well, we know that θ is in the III Quadrant, where the sine is negative and the cosine is negative as well, or if you wish, where "x" as well as "y" are both negative, now, the hypotenuse or radius of the circle is just a distance amount, so is never negative, so in the equation of cos(θ) = - (2/5), the negative must be the adjacent side, thus
[tex]cos(\theta)=\cfrac{\stackrel{adjacent}{-2}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2 - (-2)^2}=b\implies \pm\sqrt{25-4}\implies \pm\sqrt{21}=b\implies \stackrel{III~Quadrant}{-\sqrt{21}=b}[/tex]
[tex]\dotfill\\\\ csc(\theta)\implies \cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{-\sqrt{21}}}\implies \stackrel{\textit{rationalizing the denominator}}{-\cfrac{5}{\sqrt{21}}\cdot \cfrac{\sqrt{21}}{\sqrt{21}}\implies -\cfrac{5\sqrt{21}}{21}} \\\\\\ tan(\theta)=\cfrac{\stackrel{opposite}{-\sqrt{21}}}{\underset{adjacent}{-2}}\implies tan(\theta)=\cfrac{\sqrt{21}}{2}[/tex]
What is the value of the expression below? (4^2)^1/4
Answer:
the value for the expression for below is (4^2) ^1/4 is 2
Answer:
2
Step-by-step explanation:
Exponent law[tex]\sf \boxed{(a^m)^{n}=a^{m*n}}[/tex]
[tex]\sf (4^2)^\frac{1}{4}=4^{2*\frac{1}{4}}[/tex]
[tex]\sf = 4^{\frac{1}{2}}\\\\ = \sqrt{4}\\\\=2[/tex]Divide. Give the quotient and the remainder.
1197/2
Answer:
1197/2
598 R 1
598½
Step-by-step explanation:
use division method
Answer:
2 divided by 1197 equals 598 with a remainder of 1.
Step-by-step explanation:
There is also another way to do divison if it is confusing for others.
If you multiply 598 and 2 that equals 1196. That is the closest number that can go into 2 598 times. So what i am trying to say is that since the problem is 2 divided by 1197 you have to figure out what number you need to multiply that can go into two. So 2 divided by what equals 1197 OR 2 divided by what number can equal 1197 or any number that is close to 1197. So 598 times 2 equals 1196. With a remainder of 1
I hope this helps because this strategy worked for me when i first learned division so i hope this helps as well :)
factor 8x^3y + 38x^2y - 10xy
Answer:
2xy(x+5)(4x−1)
Step-by-step explanation:
1 Find the Greatest Common Factor (GCF).
GCF = 2xy
2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2xy (8x^3y + 38x^2y/2xy + −10xy/2xy)
3 Simplify each term in parentheses.
2xy(4x^2 +19x−5)
4 Split the second term in 4x^2+19x-5 into two terms.
2xy(4x^2 +20x−x−5)
5 Factor out common terms in the first two terms, then in the last two terms.
2xy(4x(x+5)−(x+5))
6 Factor out the common term x+5.
2xy(x+5)(4x−1)
What is 2x-x^2=1 in standard form
Answer:
Answer is in attachment
Mark brainliest pls :)
Twice x increased by five is 27. What is x?
Answer:
x=11
Step-by-step explanation:
2x+5=27
2x=22
x=11
D. When a number is subtracted from the numerator and denominator of 4/3 the result is more than 2/3. Find the number
Answer:
Let us solve this
We’ll do it by the elementary method
Suppose the original fraction be x/y
Given, x : y = 2:3 ……(i)
then y = 3/2x
Now , by condition,
(x-6)/y = 2/3 * x/y
=> (x-6)/y = 4/9 [ from (i) ]
=> x-6 = 4/9y = (4/9)(3/2)x = 2/3x
=> 3x-18 = 2x [cross multiplication]
=> x = 18
Your Answer: the numerator of the original fraction is = 18
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A store buys 17 sweaters for $204 and sells them for $646. how much profit does the store make per sweater?
Total profit: 646 - 204 = 442
profit per shirt = 442 / 17 = 26
Answer: $26
a number that has four identical even
factors. Each factor must be greater than 1 and
can have only 1 and itself as factors.
Answer:
210?
Step-by-step explanation:
210 has factors of 2, 3, 5, and 7
Justine ran for 35 minutes on monday, for 1 hour and 10 minutes on Wednesday , and for 1 hour and 15 minutes on friday. How many total minutes did Justine run?
Answer:
3 hours or 180 minutes
Step-by-step explanation:
This one should be an easy one
First, lets convert everything to units
35 + (1 hour and 10 minutes or 70 minutes) + (1 hour and 15 minutes or 75 minutes) = 35 + 70 + 75 = 180 minutes, or 3 hours.
Hope it helps :)
The ratio of two angles is 5:3. The two angles are supplementary,
What is the measure of each of the angles in the angle pair?
Help me on this math problem please!! DUE TONIGHT!!
Answer:
48 + 2x = 120
x = length od long side.
Can someone please help me
Answer:
1 true
2 false
3 false
4 true
[tex] \huge \rm \color{red}help \: pls[/tex]
Choises :
• 1260°
• (n-2) × 180°
• 360°
• (n- 2)×180°
----------------
n
• 180°
•30m
1. YOU ARE ASKED TO FIND THE SUM OF THE MEASURES OF THE EXTERIOR ANGLES OF A DECAGON, WHAT DO YOU THINK IS THE TOTAL MEASUREMENT OF THE EXTERIOR ANGLES OF A DECAGON? _________
2. NINA IS CONFUSED ON WHAT FORMULA SHE WILL USE TO FIND THE MEASURES OF EACH INTERIOR ANGLE OF AN OCTAGON, CAN YOU GIVE HER THE APPROPRIATE FORMULA TO USE? ____________
3. VINCE WANTS TO BUILD A REGULAR HEXAGON PLAYGROUND IN HIS GARDEN. HOW MUCH FENCING HE WILL NEED TO BUY IF EACH SIDE MEASURES 5M? ___________
4. THE SURFACE OF A WARNING SIGN IS IN THE SHAPE OF A REGULAR TRIANGLE. WHAT IS THE SUM OF THE INTERIOR ANGLE OF THE SIGN?
_____________
5. LOU IS TRYING TO FIND OUT WHAT IS THE SUM OF ALL THE INTERIOR ANGLES OF A PENTAGON, WHAT IS THE APPROPRIATE FORMULA TO USE?
______________
The sum of the exterior angles of a decagon is 360 degree if each exterior angle measure is 36 degree.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have:
Decagon, in which the number of sides is 10
The formula for the sum of the interior angles in n number of polygon:
Sum = 180(n - 2)
Plug n = 10
Sum = 180(10-2)
Sum = 1440
Each interior angle = 1440/10 = 144 degree
Each exterior angle = 180 – 144 = 36 degree
The sum of the exterior angles = 36×10 = 360 degree
Similarly, we can find any angle measure for interior or exterior by using the formula:
Sum = 180(n—2)
Where n is the number of sides.
Thus, the sum of the exterior angles of a decagon is 360 degree if each exterior angle measure is 36 degree.
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what is (4/9) to the power of 2 AS a fraction??
Step-by-step explanation:
[tex] = ( \frac{4}{9} {)}^{2} \\ [/tex]
[tex] = \frac{ {4}^{2} }{ {9}^{2} } \\ [/tex]
[tex] = \frac{16}{81} \\ [/tex]
The required power 2 of 4/9 in fraction form is 16/81.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
The given fraction is,
(4/9)
To find the power 2 of fraction 4/9,
Use mathematical operations,
4/9 to the power 2 = (4/9)²
= (4/9)x(4/9)
= 16 / 81
The power 2 of 4/9 as a fraction is 16/81.
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Which of the following systems is dependent?
x − y = 2 and x y = −2
x − y = 2 and −2x 2y = −4
x − y = 2 and 3x − 3y = 2
x − y = 2 and −x − y = −2
The system of equation x − y = 2 and −2x+2y = −4 is dependent becasue the they have same coefficient of x and y option second is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
As we know, if the two linear equations have the same coefficient of x and y they are dependent or if the graph of two linear equations is the same then the equations are dependent.
From the given options, we can see the system of equations:
x − y = 2 and −2x + 2y = −4 are the same equation.
Take the equation −2x + 2y = −4 and divide by -2 on both sides, we get:
x - y = 2
This is the same equation as x − y = 2
Thus, the system of equation x − y = 2 and −2x+2y = −4 is dependent becasue the they have same coefficient of x and y option second is correct.
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Help Please…. I don’t really understand the question
Step-by-step explanation:
if you don't even understand the question, this is also something you need to tell your teacher. it is his/her job to make you understand it.
a probability is always
desired cases / possible cases
so, if we pick a single student randomly, how many possible options do we have ?
we have 2+5+6+9 = 22 students (as the 4 categories in the table are mutually exclusive).
therefore, our possible cases to pick a student are 22.
now, how many of these 22 students represent our desired cases ?
male, who does not have an A : 9
so, the probability to pick a student who is male and does not have an A is
9/22 = 0.409090909...
Find the volume and surface area of the figure below.
The volume of the prism is determined as 1,416 m³ and the surface area of the prism is 664.8 m².
Volume of the prismThe volume of the prism is determined from the product of base area and slant height of the prism.
Base of the prism, A = ¹/₂bh = ¹/₂ x 12 x 20 = 120 m²
Volume = AL
where;
L is the slant heightL² = (12/2)² + (20.3/2)²
L² = 6² + 10.15²
L² = 139.0225
L = 11.8 m
V = AL
V = 120 x 11.8 = 1,416 m³
Surface area of the prismA = bh + pL
A = (12 x 20) + 11.8(12 + 12 + 12)
A = 664.8 m²
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(30 BRAIN POINTS ) HELP ME I MUST WIN THIS TEST >:(
Answer:
it is greater for group B than group A
If Hal usually mows 21 yards per week, how many yards does he average per day?
(will mark brainliest)
Answer:
3 yards per weekStep-by-step explanation:
21÷7=3
3 yards per week
hope this helps
Answer:
3 yards per day
Step-by-step explanation:
Given :
Hal mows an average of 21 yards per weekTo Remember :
There are 7 days in a weekSolving :
Avg. yards per day = Avg. yards per week / No. of days in a weekAvg. yards per day = 21/7Avg. yards per day = 3 yards per dayA rectangle has a length of 11.8cm and a width of 8.3. What is the area of this rectangle?
A. 48.36cm
B. 96.76cm
C. 107.2cm
or 140.76cm?
Big thanks to anyone that helps
Answer:
a
Step-by-step explanation:
Answer:97.94
Step-by-step explanation:
11.8*8.3 = 97.94
PLS HELP ILL GIVE BRAINIEST PLSSSSS
An art test has 15 questions. A student answers 80% correctly.
How many questions does the student answer correctly?
Enter your answer in the box.
questions
Answer:
The student gets 12 questions correctly.
Step-by-step explanation:
The test has 15 questions, multiply this by .8 to get how many questions he got correct.
Questions answered correctly
80% of 150.8(15)120/1012QuestionsDone
A small bottle of water weighs 5/8 pound. A carton hdds 30 small bottles of water.
How many pounds do the 30 small water bottles weigh? Move numbers to the boxes to show the answer. If there is no whole number, put a 0 in the first box
in the first box
The weight in pounds do the 30 small water bottles when the weight of one bottle is 5/8 pound is 75/4 pounds.
How to measure the weight?Weight measurement is the measurement of the heaviness of a object. The units of weight measurement are pounds, grams, kilograms etc.
A small size bottle of water which has the weighs 5/8 pound. One carton has total 30 small bottles of water.
Let the weight in pounds do the 30 small water bottles has is x. Thus,
[tex]x=\dfrac{5}{8}\times30\\x=\dfrac{5}{4}\times15\\x=\dfrac{75}{4}\rm\; pounds[/tex]
Thus, the weight in pounds do the 30 small water bottles when the weight of one bottle is 5/8 pound is 75/4 pounds.
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A rectangle has a length of 10 cm and the width of 7 cm. what the perimeter
A, B and C form a triangle where ∠BAC = 90°
AB = 4.4mm and BC = 14.8mm
Find the length of AC, giving your answer rounded to 1 decimal place.
Answer:
............ .. .......
Answer:
14.1 mm
Given:
∠BAC = 90° (angle A should be 90°)
AB = 4.4mm
BC = 14.8mm
See the diagram given below.
Solving using Pythagoras Theorem: a² + b² = c²
x² + 4.4² = 14.8²
x = 14.8² - 4.4²
x = 219.04 - 19.36
x = 199.68
x = √199.68
x = 14.13 ≈ 14.1 mm (rounded to 1 decimal place)
A rectangle is four times as long as it is wide. If it has an area of 36 square inches, what are its dimension?. a. 6 by 6 c. 4 by 9 b. 3 by 12 d. 4 and 8 Please select the best answer from the choices provided A B C D
Answer:
B. 3 by 12
Step-by-step explanation:
[tex]x(4x) = 36[/tex]
[tex]4 {x}^{2} = 36[/tex]
[tex] {x}^{2} = 9[/tex]
[tex]x = 3[/tex]
[tex]4x = 12[/tex]
So the length is 12 inches, and the width is 3 inches.
Doreen Short was looking over the repayment schedule for a loan of $40,000. 00 at 9% for 4 years with a monthly payment of $995. 40.
Find the final payment and amount saved if :
A. ) The loan is paid off with payment 30 with a previous balance of $17,565. 74
B. ) The loan is paid off with payment 36 with a loan balance of $12,285. 66
C. ) The loan is paid off with payment 48 with a previous balance of $988. 9
Doreen Short was looking over the repayment schedule for a loan of $40,000, the final payment and amount saved for the options are mathematically given as
F=17697.5 , AS=1215.12F=12377.80, AS=$562.40F=$995.40, Amount saved is zeroWhat is the loan is paid off with payment 30 with a previous balance of $17,565. 74?Generally, the equation for the interest is mathematically given as
I= balance*percentage/12
Therefore
I=17,565. 74*0.09/12
I=131.7
The final payment
F=I+B
F=131.7+17,565. 74
F=17697.5
Amount saved
AS=19*995.40 -17697.5
AS=1215.12
b) For the loan is paid off with payment 36 with a loan balance of $12,285. 66
I= balance*percentage/12
Therefore
I= 12,285. 66*0.09/12I92.142
I=92.142
Final payment
F=I+B
F=92.142+12377.80
F=12377.80
Amount saved
AS=13*995.40-12377.80
AS=$562.40
c) For the loan is paid off with payment 48 with a previous balance of $988. 9
I= balance*percentage/12
I= 988.09*0.09/12
I=7.41
Therefore
F=7.41* +988.09
F=$995.40
The Amount saved is zero
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How many solutions does the equation have? 0=3x^2-5x-5
Answer:
2 real solutions
Step-by-step explanation:
Since the degree of the polynomial is 2, then there are 2 solutions for the equation, but we don't know if they are both complex or both real.
Since the discriminant is [tex]b^2-4ac=(-5)^2-4(3)(-5)=25+60=85 > 0[/tex], then there are 2 real solutions.
how do you show that 2/11 is a repeating decimal
A circle's radius is 6 inches. What is the circle's area?
Use 3.14 for pi and round your answer to the nearest tenth.
Answer:
9*9*3.14= 254.34
Area= 3.14 (pi)*radius suqare
Step-by-step explanation:
:)
What’s the circumference?
Answer:
if you want in terms of π, then 3π
if you want it without π, then 9.42
Step-by-step explanation:
plug into formula
3= diameter
c=πd
c=π*3
3π or
π=3.14
so 3.14*3, which is 9.42
Answer:
3π if in terms of pi or 9.42 if π= 3.14
Step-by-step explanation: