 3 + 2} \\ = {2}^{8} [/tex]
I.
[tex] 0.25 \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = {(0.25)}^{1} \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = \times {(0.25)}^{1+4+0} \\ = \times {(0.25)}^{5} [/tex]
J.
[tex] {7}^{3} \times {7}^{2} \times 7 \\ = {7}^{3} \times {7}^{2} \times {7}^{1} \\ = {7}^{3+2+1} \\ = {7}^{6} [/tex]
Find the derivative of this with respect to x
Answers
To solve we can use chain rule and the knowledge that the derivative of the natural log is 1/x
So we have 1/((1 + x) / (1 - x))
Multiplied by the derivative of the stuff inside the natural log
We solve the derivative of what is inside the natural log and we get 2/(1 - x)
Then we can simplify this:
(2 / (1 - x)) / ((1 + x) / (1 - x))
Canceling the 1 - x term
To get the final answer of 2/(1 - x)
I hope this helps :)
I can help with the algebra simplifying if you want also :))
At the first school , there were 5 Sixth graders for every 2 seventh graders. At the second school dance, there were 7 sixth graders for 8 seventh graders . Are the ratios of sixth to Seventh on graders at both school dance equivalents. Explain
Answers
Answer:
No
Step-by-step explanation:
The ratio of the first school is 5/2. The ratio of the second school is 7/8.
how many cups is it?
Answers
The number of cups that will be in 3 gallons is 48 cups.
How to calculate the number of cups?It is important to note that ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Based on the information, the number of cups won a gallons will be:
= 64 / 4
= 16 cups.
Therefore, the cups that will be in 3 gallons will be:
= 3 × 16. cups
= 48 cups.
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Rachael’s Restaurant, a fast-food restaurant company, operates a chain of restaurants across the nation. Each restaurant employs eight people; one is a manager paid a salary plus a bonus equal to 4 percent of sales. Other employees, two cooks, one dishwasher, and four servers, are paid salaries. Each manager is budgeted $3,000 per month for advertising costs.
Answers
The cost incurred by Rachael's restaurant as fixed, variable or mixed are given below.
What is restaurant?
A restaurant is a location where you can consume food while paying for it. In restaurants, a waiter or waitress will typically bring your food to your table. Breakfast, lunch, and dinner are all offered at the restaurant. The restaurant's food was delectable, and the waitstaff was courteous.
Given:
Rachael’s Restaurant, a fast-food restaurant company, operates a chain of restaurants across the nation.
Each restaurant employs eight people; one is a manager paid a salary plus a bonus equal to 4 percent of sales.
Other employees, two cooks, one dishwasher, and four servers, are paid salaries. Each manager is budgeted $3,000 per month for advertising costs.
The cost incurred by Rachael's restaurant as fixed, variable or mixed are,
a. Advertisement c cost relative to number of customers Fixed
b. Rental cost relative to number of restaurant Variable
c. Cooks salaries relative to number of customer Fixed
d. Cost of Supplies (cups, plates, spoons, etc.) relative
to number of customer Variable
e. Manager's compensation relative to number of customer Mixed
f. Servers' salaries relative to number of Restaurants Variable
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Complete question:
Complete question is attached below.
Max is already 224 miles into his road trip. if he is averaging 52 miles per hour and the trip is 640 miles total, how many more hours does he have left to drive.
Answers
a scientist wants to determine whether or not the height of cacti, in feet, in africa is significantly higher than the height of mexican cacti. he selects random samples from both regions and obtains the following data.
Africa:
Mean = 12.1
Sample size = 201
Mexico:
Mean = 11.2
Sample size = 238
(a) Which of the following would be the correct hypothesis test procedure to determine if there is a difference between the mean height of two cacti?
-Two-sample test for proportions
-Two-sample t-test
- Paired t-test
(b) What is the value of the sample statistic to test those hypotheses? (2 decimal places)
(c) If the T test statistic is 2.169, and df = 202, find the p-value. (3 decimal places)
(d) Select the correct conclusion at alpha = 0.05.
-The null hypothesis is not rejected. There is insufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is not rejected. There is sufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is rejected. There is insufficient evidence of a difference between the mean height of two cacti.
(e) Mark the correct statement at alpha = 0.05:
-The test result is statistically significant.
-The test result is not statistically significant.
(f) Explain the type of error, in context, that might have been made.
-Type II error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
-Type II error, which means the scientist concluded there is not a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is a difference.
-Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
-Type I error, which means the scientist concluded there is not a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is a difference.
(g) What would the p-value have been if we had done a two-tailed test? (3 decimal places)
Answers
The correct options for the given parts are as follows
(a) Two-sample t-test.
(b) x1 bar - x2 bar = 12.1 - 11.2 = 0.9
(c) p - value = 0.031
(d) The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
(e) The test result is statistically significant.
(f) Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
What is sample statistics?
Any number calculated from your sample data is referred to as a sample statistic (or simply a statistic). The sample average, median, sample standard deviation, and percentiles are a few examples. Because a statistic is based on data obtained through random sampling, which is a random experiment, it is a random variable.
a) Since there are two independent samples and we want to compare population means. We must use: Two-sample t-test.
b) The value of the sample statistic to test those hypotheses is:
x1 bar - x2 bar = 12.1 - 11.2 = 0.9
c) This is two-tailed test. For p-value, use excel formula =TDIST(2.169,202,2).
p - value = 0.031
d) Since p-value is less than 0.05, correct option is:
The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
e) Since p-value is less than 0.05, correct option is:
-The test result is statistically significant.
f) Since null hypothesis is rejected, we might have been made Type I error. The correct option is:
-Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
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adam is racing around a circular running track. the time he takes to run each lap is 5 seconds less than he took for the previous one. he completes the first lap in 1 minute and 58 seconds. how long (in seconds) does he take to run his seventh lap?
Answers
Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.
As given in the question,
Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec
First term t₁ = 1 minute 58seconds
Time taken by each successive lap is 5seconds less then the previous lap
Common difference 'd' = -5seconds
let time taken to complete the seventh lap be t₇
t₇ = t₁ + ( 7 - 1 ) d
⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)
= 1 minute 58 seconds - 30seconds
= 1 minute 28 seconds
Therefore, the time taken by Adam to complete his seventh lap is equal to
1 minute 28 seconds.
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Consider the line y = 2x - 3. Write the equation of the line that is perpendicular to this line and that contains the point (-5, 3) Please help!!!
Answers
Considering the definition of perpendicular line, the equation of the perpendicular line is y= -1/2x + 1/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 2x -3
where:
The slope m is 2.The ordinate to the origin b is -3.If you multiply the slopes of two perpendicular lines, you get –1, you get:
2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 2
slope perpendicular line= -1/2
The line passes through the point (-5, 3). Replacing the point and the slope in the expression for a line:
3= (-1/2)× (-5) + b
3= 5/2 + b
3 -5/2 = b
1/2= b
Finally, the perpendicular line is y= -1/2x + 1/2.
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2 flower shops sell tulip for different,prices as shown below. What is the cheaper peice for 12 tulips?Give your answer in (£) £9.80 for 4 tulips were £4.20 each now 1/3 off
Answers
The cost of 12 tulips in the first shop (£29.40) is cheaper than the second shop (£33.60).
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
2 bloom shops sell tulips at various costs as displayed underneath.
£9.80 for 4 tulips and £4.20 every now 1/3 off.
The cost of the 12 tulips in the first shop, then we have
⇒ (£9.80 / 4) x 12
⇒ £2.45 x 12
⇒ £29.40
The cost of the 12 tulips in the second shop, then we have
⇒ £4.20 x 12 x (1 - 1/3)
⇒ £50.40 x 2/3
⇒ £33.60
The cost of 12 tulips in the first shop (£29.40) is cheaper than the second shop (£33.60).
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Gabriella owned so many CDs that she gave 64 of them away. After donating the CDs she had 147 left. Write an equation to find the number of CDs c gabriella had originaly
Answers
Answer:
147+64=c
Step-by-step explanation:
you would add the two numbers together to get the original.
if f(x)=2x²-6, then find f(4)
Answers
Answer:
Substitute x = 4 into the equation.
f(4) = 2(4)² - 6
= 2(16) - 6
= 32 - 6
= 26
Damon and Nicholas are racing to see who can get his community service hours for scouting completed first. Damon, who has already completed 2 hours, plans to volunteer for 2 hours per week going forward. Nicholas hasn't started yet, but plans to dedicate 3 hours per week to his volunteer project from now on. Before too long, the boys will be tied, with the same number of volunteer hours. How long will that take? How many hours will each boy have volunteered by then?
Answers
The number of hours when Damon and Nicholas will be tied is 2 hours.
The number of hours for the volunteer is 6 hours.
How long will it take for them to be at same project?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the information, Damon, who has already completed 2 hours, plans to volunteer for 2 hours per week going forward. Nicholas hasn't started yet, but plans to dedicate 3 hours per week to his volunteer project from now on.
Let the number of hours be h.
Damon's equation will be 2 + 2h
Nicholas equation will be 3h
The number of hours to be tied will be:
2 + 2h = 3h
3h - 2h = 2
h = 2
The number of hours is 2.
The number of hours for the volunteer will be:
= 3h
= 3(2)
= 6 hours.
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a company surveyed college students to determine their need and want for a new portable computer accessory. once the data was gathered, the company began designing the accessory to specifications determined by the data. this is an example of .
Answers
On solving the provided question, from the information we can say that this is a example of Research and development (R&D).
What means research and development?Research and development (R&D) refers to the knowledge a business accumulates to create new items or discover innovative ways to enhance current goods and services. Before using their products or processes for commercial purposes, large corporations may have their own R&D teams that test and improve them.
What is the role of research and development?Research and development (R&D) refers to the processes businesses use to innovate and launch new goods and services. It is frequently the initial stage of the development process. Typically, the objective is to expand the company's revenue while introducing a new good or service to the market.
This is an example of Research and development (R&D)
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What is the length of the sides of this equilateral triangle?
3x + 6
6x - 3
9x - 12
Answers
Answer:
15
Step-by-step explanation:
In an equilateral triangle all the sides length are the same. Set two sides equal to each other and solve for x
3x + 6 = 6x - 3 Subtract 3x from both sides
6 = 3x -3 Add 3 to both sides
9 = 3x Divide each side by 3
3 = x
Now that we know x is 3, plug this into the expression for any side and find the side length
3x + 6
3(3) + 6
9 + 6 = 15
5x4x5x3+56
help ma pls why they got such long multipictacion in -8th garde
Answers
[tex]\fbox{356}[/tex]
[tex](5\times4\times5\times3)+56[/tex]
[tex]5\times4=20\\5\times3=15\\20\times15=300[/tex]
[tex]300+56=356[/tex]
Answer: 356
Step-by-step explanation:
-start by grouping numbers into smaller portions (ex. the 5x5)
-5x5=25
-4x3=12
-Now we have 25x12.
-10x25=250, now add two more 25's
-250+50=300 or 25x12=300
-Add 56 to get 356
Solve the equation.
4/7 = 10/X
x=
Answers
Answer:
x = 17.5
Step-by-step explanation:
4/7 = 10/X
We can use cross products to solve for x
4*x = 7 * 10
4x = 70
Divide by 4
4x/4 = 70/4
x = 17.5
Answer:
17.5
Step-by-step explanation:
[tex] \frac{4}{7} = \frac{10}{x} \\ [/tex]
Use cross multiplication.
4x = 7 × 10
4x = 70
Divide both sides by 4.
x = 70/4
x = 17.5
Which of the following is the discriminant of the quadratic equation: ax- bx +c= 0, where a,b,c are real number and a 0? A. b2
B. Vb2 - 4ac
C. b2 - 4ac
D. -b + Vb2 - 4ac
Answers
The required discriminant of the quadratic equation ax-bx+c= 0 is D = b² - 4c.
What is discriminant?In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows some root properties to be inferred without having to compute them.
It is essentially a polynomial function of the coefficients of the initial polynomial.
So, we have the quadratic equation:
ax- bx +c= 0
We know that the discriminant formula is as follows:
Discriminate = b² - 4c
Now, get the discriminant:
D = b² - 4c
Therefore, the required discriminant of the quadratic equation ax-bx+c= 0 is D = b² - 4c.
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A pizza lover wants to compare the average delivery times for four local pizza restaurants. Over the course of a few weeks, he orders a number of pizzas from each restaurant, and he records the time it takes for each pizza to be delivered.
a) When performing an ANOVA with this data, what is the alternative hypothesis?
- All of the restaurants have different mean delivery times
- At least two of the restaurants have different mean delivery times
- Two of the restaurants have different mean delivery times
- One of the restaurants has a different mean delivery time than the others
b) A partial ANOVA table for his data is shown below. What is the value of B?
Source DF SS MS F P-value
Treatment B 19.31 D F G
Error C 15.667 E
Total 18 34.977
What is the value of C in the ANOVA table?
d) What is the value of D in the ANOVA table? Give your answer to three decimal places.
e) What is the value of E in the ANOVA table? Give your answer to three decimal places.
f) What is the value of F in the ANOVA table? Give your answer to two decimal places.
g) What is the value of G in the ANOVA table? Give your answer to four decimal places.
h) Using a 0.1 level of significance, what should his conclusion be in this case?
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is less than 0.1.
- He should fail to reject the claim that at all of the restaurants have the same mean delivery times because the P-value is greater than 0.1.
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is greater than 0.1.
- He should conclude that at all of the restaurants have the same mean delivery times because the P- value is less than 0.1.
Answers
(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.
(b)75.8
Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.
The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.
It is given that a pizza lover wants to compare the average delivery times.
Therefore the null hypothesis and alternate hypothesis implies that,
H₀ = all restaurants have equal mean delivery time
Hₐ = at least two restaurants have different two deliveries
Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.
The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.
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a manufacturer of mp3 players conducts a set of comprehensive tests on the electrical functions of its product. all mp3 players must pass all tests prior to being sold. of a random sample of 500 mp3 players, 15 failed one or more tests. find a 90% confidence interval for the proportion of mp3 players from the population that pass all tests.
Answers
0.957 < p < 0983 is a 90% confidence interval for the proportion of mp3 players from the population that pass all tests
How do I calculate 90% confidence interval?Add and subtract the margin of error from the sample mean to get this confidence interval. The confidence interval's top and lower limits are represented by this result.We can be 90% certain that the interval contains the population mean,, if the degree of confidence is 90%. The associated z-scores are 1.645. In order to calculate a confidence interval, the sample mean (X) and, if applicable, the population standard deviation () must be known. When the sample size is more than 30, the sample standard deviation, s, can be used in place of the population standard deviation..Given :
a random sample of 500 mp3 players, 15 failed one or more tests.
no of passed mp3 players = 500-15 =485
p = 485/500 =0.97
q = 1-p = 1-0.97 =0.03
90% confidence interval.
1- [tex]\alpha[/tex] = 90%
[tex]\alpha = 0.1[/tex]
[tex]Z_{\alpha/2}[/tex] = [tex]z_{.05} =1.645[/tex]
[tex]\hat{p} -[/tex] [tex]Z_{\alpha/2}[/tex][tex]\sqrt{\frac{\hat p \hat q}{n} }[/tex]< p< [tex]\hat{p} +[/tex] [tex]Z_{\alpha/2}[/tex][tex]\sqrt{\frac{\hat p \hat q}{n} }[/tex]
0.957 < p < 0983
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A 90% confidence interval for the percentage of mp3 players in the population that pass all tests is 0.957 < p <0983.
How can I determine the confidence interval at 90%?To obtain this confidence interval, add and subtract the margin of error from the sample mean. This result represents the upper and lower bounds of the confidence interval.
If the level of confidence is 90%, we can be 90% confident that the interval contains the population mean. The corresponding z-score is 1.645.
The sample mean (X) and, if relevant, the population standard deviation must be known in order to compute a confidence interval. The sample standard deviation, s, can be used in place of the population standard deviation when the sample size is greater than 30.
According to the given information
15 out of 500 mp3 players in a random sample failed one or more tests.
MP3 players that have been passed: 500-15 = 485
p = 485/500 =0.97
q = 1-p = 1-0.97 =0.03
Confidence interval of 90%.
[tex]1-\alpha[/tex] = 90%
[tex]\alpha[/tex] = 0.1
[tex]Z_{\frac{\alpha }{2} } = Z_{.05} = 1.645[/tex]
[tex]p-Z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }[/tex]<p<[tex]p+Z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }[/tex]
0.957 < p < 0983
A 90% confidence interval for the percentage of mp3 players in the population that pass all tests is 0.957 < p <0983.
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Solve for X. Please help me
Answers
Answer:
x = 9
Step-by-step explanation:
If the perimeter of triangle is 15 centimeters what is value of n
Answers
Answer:
5 cms
Step-by-step explanation:
This is assuming that it is equilateral and that n is the length of one side
point) The number of Drosophila fruit flies in controlled experiment assumes the following growth pattern when the food source is limited: 600 N(t) 1+ Me-0.3t where measured in days. A. How many fruit files were there in the beginning? What is the limiting number of fruit flies 600 C.At what time was the population increasing most rapidly? D. At what rate is the number of fruit flies increasing after days? 600/(1+11e
Answers
time was the population increasing most rapidly. At rate is the number of fruit flies increasing after days A. 600 B. 600 C. t=0 D. 0.09
The equation 600/(1+Me-0.3t) is a model for the population of Drosophila fruit flies, with time representing the number of days the experiment has gone on for. A. The population of fruit flies in the beginning is given by the equation as 600. B. The limiting number of fruit flies is also given by the equation as 600. C. The population is increasing most rapidly when t=0. D. After days, the number of fruit flies is increasing at a rate of 0.09, which can be calculated by taking the derivative of the equation with respect to t.
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Which of the following is true about k-means clustering Group of answer choices A tree diagram is used to illustrate the steps in the clustering analysis We choose the value for k before doing the clustering analysis It is a type of hierarchical clustering The cluster analysis will give us an optimum value for k In a cluster analysis, the distance between the clusters should be: Group of answer choices Maximized Minimized Even Zero THANK YOU :)
Answers
Prior to performing the clustering analysis, we choose the value for k. In a cluster analysis, the distance between the clusters should be minimized.
K-means clustering is an unsupervised machine learning technique used to identify clusters of data points. Before performing the clustering analysis, we must first choose the value of k (the number of clusters we wish to identify). The cluster analysis will then attempt to find the k clusters by minimizing the distances between the data points in each cluster. Once the clusters have been identified, the distance between them should be minimized to ensure that the clusters are as distinct as possible.
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Graph the function f(x) = -3 log₂ (-x-4) - 8 on the
axes below. You must plot the asymptote and any two points
with integer coordinates.
Answers
The graph of the function is attached below:
The asymptote of the function is:
(-3 log(-x-4)/log2)-8 →∞ as x→ -4
What is meant by a function?Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. The sets X and Y are referred to together as the function's codomain and domain, respectively.
Al-Biruni and Sharaf al-Din al-Tusi were two Persian mathematicians who are credited with developing the earliest known approach to the concept of function. The basic conception of functions was the relationship between fluctuating quantities and other variables. An illustration of this is how time affects a planet's position. The idea was developed historically with the infinitesimal calculus towards the end of the 17th century, and until the 19th century, the functions that were taken into consideration were differentiable.
Given function is,
f(x)= -3 log₂ (-x-4) - 8
The graph of the function is attached below:
The asymptote of the function is:
(-3 log(-x-4)/log2)-8 →∞ as x→ -4
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HELPPPP!!!
Identify the vertex, focus, and directrix of the graph. Which of the following equations represents the parabola in the graph?
x=1/12(y+4)^2-2
y=1/12(x+4)^2+2
x=-1/12(y+4)^2+2
y=-1/12(x+4)^2-2
Answers
Following equation represents the parabola in the graph:
x=1/12(y+4)^2-2
How to find the focus and directrix of a parabola?From the graph, we see that;
Focus = (-4, -2)
We use the equation x=h−p to find the directrix.
General form of equation of a parabola is;
(y - k)² = 4p(x - h)
where;
focus is (h + p, k)
directrix is x = h - p
Can a parabola not cross the y-axis?If we are talking about the function y = ax² + bx + c, then since it is a continuous function on the whole real line, it must cross the y–axis at (0 , c).
However x = y² + 1 is a parabola(not a function) that does not cross the y–axis.
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Express 2log 4 + 3log 2 as a single logarithm.
A 6log 8
B log 48
C 5log 6
D log 128
Answers
To express 2log 4 + 3log 2 as a single logarithm, you can use the property of logarithms that states that loga(mn) = logam + logan. This property can be used to rewrite the given expression as follows:
2log 4 + 3log 2 = log 4^2 + log 2^3
= log 16 + log 8
= log 16 * 8
= log 128
here 2log 4 + 3log 2 equals to log 128
Therefore, 2log 4 + 3log 2 = log 128, which is answer choice (D) log 128.
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Mawsynram, a village in India, is the wettest place on earth. It gets about 11,850 millimeters of rain per year.
About how many centimeters of rain fall in the village?
About how many inches if rain fall in the village?
Answers
Answer: 467 inches and 1185 centimeters
Step-by-step explanation:
1. Divide by 10 to find centimeters
2. Divide by 25.4 and round to find inches
Which equation best describes the line whose graph is shown?
A y=x+3
By = 3x
Cy=3
D x=3
Answers
Answer:
i have done this mano time ago, but problaply the answer is x=3
20
Use the box and whisker plot to answer the following question.
73
81 84
70
→
65 70 75
80
Low temperatures (°F)
85
87
王
90
What is the interquartile range IQR of the data set? (IQR = Q3 - Q1)
Answers
The interquartile range IQR for the given data set is IQR=10
What is block and whisker plot?A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.
How do you calculate box and whisker plot?Finding the median, lower quartile, and upper quartile of a given set of data (Q2, Q1, and Q3) is the first stage in creating a box-and-whisker figure. Now that you know how to calculate the interquartile range (IQR). The distance between the upper and lower quartiles is known as the interquartile range.
Lower data set:
70 73 81 84
Q1=73+81/2=77
Middle data set
65 70 75 80
Q2= 70+75/2=72.5
Upper data set
85 87 90
Q3=87
IQR=Q3-Q1=87-77=10
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