Answer: [tex](r,\theta) = \left(\sqrt{6}, \frac{\pi}{4}\right)[/tex]
In other words, [tex]r = \sqrt{6} \ \text{ and } \ \theta = \frac{\pi}{4}[/tex] where theta is in radians.
=====================================================
Work Shown:
[tex](\text{x},\text{y}) = (\sqrt{3},\sqrt{3})\\\\r = \sqrt{\text{x}^2+\text{y}^2}\\\\r = \sqrt{(\sqrt{3})^2+(\sqrt{3})^2}\\\\r = \sqrt{3+3}\\\\r = \sqrt{6}\\\\[/tex]
and,
[tex]\theta = \tan^{-1}\left(\frac{\text{y}}{\text{x}}\right)\\\\\theta = \tan^{-1}\left(\frac{\sqrt{3}}{\sqrt{3}}\right)\\\\\theta = \tan^{-1}\left(1\right)\\\\\theta = \frac{\pi}{4} \text{ radians}\\\\[/tex]
Use a calculator or the unit circle to arrive at the last step. Keep in mind that (√3, √3) is in the first quadrant where [tex]0 < \theta < \frac{\pi}{2}[/tex] since both x and y are positive.
Right triangle DEF is shown below.What is DF to the nearest tenth of a meter?
Answer: 25.1º
Explanation
As the given triangle is a right triangle, we can use trigonometric functions to find DF, specifically:
[tex]\cos x=\frac{adjacent}{hypotenuse}[/tex]where the adjacent is the side adjacent to our angle and the hypotenuse is the longest side (side opposite to the 90º angle).
Based on this, we can replace the values as follows:
[tex]\cos(23\degree)=\frac{DF}{27.3}[/tex]Solving for DF:
[tex]DF=27.3\cdot\cos(23\degree)[/tex][tex]DF=27.3\cdot\cos(23\degree)[/tex][tex]DF\approx25.1[/tex]Find the value of x.
Check the picture below.
solve . -9 2/7 - (-10 3/7)
Answer: 8/7 is your answer
Step-by-step explanation:
Answer:
Exact Form:
8/7
Decimal Form:
1.42857
Mixed Number Form:
1 1/7
glad i could hep
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
If (a) (b) = 0 then a = 0 and b = 0 or a = b = 0. This states what law? Answer:
Answer: Zero Product Property
Step-by-step explanation:
Answer:
Well, am not sure if am correct, if a = 0 and if b = 0, then both terms have the same value. The law this equation ab = 0 is following is called Zero Product Property.
Step-by-step explanation:
a x b
Suppose a x b = 0
Then either a = 0 or b = 0
so these are the two possible cases.
1. 0 x b = 0
2. a x 0 = 0
Therefore, the product of the a and b is equal to zero when a is equal to zero or b is equal to zero. This rule is the zero product property.
A line passes through the points (7, 10) and (7, 20). What is true about the slope of the line? *
The slope of the line is indefinite (∞). Also, the line will be parallel to the x-axis.
It is given in the question that a line passes through the points (7, 10) and (7, 20).
We have to find the slope of the line.
We know that,
Slope of a line with coordinates (a,b) and (c,d) is given by:-
(d - b)/( c - a)
Here,
a = 7,
b = 10,
c = 7 and,
d = 20
Hence, we can write,
Slope of the line = (20 - 10)/( 7 - 7) = 10/0 = ∞.
Hence, the slope of the line is indefinite.
Here, as the x -coordinate of both the points are same, this line will be parallel to the x - axis.
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The elevation of Desert Shores, California, is less that -55 meters. Which of the following best describes Desert Shores.
A. Desert Shores is lower than 55 meters below sea level.
B. Desert Showers is lower that 55 meters above sea level
C. Desert Shores is higher than 55 meters below sea level.
D. Desert Shores is higher than 55 meters above sea level.
The option that best describes the elevation of Desert Shores is; A. Desert Shores is lower than 55 meters below sea level.
What is the Elevation below sea level?We are told that the elevation of Desert Shores, California, is less than -55 meters.
Now, an elevation of a natural landmass like this is usually given with reference to the sea level. If above sea level, it is positive but if below sea level, it is negative.
Now, the elevation is negative as we can see that it is given as -55 meters. Thus, we can easily conclude that Desert Shores is lower than 55 meters below sea level.
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A citizen wants to propose to the city council extending the hours at the local public library on some weekdays. To measure support for extended hours, the citizen visits neighborhood homes and asks adults the following: "Would you agree that the closing time of the library should be extended by one hour on weekdays to accommodate working families?” Of the 212 adults surveyed, 86% agreed with the statement. Which of the following statements about the results is true?
(A)The 86% support provides substantial evidence that the library hours should be extended.
(B)More families should be asked the same question to be sure of community support.
(C)The survey suffers from question wording bias and may not represent true support for the extended hours.
(D)The survey suffers from voluntary response bias and may not estimate true support for the extended hours
The true statement about the result is that D. The survey suffers from voluntary response bias and may not estimate true support for the extended hours
How to illustrate the information?From the information, in order to measure support for extended hours, the citizen visits neighborhood homes and asks adults the research question.
This illustrates bias as the citizen wants to propose to the city council extending the hours at the local public library on some weekdays.
Therefore, the true support may not be illustrated. In conclusion, the correct option is D.
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Simplifying a Rational Expression Simplify (a ^ 2 * b ^ 8)/(a ^ 2 * b ^ 3 - a ^ 4 * b ^ 2); (a * b ^ 2)/(1 - a ^ 4 * b ^ 2); (a ^ 3 * b ^ 8)/(a ^ 2 * b ^ 2 * (b - a ^ 2)); b/(1 - a); (a * b ^ 4)/(b - a ^ 2)
Answer:
ab^4/b-a^2
Step-by-step explanation:
...........
Lynn writes this problem:
315 divided by 1700
Which expressions represent Lynn's problem?
Select each correct answer.
Responses
3151700
315 over 1700
3151700
315 long division enclose 1700
1700 ÷ 315
1700 ÷ 315
1700315
1700 long division enclose 315
315 ÷ 1700
315 ÷ 1700
1700315
1700 over 315
Answer:
315 over 1700
1700 long division enclose 315
315 ÷ 1700
Step-by-step explanation:
315 divided by 1700 can be written in each of the three ways listed above.
Angle C is an acute angle with sec C = 9/4 and sin C =
√65/9. What are the values of cos C and csc C?
From trigonometric ratios we calculate the value of the cos C is 4/9 and the value of cosec C is 9/√65 .
Real functions known as trigonometric functions in mathematics connect right-angled triangle angles and the ratios of their two side lengths.
The terms trigonometric functions, circular functions, and angle functions are also used to describe them. Trigonometric functions are frequently employed in all fields of study involving geometry, including geodesy, solid mechanics, celestial mechanics, and many more. Given that one of the most fundamental periodic functions is the Fourier transform, it is frequently employed to examine periodic phenomena.Sine, cosine, and tangent are the three trigonometric functions that are employed in modern mathematics the most frequently. The less common cotangent, secant, and cosecant are their reciprocals. The hyperbolic functions and their corresponding inverse functions have analogues for each of these six trigonometric functions.We know that sec C = 1/cos C
Hence the value of cos C = 4/9 .
Again we know that the value of sin C=1/cosec c
Therefore the value of cosec C is 9/√65 .
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Please show work
I will mark brainliest
As a result, the value of x is 20. Vertically opposite angles are formed by two straight intersecting lines that are opposite one another at a specific vertex.
What is vertical opposite angle?Vertically opposite angles are formed by two straight intersecting lines that are opposite one another at a specific vertex. Angles that are vertically opposite each other are equal. These are sometimes referred to as vertical angles.Here to find y,
∠A = ∠B ( vertically opposite angles are equal ).
5y - 8 = 42
5y = 42 +8
5y = 50
y = 10
To find ∠A,
∠ A = 5y - 8
= 5 x 10 - 8
= 50 -8
= 42°.
we know that angle on a straight line is 180°.
So , ∠A + ∠C = 180°
42 + ∠C = 180°
∠C = 180 - 42
∠ C = 138°.
Since ∠C = ∠D (vertically opposite angle ).
∠D = 138°
As a result, the value of x is 20.
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Mariam wants to buy strawberries and apples to
make a fruit tart. Strawberries cost $3 per pound
and apples cost $3.25 per pound. How many pounds
of fruit does she buy if she buys 0.5 pounds of
strawberries and 3 pounds of apples? How many
pounds of fruit does she buy if she buys x pounds of
strawberries and y pounds of apples?
Answer:
Answer bellow with explanations
Step-by-step explanation:
if Miriam buys 0.5 pounds of strawberries and 3 pounds of apples she will in total would have bought 3.5 pounds of fruit.
if you are looking for the price she had to pay for the fruits above the equation to solve that is as following.
0.5 x 3$ = 1.5$
3.0 x 3.25 = 9.75$
total for the fruits needed above would be 1.5$ + 9.75$ = 11.25$
if you are looking for the amount of pounds converted into the amount of fruit
0.5/3$ = 0.16(6) pounds of strawberries
3/3.25$= 0.92307692307 pounds of apples
total of pounds of fruit that have been purchased is equal to 0.16(6) + 0.92307692307 = 1.08974358973 pounds
If Miriam buys x pounds of strawberries and y pounds of apples
it can be shown in an equation using 2 unknown values
X(strawberries)
Y(apples)
x/3$ + y/3.25$
to calculate the amount of pounds that have been purchased
Ver en españolWhat is the area?5 in5 in square inches
From the question, we are asked to find the area.
Since all the sides of the figure are the same, then it is a square.
So we will be using the area of a square formula to solve it.
Formula for area of a square is:
Area = a x a = a²
a = 5 in
So,
Area = 5 x 5 = 5² = 25
Therefore, the area of the square is 25 in²
20) A gas station charges $4.09 for a gallon of premium unleaded. The gas station charges
$.20 less per gallon of gasoline if a customer also gets a car wash. A car wash cost $10.
Write an inequality and solve to find the possible amounts (in gallons round to the nearest
hundredth) of gasoline that you can buy if you also get a car wash and can spend at most
$30?
He can buy $100 of gasoline that you can buy if you also get a car wash and can spend at most $30.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
Given Data
The gas station charges $0.20 less per gallon of gasoline if a customer also gets a car wash. A car wash cost $10.
Inequality-
$0.2x + $10 = $30
0.2x = $20
x = 100
He can buy $100 of gasoline that you can buy if you also get a car wash and can spend at most $30.
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Represent the system with a matrix.
2x+3y+5z=9
-x+4z=10
-6x+z-12=y
The given system of equations represented as a matrix is
[tex]\left[\begin{array}{ccc}2&3&5\\-1&0&4\\-6&-1&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}9\\10\\12\end{array}\right][/tex]
Representing system of linear equations with a matrixFrom the question, we are to represent the given system of linear equations with a matrix.
The given system of equations is
2x + 3y + 5z = 9
-x + 4z = 10
-6x + z -12 = y
First, we will write the third equation in standard form
-6x + z -12 = y
This becomes
-6x - y + z = 12
Thus,
The system of equations becomes
2x + 3y + 5z = 9
-x + 4z = 10
-6x - y + z = 12
Thus,
The system of equations can be written as a matrix as shown below
[tex]\left[\begin{array}{ccc}2&3&5\\-1&0&4\\-6&-1&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}9\\10\\12\end{array}\right][/tex]
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Please help with finding the approximate mean pretty easy 7th grade math.
2/3 ÷ 4/9 What is the answer.
Answer:
3/2Step-by-step explanation:
2/3 ÷ 4/9 What is the answer?
2/3 : 4/9 =
2/3 * 9/4 =
3/2
2(64x² - 25) (x² + 49) = 0
Answer:
[tex]x=-7i, 7i, 5/8, -5/8[/tex]
Step-by-step explanation:
[tex](64x^2-25)(x^2+49)=0 \\ \\ (8x-5)(8x+5)(x+7i)(x-7i)=0 \\ \\ x=-7i, 7i, 5/8, -5/8[/tex]
What is the area of a quadrilateral with vertices at (-2,-6),
(1,6), (-2,0), and (1,0)? Enter the answer in the box.
units squared
Check the picture below.
so the quadrilateral is really two triangles, each with a base of 3 and a height of 6
[tex]\stackrel{\textit{area of the two triangles}}{2\left[ \cfrac{1}{2}(\underset{b}{3})(\underset{h}{6}) \right]\implies 2(9)\implies} \text{\LARGE 18}[/tex]
WELL GIVE U BRAINLIEST ASAP
Drag the numbers to order them from least to greatest.
Answer:
3/5 is the smallest, 7/9 is in the middle and 5/6 is the biggest
Step-by-step explanation:
Brainlest, Please!
Answer: 3/5 is first, 7/9 is second, and 5/6 is last.
Please answer with if the slope is positive or negative and what the slope is.
Answer:negative slope, slope=-3/5
Step-by-step explanation:
To find slope:
Rise/Run
Rise/Run: down 3 left 5 so -3/5
I think I got this right is it right ?
Answer:
1. Correct
2. Incorrect
3. Correct
4. Correct
5. Incorrect
Step-by-step explanation:
For the ones you got wrong:
1 / (-3)² = 1/9
and
[tex]3^{-2}[/tex] = 1/9
Answer:
First one is correct
Second one is 1/9
Third one is -1/9
Fourth one is 1/9
Fifth one is 1/9
Step-by-step explanation:
Second one -
Use the rules of exponents to simplify the expression;To raise a power to another power multiply the exponents(-3)^2(-1)Multiply 2 times -1(-3)^2Raise -3 to the power of -2 1/9Third one - Calculate 3 to the power of -2 to get -1/9Fourth one - Calculate -3 to the power of -2 to get 1/9Fifth one - calculate 3 to the power of -2 to get
1/9
The Good Ole Times magazine charges for ads by the "column inch." A column inch is as wide as one column, and it is one inch high. The cost is $67 per column inch. How much would the magazine charge to print a 2 ½-inch ad?
Cost of the ad is $167.5
What is cost?
A cost is the worth of money that has been used up to create something or supply a service and is thus no longer accessible for use in production, research, retail, or accounting. In business, the cost might be one of acquisition, in which case the money spent to obtain it is recognized as cost. In this situation, money is the input that is used to purchase the item. This acquisition cost might be the total of the original producer's production expenses and the acquirer's additional transaction costs over and above the amount paid to the producer. Typically, the price includes a profit margin above the cost of manufacture.
The cost of the ad per column inch = $67
So, the cost of 2¹/₂ inch = 67 x 2¹/₂ = $167.5
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what is the answer to -3(x+4)=-6x+18
Answer:x=10
Step-by-step explanation:
1. Simplify both sides of the equation. -3(x+4)=-6x+18 to -3x - 12=-6x + 18
2. Add 6x to both sides. -3x - 12=-6x + 18 to -3x - 12 + 6x=-6x + 18 +6x which would equal to 3x - 12=18
3. Add 12 to both sides. 3x - 12 + 12=18 + 12.
4. Divide both sides by 3. 3x/3=30/3 which equals x=10.
Solve for x. 9 + x/2=14 x=
please help see picture above^^ thank you
From the calculations, we could obtain the maximum speed of the car as 72.6 miles/hr.
What is proportionality?The term proportionality gives us an idea of the nature of the relationship that does exist between the variables in a given situation. The proportionality could be;
1) Direct
2) Inverse
3) Joint
Given that the stopping distance (D) varies directly as the speed (S), we could say;
D α S
Introducing the constant k
D = kS
k = D/S
k = 0.027 miles/40 mile/hr
k = 6.75 * 10^-4 hours
Maximum speed = D/k
= 0.049 miles/ 6.75 * 10^-4 hours
= 72.6 miles/hr
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Which lines are parallel if m<5 =m<6? Need answers right now
○ line p is parallel to line q ; converse of alternate interior angles theorem
○ line p is parallel to line q ; converse of corresponding angles postulate
○ line l is parallel to line m; converse of corresponding angles postulate
○ line p is parallel to line q; converse of same side interior angles theorem
Answer:
line I is parallel toM to know how you got follow me and ask the the question
Explanation:
Erase line L since we won't be using it. Erase every angle but angle 5 and angle 6.
If angle 5 and angle 6 are congruent, then we can use the converse of the corresponding angles postulate to show that lines p and q are parallel.
Angle 5 and angle 6 are corresponding angles since they are both in the same northeast corner, i.e. they're both in the same corresponding position so to speak.
Can someone please help me with this geometry question
Triangles 2, 4, 6, 8, 9, 10, 12, 14, and 15 are not translations of triangle 1.
What is translation?In mathematics, a translation is an up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered. There is no change in the shape because it is simply being moved from one location to another.
The object may move left at first, then right, and so forth. The object's position can change, as well as the manner in which it does so. Each point on the shape will move by the same number of units during translation.
Therefore, triangles 2, 4, 6, 8, 9, 10, 12, 14, and 15 are not translations of triangle 1.
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Q3. If the sum of three consecutive odd number is 81, find the numbers.
Answer:
25, 27, 29Step-by-step explanation:
If the sum of three consecutive odd number is 81, find the numbers.
remove from 81 the difference between the numbers (2 + 2 + 2) divide by three and find the first, add 2 and find the second, to the result add 2 again and you have the third number(81 - 6) : 3 = 25
25 + 2 = 27
27 + 2 = 29
--------------------------
check
25+27+29=81
the answer is good
24 and 27 are vertical angles.
Select Choice the angles are Select Choice and are formed by two Select Choice lines.
Yes/no
Adjacent/non adjacent
Parallel/intersecting
Yes they are vertical angles, the angles are nonadjacent and are formed by intersecting lines.
What are Vertical Angles?When two lines that are straight intersect with each other, they form two pairs of opposite angles that are called vertical angles.
Vertical angles share a common vertex both no common sides and are therefore referred to as non-adjacent angles.
Thus, the image shows that lines intersect to form angle 4 and angle 7.
Angle 4 and angle 7 share a common vertex but do not share a common side, hence they are nonadjacent to each other, as shown in the diagram.
We can conclude that they are vertical angles because they are nonadjacent and are formed by intersecting lines.
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