Answers
Step-by-step explanation:
i) [tex]\overline{AB} = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}[/tex]
[tex]\:\:\:\:\:\:\:=\sqrt{(2)^2 + (12)^2} = 12.3[/tex]
ii) [tex]m = \dfrac{y_A - y_B}{x_A - x_B} = \dfrac{-12}{2} = -6[/tex]
iii) [tex](\overline{x},\:\overline{y}) = \left(\dfrac{x_A + x_B}{2},\:\dfrac{y_A + y_B}{2}\right)[/tex]
[tex]\:\:\:\:\:\:\:=(3,\:-2)[/tex]
Related Questions
f(x)=2^x. show that f(x=3)=8 f(x)?
Answers
Step-by-step explanation:
[tex]f(x) = {2}^{x} [/tex]
x = 3
f(3) = 2³ = 2×2×2 = 4×2 = 8
A teapot,which has a capacity of one and half litters, can fill six identical mugs with tea.what is the capacity of the six mugs altogether?
Answers
Answer:250
Step-by-step explanation:
Write an equation that expresses the relationship. Then solve the equation for B.
T varies directly as the cube of A and inversely as B.
T= what?
(Use k as the constant of variation.)
Answers
Answer:
kkkkkkkllllll
Step-by-step explanation:
llllllllllllllllllllllllll
Please help me I need it!
Answers
PLZ answer quick i will give brainliest if right no explanation needed Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms. Joe had already reserved and paid for 161616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900. Let B represent the number of additional blocks that Joe reserves. 1) Which inequality describes this scenario? Choose 1 answer: a: 16+8B≤50 b: 16+8B≥50 c: 16+B≤50 d: 16+B≥50 2) What is the least amount of additional money Joe can spend to get the rooms they need?
Answers
Answer:
16 + 8b ≥ 50
4500
Step-by-step explanation:
He needs at least 50 rooms and has already reserved 16
They are in groups of 8
16 + 8b ≥ 50
Subtract 16 from each side
16+8b-16 ≥ 50 -16
8b≥ 34
Divide by 6
8b/8 ≥ 34/8
b≥ 4.25
We need to round up since we need at least 50
b = 5 since we want the least amount of rooms
Each block is 900
5*900 = 4500 more that he will have to spend
A rectangle’s perimeter is equal to 27 plus its width. The length of the rectangle is four times its width. What is the width of the rectangle in units?
Answers
Answer:
width: 3
Step-by-step explanation:
Given a length l and a width w, we can say that the perimeter is equal to
2 * l + 2 * w. Then, we also know that the perimeter is 27 plus its width, so
2 * l + 2 * w = 27 + w
and the length is 4 times its width, so length = 4 * width = l = 4 * w
We therefore have the two equations
2 * l + 2 * w = 27 + w
l = 4 * w
What we can do is plug 4* w for l in the first equation and solve from there. We thus have
2 * ( 4 * w) + 2 * w = 27 + w
8 * w + 2 * w = 27 + w
10 * w = 27 + w
subtract w from both sides to isolate the w and its coefficient
9 * w = 27
divide both sides by 9 to isolate w
w = 3
l = 4 * w = 12
Therefore, the width is 3 and the length is 12
The charge of eletricity for the first 20 unit is Rs 80 and Rs 7 per unit from 21 unit to 30 units. If service is Rs 75 find the total charge of 28 units
Answers
28 - 20 = 8 units
8 x 7 = Rs 35
80 + 35 = Rs 115
I drive 13 miles each way to work every day. It sometimes takes me 20 minutes to get to work, and sometimes it takes me 30 minutes. If Distance = Rate x Time, at what rate am I going if it takes me 20 minutes to get to work? At 30 minutes?
Answers
Answer:
39 mph
26 mph
Step-by-step explanation:
distance = rate * time
20 minutes:
13 miles = rate * 20 minutes
rate = (13 miles)/(20 minutes) * (60 minutes)/(hour)
rate = 39 mph
30 minutes:
13 miles = rate * 30 minutes
rate = (13 miles)/(30 minutes) * (60 minutes)/(hour)
rate = 26 mph
To which number sets of numbers does the number 3.567...belong?
Answers
Answer:
It's irrational numberIf the decimal digits do not repeat in some known pattern, then the number is irrational. We cannot write it as a ratio or fraction of two integers. If it did have a pattern, then we can use algebra to find the fractional representation of that number. Based on what is shown, it looks like there is no pattern so that's why the value is irrational. The number is also a real number as this is the case with any number you'll encounter unless you're dealing with complex numbers (but your teacher may not have introduced that topic yet).
6. If x + 2 is the only factor of the polynomial P(x),then P(2) is:
Options:
A. Cannot be determined
B. Not Zero
C. R(2)
D. Zero
Answers
Answer:
P(x) = x + 2p(2) = 2 + 2 p(2) = 4So option B is the answer.
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) is Not Zero. Therefore, the option B is the correct answer.
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
Given information;
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) :
P(x) = x + 2
p(2) = 2 + 2
p(2) = 4
The P(2) is Not Zero.
Therefore, the option B is the correct answer.
Learn more about standard form of a polynomial here:
https://brainly.com/question/15313798
#SPJ5
renea is going to the lake to visit some freinds if the lake is 60 miles away and renae is driving at 40 miles per hour the entire time how long will it take her to get to the lake
Answers
Answer:
1.5 hours
Step-by-step explanation:
Set up a proportion:
[tex]\frac{40 miles}{1 hour}[/tex] = [tex]\frac{60 miles}{x}[/tex]
Cross multiply:
40x = 60
x = 1.5
= 1.5 hours
Let
A ={1,2,6,7,8,13,15} and B= {1,2,5,6,8,12,15, 18, 20}
Find the following:
LIST the elements in the set
A∪B :
A∪B = { }
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
LIST the elements in the set
A∩B :
A∩B= { }
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
Answers
Answer:
AUB=(1,2,5,6,7,8,12,13,15, 18,20)
AnB={1,2,6,7,8}
Answer:
Hello,
Step-by-step explanation:
[tex]A =\{1,2,6,7,8,13,15\} \\B= \{1,2,5,6,8,12,15, 18, 20\}\\\\A\ \bigcup\ B=\{1,2,5,6,7,8,12,13,15,18,20\}\\\\A\ \bigcap\ B=\{ 1,2,6,8,15\}\\[/tex]
Jack is going to the fair. The fair charges $10 to enter and $0.25 per ticket. How much will be spent by Jack? t = tickets 0.25 + 10 10 + 0.25t
Answers
there is a base charge of 10 (+10)
and each ticket is multiplied by 0.25 (0.25t)
10+0.25t
hope this helped :)
Answer:
10 + .25t
Step-by-step explanation:
The total amount spent is equal to the amount to get in plus the cost of the tickets times the number of tickets
cost = 10 + .25t
The sum of triple a number
and nineteen.
Answers
Answer:
3x+19
Step-by-step explanation:
Let x be the unknown number
triple means 3 times
sum means add
3x+19
PLEASE HELP
2/3x =10
Show your work in details if you can, I have a hard time understanding this.
Answers
[tex]\\ \sf\longmapsto \dfrac{2}{3}x=10[/tex]
[tex]\\ \sf\longmapsto \dfrac{2x}{3}=10[/tex]
[tex]\\ \sf\longmapsto 2x=3(10)[/tex]
[tex]\\ \sf\longmapsto 2x=30[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{30}{2}[/tex]
[tex]\\ \sf\longmapsto x=15[/tex]
[tex] \begin{cases}\large\bf{\red{ \implies}} \tt \frac{2}{3} x \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt \frac{2x}{3} \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 3 \: \times \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 30 \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \:\frac{ \cancel{30} \: \: ^{15} }{ \cancel{2}} \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \: 15 \end{cases}[/tex]
Factor the following
9t^2-42t+49
Answers
Answer:
(3t -7)²
Step-by-step explanation:
We know that the square of a binomial is ...
(a -b)² = a² -2ab +b²
So, when we see the first and last terms are both perfect squares, we suspect that the trinomial is a perfect square trinomial.
9t² = (3t)²
49 = 7²
-42t = -2(3t)(7) . . . . confirming we have a perfect square
The factorization is ...
(3t -7)²
There are 9 students at the math club picnic. If 3 students are drinking punch and 6 are drinking lemonade, what fraction are drinking lemonade
Answers
Therefore 2/3 of the students are drinking lemonade.
Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.
What is the probability that the pianist will be a boy and the alternate will be a girl? Express your answer as a percent.
30%
40%
50%
60%
Answers
Answer:
30% is the correct answer.
Step-by-step explanation:
Total number of boys = 2
Total number of girls = 3
Total number of students = 5
To find:
Probability that the pianist will be a boy and the alternate will be a girl?
Solution:
Here we have to make 2 choices.
1st choice has to be boy (pianist) and 2nd choice has to be girl (alternate).
[tex]\bold{\text{Required probability }= P(\text{boy as pianist first}) \times P(\text{girl as alternate})}[/tex]
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
For [tex]P(\text{boy as pianist})[/tex], number of favorable cases are 2 (total number of boys).
Total number of cases = Total number of students i.e. 5
So, [tex]P(\text{boy as pianist})[/tex] is:
[tex]P(\text{boy as pianist}) = \dfrac{2}{5}[/tex]
For [tex]P(\text{girl as alternate})[/tex], number of favorable cases are 3 (total number of girls).
Now, one boy is already chosen as pianist so Total number of cases = Total number of students left i.e. (5 - 1) = 4
[tex]P(\text{girl as alternate}) = \dfrac{3}{4}[/tex]
So, the required probability is:
[tex]\text{Required probability } = \dfrac{2}{5}\times \dfrac{3}{4} = \dfrac{3}{10} = \bold{30\%}[/tex]
Answer:
30% A
Step-by-step explanation:
Which of the following is NOT a requirement of testing a claim about two population means when 1 and 2 are unknown and not assumed to be equal? Choose the correct answer below. A. The two samples are dependent. B. Both samples are simple random samples. C. Either the two sample sizes are large (30 and 30) or both samples come from populations having normal distributions, or both of these conditions are satisfied. D. The two samples are independent.
Answers
Answer:
b
Step-by-step explanation:
In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. Question 9 (2.5 points) If 2000 students are randomly selected, how many would you expect to have a score between 250 and 305?
Answers
Answer:
The number is [tex]N =1147[/tex] students
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 281[/tex]
The standard deviation is [tex]\sigma = 34.4[/tex]
The sample size is n = 2000
percentage of the would you expect to have a score between 250 and 305 is mathematically represented as
[tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]
So
[tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]
[tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]
From the z table the value of [tex]P( z_2 < 0.698) = 0.75741[/tex]
and [tex]P(z_1 < -0.9012) = 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.57[/tex]
The percentage is [tex]P(250 < X < 305 ) = 57\%[/tex]
The number of students that will get this score is
[tex]N = 2000 * 0.57[/tex]
[tex]N =1147[/tex]
I need help to fine the statement that is true
Answers
Answer:
option A
Step-by-step explanation:
wx and zy making 90 angle with each other therefore they are perpendicular.
wx and ab making 0 angle with each other therefore they are parallel
what is empowerment and radication please that is not from google
Answers
Answer:
In MATH:
Empowerment - Gaining the skills required in language and practices to fully understand math.
Radication - The process of extracting a number's root.
In ENGLISH:
Empowerment - The process of gaining more power over anything, including yourself, others, society, government, and corporations.
Ex - In the spirit of empowerment, the company has implemented a new system that asks employees to nominate one another for bonuses.
Radication - The process of establishing, fixing, or creating.
Ex - The high prestige of the premier is radicated in the hearts of the people.
Find the cost of fencing a square plot area 11025 sq m. at the rate of rupees 85 per sq m.
Answers
Answer:
Rate per meter=85 Rs. hence , the cost of fencing the square plot at rate of 85 rs. per meter is 937125 Rs.
In a geometric sequence, t4 = 8 and t7 = 216. Find the value of t2
Question 14 plz show ALL STEPS ASAP
Answers
Answer:
8/9
Step-by-step explanation:
Let the geometric series have the first term=a and common ratio=r. ATQ, ar^3=8 and ar^6=216. r^3=27. r=3. a=8/3^3=8/27. t2=ar=8/9
You have a $5,000 limit on your credit card. What is the largest balance you should carry on this card to maintain an acceptable debt ratio? Recall that your debt ratio should never exceed 50% of your limit
Answers
Answer:
Amount of balance maintain = $2,500
Step-by-step explanation:
Given:
Limit of credit card = $5,000
Debt ratio = 50%
Find:
Amount of balance to maintain
Computation:
Amount of balance to maintain = Limit of credit card × Debt ratio
Amount of balance to maintain = $5,000 × 50%
Amount of balance to maintain = $2,500
Consider the following.
3^5x − 1 = 7
(a) Find the exact solution of the exponential equation in terms of logarithms.
(b) Use a calculator to find an approximation to the solution rounded to six decimal places.
Answers
Answer:
Step-by-step explanation:
You've typed the equation incorrectly. 3^5x-1 = 3⁵x-1.
It needs to be typed as 3^(5x-1) = 7.
Can you help me? Please
Answers
9514 1404 393
Answer:
a.
Step-by-step explanation:
For an even-index radical, ...
[tex]\sqrt[n]{x^n}=|x|\qquad\text{n even}[/tex]
This lets us simplify the given expression as follows:
[tex]\sqrt[4]{81x^6y^4}-|y|\sqrt[4]{x^6}-\sqrt[4]{16x^2}=\sqrt[4]{(3xy)^4x^2}-|y|\sqrt[4]{x^4x^2}-\sqrt[4]{2^4x^2}\\\\=3|xy|\sqrt[4]{x^2}-|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}=\boxed{2|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}}[/tex]
Sketch a graph to envision the following scenario. Place time on the x-axis. A rock climber is 25 feet above sea level. After 8 seconds he is at sea level. (He did not fall). What is the slope of the line depicted (no units)
Answers
Answer:
Please refer to the attached graph.
Slope = -3.125
Step-by-step explanation:
Given
Time is placed on x axis.
Initially, height of rock climber is 25 feet above sea level.
[tex]t_1 =0\ sec[/tex]
[tex]h_1[/tex] = 25 feet
After 8 seconds, he is at sea level.
[tex]t_2 =8\ sec[/tex]
[tex]h_2[/tex] = 0 feet
To find:
Graph of the given points and Slope of the line depicted.
Solution:
Kindly refer to the attached graph.
Here, we have been given two points to be plotted on the xy coordinate plane.
1st point is (0, 25): Time is 0 and height above sea level is 25 ft
2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)
First of all, mark these points and join them with a straight line.
Please refer to attached graph.
Slope of a line is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0[/tex]
Using the formula:
[tex]m=\dfrac{0-25}{8-0}\\\Rightarrow m=-\dfrac{25}{8} = \bold{-3.125}[/tex]
Working together, it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 50 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? don't round
Answers
Answer:
12.5 minutes
Step-by-step explanation:
When working together,It takes two computers 10 minutes to send out an email
It takes the slower computer 50 minutes to send out an email
Let x represent the time taken by the faster computer to do the job in its own
Therefore, the time required by the faster computer can be calculated as follows
1/x + 1/50= 1/10
Collect the like terms
1/x= 1/10-1/50
1/x= 4/50
Cross multiply both sides
4 × x = 50×1
4x=50
Divide both sides by the coefficient of x which is 4
4x/4=50/4
x= 12.5
Hence the time taken by the faster computer to finish the job on its own is 12.5 minutes
Anna is paid $14.75 per hour. She works a
12 hour shift, the last 4 hours being at a double
time pay rate. What is Anna's wage before
tax?
HELP
Answers
Answer:
$336
Step-by-step explanation:
$14.75(8) + $14.75(2)(4) - (8 hours of normal shift) + (double pay rate)(for 4 hours)
= $118 + $118 - Add
= $336