The two pairs of polar coordinates for the given point (3, -3) with 0° ≤ θ < 360° are (3√2, 135°) and (3√2, 315°).
What is a polar coordinate?A polar coordinate is a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).
Next, we would determine the distance (r) and angle (θ) as follows:
r = √(3² + (-3)²)
r = √(9 + 9)
r = 3√2.
θ = tan⁻¹(-3/3)
θ = tan⁻¹(-1)
θ = 3π and 7π/4 (second and fourth quadrants).
Converting to degrees, we have:
θ = 135° and 315°.
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Complete Question:
Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°
I need some help guys!
Answer:
0.18
Step-by-step explanation:
GEOMETRY - FIND X ON THIS TRIANGLE
Answer: [tex]\frac{7\sqrt{3}}{2}[/tex]
Step-by-step explanation:
[tex]\sin 60^{\circ}=\frac{x}{7}\\\\\frac{\sqrt{3}}{2}=\frac{x}{7}\\\\x=\frac{7\sqrt{3}}{2}[/tex]
(x-2)(x+2)(x²+4)-(x²+3)(x²-3)+2022
The simplified form of the given expression is 2015
Simplifying expressionsThe given expression is (x-2)(x+2)(x²+4)-(x²+3)(x²-3)+2022
The expression can be simplified as shown below
(x-2)(x+2)(x²+4) - (x²+3)(x²-3) + 2022
x(x+2)-2(x+2)(x²+4) - x²(x²-3) +3(x²-3) + 2022
(x²+2x-2x-4)(x²+4) - (x⁴-3x²+3x²-9) + 2022
(x²-4)(x²+4) - (x⁴-9) + 2022
x²(x²+4) -4(x²+4) - (x⁴-9) + 2022
(x⁴+4x²-4x²-16) - (x⁴-9) + 2022
(x⁴-16) - (x⁴-9) + 2022
x⁴ -16 -x⁴ +9 + 2022
x⁴ -x⁴ -16 +9 +2022
= 2015
Hence, the simplified expression is 2015
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Vertical lines have an undefined slope.
True or False
Answer:
True
Step-by-step explanation:
The 'base' of the line has length zero.
Answer:
True.
Step-by-step explanation:
You take 2 points and find gradient of a line and if you get a constant. For example, m=5. Then 5 over 0 (the denominator is what matters, it must be 0) and that's how you know it's a vertical line and has undefined slope.
Which of the following gives a single solution of the inequality |x+3|-2<0 and shows a graph that can be used to determine the entire solution set of the inequality?
The solution to the inequality |x + 3| - 2 < 0 is -5 < x < -1 as shown in the graph attached
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality is an expression used to show the non equal comparison of two or more numbers and variables.
Given that:
|x + 3| - 2 < 0
Hence:
(x + 3) - 2 < 0 and -(x + 3) - 2 < 0
x < -1 and x > -5
The solution to the inequality |x + 3| - 2 < 0 is -5 < x < -1 as shown in the graph attached
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Answer: The answer to the question is Answer Choice "B"
Step-by-step explanation:
Proof that It's actually correct as you can see it on the screenshot :)
At a school book fair, 3/5 of the books are nonfiction books. of the nonfiction books, 1/4 are animal books. what fraction of the book fair books are animal books? move numbers to the boxes to show the fraction.
Answer:
Animal books make up (3/20) of all books
Step-by-step explanation:
Let X be the total number of books, made up of nonfiction, animal, and all others.
(3/5)X are nonfiction books.
Of the nonfiction books, 1/4 are animal books: (3/5)*(1/4)X = (3/20)X are animal books
[This means that Nonfiction, less animal books is: (3/5)X - (3/20)X]
Animal books make up (3/20) of all books.
When two musical notes are a "fifth" apart, the frequency of the lower note is 2/3 the frequency of the higher note. Using f as the frequency of the higher note, write an expression for the frequency
of the lower notes
Frequency is a physical quantity that relates to the number of cycles made by a wave per second. Therefore the required expression for the frequency of the lower note is: [tex]\frac{2}{3}[/tex] f
A wave is a phenomenon that propagates through a material medium without any permanent effect on the molecules of the medium. It transmits energy from one end of the medium to another. Examples are sound waves, light waves, electromagnetic waves, etc.
The propagation of a wave gives rise to frequency. Which can be defined as the number of cycles made by a wave per second. And it is measured in Hertz.
Let the frequency of the higher note be represented by f, and that of the lower note by [tex]f_{l}[/tex]. Thus, we have;
[tex]f_{l}[/tex] = [tex]\frac{2}{3}[/tex] f
Therefore, the expression for the frequency of the lower notes is [tex]\frac{2}{3}[/tex] f.
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Select the correct answer. This table represents a quadratic function. x y 1 3 3 -3 5 -5 7 -3 9 3 Which statement about this function is true? A. The value of a is negative, so the vertex is a maximum. B. The value of a is positive, so the vertex is a maximum. C. The value of a is positive, so the vertex is a minimum. D. The value of a is negative, so the vertex is a minimum. Reset Next
The statement "The value of a is positive, so the vertex is a minimum" is correct.
What is a quadratic function?
Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
From the table we can find the quadratic function:
f(x) = ax² + bx + c
Plug (x, y) on the above function.
a + b + c = 3 ...(1)
9a + 3b + c = -3 ...(2)
25a + 5b + c = -5 ...(3)
After solving the above equations:
a = 0.5
b = -5
c = 7.5
The value of a is positive.
Thus, the statement "The value of a is positive, so the vertex is a minimum" is correct.
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This coordinate plane shows the journey of a plane between two cities. The journey starts from City A, indicated by a green point, and ends in City B, indicated by a red point. In which quadrant did the journey start and in what quadrant did it end?
A. Started in Quadrant III and ended in Quadrant I.
B. Started in Quadrant I and ended in Quadrant II.
C. Started in Quadrant II and ended in Quadrant IV.
D. Started in Quadrant I and ended in Quadrant III.
Started in Quadrant II and ended in Quadrant IV.
==========================================================
Explanation:
Refer to the diagram below. It shows how the four quadrants are labeled using roman numerals. We start in the upper right corner (aka northeast corner) and work counterclockwise when labeling quadrant I, II, III, and IV in that order.
The green point A is located in quadrant II in the northwest. Meanwhile point B in red is in the southeast quadrant IV.
Therefore, we started in quadrant II and ended in quadrant IV which points us to choice C.
Solve The Following
( Solving equations)
Answer:
a) x = 4
b) x = 1
Step-by-step explanation:
a) [tex]\frac{4x-1}{2} = x + 7[/tex] multiply both sides by 2 so we can simplify the fraction by getting rid of 2
4x - 1 = 2x + 7 transfer like terms to the same side of the equation
4x - 2x = 7 + 1
2x = 8 divide both sides by 2
x = 4
b) [tex]3x + 2 = \frac{2x+13}{3}[/tex] again, get rid of the fraction by multiplying both sides by 3
9x + 6 = 2x + 13 transfer like terms to the same side of the equation
9x - 2x = 13 - 6
7x = 7 divide both sides by 7
x = 1
What number is it that, when multiplied by 18,27,36,45,54,63,72,81, or 99, gives a product in which the first and last figures are the same as those in the multiplier, but which when multiplied by 90 gives a product in which the last two figures are the same as those in the multiplier?
The given multipliers are factors of 9, the possible number will have 1 as first and last digit which gives the number as 101
How can the correct number be found?The given numbers are;
18, 27, 36, 45, 54, 63, 72, 81, 99
Given that the first and the last figures are those of the multipliers, we have;
The first and last and last digit of the number can be 1, which gives;
Possible numbers includes; 11 and 101
By trying the possible numbers, the difference found is presented as follows;
99 × 11 = 1089 (The first and the last digit are not the same as the multiplier)
99 × 101 = 9999 (First and last digit are not the same as the multiplier)90 × 11 = 990
90 × 101 = 9090
The correct option is therefore 101
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Which of the following lines is parallel to the given line?
Answer:
y=10x
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula
y−y1=m(x−x1) to find the line parallel to y=10x−45
.
Guided Practice
Cans of Soup
Number of Servings
1
4
2
8
3
12
4
16
Write a function rule for the table.
A.
s = 4c
B.
c = 4s
C.
s = c + 4
D.
c = 4 + s
The function rule for the table is A. s = 4c
How to depict the function?From the table, it can be seen that when the cans of soup is 1, the number of serving is 4. Also, when it's 2, the number or servings is 8.
This implies that:
4/1 = 8/2
= 4.
Therefore, the function rule for the table is s = 4c
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PLEASE HELP
Select the correct answer.
Which statement is true about this function for all values of x<4
A) The function is negative
B) The function is decreasing
C) The function is positive
D) the function is increasing
Answer: B) The function is decreasing
Step-by-step explanation:
As x increases, y decreases.
1) The dimensions of an irregular solid are as shown in the figure below.
a) Write a polynomial function, in standard form, to model the volume of this solid.
b) If the volume of the solid is 208 cubic inches, what is the value of x?
Hello,
a) Volume of the figure = Volume of light blue rectangular parallelepiped - volume of dark blue rectangular parallelepiped
Volume of rectangular parallelepiped = lengh × high × height
Volume of light blue rectangular parallelepiped :
V = (x + 2) × (x + 5) × (2x + 1)
V = (x² + 5x + 2x + 10) × (2x + 1)
V = (x² + 7x + 10) × (2x + 1)
V = 2x³ + 15x² + 27x + 10
Volume of dark blue rectangular parallelepiped :
V = x × 3 × (x + 5)
V = 3x(x + 5)
V = 3x² + 15x
Polynomial function, in standard form, to model the volume of this solid :
V = 2x³ + 15x² + 27x + 10 - (3x² + 15x)
V = 2x³ + 15x² - 3x² + 27x - 15x + 10
V = 2x³ + 12x² + 12x + 10
b) We have to solve 2x³ + 12x² + 12x + 10 = 208
⇔ 2x³ + 12x² + 12x - 198 = 0
⇔ 2(x - 3)(x² + 9x + 33) = 0
⇔ x = 3 or x² + 9x + 33 = 0
a = 1 ; b = 9 ; c = 33
Δ = b² - 4ac = 9² - 4 × 1 × 33 = -51 < 0 ⇔ Δ < 0 ⇒ no solution
So if the volume of the solid is 208 cubic inches, the value of x is 3
HELLP HEELEP SOS EMERGENCY
Answer:
15 in.
Step-by-step explanation:
P = 2(L + W)
36 = 2(L + 3)
18 = L + 3
L = 15
Answer:
Hello! The answer is 15 in.
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2l + 2w. We can substitute our w-value since it's provided for us:
2l + 2(3) = 36
Now, we can solve the equation:
2l + 6 = 36
-6. -6
----------------
2l = 30
-- --
2 2
l = 15 in
Given that
y=1/27x^3
express each of the following in the form kx^n where k and n are constants.
(a) y^1/3
(b) 3y^-1
(c) √(27y)
Express the following in the form kx^n where k and n are constants.
(a) y=x^3
(b)y=3x^-1
(c) y=x^3/27
To express each of the following in the form kx^n where k and n are constants.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given that:
y=1/27x^3
express each of the following in the form kx^n where k and n are constants.
(a) y^1/3
Let y^1/3=x
by cubing both sides we get,
y=x^3
The equation in the form of kx^n
where,
k=1
n=3
(b) 3y^-1
Let 3y^-1=x
3/y=x
y=3/x
By simplify
y=3x^-1
The equation in the form of kx^n
where,
k=3
n=-1
(c) √(27y)
Let (27y)^1/3=x
by cubing both sides we get,
27y=x^3
y=x^3/27
The equation in the form of kx^n
where,
k=1/27
n=3
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What is the y-intercept of the graph that is shown below?
On a coordinate plane, a line goes through points (negative 2, 0) and (4, 0).
(–2, 0)
(–1, 2)
(0, 4)
(4, 0)
Answer:
0,4
Step-by-step explanation:
X is 0 and Y is 4 it'll be touching the vertical line
Answer:
0,4
Step-by-step explanation:
Adriana and Sophie have summer jobs selling newspaper subscriptions door-to-door, but their
compensation plans are different. Adriana earns a base wage of $6 per hour, as well as $2 for
every subscription that she sells. Sophie gets $3 per subscription sold, in addition to a base
wage of $4 per hour. If they each sell a certain number of subscriptions in an hour, they will
end up earning the same amount. How much would each one earn?
Write a system of equations, graph them, and type the solution.
Answer:
The each have to place 2 subscriptions
Step-by-step explanation:
Adriana
E (earnings) = 6 + 2*x where x is the number of subscriptions
Sophie
E (earnings) = 4 + 3x
For them to earn the same amount, their right sides must be equated.
4 + 3x = 6 + 2x Subtract 2x from both sides
4 + 3x - 2x = 6+ 2x - 2x Combine
4 + x = 6 Subtract 4 from both sides
4 - 4 + x = 6 - 4
x = 2
if p is a prine number greater than 5 and q is an odd number greater than 5 whihc of the following is true
The first statement p + q is not a prime number is a true option (A) correct.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
First statement:
p + q is not a prime number.
Let p = 7
q = 9
= 7 + 9 = 16 (16 is not a prime)
= 7×9 = 63 (no factor of 63)
p = 7, q = 7
q/p = 7/7 = 1 (1 is integer)
Thus, the first statement p + q is not a prime number is a true option (A) correct.
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Geometry question I need help with true of false
Answer:
RS = 12 False
x=4 True
x=3 False
QT=16 True
Step-by-step explanation:
A measure of the strength of the relationship between two variables is referred to as the.
A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.
What is the correlation coefficient?Correlation coefficients are used to evaluate the strength of the linear relationship between two variables.
When the correlation coefficient value is less than zero, it indicates a bad association, while a number higher than zero indicates a good relationship.
There is no correlation between the two variables being compared, as shown by a correlation coefficient of zero.
The idea of a negative correlation, also referred to as an inverse correlation, is essential to the construction of diversified portfolios that may be better able to withstand portfolio volatility.
It is often done by entering data into a calculator, computer, or statistics application because computing the correlation coefficient requires time.
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The purpose of statistical inference is to make estimates or draw conclusions about a _____. a. population based upon information obtained from the sample b. mean of the sample based upon the mean of the population c. sample based upon information obtained from the population d. statistic based upon information obtained from the population
a)The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.
Statistical inference is the process of drawing conclusions about populations or scientific truths from data. There are many ways to make inferences, including statistical modeling, data-driven strategies, and the explicit use of designs and randomization in analyses.
Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or population probability distribution.
First, a preliminary assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted H0.
An alternative hypothesis (denoted Ha) is then defined, which is the opposite of what is stated in the null hypothesis. The hypothesis testing procedure involves using sample data to determine whether or not H0 can be rejected. If H0 is rejected, the statistical conclusion is that the alternative hypothesis Ha is true.
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Question 3 (Essay Worth 10 points)
(05.07 MC)
The scatter plot shows the number of strawberries that have been picked on the farm during the month of February:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Strawberries and the x axis is labeled Days in February
Part A: Using computer software, a correlation coefficient of r = 0.01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm. (5
It's not an accurate value for the data based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means practically no correlation, while the points on the graph are moderately correlated
How to illustrate the information?1. Part A:
Since the points in the scatter plot shows a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.
The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to 1.
Here, r = - 1 is a perfect negative correlation as the points will adjust perfectly to a line with a negative slope.
r = + 1 is a perfect positive correlation: the points will adjust perfectly to a line with a positive slope.
r = 0 means that the variables are not correlated at all.
Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows another thing.
Therefore, the calculated value of r = 0.01 is not accurate for this scatter plot.
2. Part B.
A causal relationship means that the explanatory variable (the independent variable) is the cause of the dependent variable.
Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.
Thus, the scenario could be:
Amount of rainfall in mm (x) Number of strawberries picked (y)
100 20
50 40
25 80
12.5 160
6.25 320
The amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.
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A certain big company classifies its employees according to gender, age-group (6 categories) and employment type (10 categories). How many classifications are there
We don’t know the number of employees remaining at the company.
We don’t know the total number of employees remaining at the company.
The classification consists of gender, division, and employment type.
It doesn’t matter what order those attributes come in. A person who is male, age group 6, and employment type 10 has the same classification as someone who is of employment type 6, male, and age group10.
Therefore since order does not matter it is a combination question.
Assuming only two genders are allowed (you didn’t say and some people think there are about 10 of them)
It is either 120 (2 times 6 times 10) or "None of the above" if you believe there are more than 2 genders.
2×6×10=120
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Convert the degree measurement to radians. Express answer as multiple of π: 126°
Answer:
.7 pi Radians
Step-by-step explanation:
There are pi radians in a 180 degrees :
pi / 180 * 126 = .7 pi Radians
Answer:
[tex]\frac{7}{10} \pi[/tex] or 0.7π radians
Explanation:
For converting degree to radians, multiply by π/180
Here given:
126°Conversion:
126° × π/180 = [tex]\frac{7}{10} \pi[/tex] or 0.7π
Similarly (additional),
1) 100° = 100 × π/180 = [tex]\frac{5}{9} \pi[/tex]
2) 320° = 320 × π/180 = [tex]\frac{16}{9} \pi[/tex]
I need a helping hand!
Answer:
x = 145°
Step-by-step explanation:
x and 35° are a linear pair and sum to 180° , that is
x + 35° = 180° (subtract 35° from both sides )
x = 145°
By rounding each number to 1 significant figure,
estimate the answers to:
a)763 x 42
_______
82
b)39 × 52
_______
3.8 x 4.9
Answer:
see explanation
Step-by-step explanation:
rounding each number to 1 significant figure
(a)
763 × 42
≈ 800 × 40
= 32000
(b)
39 × 52
≈ 40 × 50
= 2000
(c)
3.8 × 4.9
≈ 4 × 5
= 20
A dilation is a nonrigid transformation that can produce enlarged or reduced images from a given pre-image. How do you know that a dilation will produce similar figures? Explain
The dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
What is dilation?It should be noted that dilation simply means a transformation to resize an object
In this case, the dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
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Answer:
The dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
Step-by-step explanation:
Write an equation for the nth term of the given arithmetic sequence. 7, 13, 19, 25
Hello,
U (n +1) = Un + 6
Un = Uo + nr
U9 = 7 + 9 × 6 = 7 + 54 = 61
Answer:
nth term = 6n + 1.
Step-by-step explanation:
The first term a1 = 7 and the common difference d = 6.
nth term = a + d(n - 1)
= 7 + 6(n - 1)
= 6n + 1.