Recall that the distance formula is given by
[tex]d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}[/tex]We are asked to find out which of the given points have a distance of 6 units?
Let us analyze each option.
A. (2, 4) (2, 2)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({2-2_{}})^2+({2-4})^2} \\ d=\sqrt[]{({0})^2+({-2})^2} \\ d=\sqrt[]{4}^{} \\ d=2 \end{gathered}[/tex]Option A does not have a distance of 6 units, so it is not the correct option.
B. (1,8) (1,2)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1-1})^2+({2-8})^2} \\ d=\sqrt[]{({0})^2+({-6})^2} \\ d=\sqrt[]{36}^{} \\ d=6 \end{gathered}[/tex]As you can see, the distance between these points is exactly 6 units.
Therefore, Option B is the correct answer.
c. (3, 1) (3,6)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({3-3})^2+({6-1})^2} \\ d=\sqrt[]{(0)^2+({5})^2} \\ d=\sqrt[]{25} \\ d=5 \end{gathered}[/tex]Option C does not have a distance of 6 units, so it is not the correct option.
D. (5,6) (5,5)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({5-5})^2+({5-6})^2} \\ d=\sqrt[]{({0})^2+({-1})^2} \\ d=\sqrt[]{1}^{} \\ d=1 \end{gathered}[/tex]Option D does not have a distance of 6 units, so it is not the correct option.
rewrite csc(theta) / sec(theta) as a single trig function with no fractions
The given expression is
[tex]\frac{\csc \theta}{\sec \theta}[/tex][tex]\text{ We know that }csc\theta=\frac{1}{\sin x}\text{ and }\sec \theta=\frac{1}{cos\theta}\text{.}[/tex]Using the reciprocal, we get
[tex]\frac{\csc\theta}{\sec\theta}=\frac{\frac{1}{\sin\theta}}{\frac{1}{\cos \theta}}[/tex][tex]\text{ Use }\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}[/tex][tex]\frac{\csc\theta}{\sec\theta}=\frac{1}{\sin\theta}\times\frac{\cos \theta}{1}[/tex][tex]\text{ Use }\frac{\cos\theta}{\sin\theta}=\cot \theta.[/tex][tex]\frac{\csc\theta}{\sec\theta}=\cot \theta[/tex]Hence the answer is
[tex]\cot \theta[/tex]Which of the following functions shows the quadratic parent function,
Given the function f(x);
[tex]f(x)=x[/tex]When the function is flipped across the x-axis, we'll have the sign reversed.
So, the new function formed is;
[tex]undefined[/tex]Which choices are equations for the line shown below? Check all that apply.(-2,5) 51(2-3)A. y + 3 = -2(x-2)B. y-5= -2(x + 2)O C. y = 2x + 1I D. y=-0.5x + 1E. y-5--2(x-2)OF. y=-2x + 1
Solution
For this case we have two points given :
(-2,5) and (2,-3)
We can find the slope on this way:
[tex]m=\frac{-3-5}{2-(-2)}=-2[/tex]And the intercept would be:
5 = -2(-2)+b
5 = 4 +b
b= 1
Then the original equation is:
y= -2x+1
And we need to find equivalent equations so we can analyze one by one the options like this:
A. y+3 = -2(x-2)
y+3 = -2x+4
y =-2x+1
B. y-5 = -2(x+2)
y-5 =-2x-4
y = -2x +1
C. y=2x+1
D. y= -0.5x +1
E. y-5 = -2(x-2)
y-5 = -2x +4
y= -2x+9
Then the correct options are A and B
The five‐number summary of a distribution consists of(a) mean, median, standard deviation, and two quartiles.(b) minimum, maximum, mean, median, and standard deviation. (c) minimum, maximum, median, and two quartiles(d) mean, standard deviation, correlation, and two quartiles
The five-number summary of a distribution consists of
1)The minimum(smallest observation)
2)The maximum ( Largest observation)
3)median
4)Two quartiles( The first quartile and the third quartile)
That is option C
3) Mary made 1/5 of a batch of cookies in 1/10 of an hour. How many batches of cookies can she make in one hour?
Given in the scenario:
a.) Mary made 1/5 of a batch of cookies in 1/10 of an hour.
Let's determine how many batches of cookies can she make in one hour.
Step 1: Let's convert the given into a ratio and proportion.
Mary made 1/5 of a batch of cookies in 1/10 of an hour = 1/5 : 1/10
At x = number of batches of cookies in one hour, we get = x : 1
Step 2: Let's determine the value of x.
[tex]\frac{\frac{1}{5}}{\frac{1}{10}}\text{ = }\frac{x}{1}[/tex][tex](1)(\frac{1}{5})\text{ = (x)(}\frac{1}{10})[/tex][tex]\frac{1}{5}\text{ = }\frac{1}{10}x[/tex][tex](1)(10)\text{ = (1)(5)(x) }\rightarrow\text{ 10 = 5x}[/tex][tex]\frac{5}{5}x\text{ = }\frac{10}{5}[/tex][tex]\text{ x = 2}[/tex]Therefore, Mary can make 2 batches of cookies in one hour.
Jamal works as a computer network technician and last year they paid $4061 in social security tax. what was their annual income last year? Take the tax percentage as 6.2%
We know that Jamal paid 4061 of taxes and
[tex]4061=P\cdot(0.062)[/tex]where P is Jamal's income and 6.2% correspond to 0.062. Now, we must isolate P. It yields,
[tex]\begin{gathered} P=\frac{4061}{0.062} \\ P=65500 \end{gathered}[/tex]this means that Jamal's income was $65500 last year
Consider the following functions.f(x) = x + 4 and g(x) = x - 7=Step 2 of 4: Find (f - 3)(x). Simplify your answer.Answerf-8)(x) =
Solution
[tex]\begin{gathered} f(x)=x+4 \\ g(x)=x-7 \end{gathered}[/tex]Now
[tex]\begin{gathered} (f-g)(x)=x+4-(x-7) \\ (f-g)(x)=x+4-x+7 \\ (f-g)(x)=11 \\ \end{gathered}[/tex]The final answer
[tex]11[/tex]Find the area of the sector of a circle with diameter 30 feet and an angle of 3Pi/5 radians. Round your answer to four decimal places.
half the diameter is the radius, so
[tex]r=15[/tex]now we can calculate the total area of the circle , and then will calculate the area for the angle
[tex]\begin{gathered} A=\pi\times r^2 \\ A=\pi\times15^2 \\ A=225\pi \end{gathered}[/tex]the area of the circle is 225pi, this is the corresponding area for the complete angle of the circle, therefore it is equivalent to 2pi
now we create a relation to find the area corresponding to the indicated angle
if 225pi is equal to 2pi how much is 3pi / 5
[tex]\begin{gathered} 225\pi\longrightarrow2\pi \\ x\longrightarrow\frac{3}{5}\pi \end{gathered}[/tex]where x is the area covered by the angle
we solve ussing cross multiplication, x is equal to: multiply the values that are found diagonally and make them equal
[tex]\begin{gathered} x\times2\pi=\frac{3}{5}\pi\times225\pi \\ \end{gathered}[/tex]and solve for x
[tex]\begin{gathered} x=\frac{\frac{3}{5}\pi\times225\pi}{2\pi} \\ \\ x=\frac{135\pi^2}{2\pi} \\ \\ x=67.5\pi\approx212.0575 \end{gathered}[/tex]The rounded area is 212.0575 square feet
Given the figure above, determine the angle that is an alternate interior angle with respect to
Explanation
When two lines are crossed by another line (called the Transversal): Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
so, the angle is
[tex]\measuredangle3[/tex]I hope this helps you
What is the solution to -4y=28 please explain
You have the equation -4y=28
To solve this equation you need to clear the value of the unknown variable y, meaning, you have to simplfy the equation until you reach y=
For this, since y is multiplied by -4 you have to divide it by -4 to leave y alone, and what you do in one side of the equation must be done to the other side to keep the equality:
[tex]\begin{gathered} -4y=28 \\ \frac{-4y}{-4}=\frac{28}{-4} \\ y=-7 \end{gathered}[/tex]The value of y=-7
Mr. Smith took a job that the employment agency. The job pays $76k per year. The employment agency is charging a fee of 19% of his first 4 weeks' pay. How much money does Mr. Smith give to the agency.
Answer:
Mr. Smith gave $1110.7 to the agency
Explanation:
Given that the job Mr. Smith took pays $76k per year.
In his first 4 weeks, taking the number of weeks per year to be 52, he is paid:
4 × ($76000)/52
= 4 × $1461.5 (Approximately)
= $5846
He is charged 19% of this earnings:
19% of $5846 is:
0.19 × $5846
= $1110.7
What he has in the end is:
$17000 - $1110.7
= $15889.3
Using the function f(x)=-x+7, find f(1).
For this type of questions you just have to substitute x by the given number ( in this case 1) anywhere x shows in the equation
f(1)= -1+7 = 6
Gordon works for a graphic design firm and is creating a label for a food truck vendor. The vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. To complete his label, Gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. Gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches.
Part A
Find out the slant height of the cone
Applying the Pythagorean Theorem
AC^2=AB^2+BC^2
we have
AC ----> slant height
AB=4/2=2 in
BC=6 in
substitute given values
AC^2=2^2+6^2
AC^2=40
AC=2√10 in
Part B
Find out the measure of the angle formed between the base and the slant height
we have that
tan( by opposite side divided by adjacent side
tan(mm
Part C
see the figure below to better understand the problem
we have that
AC and DC are slant height
triangle ADC is an isosceles triangle
because AC=DC
that means
mmmmthe answer part C is 36.86 degrees
James deposits $12,500 in a simple interest account with an annual interestrate of 1.5%. After a few years, he notices that he has earned $1,687.50 ininterest. How long has James had this account?
Recall that the simple interest means that you will calculate interest only based on the initial deposit amount. This means that the generated interests do not generate any interests.
To find the number of years James has had this account, we will first find a formula for the amount available in the account each year.
At year 0, James deposits 12500. So, at year 0 the account has 12500
At year 1, James earns 1.5% over the 12500. So we add to what we had at year 0, the interest. That is
[tex]12500+\text{ 12500}\cdot i[/tex]where i is the interest annual rate of 1.5%.
At year 2, James earns 1.5% over 12500 again. So we add this value to what we had at year 1, so at year 2 he has
[tex]12500+12500\cdot i+12500\cdot i\text{ = 12500+12500}\cdot2\cdot i[/tex]Finally, at year 3, James earns another 1.5% over the 12500. So we add this value to what he had at year 2, so he has
[tex]12500+12500\cdot2\cdot i+12500\cdot i\text{ = 12500+12500}\cdot3\cdot i[/tex]In general, from this we can see a pattern. At year n, the amount available would be
[tex]12500+12500\cdot i\cdot n\text{ = 12500}\cdot(1+i\cdot n)[/tex]In this formula the amount of interest is given by the expression
[tex]12500\cdot i\cdot n[/tex]We are told that this amount is 1687.5. So we have the following equation
[tex]12500\cdot i\cdot n=1687.5[/tex]so, if we divide both sides by 12500*i, we get
[tex]n=\frac{1687.5}{12500\cdot i}[/tex]we know that i=1.5%. = 0.015. So we have
[tex]n=\frac{1687.5}{12500\cdot0.015}=9[/tex]so James has had the account for 9 years.
Given ST is tangent to circle Q, find the value of r
Given the figure of the circle Q
As shown, ST is tangent to circle Q
So, ST is perpendicular to the radius QS
So, the triangle QST is a right-angle triangle
We can apply the Pythagorean theorem where the legs are QS and ST
And the hypotenuse is QT
The side lengths of the triangle are as follows:
QS = r
ST = 48
QT = r + 36
So, we can write the following equation:
[tex]\begin{gathered} QT^2=QS^2+ST^2 \\ (r+36)^2=r^2+48^2 \end{gathered}[/tex]Expand then simplify the last expression:
[tex]\begin{gathered} r^2+2*36r+36^2=r^2+48^2 \\ r^2+72r+1296=r^2+2304 \end{gathered}[/tex]Combine the like terms then solve for (r):
[tex]\begin{gathered} r^2+72r-r^2=2304-1296 \\ 72r=1008 \\ \\ r=\frac{1008}{72}=14 \end{gathered}[/tex]So, the answer will be r = 14
5x+4=x+44 solve for x
5x + 4 = x + 44
x is adding on the right, then it will subtract on the left
4 is adding on the left, then it will subtract on the right
5x - x = 44 - 4
4x = 40
4 is multiplying on the left, then it will divide on the right
x = 40/4
x = 10
Find the absolute change and the relative change in the following cases.The number of refugees in the world increased from 8.7 million in 2005 to 16.1 million in 2015.
absolute change is determined by the absolute value of the subtraction of the number of refugees in both years:
absolute change = | 16.1 million - 8.7 million | = 7.4 million
Relative change is given by the quotient between final value and initial value, just as follow:
relative change = final value / initial value
= 16.1 million / 8.7 million
= 1.85
Hence, the absolute change is 7.4 million and relative change is of 1.85
Beatrice invests $100 at 7% per year simple interest. i) Show that after 20 years, Beatrice has $240.
Answer:
P(1+rY) (r=Interest in Decimal Form) (Y=Number of years investing)
Step-by-step explanation:
The expression you want to use for simple interest is P(1 + rY), where r = the interest (in decimal, so 0.07) and Y = the number of years you are investing.
100(1+(0.07)(20))
This turns into
100(1+1.4)
100(2.4)
And with simple multiplication (100 x 2.4) you would receive 240 as an answer.
Hope that helps.
This one is simple But I dont exactly know whats a function
ANSWER
B. False
EXPLANATION
We want to identify if the statement is true or false.
A function is a type of relation in which each input value is mapped directly to only one output value. In other words, each value of x has only one value of y.
To identify the graph of a function, if a vertical line can be drawn at any value of x such that it connects more than one point on the graph, then, the graph does not represent a function.
From the given graph, we see that a vertical line can be drawn to touch more than one point at several values of x.
This implies that the graph does not represent a function, hence, the statement is false.
The answer is option B.
The sum of 3 times a number and another number is 34. Five times the first number minus the other number is 38. What are the two numbers. The numbers are 3 and 11. The numbers are 9 and 7.
The sum of 3 times a number and another number is 34. Five times the first number minus the other number is 38. What are the two numbers. The numbers are 3 and 11. The numbers are 9 and 7.
Let
x -----> first number
y -----> another number
we have that
3x+y=34 -------> equation A
5x-y=38 -----> equation B
solve by elimination
Adds the equations
so
8x=72
x=72/8
x=9
substitute
3(9)+y=34
y=34-27
y=7
therefore
the numbers are 9 and 7There is a population of 2,363 bacteria in a colony. If the number of bacteria doubles every 157 minutes, what will the population be 314 minutes from now?
9452
Explanation
an exponential function is given by:
[tex]\begin{gathered} y=a(b)^x \\ \text{where a is the initial amount} \\ b\text{ is the rate of change} \\ x\text{ is the time} \end{gathered}[/tex]so
Step 1
Set the equations
a) initial population = 2363
time=0
replace
[tex]\begin{gathered} y=a(b)^x \\ 2363=a(b^0) \\ 2363=a\cdot1 \\ 2363=a \end{gathered}[/tex]b) If the number of bacteria doubles every 157 minutes
[tex]\begin{gathered} (2363\cdot2)=2363(b^{157}) \\ (2363\cdot2)=2363(b^{157}) \\ 4726=2363b^{157} \\ \text{divide both sides by }2363 \\ \frac{4726}{2363}=\frac{2363b^{157}}{2363} \\ 2=b^{157} \\ 2^{(\frac{1}{157})}=(b^{157})^{\frac{1}{157}} \\ 1.00442471045\text{ =b} \end{gathered}[/tex]so, the function is
[tex]y=2363(1.00442471045)^x[/tex]Step 2
what will the population be 314 minutes from now?
Let
time=x =314
replace
[tex]\begin{gathered} y=2363(1.00442471045)^x \\ y=2363(1.00442471045)^{314} \\ y=2363\cdot4 \\ y=9452 \end{gathered}[/tex]therefore, the answer is
9452
I hope this helps you
20.Dilate Point B by a scale factor of 1/2Va) (1.5,-4)c) (-1,-1.5)b) (-1.5,1)d) (-2,-2)
the coordinate of point B is (-3,2)
In order to dilate the point with a scale factor of 1/2 we need to multiplicate the scale factor by the coordinate-x and the coordinate-y
coordinate x
[tex]-3\cdot\frac{1}{2}=-1.5[/tex]coordinate y
[tex]2\cdot\frac{1}{2}=1[/tex]the coordinate dilate is
B'(-1.5,1)
the correct answer is b
LEO AND OLIVER HAVE TLO CLEAN THIER BEDROOMS. OLIVER CLEANS HIS ROOM IN 3/4 OF AN HOUR.LEO TAKES TWICE AS LONG AS OLIVER. HOW DID IT TAKE LEO TO CLEAN HIS ROOM?
It took 1.5 hour for Leo to clean the room .
In the question ,
it is given that
Leo and Oliver clean their their room
time taken by Oliver to clean the room is = 3/4 of an hour = 0.75 hours .
and also given that Leo takes twice as long as Oliver
which means
time taken by Leo to clean the room = 2*(time taken by Oliver to clean the room )
On substituting the values
we get ,
time taken by Leo to clean the room = 2*(0.75 hours)
= 1.5 hours
Therefore , Leo takes 1.5 hours to clean the room .
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Three time a number is two times the difference of that number and one
Please help. Write an algebriac expression
Answer:
[tex]3x = 2(x - 1)[/tex]
Suppose you are riding in a roller coaster which
follows the curve in the graph and when you reach the point
(1.1) your hat falls off. This curve is defined by the equation
23 + 43
=2y. Find an equation of the line that the hat will
follow if you ignore gravity and air resistance.
x + y = 2 is the equation of the line that the hat will follow if we ignore the gravity and air resistance.
Given, we are riding in a roller coaster which follows the curve in the graph and when we reach the point (1 , 1) our hat falls off.
Now, we have to find the equation of the line that the hat follow,
The slope of the tangent to the curve x³ + y³ = 2xy is given by,
3x² + 3y²y' = 2y + 2xy'
at the point (1 , 1)
3 + 3y' = 2 + 2y'
y' = -1
Now, the slope of the line perpendicular to the tangent of the curve is,
-1
Now, the equation of the line that hat follows is,
(y - 1)/(x - 1) = -1
y -1 = 1 - x
x + y = 2
Hence, x + y = 2 is the equation of the line that the hat will follow if we ignore the gravity and air resistance.
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A binomial experiment consists of 18 trials. The probability of success on trial 11 is 0.79. What is theprobability of success on trial 15?0.790.280.610.460.560.72
Answer:
0.79
Explanation:
Given a binomial experiment with 18 trials; and
[tex]P(\text{ success on trial 11\rparen}=0.79[/tex]By the conditions required for a binomial experiment, the probability of success (or failure) remains the same throughout the experiment and for each and every trial.
Therefore:
[tex]P(\text{ success on trial 15\rparen}=0.79[/tex]The answer is 0.79
what do 13% and 0.125 and 1/5 and 10 % have in common
Comparing 13%, 0.125 , 1/ 5 and 10%
1. 13 % = 0.13
2. 0.125 = 0.13 ( 2 decimal places)
3. 1/5 = 0.2
4. 10 % = 0.1
Conclusion : 13% and 0.125 have things in common
I have started number 7 but am not so sure about my answer just wanted to see if I was doing the problem right way.
To get a probability in a given set, we need to count the events we want to happen and divide by the total possibilities.
a) Here, we have a set that goes from 1 to 12, so there is 12 possibilities. We want to pick a prime number, so we need to count how many primes we have in this set.
1 is not prime.
Also, 4, 6, 8, 9, 10 and 12 are not primes.
So, we have the primes: 2, 3, 5, 7 and 11. There are 5.
So, the probability will be:
[tex]P=\frac{5}{12}\approx0.42[/tex]b) Assuming the die are 6-sided going from 1 to 6, we can obtain the numbers from 1 + 1 = 2 until 6 + 6 = 12. However, there are differento number of possibilities. We still are looking for 2, 3, 5, 7 and 11, however now we have a total of 6 times 6 possibilities:
[tex]C_T=6\cdot6=36[/tex]And we have to calculate the combinations for each prime and add them.
2: there is only 1 + 1, so:
[tex]C_2=1[/tex]3: We can do 1 + 2 and 2 + 1, so there are 2:
[tex]C_3=2[/tex]5: We have 1 + 4, 2 + 3, 3 + 2 and 4 + 1, so 4 possibilities:
[tex]C_5=4[/tex]7: We have 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2 and 6 + 1, 6 possibilities:
[tex]C_7=6[/tex]11: We have 5 + 6 and 6 + 5 only. 2 possitilities:
[tex]C_{11}=2[/tex]In total, we have:
[tex]C_2+C_3+C_5+C_7+C_{11}=1+2+4+6+2=15_{}[/tex]So, the probability will be:
[tex]P=\frac{15}{36}\approx0.42[/tex]It ended up being the same.
A. Step 1 B. Step 2 C. Omar did not make a mistake
To find out if Omar made a mistake, we must solve the equation step by step.
Step 1
[tex]\begin{gathered} 3x=4.5 \\ \text{divide through by 3} \\ \frac{3x}{3}=\frac{4.5}{3} \end{gathered}[/tex]Step 2
Simplify the final part in step 1
[tex]\begin{gathered} \frac{3x}{3}=\frac{4.5}{3} \\ x=\frac{3}{2}=1.5 \end{gathered}[/tex]Since, we have gone through all the steps and gotten exactly the same steps and solution as Omar, we can conclude that Omar did not make a mistake.
How do you graph y= -1/2x
Step-by-step explanation: move down 1 and right 2 because it has to be a negative slope.
Answer: See attached, or read below.
Step-by-step explanation:
First, we see there is no b value, so there is no y-intercept. The line will intercept the graph at (0, 0), also known as the origin.
Next, we see a negative slope of -1/2. This means, starting at the origin, we will move down one unit and right two. Then repeat. Lastly, draw a straight line through all three points for our graph.