Answer:
16 and 56
Step-by-step explanation:
gcf of 24 and 48 is 24
gcf of 14 and 32 is 2
gcf of 16 and 28 is 4
Let's find one by one
#1
24 and 48
GCF=24No
#2
14 and 32
GCF is 2No
#3
16 and 28GCF is 4
No
#4
16 and 56
GCF is 8Yes
26. Given that tanθ almost equal to≈ 2.773 where 0<θ<π2, find the values of sinθ and cosθ. 27. Given that tanθ ≈ -1.559 where 3π2<θ<2π , find the values of sinθ and cosθ.
Answer:
a. i. sinθ = +0.941
ii. cosθ = +0.339
b. i. sinθ = -0.842
ii. cosθ = +0.540
Step-by-step explanation:
a. Given that tanθ almost equal to≈ 2.773 where 0<θ<π/2, find the values of sinθ and cosθ.
i. sinθ
Given that 1 + cot²θ = cosec²θ
cotθ = 1/tanθ
Since tanθ = 2.773, cotθ = 1/tanθ = 1/2.773 = 0.3606
So, 1 + cot²θ = cosec²θ
1 + (0.3606)² = cosec²θ
1 + 0.13 = cosec²θ
1.13 = cosec²θ
cosec²θ = 1.13
cosecθ = ±√1.13
cosecθ = ±1.063
1/sinθ = ±1.063
sinθ = ±1/1.063
sinθ = ±0.9407
sinθ ≅ ±0.941
Since we have 0<θ<π/2, sinθ is in the first quadrant, so we choose the positive value.
So, sinθ = +0.941 where 0<θ<π/2
ii. cosθ
Given that 1 + tan²θ = sec²θ
Since tanθ = 2.773,
So, 1 + tan²θ = sec²θ
1 + (2.773)² = sec²θ
1 + 7.6895 = sec²θ
8.6895 = sec²θ
sec²θ = 8.6895
secθ = ±√8.6895
secθ = ±2.9478
1/cosθ = ±2.9478
cosθ = ±1/2.9478
cosθ = ±0.3392
cosθ ≈ ±0.339
Since we have 0<θ<π/2, cosθ is in the first quadrant, so we choose the positive value.
So, cosθ = +0.339 where 0<θ<π/2
b. Given that tanθ ≈ -1.559 where 3π/2<θ<2π, find the values of sinθ and cosθ.
i. sinθ
Given that 1 + cot²θ = cosec²θ
cotθ = 1/tanθ
Since tanθ = -1.559, cotθ = 1/tanθ = 1/-1.559 = -0.6414
So, 1 + cot²θ = cosec²θ
1 + (-0.6414)² = cosec²θ
1 + 0.4114 = cosec²θ
1.4114 = cosec²θ
cosec²θ = 1.4114
cosecθ = ±√1.4114
cosecθ = ±1.1880
1/sinθ = ±1.1880
sinθ = ±1/1.1880
sinθ = ±0.8417
sinθ ≈ ±0.842
Since we have 3π/2<θ<2π, sinθ is in the fourth quadrant, so we choose the negative value.
So, sinθ = -0.842 where 3π/2<θ<2π
ii. cosθ
Given that 1 + tan²θ = sec²θ
Since tanθ = -1.559,
So, 1 + tan²θ = sec²θ
1 + (-1.559)² = sec²θ
1 + 2.4305 = sec²θ
3.4305 = sec²θ
sec²θ = 3.4305
secθ = ±√3.4305
secθ = ±1.8522
1/cosθ = ±1.8522
cosθ = ±1/1.8522
cosθ = ±0.5399
cosθ ≈ ±0.540
Since we have 3π/2<θ<2π, cosθ is in the fourth quadrant, so we choose the positive value.
So, cosθ = +0.540 where 3π/2<θ<2π
Use the perfect square trinomial identity to write this expression in factored form:
x2 + 10x + 25.
Answer:
[tex] {x}^{2} + 10x + 25 \\ = ( {x}^{2} + 10x + {5}^{2} ) + (25 - {5}^{2} ) \\ = {(x + 5)}^{2} [/tex]
help me with my last question for 30 to 100 points if correct
Answer
Ok i will help
Step-by-step explanation:
Yay!
Need help please. Giving 15 points for answering correct!!
Answer:
the first one
Step-by-step explanation:
what is the √n^3 in simplest radical form?
Answer:
Surds. Note: a root we can't simplify further is called a Surd. So √3 is a surd.
The graph shows the relationship between time
and the number of soda bottles a machine can
make. Use the points (4,96) and (6,144) to find
the number of soda bottles the machine can make
each minute.
Answer:
The machine can make 24 bottles of soda per minute
Step-by-step explanation:
Looking at the graph of the relationship, we can see that the number of bottles per minute simply represent the slope of the line
Thus, by calculating the slope using the given points, we can have the number of bottles per minute
We have the formula as;
m = (y2-y1)/(x2-x1)
(x1,y1) = (4,96)
(x2,y2) = (6,144)
m = (144-96)/(6-4) = 48/2 = 24
how do u solve -2x=-26
Answer:
x=-14
Step-by-step explanation:
because -2(-14)=-26
In the month of agust, joes snack shack sold 400 sandwiches. If 40% of them were made with chicken, how many chicken sandwiches were sold?
Answer: 160 chicken sandwiches were sold.
To convert a percentage into a decimal, move the decimal two places back.
40%=0.40, or 0.4
This means that 0.4 is still equivalent to 40%
Remember that "of" means multiplication.
So 0.4*400=160
160 chicken sandwiches were sold
the Angle opposite The OPP is
Answer:
Theta
Step-by-step explanation:
Indeed all angles of a triangle have a opposite side. And in trigonometry, the side opposite to theta is opposite side
what is the 66th term in the following arithmetic sequence
-93, -85, -78, -71
Answer:
d= a2- a1
hence d= -85-(-93) = -85+93 = 8
a1= -93
d= 8
n=66
hence a66=a1+(n-1)d
a66= -93+ 65(8)
=-93+520
=427
66th term=427
pls mark as brainliest
What is the slope of the line? Khan academy 15 points
Answer:
m = -8/5
Step-by-step explanation:
First determine how much x changes as we go from the first point to the second: -1 to +4. This change (the 'run') is 5 units.
Then find the change in y: -4 - (4) = -8. This change (the 'rise') is -8.
Thus the slope m = rise / run is m = -8/5
Maggie started collecting teacups on her 13th birthday when she was given 4 teacups. She has purchased a new teacup every month since then. How many teacups will she
have on her 17th birthday?
A.52
B.64
C.38
D.48
Answer:
A. 52
Step-by-step explanation:
Find how many months are in 4 years, since there are 4 years between her 13th and 17th birthdays.
There are 12 months in a year, so multiply 12 by 4:
12(4)
= 48
So, there are 48 months in 4 years. Since she buys a new teacup every month, this means she will have bought 48 more teacups.
Add this to the 4 teacups she got on her 13th birthday:
48 + 4
= 52
So, on her 17th birthday, she will have A. 52 teacups
What is the volume of a rectangular prism with a length of 5 cm, width of 4cm, and height of
9cm?
Answer:
180cm^3
Step-by-step explanation:
All you have to do is multiply everything together to get the volume. l x w x h
Answer:
The answer is 180 cubic centimeters.
Step-by-step explanation:
To find the volume of the rectangular prism, use the formula V= LWH. Next, plug in the information given from the question, and the formula will look like V= (5cm) (4cm) (9cm).
Then, solve the equation for the answer, and the answer will be 180 cubic centimeters.
20% of j is 12 what is j
Answer:
60
Step-by-step explanation:
20/100 * j = 12
j = 12 * 100/20
j = 60
this is timed and I just need to see if i’m right! please check my work :)
what is the area of the figure below
Answer:
58cm2
Step-by-step explanation:
put it in section and them slove
so area of triangle = b×h÷2= 6×3/2=9cm2
area of terpizium = 5(4+6)/2=25cm2
area of triangle = 8×6÷2=20cm2
add all these together You get 58cm2
hope this helps :)
The length of the diameter of a sphere is 8 inches. The volume of the sphere is
_______. the surface area of the sphere
A. equal to
B. less than
C. greater than
Please help me on this question.
Answer:
This is the ans i think this is right
(I NEED HELP ASAP) In a class, there are 25 boys and 15 girls. If a student is selected at random, what is the probability that the student is a boy?
15/25
3/8
25/15
5/8
Answer: 3rd
Answer: 3rd
25/15
Will rank brainliest!!
Answer:
x=46 degree
Step-by-step explanation:
32 +x=Angle ABC
32 + x =78 degree
x=78 - 32
x=46 degree
If x-y = b which statement is right b - y = x, X x Y = b2, b = x - y or b = y x X (this is a question to see if the site works, I know the answer)
Answer:
b = x - y
Step-by-step explanation:
Given the expression x - y = b
We are to rewrite the value of b;
We can simply do this by swapping both sides that are putting b at the Left hand side and x - y at the right as shown
b = x - y
Hence the correct expression will be b = x - y
Match each product of powers with its simplified expression
= 5-³ -³
= 5-⁶
= 1/5⁶
5⁷ × 5³= 5⁷+³
= 5¹⁰
5⁶×5 -⁴= 5⁶ - ⁴
= 5²
5-⁴×5⁴×5⁰= 5-⁴ + ⁴ × 1
= 5⁰
Answer:
answser in picturew
Step-by-step explanation:
Select the correct answer.
Joseph plots the speed of his car and time on a scatter plot. The equation for the line of best fit on his scatter plot is y = -15x + 60, where x is the time in hours and y is the speed in miles/hour. Which statement describes the situation correctly?
A.
The initial speed is 60 miles/hour, and his speed decreases by 15 miles/hour every hour.
B.
The initial speed is 60 miles/hour, and his speed increases by 15 miles/hour every hour.
C.
The initial speed is 0 miles/hour, and his speed increases by 15 miles/hour every hour.
D.
The initial speed is 5 miles/hour, and his speed increases by 30 miles/hour every hour.
Answer:
its be without a doubt
Step-by-step explanation:
Simplify (6x^2 − 8x) ÷ (2x) step by step
a. 2x − 3
b. 2x + 3
c. 3x − 4
d. 3x − 8
Answer:
3x - 4
Step-by-step explanation:
(6x^2 − 8x) ÷ (2x) =
(6x^2)/2x - 8x/2x =
3x - 4
Answer:
(C). 3x - 4
Step-by-step explanation:
It will be easily to break this down so,
6/2=3
x^2/x=x
therefore, 6x^2/2x = 3x
Minus stay minus
8/2 = 4
x/x=1
therefore, 8x/2x=4
If we put it all together,
3x - 4
if this helps you, please give brainliest!
Can someone please help
Answer:
ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm and i Oop
Step-by-step explanation:
Use the discriminant to determine the number of solutions to the quadratic equation 3x^2+5x=-1
Answer:
Two real distinct solutions
Step-by-step explanation:
Hi there!
Background of the Discriminant
The discriminant [tex]b^2-4ac[/tex] applies to quadratic equations when they are organised in standard form: [tex]ax^2+bx+c=0[/tex].
All quadratic equations can be solved with the quadratic formula: [tex]x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}[/tex].
When [tex]b^2-4ac[/tex] is positive, it is possible to take its square root and end up with two real, distinct values of x.
When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.
When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.
Solving the Problem
[tex]3x^2+5x=-1[/tex]
We're given the above equation. It hasn't been organised completely in [tex]ax^2+bx+c=0[/tex], but we can change that by adding 1 to both sides to make the right side equal to 0:
[tex]3x^2+5x+1=0[/tex]
Now that we can identify the values of a, b and c, we can plug them into the discriminant:
[tex]D=b^2-4ac\\D=(5)^2-4(3)(1)\\D=25-4(3)(1)\\D=25-12\\D=13[/tex]
Therefore, because the discriminant is positive, the equation has two real, distinct solutions.
I hope this helps!
Find the y-coordinates of points on the line y = −0.5x that have x-coordinates of 6[tex]coordinates[/tex]
Answer:
y = -3
Step-by-step explanation:
y = -0.5(6)
y = -3
What inverse operation should be used to isolate the variable in the equation c ÷ 7 = 2?
synthetic division problem... pls help asap
please please HELP me! this is due tonight
explaining your answer = brainliest/five star rating
the peremiter is 15 cm. c = ___ cm?
Answer:
4
Step-by-step explanation:
the perimeter is the the total length of the shape. we already know that the two sides is 8, and 3 cm. we also know that the perimeter is 15cm. 8+3 is 11 so we need to figure out the remaining length of the side. 15-11 is 4 so the missing length, c, is 4 cm.