I need help with this practice problem solving My attempted answer is in the pic, though I am not sure if I am correct or not
Answers
Solution
To convert from polar coordinate to rectangular coordinate,
[tex]\begin{gathered} (r,\theta)\to(r\cdot\cos \theta,r\cdot\sin \theta) \\ \\ \Rightarrow(3\sqrt[]{5},-\frac{\pi}{8})\to(3\sqrt[]{5}\cdot\cos (-\frac{\pi}{8}),3\sqrt[]{5}\cdot\sin (-\frac{\pi}{8})) \\ \\ \Rightarrow(3\sqrt[]{5}\cdot\cos (-\frac{\pi}{8}),3\sqrt[]{5}\cdot\sin (-\frac{\pi}{8}))=(6.20,-2.57) \end{gathered}[/tex]Related Questions
549 vehicles in 9 acres. How many in 1 acre?
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We have that there are 549 vehicles in 9 acres, we want to know how many are in 1 acre. We see that those quantities are proportional and therefore:
[tex]v=\frac{549\cdot1}{9}\Rightarrow v=61[/tex]We will have that there are 61 vehicles in 1 acre.
I need a little help understanding this
Answers
I'm going to use the letters L and W for the length and the width of the granite rectangle. We know that the length is 3 times the width. With this information we can build the following equation:
[tex]3W=L[/tex]We also know that the perimeter of the section must be less than 320 inches. The perimeter of a rectangle is giving by two times its length plus two times its width. Then we have the equations:
[tex]\begin{gathered} \text{Perimeter}=2L+2W \\ \text{Perimeter}<320 \\ 2L+2W<320 \end{gathered}[/tex]Since we know that L=3W then:
[tex]\begin{gathered} L=3W \\ W=\frac{L}{3} \end{gathered}[/tex]Now that we know that W=L/3 we can substitute L/3 in place of W on the inequality I wrote before:
[tex]\begin{gathered} 2L+2W<320 \\ 2L+2\cdot\frac{L}{3}<320 \\ \frac{8}{3}L<320 \\ L<320\cdot\frac{3}{8} \\ L<120 \end{gathered}[/tex]This means that the length must be less than 120 inches. This is the same as statement D which is the answer for this problem.
Is the line through points P(3, -5) and 2(1, 4) parallel to the line through points R(-1, 1) and S(3,Explain.
Answers
As given by the question
There are given that the two-point;
[tex]\begin{gathered} P(3,\text{ -5) and Q(1, 4)} \\ R(-1,\text{ 1) and S(3, -3)} \end{gathered}[/tex]Now,
First, find the slope of both of the lines from the point
Then,
For first line:
[tex]\begin{gathered} PQ(m)=\frac{y_2-y_1}{x_2-x_1} \\ PQ(m)=\frac{4_{}+5_{}}{1_{}-3_{}} \\ PQ(m)=\frac{9}{-2} \\ PQ(m)=-\frac{9}{2} \end{gathered}[/tex]Now,
For the second line:
[tex]\begin{gathered} RS(m)=\frac{y_2-y_1}{x_2-x_1} \\ RS(m)=\frac{-3_{}-1_{}}{3_{}+1_{}} \\ RS(m)=-\frac{4}{4} \\ RS(m)=-1 \end{gathered}[/tex]Since both slopes are different, they are not parallel lines, which means parallel lines have the same slope.
Hence, the correct optio
ok Find the distance from M to N on the coordinate plane if M(-5,8) and N(9,-2).
Answers
The above formula is used to find the distance betweent two points on the coordinate plane
let x1 = -5
let y1 = 8
let x2 = 9
let y2 = -2
inputing the following values in the above equation
[tex]\sqrt[]{(-5-9)^2+(8-(-2)^2}[/tex][tex]\sqrt[]{(-14)^2+(8+2)^2}[/tex][tex]\sqrt[]{(-14)^2+10^2}[/tex][tex]D=\sqrt[]{196\text{ + 100}}\text{ }[/tex][tex]\sqrt[]{296}[/tex][tex]undefined[/tex]When simplified, what is the value if i2 = −1?
Answers
Solution:
Given:
[tex]\begin{gathered} \sqrt[]{-128} \\ \\ \text{also,} \\ i^2=-1 \end{gathered}[/tex]To simplify, we break the radical down into bits.
[tex]\begin{gathered} \sqrt[]{-128}=\sqrt[]{-1}\times\sqrt[]{128} \\ To\text{ simplify }\sqrt[]{128}\text{ , we split it into a number that is a p}\operatorname{erf}ect\text{ square and another number,} \\ \text{Hence,} \\ \sqrt[]{128}=\sqrt[]{64\times2}=\sqrt[]{64}\times\sqrt[]{2} \\ \text{This means,} \\ \sqrt[]{-128}=\sqrt[]{-1}\times\sqrt[]{64}\times\sqrt[]{2} \\ \text{But recall that;} \\ i^2=-1 \\ \text{Taking the square root of both sides,} \\ i=\sqrt[]{-1} \\ \text{Substituting it in the expression below,} \\ \sqrt[]{-128}=\sqrt[]{-1}\times\sqrt[]{64}\times\sqrt[]{2} \\ \sqrt[]{-128}=i\times8\times\sqrt[]{2} \\ \sqrt[]{-128}=8i\sqrt[]{2} \end{gathered}[/tex]Therefore, the simplified form is;
[tex]8i\sqrt[]{2}[/tex]Person A went to the store and bought some books at $12 each and some DVDs at $15 each. The bill (before tax) was less than $120. Which inequality represents the situation if x=books and y=DVDs?A) 12x+15y = 120B) 12x+15y < 120C) 12x+15y >-D) none of the above
Answers
Since the cost of each book is $12, and x is the number of books, the total cost of books will be 12x.,
Similarly, since the cost of each DVD is $15, and y is the number of DVDs, the total cost of DVDs will be 15y.
Thus, the total cost of books and DVDs will be 12x + 15y.
We know that the total cost was less than $120, so this expression should be less than 120.
Thus, the inequality is:
[tex]12x+15y<120[/tex]Which corresponds to alternative B.
To check wether the amount in the alternatives can be purchased, we just need to substitute x and y and check wether the inequality is valid:
A
[tex]\begin{gathered} 12\cdot5+15\cdot5<120(?) \\ 60+75<120(?) \\ 135<120\to invalid \end{gathered}[/tex]B
[tex]\begin{gathered} 12\cdot6+15\cdot2<120(?) \\ 72+30<120(?) \\ 102<120\to valid \end{gathered}[/tex]C
[tex]\begin{gathered} 12\cdot2+15\cdot6<120(?) \\ 24+90<120(?) \\ 114<120\to valid \end{gathered}[/tex]D
[tex]\begin{gathered} 12\cdot0+15\cdot10<120(?) \\ 0+150<120(?) \\ 150<120\to invalid \end{gathered}[/tex]E
[tex]\begin{gathered} 12\cdot8+15\cdot0<120(?) \\ 96+0<120(?) \\ 96<120\to valid \end{gathered}[/tex]Thus, the amounts that could have been purchased are thouse in alternatives B, C and E.
Calculate the volume of the figure.*2 pointsCaptionless ImageA) 273 in^3B) 50 in^3C) 260 in^3D) 176 in^3
Answers
The volume of a rectangle is:
[tex]\begin{gathered} V=\text{ lenght x width x height} \\ V=\text{ 13 in x 10 in x 2 in} \\ V=\text{ 260 in}^3 \end{gathered}[/tex]The answer is C. 260 in^3
which figure can we transformee into figure k by a reflection across the x-axis and dilation of 1/2.
Answers
The rule for reflecting a point through the x-axis is (x, -y) and to dilation is (1/2x, 1/2y):
Now, let's se what figure can be transformed into figure K:
J
(8, 4), reflecting through x-axis (8, -4), dilation (4, -2) --> This point meets figure K
Let's prove with another point of J:
(4, 4) ---> (4, -4) ---> (2, -2) --> This point also meets figure K
Then we can say that figure J can be transformed into figure K
which of the following numbers is a power of 10 options 1010 500 1000 or 20
Answers
Answer
Answer = 1000
Explanation
A power of 10 would be a number that can result from multiplying 10 by itself a number of times.
And from the options, we can see that only
1000 = 10 × 10 × 10
Hope this Helps!!!
Use the followingA test has 28 questions that total 100 points. The test contains multiple choice questions that areworth 3 points each and short answer questions that are worth 5 points each15. Write a system of finear equations to represent the situation16. Write a matrix equation that corresponds to the system in question 15.17. Solve the system using matrices to determine how many multiple choice and short answerquestions are on the test
Answers
The equations are:
x + y = 28 ...............................................(1)
3x + 5y = 100 .........................................(2)
Explanation:Parameters:
Total questions = 28
Total points = 100
Mulitple choice questions = 3 points each
Short answer quesitons = 5 points
Let x represent the number of multiple choice question, and y be the number of short answer
x + y = 28 ...............................................(1)
3x + 5y = 100 .........................................(2)
In a matrix form, this is:
[tex]\begin{bmatrix}{1} & {1} \\ {3} & {5}\end{bmatrix}\begin{bmatrix}{x} \\ {y}\end{bmatrix}=\begin{bmatrix}{28} \\ {100}\end{bmatrix}[/tex]Solving the above, we have:
[tex]undefined[/tex]Consider the first 2 terms of the sequence 28, 14, ...
Determine whether the sequence is arithmetic or geometric. Explain your reasoning.
please help me with 1 and 2
Answers
With the first term being 28 and the difference being 2, this geometric progression is finite because 28 is divided by 14 and then that number is divided by 2 and so on.
What is geometric progression?
A mathematical sequence known as a geometric progression (GP) is one in which each succeeding term is generated by multiplying each preceding term by a fixed number, or "common ratio." This progression is also referred to as a pattern-following geometric sequence of numbers. A geometric progression is a series in which each term can be obtained by multiplying or dividing the term before it by a predetermined amount. Infinite GP sum refers to the total number of terms in an infinite GP. S_ = a/(1 - r), where an is the first term and r is the common ratio, is the formula for calculating the sum of an infinite geometric progression.
Here,
This is geometric progression with first term 28 and difference 2 and this is finite GP as 28 is divided by 14 then 14 is divided by 2 so on as the definition of GP says, "a series of numbers with a fixed ratio between each and the previous one (e.g., each subsequent number is increased by a factor of 3 in the progression 1, 3, 9, 27, 81 )".
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Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the
option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, Interest will accrue at 4.29%.
Suppose Rich only paid the interest during his 4 years in school and the six-month grace period. What will he now pay in interest over the term of his loan?
Answers
Rich will incur interest totaling $1,525.095 throughout the course of the 4.5-year non-payment period.
What is simple intrest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.acc to our question-
Given that he is aware that he has the option to start loan payback in 4.5 years at the current interest rate of 4.29% on a $7,900 loan, the following will apply:
4.29% of 7900 after the first year.In order to calculate the total interest after the 4.5-year term, multiply the interest by 4.5:=338.91*4.5=1525.095
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Given the following exponential function, identify whether the change representsgrowth or decay, and determine the percentage rate of increase or decrease y=5600(1.07)^x
Answers
y= 5600 (1.07)^x
Base = 1.07
When the base of an exponential function is greater than one, it represents growth.
We can rewrite the base as:
1.07 = 1+r= 1 +0.07
r=0.07
r= increase rate
Percentage rate of increase = 0.07 x 100 = 7%
Translate the figure 1 unit right and 4 units up.Draw a vector from the origin 1 unit right and 4 units up.I need help pls
Answers
We want to translate the figure 1 unit right and 4 units up. This means we are going to add +1 to each x cordinate and +4 to each y cordinate.
To do this, the coordinates of the figure will change as follows:
(-9, -4) = (-9 + 1, -4 + 4) = (-8, 0) (starting point)
(-6, -9) = (-6 + 1, -9 + 4) = (-5, -5)
(-5, -5) = (-5 + 1, -5 + 4) = (-4, -1)
(-1, -5) = (-1 + 1, -5 + 4) = (0, -1)
(-2, -1) = (-2 + 1, -1 + 4) = (-1, 3)
(-9, -4) = (-9 + 1, -4 + 4) = (-8, 0) (ending point)
Now, we have to plot these new cordinates:
The figure has been translated
Given f(x)= -3x^3 - 8x^2 - x + 8 andg(x)= 3x^3 - 6x^2 - 8x - 8What would (f-g)(x) and (f-g)(-1) be?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
f(x)= -3x³ - 8x² - x + 8
g(x)= 3x³ - 6x² - 8x - 8
Step 02:
functions:
(f - g)(x):
(f - g)(x) = -3x³ - 8x² - x + 8 - (3x³ - 6x² - 8x - 8)
(f - g)(x) = -3x³ - 8x² - x + 8 - 3x³ + 6x² + 8x + 8
(f - g)(x) = - 6x³ - 2x² + 7x + 16
(f - g)(-1):
(f - g)(-1) = - 6(-1)³ - 2(-1)² + 7(-1) + 16
(f - g)(-1) = - 6(-1) - 2(1) + 7(-1) + 16
(f - g)(-1) = 6 - 2 - 7 + 16
(f - g)(-1) = 13
That is the full solution.
use the distributive property to evaluate the expression (3+6)(-8)
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We have the following:
The distributive property of multiplication over addition can be used when multiplying a number by a sum.
[tex]\begin{gathered} \mleft(3+6\mright)\mleft(-8\mright)=9\cdot-8 \\ -72=-72 \end{gathered}[/tex]The probability distribution for arandom variable x is given in the table.Х- 10-505101520Probability.20.15.05.1.25.1.15Find the probability that x = -10
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To find the probability of a distribution given in table form we have to look for the x we are searching and see its corresponding probability in the table.
In this case we notice that to x=-10 corresponds the probability .20, therefore:
[tex]P(x=-10)=0.20[/tex]True or False. Given the following vectors:a=(3,4,-2)b=(2,-7,1)c=(-6,5,4)The value of a +cxb is (36,18,30)
Answers
Answers
False
Explanation
Given vectors:
a = (3, 4, -2)
b = (2, -7 ,1)
c = (-6, 5, 4)
What to find:
The value of a + c x b
Step-by-step solution:
c x b = (-6, 5, 4) x (2, -7, 1)
c x b = (-12, -35, 4)
a = (3, 4, -2)
Therefore, a + c x b = (3, 4, -2) + (-12, -35, 4)
a + c x b = (-9, -32, 2)
Thus, (-9, -32, 2) ≠ (36, 18, 30)
Hence the answer is False
1 What is the image of (12,-8) after a dilation by a scale factor of 4 centered at the origin? 12.4) b 18-32) 13,-2)
Answers
A dilation of a point by a factor of 4 means that its coordinates will be multiplied by 4, so the image of the point (x,y) after the dilation will be (4x,4y). With this in mind, let's solve the problem:
[tex]H\text{ = }(12\cdot4,-8\cdot4)=(48,-32)[/tex]The answer is (48,-32).
a monument that is 169.4 ft tall is built on a site that is 67.3 Ft below sea level how many feet above sea level is the top of the monument
Answers
Answer:
102.1 ft
Explanation:
We can represent the situation as follows:
So, we need to find the value of H. Therefore, H is equal to:
H = 169.4 ft - 67.3 ft
H = 102.1 ft
So, the top of the monument is 102.1 ft above sea level.
The aquarium has 6 fewer yellow fish than green fish. 40% of the fish are yellow. How many green fish are in the aquarium? Show your work.
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The total number of green fish are in the aquarium is 18.
What is called the linear equation?A linear equation is just an algebraic equation of the form y=mx+b, where the slope is m and b is the y-intercept, and just a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."T = Total fishes in aquarium.
G = Green fishes
Y = Yellow fishes
Thus, the linear equation for all fishes are-
T = G + Y ...eq 1
The aquarium has 6 fewer yellow fish than green fish.
G = Y+6 Put in eq 1
T = (Y+6) + Y
T = 2Y+6
40% of the fish are yellow = 0.4.
Y = 0.4×T
T = 2×(0.4×T) + 6
Solve for total fishes
T = 0.8T + 6
0.2T = 6
T = 30
Solve for Green fishes.
G = 0.6×T (given)
G = 18
Thus, the number of green fish are in the aquarium is 18.
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Find the area of the polygon. 17 ft 14 ft 4 ft- 3 ft 4 ft The area of the polygon is (Type a whole number.)
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Notice that the polygon can be divided on 3 rectangles, as shown in the following diagram:
The 14 ft side on the original image was split on a segment of 10ft and another of 4ft.
The areas of these rectangles, are:
[tex]\begin{gathered} A_1=(17ft)(10ft)=170ft^2 \\ A_2=(4ft)(3ft)=12ft^2 \\ A_3=(4ft)(4ft)=16ft^2 \end{gathered}[/tex]The total area of the polygon is the sum of the areas of the three rectangles:
[tex]\begin{gathered} A=170ft^2+12ft^2+16ft^2 \\ =198ft^2 \end{gathered}[/tex]Therefore, the area of the polygon is:
[tex]198ft^2[/tex]Super Yoga Program has two plans, basic plan and trial plan. In basic plan, you will pay $20 per month as a membership fee and $8 per each session. In trial plan, you pay $12 per each session.a. If you go to Yoga sessions 4 times in a month, which plan is better for you? Explain.b. If you go to Yoga sessions 8 times in a month, which plan is better for you? Explain.c. If you go to Yoga sessions n times in a month, express the total cost of basic plan as an expression.d. If you go to Yoga sessions n times in a month, express the total cost of trial plan as an expression.
Answers
ANSWER:
a. trial plan
b. basic plan
c. 20 + 8n
d. 12n
STEP-BY-STEP EXPLANATION:
a.
We calculate the price in each case, like this:
[tex]\begin{gathered} p_b=20+8\cdot4=52 \\ p_t=12\cdot4=48 \end{gathered}[/tex]Therefore, if you go 4 times a month, the trial plan is better.
b.
We calculate the price in each case, like this:
[tex]\begin{gathered} p_b=20+8\cdot8=84 \\ p_t=12\cdot8=96 \end{gathered}[/tex]Therefore, if you go 8 times a month, the basic plan is better.
c.
Let n be the number of times you go per month, the cost expression of basic plan would be:
[tex]p_b=20+8n[/tex]d.
Let n be the number of times you go per month, the cost expression of the trial plan would be:
[tex]p_t=12n[/tex]To help pay for culinary school, Susan borrowed money from an online lending company.
She took out a personal, amortized loan for $52,000, at an interest rate of 5.65%, with monthly payments for a term of 15 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Susan's monthly payment.
$0
(b) If Susan pays the monthly payment each month for the full term,
find her total amount to repay the loan.
$0
(c) If Susan pays the monthly payment each month for the full term,
find the total amount of interest she will pay.
$0
Answers
Susan's monthly payment is $4578.2, Susan pays the monthly payment each month for the full term, then 54938 is amount to repay the loan and If Susan pays the monthly payment each month for the full term, then 2938 is the total amount of interest she will pay.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Susan took out a personal, amortized loan for $52,000, at an interest rate of 5.65%, with monthly payments for a term of 15 years.
5.65% of 52000
5.65/100×52000
0.0565×52000
2938
2938+52000=54938
Ina year we will have 12 months.
So let us divide 54938 by 12
54938/12=4578.2
Susan's monthly payment is $4578.2
If Susan pays the monthly payment each month for the full term, then 54938 is amount to repay the loan.
If Susan pays the monthly payment each month for the full term, then 2938 is the total amount of interest she will pay.
Hence Susan's monthly payment is $4578.2, Susan pays the monthly payment each month for the full term, then 54938 is amount to repay the loan and If Susan pays the monthly payment each month for the full term, then 2938 is the total amount of interest she will pay.
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Name an angle supplementary to
Answers
Supplementary angles are angles that add up to 180 degrees.
To find the supplementary angle to ∠EOD, we find the angle with ∠EOD that makes up a straight line.
Looking at the figure, EC is a straight line and both ∠EOD and ∠DOC fall on this line. These two angles make up 180 degrees.
Thus,
The one supplementary angle to ∠EOD is ∠DOC.
AnswerBWhen solving the equation 15 = -3x + 3, the first step would be
Answers
12=-3x
Answer:
Subtract 3 from both sides
Step-by-step explanation:
When solving a linear equation, you need to get all the constants to one side and all the variable terms to the other side. In the equation 15=-3x+3, there is one constant on the left, and a variable term and a constant on the right. You have to move the constant, in this case 3, to the left side in order to solve. To do this, you perform the opposite operation, so in this case, you would subtract 3 from both sides. The 3 on the right will cancel out with the minus three, so you will have a zero on the right side, which can just be removed. You are left with 12=-3y.
Write the slope-intercept form of the equation of the line described. 11.) through: ( 1 , 2 ) , perpendicular to Y= -1/5x +2
Answers
We would like to find the equation of the line that passes through the point (1.2) and is perpendicular to the line y=-1/5 x +2, and write in slope intercept form. To do this first we have to remeber that the equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]and that to find it we need a point and the slope. In this case we have the point but we don't know the slope yet. To find the slope we notice that the line has to be perpendicular to the line y=-1/5 x +2. We need to remember that two lines are perpendicular if and only if
[tex]m_1m_2=-1[/tex]where m1 and m2 are the slopes of the lines.
The line y=-1/5 x +2 is wirtten in the slope-intercept form:
[tex]y=mx+b[/tex]from this we notice that its slope is -1/5, then using the relation for perpendicular lines we have that
[tex](-\frac{1}{5})(m)=-1[/tex]Solving for m we have that
[tex]\begin{gathered} m=\frac{-1}{-1}(5) \\ =5 \end{gathered}[/tex]So, our line passes through the point (1,2) and has an slope equal to 5. Plugging this values on the equation for a line we have
[tex]\begin{gathered} y-2=5(x-1) \\ y-2=5x-5 \\ y=5x-5+2 \\ y=5x-3 \end{gathered}[/tex]so the equation of the line we were looking for is y=5x-3. (Notice that it is already written in the adequate form).
Someone help how do I find if it’s a function
Answers
To know if this is a function, simply perform a vertical line test on it.
If it passed the vertical line test then it is a function but if it fails it then it is not a function
In the graph given, if you draw a vertical point at any point, we woulld not have two points on the vertical line, hence it is a function
if you can make one scarf with 3/5 of a ball of yarn how many can you make with 15 balls of yarn?
Answers
Explanation:
To find out how many scarfs you can make with 15 balls of yarn we have to divide 15 by 3/5, because with 3/5 you can make 1 scarf:
[tex]15\colon\frac{3}{5}=\frac{15\cdot5}{3}=\frac{75}{3}=25[/tex]Answer:
WIth 15 balls of yarn you can make 25 scarfs
Select the expression equivalent to:(4x + 3) + (-2x + 4)A: 2x + 7B: -2x + 12C: -8x + 12D: 6x + 7
Answers
(4x + 3) + (-2x + 4)
Eliminating the parentheses:
4x + 3 - 2x + 4
Reordering:
4x -2x + 3 + 4
2x + 7