[tex]\text{Given that,}\\\\\cos \theta = - \dfrac 23\\\\\implies \cos^2 \theta = \dfrac 49\\\\\implies 1- \sin^2 \theta = \dfrac 49\\\\\implies \sin^2 \theta =1-\dfrac 49\\\\\implies \sin^2 \theta =\dfrac 59\\\\\\\text{Now,}\\\\\cot^2 \theta = \dfrac{\cos^2 \theta}{\sin^2 \theta} \\\\\\\implies \cot^2 \theta = \dfrac{\tfrac 49}{\tfrac 59}\\\\\\\implies \cot^2 \theta = \dfrac 49 \times \dfrac 95\\\\\\\implies \cot^2 \theta = \dfrac 45\\\\\\[/tex]
[tex]\implies \cot \theta = \pm\sqrt{\dfrac 45} = \pm \dfrac 2{\sqrt 5}\\\\\\\text{Since}~ \theta ~ \text{lies in the second quadrant,} \cot \theta ~\text{will be negative.}\\\\\text{Hence,}~ \cot \theta = - \dfrac{2}{\sqrt 5}[/tex]
Answer:
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Solve.
−4/15x=1.44
Enter your answer as a mixed number in simplest form in the box.
x =
1 Simplify \frac{4}{15}x
15
4
x to \frac{4x}{15}
15
4x \frac{4x}{15}=1.44
4x =1.44
2 Multiply both sides by 1515.
4x=1.44\times 15
4x=1.44×15
3 Simplify 1.44\times 151.44×15 to 21.621.6.
4x=21.6
4x=21.6
4 Divide both sides by 44.
x=\frac{21.6}{4}
x= 4
21.65 Simplify \frac{21.6}{4} 421.6 to 5.45.4.
x=5.4
x=5.4
The value of x for the given equation in the mixed fraction will be -4 7/5.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.]
It is given that,−4/15x=1.44
Solve the equation for x,
x= -1.44 × 15/4
Convert the decimal values into the fraction as
x=-144/100 × 15/4
x= -27/5
A mixed number is one that includes both a correct fraction and a full number. Convert the given number into the mixed number as
x=-4 7/5.
Thus, the value of x for the given equation in the mixed fraction will be -4 7/5.
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this question
please help please
m=n+4b
Answer:
m=n+4b:- b=m-n/4.........
how to find the circumcenter of a triangle with given vertices
Answer:
What is the formula of area of Circumcircle?
Image result
We know that area of circle = π*r2, where r is the radius of given circle. We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3. Therefore, area = π*r2 = π*a2/3.
Step-by-step explanation:
What is the value of the expression when h = 5? h + 7
Answer:
12
Step-by-step explanation:
if h=5
then h+7 = 5+7 = 12
[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]
[tex]\implies\sf{h + 7} \\ \\ \implies\sf{5 + 7} \\ \\ \implies\sf{12}[/tex]
what is the answer to this question 1.6x + 30
Please help me Find the slope and please help me no links or bots please and thank you please actually help
Answer: slope for that is 1/2
Step-by-step explanation: rise over run y2-y1 x2-x1
A laser printer prints 9 pages per minute. Martha refilled the paper tray after it had printed 92 pages. In how many more minutes will there be a total of 245 pages printed?
17 minutes
hope this helps!
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY. A wire is needed to support a vertical pole 8 feet tall. The cable will be anchored to a stake 6 feet from the base of the pole. How much cable is needed?
Answer: The answer is 10 feet of cable.
What is the value of y in the formula show when x=4/5
Answer:
there is no way to solve for y, but if your solving for x then x=4/5 and in decimal form it is x=0.8 hope that helps
Step-by-step explanation:
what is 2 2/3 - (-3 2/6)
Answer:
6
Step-by-step explanation:
Find the y-intercept of the line: x + 4y + 8 = 0
Answer:
(0,-2)
Step-by-step explanation:
Use a Quadratic formula to solve for X
3x^2+9x=-4
Round to the nearest hundreth.
Order the side lengths from least to greatest.
Answer:
38, 40, and 102
Step-by-step explanation:
when we take a look at this problem which looks the smallest to you? 38! so then whe look again and which looks the second smallest..? 40. so then we are left with 102 which is the biggest number. Therefore your answer is 38, 40, and 102
hellp meeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
yasss its C
12 A train in France can travel at a speed
of 217.4 miles per hour. A train in
China can travel 1.23 times this speed.
How fast can the train in China travel
in miles per hour?
I WILL MARK YOU AS BRAINIEST IF YOU ANSWER THIS QUESTION WITH AN ANSWER AND EXPLANATION + 100 points
Answer: 267.402
Step-by-step explanation:
The answer is 267.402 because 217.4 times 1.23 = 267.402.
Answer:
267 mph
Step-by-step explanation:
Multiplication
i hope this helps have a great day :)
In a solid cube made up of smaller black and white cubes. The black and white cubes are at alternate places of the larger cube. How many black cubes are there in the above arrangement?
There are 168 black cubes in the arranagement.
A cube has 6 faces. Each face of the cube consists of 25 white cubes and 24 black cubes.
To get the number of black cubes in the arrangement, we will use the equation below;
Number of black cubes = Total number of black cubes on a face * number of small cubes along the edgeNumber of black cubes = 24 * 7Number of black cubes = 168Hence there are 168 black cubes in the arrangement.
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If (6^2]^p = 6^10, what is the value of p?
A.) 2
B.) 3
C.) 4
D.) 5
NEED HELP PLZ HELP ME ….
Answer:
R= -0.95
Step-by-step explanation:
HOPE THIS HELPS :)
The scale model of a building is 8.5 inches tall. How tall is the actual building if the scale
used for the model is 1 inch = 150 feet?
Answer:
1,275
Step-by-step explanation:
Answer:
1275
Step-by-step explanation:
you do 8.5 multiplied by 150
Find x, given the slope is -2. (x,-6) (-6,10)
Answer:
x= 2
Step-by-step explanation:
[tex]\boxed{slope = \frac{y _{1} - y_2}{x_1 - x_2} }[/tex]
Substitute known values into the formula:
[tex] - 2 = \frac{ - 6 - 10}{x - ( - 6)} [/tex]
[tex] - 2 = \frac{ - 16}{x + 6} [/tex]
-2(x +6)= -16
Divide both sides by -2:
x +6= -16 ÷(-2)
x +6= 8
Subtract both sides by 6:
x= 8 -6
x= 2
A girl goes on an epic 9-hour snowshoeing truck, and her velocity time graph is shown below, with velocity shown in miles per hour and time shown in hours.
A. When is her velocity at its maximum? What is that maximum velocity?
B. How far did she travel during the first 3 hours?
C. How far does she travel during her entire hike?
D. What is her average velocity during the hike?
a) She reaches a velocity of 4 miles per hour at [tex]t = 5\,h[/tex].
b) The girl travels a distance of 6 miles in the first 3 hours.
c) The girl travels a distance of approximately 22.283 miles during her entire hike.
d) The average velocity of the girl is approximately 2.476 miles per hour.
a) The maximum velocity represent the maximum value in the vertical axis reached by the girl in time. According to the graph, she reaches a velocity of 4 miles per hour at [tex]t = 5\,h[/tex].
b) Travelled distance is represented graphically by the area below the curve and above the time axis. The travelled distance ([tex]\Delta x[/tex]), in miles, during the first 3 hours is represented by the area of a rectangle, that is to say:
[tex]\Delta x = v(3)\cdot \Delta t[/tex] (1)
Where:
[tex]\Delta t[/tex] - Time interval, in hours.[tex]v(3)[/tex] - Final velocity, in miles per hour.If we know that [tex]\Delta t = 3[/tex] and [tex]v(3) = 2[/tex], then the travelled distance in the first 3 hours is:
[tex]\Delta x = (2)\cdot (3)[/tex]
[tex]\Delta x = 6\,mi[/tex]
The girl travels a distance of 6 miles in the first 3 hours.
c) The travelled distance is determined by the following geometric expression:
[tex]\Delta x = v(3)\cdot t_{1} + 0.5\pi\cdot [v(5)-v(3)]^{2}+0.5\cdot v(3)\cdot (t_{2}-t_{1})[/tex] (2)
If we know that [tex]v(3) = 2[/tex], [tex]t_{1} = 7[/tex], [tex]v(5) = 4[/tex] and [tex]t_{2} = 9[/tex], then the travelled distance is:
[tex]\Delta x = 2\cdot 7 + 0.5\pi\cdot (4-2)^{2}+0.5\cdot 2\cdot (9-7)[/tex]
[tex]\Delta x \approx 22.283\,mi[/tex]
The girl travels a distance of approximately 22.283 miles during her entire hike.
d) The average velocity ([tex]\bar v[/tex]), in miles per hour, is obtained by dividing the traveled distance ([tex]\Delta x[/tex]), in miles, found in c) by time.
[tex]\bar v = \frac{\Delta x}{\Delta t}[/tex] (3)
If we know that [tex]\Delta x \approx 22.283[/tex] and [tex]\Delta t = 9[/tex], then the average velocity of the girl is:
[tex]\bar v = \frac{22.283}{9}[/tex]
[tex]\bar v \approx 2.476\,\frac{mi}{h}[/tex]
The average velocity of the girl is approximately 2.476 miles per hour.
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Describe the possible length of the third side of the triangle given that the links of the other two sides of 5 inches and 12 inches
___in.
Answer:
60
Step-by-step explanation:
your welcome
Find the 12th term of the geometric sequence.
15, 30, 60, ...
Answer:
465
Step-by-step explanation:
The way I thought about it was I subtracted 30 from 15 and got 15. Then I subtracted 60 from 30 and got 20. My conclusion is you continue to add 5 more to what you added before. 15, 30, 60, 85, 115, 150, 190, 235, 285, 340, 400, 465.
if one rents a car from Airport Rent-a-Car, the charge is $79 plus 7 cents a kilometer. Savings Rent-A-Car charges $59 plus 9 cents a kilometer. If one will drive d kilometers, when is it cheaper to use Savings Rent-A-Car?
It will be cheaper to use Savings Rent-A-Car up to 1000 kilometers, from then on it will be cheaper to use Airport Rent-a-Car.
Given that if one rents a car from Airport Rent-a-Car, the charge is $ 79 plus 7 cents a kilometer, while Savings Rent-A-Car charges $ 59 plus 9 cents a kilometer, to determine, if one will drive D kilometers , when it is cheaper to use Savings Rent-A-Car, the following calculation must be performed:
79 + 0.07 x 30 = 79 + 2.1 = 81.1 59 + 0.09 x 30 = 59 + 2.7 = 61.7 79 + 0.07 x 300 = 100 59 + 0.09 x 300 = 86 79 + 0.07 x 600 = 121 59 + 0.09 x 600 = 113 79 + 0.07 x 900 = 142 59 + 0.09 x 900 = 140 79 + 0.07 x 1000 = 149 59 + 0.09 x 1000 = 149
Therefore, it will be cheaper to use Savings Rent-A-Car up to 1000 kilometers, from then on it will be cheaper to use Airport Rent-a-Car.
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Maya has to type a document of 2160 words. The graph below shows her initial progress. If
she continues at the same speed, how much time will Maya take to type the document?
The time it takes to type the document increases proportionately to the
number of words in the document.
The time it would take to type the document is; 36 minutesReasons:
From the possible figure from a similar question, we have;
The points on the graph are; (0, 0), (1, 60), (2, 120), (3, 180), (4, 240)
The graph is a straight line, therefore, given that the starting point is at the origin, using the points, (0, 0), (1, 60), we have;
The slope of the graph = 60
The y-intercept = 0
The equation that represents the proportional relationship shown on the graph is therefore;
y = 60·x
Where;
y = The number of words
x = The time it takes to type the document
The time it would take Maya to type the document of 2,160 words is given as follows;
2,160 = 60·x
Therefore;
[tex]\displaystyle Time, \ x = \frac{2,160 \ words}{60 \ words/minute} = \mathbf{36 \ minutes}[/tex]
The time it would take Maya to type the document is x = 36 minutes
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Freddie swam 5/7 laps on Monday, Tuesday, and Wednesday. 1/4 laps on Thursday and Friday. How many laps did he swim in total?
Answer: 27/28 or 0.9642857
Step-by-step explanation:
5/7 + 1/4 = 5 · 4/7 · 4 + 1 · 7/4 · 7 = 20/28 + 7/28 = 20 + 7/28 = 27/28
Lincoln middle school had a canned food drive. The 6th grader brought in 5.75
So the Lincoln middle school will have +5.75 pounds or ounces of ffod
Add the polynomials: x2 + 2x + 1 and y2 + 2x + 3.
Therefore, the above answer is correct.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Adding both of the polynomial equations we get [tex]x^2+y^2+4x+4[/tex].
What is a polynomial equation?A polynomial equation exists an equation where a polynomial exists set equivalent to zero. i.e., it exists an equation constructed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It includes different exponents. The highest one demonstrates the degree of the equation.
Given: [tex]x^2 + 2x + 1[/tex] and [tex]y^2 + 2x + 3.[/tex]
Adding both of these two equations, then we get
[tex]x^2+2x+1+y^2+2x+3[/tex]
Group like terms
[tex]=x^2+y^2+2x+2x+3+1[/tex]
Add similar elements [tex]x^2+y^2+4x+4[/tex]
Adding both of the polynomial equations we get [tex]x^2+y^2+4x+4[/tex].
Therefore, the correct answer is [tex]x^2+y^2+4x+4[/tex].
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An ice cream store has 31 flavors of ice cream and 10 toppings. A regular sundae has one flavor of ice cream, one topping, and comes with or without whipped cream. How many different ice cream sundaes can be ordered?
Answer:
610
Step-by-step explanation:
31 x 10= different flavour and topping combination
x2 = for the whipped cream different option
If RV = x+6, US = 5x-9, and RS = 11, find VT and ST
The values of VT and ST for the given rectangle are 13 and 23.56 respectively.
The given parameters:
RV = x + 6US = 5x - 9RS = 11The value of VT and ST is calculated as follows;
from the given diagram we can conclude the following;
2RV = RT = US
[tex]2(x + 6) = 5x - 9\\\\2x + 12 = 5x - 9\\\\12 + 9 = 5x - 2x\\\\21=3x\\\\x = 7[/tex]
RT = 2RV = 2VT = 2(7 + 6) = 26
VT = ¹/₂ x 26
VT = 13
The value of ST can be determined from Pythagoras theorem as follows;
[tex]ST = \sqrt{RT^2 - RS^2} \\\\ST = \sqrt{26^2 - 11^2} \\\\ST = 23.56[/tex]
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