Given:
[tex]\cos \theta =\dfrac{3}{5}[/tex]
[tex]\sin \theta <0[/tex]
To find:
The quadrant of the terminal side of [tex]\theta[/tex] and find the value of [tex]\sin\theta[/tex].
Solution:
We know that,
In Quadrant I, all trigonometric ratios are positive.
In Quadrant II: Only sin and cosec are positive.
In Quadrant III: Only tan and cot are positive.
In Quadrant IV: Only cos and sec are positive.
It is given that,
[tex]\cos \theta =\dfrac{3}{5}[/tex]
[tex]\sin \theta <0[/tex]
Here cos is positive and sine is negative. So, [tex]\theta [/tex] must be lies in Quadrant IV.
We know that,
[tex]\sin^2\theta +\cos^2\theta =1[/tex]
[tex]\sin^2\theta=1-\cos^2\theta[/tex]
[tex]\sin \theta=\pm \sqrt{1-\cos^2\theta}[/tex]
It is only negative because [tex]\theta [/tex] lies in Quadrant IV. So,
[tex]\sin \theta=-\sqrt{1-\cos^2\theta}[/tex]
After substituting [tex]\cos \theta =\dfrac{3}{5}[/tex], we get
[tex]\sin \theta=-\sqrt{1-(\dfrac{3}{5})^2}[/tex]
[tex]\sin \theta=-\sqrt{1-\dfrac{9}{25}}[/tex]
[tex]\sin \theta=-\sqrt{\dfrac{25-9}{25}}[/tex]
[tex]\sin \theta=-\sqrt{\dfrac{16}{25}}[/tex]
[tex]\sin \theta=-\dfrac{4}{5}[/tex]
Therefore, the correct option is B.
The growth rate of some species of bamboo is 0.0000237 miles per hour. write this in scientific notation
Answer:
2.37 x 10 ^ -5
Step-by-step explanation:
In a survey, 15 high school students said they could drive and 15 said they could not. Out of 60 college students surveyed, 30 said they could drive. Micah concluded that knowing that a person is in college means they are more likely to drive. Is Micah’s conclusion correct? Explain.
Answer:
No.
Step-by-step explanation:
#1, the sample size is not indicative of a proper high school population, unless of all there is a small amount of students in the high school (or even only 30 students in it). On a individual basis, it can vary widely, and so data analysis such as this is not correct. The data size is skewed as well for the college, especially as college campuses typically house more students then usual. To only ask 60 college students also skew the data gotten. Another sample error may be locational error, in which the location of the schools may warrant the need for a driver license, or if it is not needed, as well as the distance of the student's house and/or where needed facilities are to accommodate a student's needs and desires.
If we were to set all these problems aside and focus more on the question, 15 high school students said they could drive, and 15 said they could not, which makes the sample size of 30 high school students in all. 15 say they can drive, therefore:
15/30 = 1/2, or there is a 50% chance of obtaining a student that can drive.
On the other hand, out of 60 college students surveyed, 30 said they can drive, therefore:
30/60 = 1/2, or there is a 50% chance of obtaining a student that can drive.
∴ Micah's prediction is incorrect in obtaining a college student that can drive more easily then obtaining one that can drive in a high school.
However, remember that too small of a data size can lead to a heavy skew, and it will not represent reality as well.
~
Answer:
Sample Response: No, Micah is not correct. Since there are equal numbers in the group that drive and the group that doesn’t drive, the relative frequency for each is 50%. Because the relative frequencies are the same, there is no association between the variables.
Step-by-step explanation:
Got this from Edg 2021
Find the volume.
I need this in now like ASAP 10 points
Answer:
0.48 m^3
Step-by-step explanation:
volume = length * breadth * height
=6m * 4m * 0.02m
=0.48 m^3
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3
Answer:
y-y1=m(x-x1)
y-2=1/3(x-3)
y=1/3x+1
Which sentence explains why polygon ABCDEFGH is congruent to polygon MNOPQRST?
A.
A sequence of translations will map MNOPQRST onto ABCDEFGH.
B.
A sequence of rigid transformations will map MNOPQRST onto ABCDEFGH.
C.
A sequence of rotations will map MNOPQRST onto ABCDEFGH.
D.
A sequence of reflections will map MNOPQRST onto ABCDEFGH.
Answer:
correct option if Option D
Answer:
The answer is B.
Step-by-step explanation:
It can't be A, C, or, D because if the polygons were in a certain position, those transformations wouldn't work.
The definition of a rigid transformation is either a translation, rotation, or reflection. Therefore it must be B.
Sorry about how vague this is. It's hard to explain this without diagrams.
an estate valued at $75 000 is divided among three daughters Natasha, Natalie and Nadia in the ratio 5:8:2 respectively. Calculate the amount each receives
Answer:
Natasha: $25000
Natalie: $40000
Nadia: $10000
Step-by-step explanation:
5 : 8 : 2
5 + 8 + 2 = 15
$75000 ÷ 15
$5000
$5000 × 5 = $25000
$5000 × 8 = $40000
$5000 × 2 = $10000
A box shown below is to paint blue except the bottom. What is the area of the surface, and square inches, that will be covered with the paint?
Answer:
186
Step-by-step explanation:
Your entire surface area is
216
the area of the rectangle on the bottom is 30
substract 30 from 216
Find the median for the following list of values:
1, 2, 4, 7
Answer:
3
Step-by-step explanation:
Since there are an even number of data points (there are 4 points), and since the data has already been written in ascending order, the median is the average of the middle two terms: (2 + 4)/2 = 3
Answer:
Median: 3
Step-by-step explanation:
Median: the number in the middle
1, 2, 4, 7
Median is between 2, 4
Therefore, the median is 3
can somebody help plz
Answer:
(3,2)
Step-by-step explanation:
the other three ordered pairs do not lie in the shaded region
For the image below, state the line of reflection:
Answer choices:
y = -2
x-axis
y-axis
x = -1
Answer:20
Billions
Step-by-step explanation:
Answer:
Kjxiycdafgousdgkuafveligfasa
slope = 4, point (3,-2) is on the line
Answer:
y = 4x + b
Step-by-step explanation:
We know that (3, -2) is on this line. So 3 = m(-2)+b.
This leaves us with two variables the slope (m) and the y intercept (b).
But wait a minute, the slope is given to us since it says slope = 4.
Our equation is now, 3 = 4(-2)+b
3 = -8 + b
b = 11.
Our final equation is now y = 4x + b.
(y,x) is a point on this line.
Hope this helped!
JoeLouis2
Can someone help I’m confused
Answer:
D and E
Step-by-step explanation:
Let's double check:
D. 9 ÷ 3 = 3
E. 4 × 9 = 36
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Have a great summer :)
Answer:
the answers would be A, D, and E
Step-by-step explanation:
just replace the Cs with the number 9 and solve from there.
for example c/3=3 would say 9/3=3
What's the circumference of a circle with a diameter of 18 inches? Use 3.14 for pi, do not round the answer.
which graph is a function of x?
Answer:the one to the left
Step-by-step explanation:
Work out the perimeter of this semicircle.
Take a to be 3.142
10 cm
Answer:
perimeter=1/2*2πr
Step-by-step explanation:
1/2*2*3.142*10
=31.42
What are solutions to the equation x^2-34=864
Answer:
x=29.9
Step-by-step explanation:
x=29.9
Find the percent of markup on a T-shirt that has a store cost of $4.87 and a selling price of $15.95
Answer:
69.47%
Step-by-step explanation:
Calculation to determine Find the percent of markup
Using this formula
Percent of markup=New price-Old price/Old price
Let plug in the formula
Percent of markup=$15.95-$4.87/$15.95
Percent of markup=$11.08/$15.95
Percent of markup=0.6947*100
Percent of markup=69.47%
Therefore the percent of markup is 69.47%
How many x-intercepts appear on the graph of this polynomial function?
f(x) = x - 5x?
O 1 x-intercept
O 2 x-intercepts
O 3 x-intercepts
O 4 x-intercepts
Answer: B
Step-by-step explanation:
There are two x-intercepts: x = -√5 and x = √5. The answer is: 2 x-intercepts.
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.
To find the x-intercepts of the polynomial function f(x) = x⁴ - 5x², we set f(x) equal to zero and solve for x.
Setting f(x) = 0:
x⁴ - 5x² = 0
Factoring out the common term x²:
x²(x² - 5) = 0
Now we have two factors: x² = 0 and x² - 5 = 0.
For x² = 0, we have a double root at x = 0.
This means the graph touches the x-axis at x = 0 but does not cross it.
For x² - 5 = 0, we can solve for x by taking the square root:
x² = 5
x = ±√5
Therefore, there are two x-intercepts: x = -√5 and x = √5.
The answer is: 2 x-intercepts.
Learn more about the x-intercept here:
https://brainly.com/question/14180189
#SPJ7
la figure ci-dessus représente une pyramide du sommet S.
Sa base le rectangle EFGH et sa hauteur SO, tel que O est le centre
du rectangle EFGH.
PETIT PLUS: SE=6.5 cm , EF= 4 cm , FG=3cm.
1)- calculer la distance EG.
2)-Montrer que: SO=6 cm
3)-Calculer le volume de la pyramide SEFGH
SVP JE DOIS LE RENDRE DEMAIN .
ET MERCI
Answer:
Step-by-step explanation:
Voir le diagramme ci-attaché.
1) Distance EG
À l'aide du théoreme Pythagore, EG^2 = EF²+FG² = 4²+3² = 25
=> EG = sqrt(25) = 5
2) Distance SO
Par la symétrie, EO=OG=(EG/2)=5/2 = 2.5
Encore, à l'aide du même théoreme,SE^2 = SO²+EO²
SO^2 = SE² - EO² = 6.5²-2.5² = 42.25 - 6.25 = 36
SO = sqrt(36) = 6 QED
3) Volume de la pyramide
V = (Aire de la base * hauteur ) /3
= (EF * FG) * SO /3
= (4*3) * 6 /3
= 24 cm³
Please help :( The picutre is right below worth 20 pionts and will mark brainliest :)
oh and the question is right in the picture too also with the rest
Answer:
perpendicular
Step-by-step explanation:
peripenducular looks like a plus sign. HOPE THIS HELPS!
Branliest...
Which expressions are equivalent to the on below select all that apply 9x
Answer:
B and D
Step-by-step explanation:
Multiplying exponents just adds them.
Answer:
B + D
Step-by-step explanation:
Find the measure of DAE
Cho tam giác ABC có AB =4cm ,AC=5cm,BC=6cm.Trên tia đối của tia AB lấy điểm D sao cho AD=5cm a) chứng minh : tam giác ABC đồng dạng với tam giác CBD b) tính CD
Answer:
meta beta
Step-by-step explanation:
diem ryugudnhkng.
Jane and Tannic split the cost of buying a video game. The game costs$25, and the sales is 6% markup. How much do they each pay?
Given:
The cost of game = $25
Sales markup = 6%
To find:
How much do they each pay?
Solution:
The sales markup is 6% of the cost.
[tex]\text{Sales markup}=25\times \dfrac{6}{100}[/tex]
[tex]\text{Sales markup}=1.5[/tex]
Now, the total cost after sales markup is:
[tex]25+1.5=26.5[/tex]
Jane and Tannic split the cost of buying a video game. It means they divide the cost in two equal parts. So, the amount paid by each one is
[tex]\dfrac{26.5}{2}=13.25[/tex]
Therefore, Jane and Tannic will pay $13.25 each .
The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use
Answer:
Coordinate of points = (7 , 0)
Step-by-step explanation:
Given:
Equation of slope;
y – y1 = m(x – x1)
Equation of slope;
y = 3(x – 7)
Find:
Coordinate of points
Computation:
By comparing
y - 0 = 3(x - 7)
So,
y1 = 0
m = 3
x1 = 7
Coordinate of points = (7 , 0)
Worth 20 points Il will mark brainiest! :)
The picture is included too oh and the question is already in the picutre but just incase you cant see what it says it says this
In the diagram below lines, AB and CD are . sorry if the picture is a bit dark
A. Perpendicular!
Because they cross with a 90 degree angle :]
Answer: Perpendicular
Step-by-step explanation: Hope this helps
This is correct? I need help please :(
Answer:
well, we only no that
2l + 2w is 80
(lengths and widths on all 4 sides
and that w * l is A
so the function should be w times what's left for l, but also expressed by something with w
2l + 2w = 80 | -2w
2l = 80 -2w | devide by 2
l = 80 - w
now we can substitute l in
A = w * l
so that we only need w's
A(w) = w * (80-w)
for any w it will give us the area, makes only sense for 0<w<80
What are the solutions of x2 - 2x +17 - 0?
O A. x = 1+2, or x = 1 - 2
O B. X = 1+4, or x = 1- 47
O c. x = 2, or x = -2
O D. x = 4; or x = -4/
Answer:
option B
Step-by-step explanation:
[tex]x^2 - 2x + 17 = 0 \ , \ [ \ where \ a = 1 , \ b = - 2 \ c = 17 \ ][/tex]
[tex]x = \frac{- b \ \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{2 \ \pm \sqrt{2^2 - (4 \times 1 \times 17)}}{ 2 \times 1}\\\\x = \frac{2 \ \pm \sqrt{4 - 68}}{ 2 }\\\\x = \frac{2 \ \pm \sqrt{-64}}{ 2 }\\\\x = \frac{2 \ \pm \sqrt{8^2 \times -1}}{ 2 }\\\\x = \frac{2 \ \pm \ 8\sqrt{ -1}}{ 2 }\\\\[/tex]
[tex]x = \frac{2 \ \pm\ 8 i}{ 2 }\\\\[/tex] [tex][ \ where \ i = \ \sqrt{i} \ ][/tex]
[tex]x = 1 \ \pm \ 4i\\\\x = 1 + 4i , \ x = 1 - 4i[/tex]
Answer:
O B. [tex]x=1+4i[/tex] or [tex]x=1-4i[/tex]
Step-by-step explanation:
Use the Quadratic Formula for the Quadratic Equation!
Quadratic Equation: [tex]x^{2} -2x+17=0[/tex]
Quadratic Formula: [tex]x= \frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]
**********************************************************************
Now set up the values like this!
[tex]ax^{2} +bx+c[/tex]
**********************************************************************
[tex]x=\frac{-b±\sqrt{-2^2-(4(0)(17)} }{2(0)}[/tex]
[tex]x=\frac{-b±\sqrt{4-(1)} }{0}[/tex]
x = 1 - 4i
x = 1 + 4i
What is the volume of this. Pyramid
720 cm2
1080cm2
1440 cm2
2160 cm2
Answer:
Option (1)
Step-by-step explanation:
To calculate the volume of the given pyramid,
Formula to be used,
Volume = [tex]\frac{1}{3}(\text{Area of the triangular base)}(\text{Height})[/tex]
Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(9)(15)[/tex]
= 67.5 cm²
Now volume of the pyramid = [tex]\frac{1}{3}(67.5)(32)[/tex]
= 720 cm³
Therefore, Option (1) will be the correct option.
What is the answer to the expression -5x + 1 = 31
Answer:
x = -6
Step-by-step explanation:
-5x + 1 = 31
Subtract 1 from each side
-5x + 1-1 = 31-1
-5x = 30
Divide by -5
-5x/-5 = 20/-5
x = -6
Answer:
x = - 6
Step-by-step explanation:
- 5 x + 1 = 31
subtract 1 from 31
- 5 x = 31 - 1
- 5 x = 30
Divide 30 by - 5
x = 30 / - 5
x = - 6