[tex]\bf (\stackrel{a}{2}~,~\stackrel{b}{-1})\qquad \begin{cases} r=\sqrt{a^2+b^2}\\\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ r=\sqrt{2^2+(-1)^2}\implies r=\sqrt{5} \\\\\\ \theta =tan^{-1}\left( \cfrac{-1}{2} \right)\implies \theta \approx -26.57^o\implies \theta \approx 333.43^o \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\sqrt{5}~~,~~333.43^o)~\hfill[/tex]
Answer:
[tex](r,\theta); (\sqrt{5} , tan^{-1}(\frac{x}{y}))\\(r,\theta); (-\sqrt{5} , -tan^{-1}(\frac{x}{y}))[/tex]
Step-by-step explanation:
Here we are given our rectangular coordinates as (2,-1) . We have to convert this into polar coordinates. The formula for conversion into polar form is
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]\theta=tan^{-1}(\frac{x}{y})[/tex]
Substituting the values of x and y in the above formulas we get
[tex]r=\sqrt{2^2+(-1)^2}\\r=\sqrt{4+1}\\r=\sqrt{5}\\r=-\sqrt{5}\\[/tex]
[tex]\theta=tan^{-1}(\frac{-1}{2})[/tex]
Hence our polar coordinates are
[tex]r=(\sqrt{5},tan^{-1}(\frac{-1}{2}) )\\r=(-\sqrt{5},tan^{-1}(\frac{-1}{2}) )\\[/tex]
Each Saturday morning Janie works five hours and earned $35.75. How much does Janie earn for each hour she works?
Answer:
$7.15/hour
Step-by-step explanation:
Find Janie's unit rate of pay: Amount per Hour:
$35.75 / (5 hours) = $7.15/hour
In each hour of working on Saturday morning, Janie earns $7.15.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Each Saturday morning Janie works five hours and earned $35.75.
So, To obtain the amount of money she earns each hour can be obtained by dividing the total amount she earned by the total number of hours she worked which is,
= $(35.75/5).
= $7.15.
So, Each hour Janie earns $7.15 by working in Saturday morning.
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On in-line skates, Bradley skates 4 miles in 20 minutes. At this speed, how long would it take him to skate the entire length of a 12-mile bike path?
Answer:
1 hour (60 minutes)
Step-by-step explanation:
If his speed remains the same, that means that this is a linear relationship. y increases at the same rate as x increases. Direct variation and all of that. Because this is a linear relationship, it can be solved using proportions. Set up the given info in a ratio with miles on the top and minutes on the bottom:
[tex]\frac{miles}{minutes}:\frac{4}{20}[/tex]
Now we want to know how long (unknown number of minutes) it will take him to go 12 miles. Keep miles with miles and minutes with minutes:
[tex]\frac{miles}{minutes}:\frac{4}{20}[/tex]=[tex]\frac{12}{x}[/tex]
We can cross multiply now to get 4x = 12(20) and 4x = 240. That means that x=60. It will take him 60 minutes (1 hour) to go 12 miles.
Answer: 60 minuites
Step-by-step explanation: actully the dude thats on top of me its only 60 mins not 1hr and 60 mins
1. Two intersecting lines form how many
a. pairs of supplementary angles
b. pairs of complementary angles
c. pairs of adjacent angles
d. linear pairs of angles
e. pairs of verticle angles
This question isn't multiple choice by the way. It asks for each, and I know this may be a bit much to ask but if any of you can find images for each response that'd be great as well. But if not answering is also fine. Thanks!
Answer:
6 pairs of supplementary (when perpendicular)
a pair of complementary(0 for perpendicular)
4 pairs of adjacent
4 pairs of linear
2 pairs of vertical
If the endpoints of the diameter of a circle are (−6, 6) and (6, −2), what is the standard form equation of the circle? A) x2 + (y + 2)2 = 36 B) x2 + (y + 2)2 = 52 C) x2 + (y − 2)2 = 36 D) x2 + (y − 2)2 = 52
Answer:
D) x² + (y − 2)² = 52
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so is the average of the end points:
(h, k) = ((-6, 6) +(6, -2))/2 = (0, 4)/2 = (0, 2)
Then the distance between the center and an end point is the radius. It is found using the distance formula:
r = √((x2 -x1)² +(y2 -y1)²) = √((-6 -0)² +(6 -2)²) = √(36 +16) = √52
Putting these values into the standard form equation for a circle ...
(x -h)² +(y -k)² = r²
gives ...
(x -0)² +(y -2)² = (√52)²
x² +(y -2)² = 52 . . . . . matches choice D
Jorge wants to collect data about the amount of time 8th graders spend weekly on the internet. Which method would be the best way to collect data
Answer: Random samples
Step-by-step explanation: Jorge could ask how many hours people spend on the internet each day and then multiply that number by 7 for each person.
The best method for Jorge to collect data about 8th graders' internet usage is to conduct a survey.
Design the Survey: Create a set of questions focused on the amount of time spent on the internet. For example, 'How many hours per day do you spend on the internet?'etc
Distribution: Distribute the survey to the target group, either through paper forms during school hours or digitally through email or school platforms.
Data Collection: Collect the responses. Ensure that anonymity is maintained to get honest answers.
Analysis: Compile the data and calculate the average time spent online by 8th graders. Use graphical representations like bar charts or pie charts to visualize the data.
Presentation: Present the findings in a written report or a digital presentation, detailing the average time spent and highlighting any noticeable trends or patterns.
By conducting a survey, Jorge can efficiently gather accurate and representative data about the internet usage habits of 8th graders.
An art project requires 20 yards of fabric that costs $0.99 per yard.If 15 club members are to share the cost of fabric equally,how much should each member pay?
The answer should be 1.32
First you should multiply 20 yards by .99
Then you should get that number and divide it by 15 people
Answer:
$1.32 per person
Step-by-step explanation:
First you multiply the cost of the fabric with the amount of yards to know how much the total fabric will cost:
0.99·20=19.80
Then you divide the total cost of the fabric with the amount of people there are:
19.80÷15= $1.32
what is the distance between the points (-4, 2) and (1, -3) on the coordinate plane?
A. 7.07 units
B. 2.83 units
C. 5.83 units
D. 7.21 units
Answer:
A. 7.07 units
Step-by-step explanation:
Use the distance formula for coordinates:
[tex]d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2 }[/tex]
Fill in the coordinates accordingly:
[tex]d=\sqrt{(1-(-4))^2+(-3-2)^2}[/tex]
which simplifies down to
[tex]d=\sqrt{25+25}[/tex]
which is of course
[tex]d=\sqrt{50}[/tex]
Plug that into your calculator and you'll get the answer
PLEASE HELPP!!!
If a function, f(x) is shifted to the left four units, what will the transformed function look like?
Answer:
It would look like this basically..
Step-by-step explanation:
If a function, f(x) is shifted to the left four units, the
function that represents the transformation would be f(x+4). Adding it would make it go right..
*If you ever need help graphing, use desmos!
Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 12.../23...
Answer:
{0, 1, 2, 4, 5, 6, 8}
Step-by-step explanation:
120/230 = 12/23
121/231 = 11/21
122/232 = 61/116
123/233 -- not reducible
124/234 = 62/117
125/235 = 25/47
126/236 = 63/118
127/237 -- not reducible
128/238 = 64/119
129/239 -- not reducible
___
All even digits will make the fraction reducible, as will the digit 5. Then the digits we're not sure of are 1, 3, 7, 9. Appending 1 to the given numbers makes them divisible by 11, so that digit is included in our list.
Ending digits 3, 7, 9 result in fractions that are not reducible. (Numbers 127, 233, and 239 are prime numbers.)
Answer:
0,1,2,4,5,6,8
Step-by-step explanation:
Sarah saw a hammer that was $3.50 more than twice the cost of a screwdriver. The hammer was $15.50. What was the cost of the screwdriver?
Answer:
$6
Step-by-step explanation:
$15.50 is $3.50 more than $12. And $12 is twice $6. The cost of the screwdriver is $6.
The sum of two numbers is 11, and their difference is 9. What are the two numbers?
Answer:
10 and 1
Step-by-step explanation:
Let x and y represent the two numbers. The problem statement lets us write two equations describing their relationships:
x + y = 11
x - y = 9
Adding these equations together, we have ...
(x +y) +(x -y) = (11) +(9)
2x = 20
x = 10 . . . . . . . . . you will notice this is the average of the two given numbers
Then ...
10 + y = 11 . . . . substitute for x in the first equation
y = 1 . . . . . . . subtract 10
The two numbers are 10 and 1.
fill in the blank to make the expression a perfect square.
v^2 - 18v + ?
Answer: (v - 9)^2 - 81
Step-by-step explanation: Use the formula (b/2)^2 in order to create a new term to complete the square.
Hope this helps! :) ~Zane
Just need someone to double check if I am correct or not, thanks!
Select Yes or No to state whether each data set is likely to be normally distributed.
the number of popcorn pieces in a bag of small popcorn sold at a given movie theater <--- I think this is yes
the heights of all the people on a field trip that is made up of first-graders and their teachers <--- I think this is no
the values of the coins collected from a parking meter <--- I think this is no
the heights of the players in a basketball league <--- I think this is yes
The data set is likely to be Normally distributed is given as:
A) Yes, is in Normal DistributionB) No, not in Normal DistributionC) No, not in Normal DistributionD) Yes, is in Normal DistributionWhat is Normal Distribution?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
As per the definition,
The Data that is significantly concentrated around the mean, with progressively fewer data points for values far away from the mean in both directions, is likely to be normally distributed.
and, Insufficient Data can cause a normal distribution to look completely scattered.
So, The first statement is comes under normal distribution.
The second statement does not comes under normal distribution.
The third statement does not comes under normal distribution.
The fourth statement is comes under normal distribution.
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The answers for the statements to check whether normally distributed or not are 1.Yes,2.No,3.No,4.Yes
The number of popcorn pieces in a bag of small popcorn sold at a given movie theater - Yes, this is likely normally distributed.MATH HELP
steve is riding his bike around the block. the distance around the block is 1/2 mi. he rides around the block 3 1/2 times.
how far does steve ride his bike ?
Answer:
1.75 miles
Step-by-step explanation:
If he rides around his block 3 times it is 1.5 miles and if he only rides around his block half-way not a time it is a quarter of a mile added on instead of a half.
Answer:
1 3/4
Step-by-step explanation:
3 1/2*1/2=1 3/4. Hope this helps.
Flipping through a magazine, Hiccup sees an advertisement for Toothless Toothpaste. The ad says that it is recommended by 4 out of 7 dragons dentists. toothless If 1,500 dragon dentists were surveyed, about how many would recommend Toothless Toothpaste? Explain your reasoning!
Answer:
375
Step-by-step explanation:
So first you would want to divide 1,500 by 4 because the ratio is 4:7. The answer you get if you divide 1,500 by 4 is 375. This is your answer because if you divide 1,500 by 4 you are seeing out of how many 'dentist' would recomend this product.
1500/4
375
Use a calculator
Very helpful
Given: circle k(O),
m
JC
= 94°
Find: m∠LJC
Answer:
The measure of angle LJC is [tex]m\angle LJC=43\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of arc LC
we know that
[tex]arc\ LC+arc\ JC=180\°[/tex] ----> because the diameter divide the circle into two equal parts
substitute the given values
[tex]arc\ LC+94\°=180\°[/tex]
[tex]arc\ LC=180\°-94\°=86\°[/tex]
step 2
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle LJC=\frac{1}{2}[arc\ LC][/tex]
substitute
[tex]m\angle LJC=\frac{1}{2}[86\°]=43\°[/tex]
PLEASE HELP!!!!!! HURRY PLEASE!
You are going to create a circle graph to represent some data. How many degrees should a section representing 65 out of a hundred be?
A. 234°
B. 65°
C. 100°
D. 13°
Answer: OPTION A.
Step-by-step explanation:
We know that a circle measures 360 degrees. Then, to determine the size of a section, we need to multiply the percent of the category by 360 degrees.
First, we need to write 65 out of a hundred in decimal form:
[tex]\frac{65}{100}=0.65[/tex]
Now, let be "x" the degrees of the section representing 65 out of a hundred. We need to multiply 360 degrees by 0.65. Therefore, we get this result:
[tex]x=360\°*0.65\\x=234\°[/tex]
This matches with the option A.
The degree measurement for a section representing 65 out of 100 on a circle graph is 234 degrees. This is obtained by forming a ratio of the data point to the total data and multiplying by 360 (the total degrees in a circle).
Explanation:To determine the degree measurement for a section on a circle graph, we must understand that a full circle consists of 360 degrees. The proportion that every bit of data takes in that circle is found by making a ratio of the data point to the total data multiplied by 360 degrees. Therefore, to find the proportion of 65 out of 100, we would make a ratio of 65 to 100 and multiply that by 360. Which comes out to: (65/100) * 360 = 234 degrees. So the correct answer would be 234 degrees (Option A).
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Please help me out please
x = [5]
y = [2]
I really hope this answer helps you out! It makes my day helping people like you and giving back to the community that has helped me through school! If you could do me a favor, if this helped you and this is the very best answer and you understand that all of my answers are legit and top notch. Please mark as brainliest! Thanks and have a awesome day!
Answer x = ?
y = 0
Have good day
PLEASE HELP ME OUT !
[tex]
\sin(\beta)=\frac{y}{h} \\
\sin(27)=\frac{y}{350} \\
y=350\sin(27)\approx\boxed{158.9}
[/tex]
Which polar equation represents an ellipse?
r= 1/3+2cos theta
r= 3/2+3 sin theta
r= 5/2+2 sin theta
r= 2/2-3 sin theta
Answer:
[tex]r=\frac{1}{3+2cos\theta}[/tex]
Step-by-step explanation:
Let us write the equations in standard form:
[tex]r=\frac{1}{3+2cos\theta} \implies r=\frac{\frac{1}{3} }{1+\frac{2}{3}\cos \theta }[/tex]
We have
[tex]e=\frac{2}{3}\:<\:1[/tex] and
[tex]ep=\frac{1}{3}[/tex]
Since the eccentricity of this conic is less than 1, the conic represents an ellipse.
The second equation is [tex]r=\frac{3}{2+3\sin \theta}[/tex].
This is a hyperbola, because eccentricity is more than 1.
The third equation is [tex]r=\frac{5}{2+2\sin \theta}[/tex].
This is a parabola, because eccentricity is 1.
The fourth equation is [tex]r=\frac{2}{2-3\sin \theta}[/tex].
This is also a hyperbola, because eccentricity is more than 1.
A tree outside Ellie's house casts a 125-foot shadow. At the same time of the day, Ellie casts a 5.5-foot shadow. If Ellie is 4 feet 10 inches tall, how tall is the tree in feet?
Answer:
The tall of the tree is about 109.85 feet
Step-by-step explanation:
* Lets study the situation in the problem
- The tree and its shadow formed a right angle triangle with legs
x the tall of the tree and 125 feet the shadow of the tree
- Ellie and her shadow formed a right triangle with legs 4 feet and
10 inches the tall of Ellie and 5.5 feet the shadow of Ellie
- The two triangles are similar
- There is an equal ratio between the corresponding sides of the
similar triangles
# Ex: If triangles ABC and XYZ are similar
∴ AB/XY = BC/YZ = AC/XZ
* Lets use this rule to solve the problem
∵ The tall of the tree is x
∵ The tall of Ellie is 4 feet and 10 inches
- Lets change the tall of Ellie to feet only
∵ 1 foot = 12 inches
∴ 10 inches = 10/12 = 5/6 foot
∴ The tall of Ellie is 4 feet and 5/6 foot = 4 + 5/6 = 29/6 feet
∵ The shadow of the tree is 125 feet
∵ The shadow of Ellie is 5.5 feet
- By using similarity ratio
∴ Tall of tree/tall of Ellie = shadow of tree/shadow of Ellie
∴ x/(29/6) = 125/5.5 ⇒ using cross multiplication
∴ 5.5(x) = 125(29/6) ⇒ divide both sides by 5.5
∴ x ≅ 109.85 feet
* The tall of the tree is about 109.85 feet
Answer:
The tall tree is about 109.85
Step-by-step explanation:
Hope this helps!
The equation for a circle is x^2 + 10x + y^2 + 12y + 52 = 0
What is the equation of the circle in standard form?
(X+5)^2+(y+6)^2=61 and then to find the radius take the square root of both sides
Mrs. Smith bought breakfast tacos for her family and they cost $9.48 for a dozen tacos how much was the cost of each taco
$0.79
Just divide 9.48 by 12.
The work of a student to solve a set of equations is shown: Equation A: y = 4 − 2z Equation B: 4y = 2 − 4z Step 1: −4(y) = −4(4 − 2z) [Equation A is multiplied by −4.] 4y = 2 − 4z [Equation B] Step 2: −4y = 4 − 2z [Equation A in Step 1 is simplified.] 4y = 2 − 4z [Equation B] Step 3: 0 = 6 − 6z [Equations in Step 2 are added.] Step 4: 6z = 6 Step 5: z = 1 In which step did the student first make an error? (5 points)
ANSWER
Step 2
EXPLANATION
The system of equations are:
Equation A:
[tex]y = 4 - 2z[/tex]
Equation B:
[tex]4y=2 - 4z[/tex]Step 1: Multiply equation A by -4.
Equation A:
[tex] - 4(y) = - 4(4 - 2z)[/tex]
Equation B:
[tex]4y=2 - 4z[/tex]
Step 2: Simplify equation A in step 1,
Equation A:
[tex] - 4y= - 16 + 8z[/tex]
This is where the student made the first error.
He didn't expand the second parenthesis correctly.
Answer:
The student made the first mistake in step 2.
Step-by-step explanation:
How does the addition of a possible outlier on PLOT B affect the center of PLOT B relative to the center of PLOT A?
A) mean increases and median increases
B) median increases and mean unchanged
C) median decreases and mean decreases
D) mean increases and median is unchanged
Answer:THE ANSWER IS D
Step-by-step explanation:
Mean increases and median is unchanged. Therefore, option D is the correct answer.
What is a dot plot?A dot plot, also known as a strip plot or dot chart, is a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis. These types of charts are used to graphically depict certain data trends or groupings.
From the given dot plot A
The data is, 12, 12, 13, 13, 13, 13, 13, 14, 14
Data of plot B is 12, 12, 13, 13, 13, 13, 13, 14, 14, 20
Here, median of plot A and plot B is same.
Mean of plot B is greater than the mean of plot A.
Therefore, option D is the correct answer.
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The French club is sponsoring a bake sale. If their goal is to raise at least $135, how many pastries must they sell at $3.00 each in order to meet that goal? Write and solve an inequality.
135p ≥ 3.00; p ≥ 45
3.00p ≥ 135; p ≥ 405
3.00p ≥ 135; p ≥ 45
3.00p ≥ 135; p ≥ 132
Answer:
3.00p ≥ 135; p ≥ 45
Step-by-step explanation:
You sell each for $3 so 3(pastries sold or p).
You want to make AT LEAST 135 (you could make more but not less.)
so 3.00p ≥ 135.
To solve: divide 135 by 3.
p ≥ 45
Answer: [tex]3p\geq135[/tex] ; [tex]p\geq45[/tex]
Step-by-step explanation:
Given : The French club is sponsoring a bake sale. If their goal is to raise at least $135 (greater than of equal to $135).
Let p be the number of pastries they sell.
If they sell at $3.00 each in order to meet that goal, then the total price of p pastries will be : 3p
Then, the inequality for the given statement will become:-
[tex]3p\geq135[/tex]
Divide both sides by 3 , we get
[tex]p\geq45[/tex]
Hence, they must sell 45 or more pastries to raise at least $135.
Describe the relationship between the two sets A and B if A ⊆ B. (No picture is provided in the question)
Answer:
Set A is a subset of set B. It means that every element of set A should be present in set B.
Step-by-step explanation:
A ⊆ B
Set A is a subset of set B. It means that every element of set A should be present in set B.
i.e for all a ∈ A then a ∈ B
Example:
Let set A = {1,2,3}
and B = { 1,2,3,4,5,6}
then A ⊆ B because every element in set A {1,2,3} is also present in set B {1,2,3,4,5,6}
If 21 more than 3 times a number is -15 , what is the number?
A: 2
B: -12
C: -2
D: 12
Let X = the number.
You have 21 more than 3 times the number which is:
3x +21 = -15
Subtract 21 from both sides:
3x = -36
Divide both sides by 3:
x = -36 /3
x = -12
The answer is B.
Answer:
-13
Explanation:
Rewrite Equation:
(3 · x) + 21 = -15
Subtract 21 From Both Sides:
(3 · x) + 21 - 21 = -15 - 21
Simplify:
3x = -36
Divide Both Sides By 3:
[tex]\bold{\frac{3x}{3} \ = \ \frac{-36}{3} }[/tex]
Simplify:
x = -12
Mordancy.
PLEASE HELP:)
need to find measure of each of the angles to the right
Answer:
Step-by-step explanation:
< 1 = 110
< 2 = 180 - 110 = 70
<5 = 180 - 110 = 70
<6 = <1 = 110
==================
<9 = 103
<13 = 180 - 103 = 77
<10 = <13 = 77
<14 = <9 - 103
====================
<2 = < 4 = 70 Property of l || m
<3 = <1 = 110 Same as above
<7 = <5 = 70 Same as above and vertical angles.
<6 = <8 = 110 Same as above
=====================
<11 = < 9 = 103 Parallel line property
<15 = <13 = 77 Same as above
<12 = <10 = 77 Same as above
<16 = <15 = 103 Parallel line property.
Can someone please answer this
Answer: y = sqrt x
Explanation:
In order to draw the graph of this function you will need to identify some of the values.
If x=0, then y = sqrt 0.
If x=1, then y = sqrt 1.
If x=2, then y = sqrt 2.
(This repeats.. you get the idea)
Plot these points and draw a curve through them. Your answer should look just like the graph in your question.