Given:
An angle θ on the unit circle has a sine of [tex]\dfrac{1}{4}[/tex].
To find:
The value of cosθ.
Solution:
We have,
[tex]\sin \theta=\dfrac{1}{4}[/tex]
Since sinθ is positive, therefore, θ lies in first or second quadrant.
We know that,
[tex]\sin^2 \theta +\cos^2 \theta =1[/tex]
[tex](\dfrac{1}{4})^2+\cos^2 \theta =1[/tex]
[tex]\dfrac{1}{16}+\cos^2 \theta =1[/tex]
[tex]\cos^2 \theta =1-\dfrac{1}{16}[/tex]
Taking square root on both sides.
[tex]\cos \theta =\pm \sqrt{\dfrac{16-1}{16}}[/tex]
[tex]\cos \theta =\pm \dfrac{\sqrt{15}}{4}[/tex]
Therefore, the value of cosθ is either [tex]\dfrac{\sqrt{15}}{4}[/tex] or [tex]-\dfrac{\sqrt{15}}{4}[/tex].
wait can sm1 like pls help me i have a d in this class
1. 7p - 6pc + 3c - 2 Number of terms: Coefficients: Constant terms:
Step-by-step explanation:
Given:
7p - 6pc + 3c - 2
Find:
Number of terms
Coefficients
Constant terms
Computation:
Number of terms = 4
Coefficients = (7, -6, 3)
Constant terms = -2
you saved $250.00 to spend over the summer. You decide to budget $25.00 to spend a week. Define the variable and write a function that represents this situation
Answer:
200
Step-by-step explanation:
PLEASE SHOW FULL SOLUTIONS!!!!!! WILL MARK BRAINLIEST TO THE BEST ANSWER!!! THANK YOU AND GOD BLESS...
9514 1404 393
Answer:
x = 60y = 50Step-by-step explanation:
The linear pair at G totals 180°, so we have ...
x + 2x = 180
3x = 180 . . . . . collect terms
x = 180/3 . . . divide by 3
x = 60
__
The total of angles in the triangle is 180°, so ...
x + y + 70 = 180
60 + y + 70 = 180 . . . . substitute for x
y = 180 -130 . . . . . . . . . subtract 130
y = 50
Jan creates a pattern using the rule "add 3". Bill creates pattern using the rule "add 6." Which describes the relationship between Jan and Bill's patterns?
Answer: a. Each term in Bill's pattern is twice the value of the corresponding item in Jan's pattern.
Step-by-step explanation:
Jan created a pattern by adding 3 and Bill created a pattern by adding 6.
6 is twice the value of 3 so Bill's terms will be twice the value of Jan's corresponding terms as well.
To prove it:
12 is twice the value of 6
18 is twice the value of 9
24 is twice the value of 12
Could someone help me I’m almost done please please
y=4
Step-by-step explanation:
cube root 64
Triangle ABC is shown. DE is a straight line with D on AC and E on BC AB = 46m, EC = 18m, CD = 29m and ED = 20m. Calculate the length AD.
Answer:
37.7m
Step-by-step explanation:
Triangle ABC is shown. DE is a straight line with D on AC and E on BC AB = 46m, EC = 18m, CD = 29m and ED = 20m. Calculate the length AD.
We solve using Similarity Theorem
BA/AC =BD/DC
46/AD+29 = 20/29
Cross Multiply
46 × 29 =20 (AD + 29)
1334 = 20AD + 580
20AD = 1334 - 580
20AD = 754
AD = 754/20
AD = 37.7m
You roll a fair six sided cube and flip a coin. What is the probability that you roll an even number and the coin lands on tails?
Answer: Since flipping a coin and rolling a 6-sided die are independent events ,thus the probability of getting head and an even number is just the product of the individual probability of events.
Let A be the event of getting a head ,and B be the event of getting an even number on die.
therefore, P(A and B)=P(A) P(B)=(1/2)*(3/6)=1/4=0.25.
what is the measure of angle b?
A. 36⁰
B. 117⁰
C.63⁰
D. 56⁰
Answer:
A
Step-by-step explanation:
180⁰= a+b+81⁰
a=180⁰-117⁰=63⁰
b=180⁰-63⁰-81⁰=36⁰
Thomas drew a line of best fit for the scatter plot as shown. Enter an equation for the line of best fit in slope-intercept form. The line of best fit equation in slope-intercept form is y =
Answer:
Equation of line best fits the scatter plot is y = [tex]-\frac{30}{7} x + 108[/tex]
Step-by-step explanation:
Let the equation of line be y = mx + c
where m = slope of line and c is the intercept on y -axis
from the graph intercept on y-axis is 108
and the slope of line is given by m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] where ([tex]x_2,y_2[/tex]) and ([tex]x_1,y_1[/tex]) is the points on line
let, points be (4,96) and (18,36)
on calculating this m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = [tex]-\frac{30}{7}[/tex]
Therefore equation of line best fits the scatter plot is y = [tex]-\frac{30}{7} x + 108[/tex]
Nick divides 527 baseball cards evenly into 17 stacks. How many baseball cards are in each stack?
This is division btw.
Answer:
Its 31
Step-by-step explanation:
Just Use A Calculator
Find the coordinates of the midpoint of the segment with the endpoints M(-5,9) and N(-2,7).
Answer:
(-3.5 , 8)
Step-by-step explanation:
midpoint (x , y)
x = (-5 + -2) / 2 = -7/2 = -3.5
y = (9 + 7) / 2 = 16/2 = 8
jessie served 13 pints of orange juice at her party
how many quarts of orange juice did she serve
Answer:
6 1/2
Step-by-step explanation:
Answer:
6.5 quarts.
Step-by-step explanation:
This is rather simple math because 2 pints equal 1 quart. You divide 13 by 2, which is an uneven number so you are guaranteed a half, and you get 6.5
1) Name the triangle.
scalene and acute
() isosceles and acute
() isosceles and right
()) scalene and right
Answer:
Isosceles and right triangle
The table below shows the number of strawberries and cups of water
used to make fruit punch according to a certain recipe.
Strawberries Water (cups)
384
30
320
25
How many cups of water are needed for every 1 strawberry? Note:
Your answer may be exact or rounded to the nearest hundredth.
Answer:
5/64 of a cup.
Step-by-step explanation:
Is there two columns of data and two data points? Like this:
Strawberries Water
384 30
320 25
If so, then there are two ways to do it.
1) You can set up a ratio like this
384/30 = 1/x
Where x is the number of cups of water for 1 strawberry.
So,
x = 30/384 of a cup
x = 5/64 of a cup.
2) Look at the increase from one to the other.
64 strawberries requires 5 cups of water
Divide by 5 by 64 to get the water for one strawberry
5/64 of a cup.
if p=3+2√2 find the values of p+1/p
Answer: 1,71572875
Step-by-step explanation: (4+2rad2)/3+2rad2
Answer:
6
Step-by-step explanation:
1/p = 1/(3 + 2sqrt2)
Multiplying by the conjugate (which you should pretty much always do to simplify), we get
(3-2sqrt2)/((3+2srqt)(3-2sqrt2))
which is
(3-2sqrt2)/(9-8) = 3-2sqrt2.
Therefore p + 1/p = 3+2sqrt2 + 3 - 2sqrt2 = 6
1 over 8 + c = 4 over 5 whats x?
Write the slope-intercept form of the equation of each line.
Answer:
1) positive 2)negative 3)negative
Step-by-step explanation:
i hope thats what your asking
10) Determine which of the following are functions. 11) What are the domain and range of the following relation?
Answer:
10) The first 2 on the left are functions and the one on the top right is a function, but the bottom right is not.
11) Domain = (2, 8, -1, 0) Range = (5, -2, 4, 5)
Which of the following is an example of a unit rate?
a. John earns $15 for mowing three lawns
b. Kelly types 90 words per minute
c. Indra earns two detentions every two weeks
d. Three bags of chips cost $3.75
Answer:
I think it's b or c because a unit rate is a ratio which the two terms are in different units
I need help with this please
QUICK ANSWERS PLEASE!!!!!!
Find the measure of each angle:
Answer:
1) 63
2) 49
3) 87
4) 44
Step-by-step explanation:
In the previous election 6,400 people voted. What is the percent decrease in actual voters?
A 8.6%
B. 11.4%
C 12.5%
D. 14.3%
Answer:
14.3%
Step-by-step explanation:
6400-5600=800
800/6400×100=14.3
Answer:
14.3
Step-by-step explanation:
In a two-digit number, the unit's digit is 2 more than that of the ten's digit. The sum of the digits is 27 less than the number. Find the product of the digits of the number
Answer:
15 is the product of the digits of the number
Step-by-step explanation:
Let the two digit number be xy
Unit digit is 2 more than ten’s digit
y - x = 2 ••••••(i)
Secondly;
x + y = (10x + y) - 27 •••••(ii)
From i, y = x + 2
Put this into ii
x + x + 2 = 10x + x + 2 - 27
2x + 2 = 11x - 25
11x - 2x = 25 + 2
9x = 27
x = 27/9
x = 3
From above;
y = x + 2
y = 3 + 2 = 5
The product of the numbers xy will be 5 * 3 = 15
Solve for p. p/8 + 12 = 36
9514 1404 393
Answer:
p = 192
Step-by-step explanation:
p/8 +12 = 36 . . . . . given
p/8 = 24 . . . . . . . . .subtract 12
p = 8·24 . . . . . . . . .multiply by 8
p = 192
please help
write the fraction as a decimal
Answer:
it's 7 divided by 10
transfer the 0 up and make it 0.7
How many cubic blocks of side length 1/6 inch qould it take to fill a rectangular prism with a length, width and height of 1/3 inch, 2/3 inch, 2/3, respectively
Answer:
32 cubes
Step-by-step explanation:
I would first determine the volume in inches of the rectangular prism.
V = 1/3 x 2/3 x 2/3 = 4/27 cubic inches.
Then I would calculate the volume of the cube with 1/6 inch sides
V = 1/6 x 1/6 x 1/6 = 1/216 cubic inches.
Then I would divide the V of the large prism by the V of the small cube
(4/27) / (1/216) = (4/27) * (216/1) = 32 cubes
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Cheryl decorated a border of a birthday card with flowers. The flowers were 1/200 m apart. The length of the border was 1/5 m. There was a flower at each end of the border. How many flowers did she draw?
Answer:
She draw 40 flowers
Step-by-step explanation:
Given
[tex]Length = \frac{1}{5}m[/tex]
[tex]Flower = \frac{1}{200}m[/tex]
Required
Determine the number of flowers
To do this, we simply divide the length of the border by the length of the flower.
[tex]Number = \frac{1}{5}/ \frac{1}{200}[/tex]
Convert to multiplication
[tex]Number = \frac{1}{5}* \frac{200}{1}[/tex]
[tex]Number = \frac{200}{5}[/tex]
[tex]Number = 40[/tex]
Hence, she draw 40 flowers
A mass of 50 g decreased by 17%. What is the new
mass?
Answer:
8.5g
Step-by-step explanation:
the mass decreased by 17%,so the decrease in mass 17% of 50g.17% of 50 = 0.17 × 50 =8.5 the mass decreased by 8.5g
The mass is decreased by [tex]8.5g[/tex].
What is the percentage?
A percentage is a number or ratio expressed as a fraction of [tex]100[/tex]. It is often denoted using the percent sign, "%".
Here given that,
A mass of [tex]50[/tex] g decreased by [tex]17[/tex] %.
So, in the mass [tex]17[/tex] % of [tex]50g[/tex] and of [tex]50g[/tex] is [tex]17[/tex] % is of the form:-
[tex]50=0.17[/tex] ×[tex]50=8.5[/tex]
Hence, the mass is decreased by [tex]8.5g[/tex].
To know more about the percentage
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