Answers
Answer:
cos(α2)= −1/5√2
Step-by-step explanation:
you are given tan(α)=7/24 , so you can find the length of the hypotenuse using the Pythagorean theorem, which is a2+b2=c2 with a and b being the legs of the triangle and c being the hypotenuse of the triangle.
c2=7^2+24^2
⟹c2=49+576
⟹c2=625
⟹c=25
if π<α<3π/2 , then α has to lie in quadrant III where cosine is negative. so cos(α)= −24/25
The half-angle identity for the cosine function is cos(α2)=±√1+cos(α)/2 , so plugging the information in, we get
cos(α2)=±√ 1+(−24/25)/2
⟹ cos(α2)=±√1/25 / 2
⟹cos(α2)=±√1/50
⟹cos(α2)=±1/5√2
Related Questions
One serving of a certain brand of yogurt contains 9 g of fat. The low-fat version contains 36.75% less fat per serving. How many grams of fat does one serving the low-fat yogurt contain?
Answers
Answer:
Answer Choices??
Step-by-step explanation:
The graphed line shown below is y = 5 x minus 10. On a coordinate plane, a line goes through (2, 0) and (3, 5). Which equation, when graphed with the given equation, will form a system that has no solution? y = negative 5 x + 10 y = 5 (x + 2) y = 5 (x minus 2) y = negative 5 x minus 10 Mark this and return
Answers
Answer:
The correct option is:
y = 5(x-2)
Step-by-step explanation:
The graphed line is;
y = 5x - 10
y = mx + c
Thus, slope of graphed line is equal to m=5.
Those line will have no solution which have are parallel to the graphed line (have a slope of 5) and passes through the given points.
Following lines have the slopes 5:
y= 5(x+2)
y= 5(x-2)
Check which equation satisfied points (2,0) and (3,5)
For (2,0)
y=5(x-2)
y=5(2-2)
y=0
For (3,5)
y=5(x-2)
y=5(3-2)
y=5
Thus, correct option is y = 5(x-2)
Answer:
y = 5 (x + 2)
Step-by-step explanation:
Its this because the slopes have to be the same, but the y intercepts have to be different
Select all the expressions that are equivalent to 16x + 36.
a 16(x + 20)
b. x(16+36)
C. 4(4x + 9)
d. 2(8x + 18)
e. 2(8x + 36)
Answers
Answer:
2(8x + 18) and 4(4x + 9)
Step-by-step explanation:
16 and 36 are both evenly divisible by 2 and 4. Thus, possible equivalents of 16x + 36 are 2(8x + 18) and 4(4x + 9).
Expressions equivalent to 16x + 36 are 4(4x+9) and 2(8x + 18).
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
Given expression
16x + 36
= 4.4x + 4.9
16x + 36 = 4(4x+9)
= 2.2(4x + 9)
16x + 36 = 2(8x + 18)
Hence, 4(4x+9) and 2(8x + 18) are equivalent to 16x + 36.
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Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (7,-7) and perpendicular to the line whose equation is x - 5y-2 = 0
The equation of the line in point-slope form is...
Answers
Answer:
y=-5x+28 general form
slope point :y-(-7)=-5(x-7)
Step-by-step explanation:
definition :perpendicular slopes are negative reciprocals of each other
x-5y-2=0
y=1/5 x-2/5
slope of the perpendicular line =1/m=-1/(1/5)=-5
slope point :y-(-7)=-5(x-7)
find b :
y=-5x+b
-7=-5(7)+b
b=-7+35=28
y=-5x+28
y=1/5 x-2/5
There is $500 in each of three envelopes. The first envelope contains only $10 bills, the second envelope contains only $20 bills, and the third envelope contains only $50 bills. One bill is taken out of one of the envelopes, two bills are taken out of another envelope, and three bills are taken out of the remaining envelope (in any order). What is the least possible amount, in dollars, that can be taken out?
Answers
Answer:
order:
-3 bills from first envelope (-30 dollars)
-2 bills from second envelope (-40 dollars)
-1 bill from third envelope (-50 dollars)
total least possible amount that can be taken out: 120
Step-by-step explanation:
Any other ways results in more than 120 being taken away. Need to have the least taken away from the 50 bill envelope because 50 is the largest bill. Take away the most from the 10 bill envelope because 10 is the smallest bill.
Answer:
$120
Step-by-step explanation:
So this question isn't hard either
We can cross out excess information and just find the main points.
a. 3 Envolopes containing 10 bills, 20 bills, and 50 bills
b. 1-3 bills are taken out of each envolope
c. It wants you to find the least possible amt. that could have been token out.
So since we want the least, we must take the smallest out of the largest
In order, 1 from 50 (largest)
2 from 20 (middle)
and 3 from 10 (smallest)
this leaves us the equation (1x50) + (2x20) + (3x10) => 50+40+30 => 120
Thus, we have our answer 120
Hope this helps!
Given that m angle x is 30 degrees in the diagram above find the m angle y please help now
Answers
Answer:
m<y= 30°Step-by-step explanation:
Because they are vertically opposite angles.
Vertically opposite angles are always equal.
About vertically opposite angles:Please see the attached picture.
There,
<AOC and <BOD are formed by the intersected line segments and they lie to the opposite side of the common vertex. They are called vertically opposite angles. <AOD and <BOC are another pairs of vertically opposite angles. Vertically opposite angles are always equal.
Hope this helps ...
Good luck on your assignment...
Answer:
y = 30°
Step-by-step explanation:
X and Y are vertically opposite angles meaning they are equal
Calculate the final cost: Original price $125 Discount 25%
Tax 6.5%
Please help me
Answers
Answer:
99.84
Step-by-step explanation:
Take the original price and subtract the discount
125 - .25 * 125
125 -31.25
93.75
Now add in the tax
93.75+.065*93.75
93.75+6.09375
99.84375
Rounding to the nearest cent
99.84
PLEASE HELP!! I will award Brainliest and give 55 POINTS!!! THANK YOU
Answers
Answer:
79
Step-by-step explanation:
If we square m + 1/m we get (m + 1/m)² = m² + 2 * (m * 1/m) + 1/m² = m² + 2 + 1/m². Since m + 1/m = 9, (m + 1/m)² = 81 so that means that m² + 1/m² = 81 - 2 = 79.
Answer:
79 is correct
What is the value of the expression below? 81^5/4
Answers
Answer:
81^5/4
Rewrite 81 in index form that is 3⁴
So we get
3⁴ × ^5/4
= 3^5
= 243
Hope this helps
Answer:
243 is correct
Step-by-step explanation:
What is the product of (7/8)(-16)(-7)(- 1/14)
Answers
Answer:
-7
Explanation:
7/8 x - 16 x -7 x -1/14 = -7
Answer: -7
7/8 x -16 = -14
-14 x -7 = 98
98 x 1/14 = -7
ANSWER IS -7
What is the value of (Negative 5) Superscript 4?
Answers
Answer:
625
Step-by-step explanation:
-5⁴
-5 × -5 × -5 × -5
= 625
the simplified value of the given Expression (Negative 5) Superscript 4 will be 20.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given a mathematical expression (Negative 5) Superscript 4
Simplifying the expression
=> (Negative 5) Superscript 4
in other terms
=> (-5)⁴
=> -5*-5*-5*-5
=> 20
Therefore, the simplified value of the given Expression will be 20.
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select the correct statement about the function represented by the table. A. It is an exponential function because the y-values increase by an equal factor over equal intervals of x values. B. It is a linear function because the difference y - x for each row is constant. C. It is an exponential function because the factor between each x and y value is constant. D. It is a linear function because the y values increase by an equal difference over equal intervals of x-values.
Answers
Answer: D.
Step-by-step explanation:
The common difference between each y-value is 18.
80 - 62 = 18
62 - 44 = 18
44 - 26 = 18
The function stays the same for every interval of the x-values
(1, 26)
(2, 44)
(3, 62)
Since the increase in the y-value is the same with equal intervals of x-values, the function represents the linear function. Thus, option D is correct.
What is function?Function is the expression that defines the relationship between the independent and dependent variables.
Determine the difference between the consecutive y-values.
44-26=18
62-44=18
80-62=18
98-80=18
It can be observed that the difference in the consecutive y-values is same, which is, 18.
Since the increase in the y-value is same with equal interval of x-values, the function represents the linear function.
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Determine the equation of a circle whose diameter has the endpoints (-1, 2) and (7.
-4).
1) (x - 3)2 + (y + 1)2 = 5
2) (x - 3)2 + (y + 1)2 = 25
3) (x - 3)2 + (y + 1)2 = 100
4) (x - 3)2 + (y + 1)2 = 10
Answers
Answer:
(x - 3)^2 + (y + 1) = 25
Step-by-step explanation:
First find the midpoint of the diameter, because that represents the center of the circle.
-1 + 7
The x-coordinate of the midpoint is xm = ---------- = 3
2
2 - 4
and the y-coordinate is ym = ---------- = -1
2
And so the center of this circle is at (3, -1).
Use the Pythagorean Theorem to determine the square of the radius:
square of radius = 4^2 + (-3)^2 = 16 + 9 = 25
And so the equation of this circle is (x - 3)^2 + (y + 1) = 25
Answer:
option 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The centre is at the midpoint of the endpoints of the diameter.
Using the midpoint formula with (- 1, 2) and (7, - 4), then
centre = ( [tex]\frac{-1+7}{2}[/tex] , [tex]\frac{2-4}{2}[/tex] ) = (3, - 1 )
The radius is the distance from the centre to either of the endpoints of the diameter.
Using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (3, - 1) and (x₂, y₂ ) = (- 1, 2)
r = [tex]\sqrt{(3+1)^2+(2+1)^2}[/tex]
= [tex]\sqrt{4^2+3^2}[/tex]
= [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5
Thus
(x - 3)² + (y - (- 1))² = 5² , that is
(x - 3)² + (y + 1)² = 25 ← equation of circle
Find the value of $B - A$ if the graph of $Ax + By = 3$ passes through the point $(-7,2),$ and is parallel to the graph of $x + 3y = -5.$
Answers
Answer:
A=-3
B=-1
ans:-1-(-3)=2
Step-11by-step explanation:
Ax+By=3,m1= -A/B
x+3y= -5,m2= -1/3
A/B=1/3(parallel)
3A=B
(-7,2)
-7A+2B=3
-7A+6A=3
A= -3
B=-3/3= -1
-1-(-3)=2
Martina creates the graph of function g by applying a transformation to function f
f(x) = 4^x-2
g(x) = 4^x+7
Which transformation did Martina apply?
Answers
Answer:
A
Step-by-step explanation:
f(x)=4^x-2
g(x)=4^x+7
it is horizontal shift 9 unit to the left
hope it works
Answer:
A: A horizontal shift of 9 units left
Hope this helps! :D
Step-by-step explanation:
Round 65.65 to the nearest whole number
Answers
Answer:
66
Step-by-step explanation:
We know that whole number means the digits before the decimal point, meaning we have to take a look at .65 since that is after the decimal point.
So
We take a look at .6, since that is the number directly after the decimal point.
If the digit is 5 and up we round up, if the digit is 4 and down we round down
."6" is our digit meaning we round up
So we take 65 and round up to 66, making the number a whole number with no decimals after it
a line in a cartesian plane passes through the points 5,8 and 9,15. what's the slope of the line
Answers
Answer:
B. 7/4
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]
Plug in the coordinates:
m = (15 - 8)/(9 - 5)
m = 7/4
The expression is now simplified to 3−6i+5i. What is the a+bi form? Type in your final solution in a+bi form, like this: 4+2i Algebra 2
Answers
Answer:
3 - 1i
Step-by-step explanation:
3 - 6i + 5i
Add like terms.
3 - 1i
3 + -1i
a = 3
b = -1
Use the graph of f to describe the transformation that results in the graph of g. f(x) = log x; g(x) =
Answers
Answer:
The function was expanded vertically by 5, and then translated vertically upwards 6 units.
Which is the third option in the list of possible answers.
Step-by-step explanation:
Recall that the types of transformations associated with:
A) a function multiplied by a positive factor larger than one consists on the function expanded vertically by that factor.;
B) a positive number added to the function consists on the vertical translation of the function upwards as many units as the number added.
Therefore, the function [tex]f(x) = log(x)[/tex] being transformed into [tex]g(x)=5\,log(x)+6[/tex]
consists of the initial function expanded vertically by 5, and then translated vertically upwards 6 units.
THE IMAGE DOWN BELOW MATH PLEASE HELP ME WITH THIS ALEGEBRA IM CRYING YALL
Answers
Answer:
50%
Step-by-step explanation:
Percent increase formula for your problem:
#wolves increased / # of wolves there were originally
We have
(27-18) / 18
9 / 18
1 /2
1/2=50% So, there was a 50% increase!
Hope this helps
Which of the following are techniques used in geometric constructions with paper folding?
Check all that apply.
A.Creating arcs and circles with the compass
B.Marking points
C.Measuring line segments by folding the paper and matching the endpoints
D.Folding the paper and aligning marks seen through the paper
Answers
The techniques used in geometric constructions with paper folding are marking points and folding the paper and aligning marks seen through the paper.
What is geometric constructions?The geometric construction is the method by which the figures of geometry are drawn using the different geometric instruments.
The techniques used in geometric constructions with paper folding are listed below.
Marking the points on the paper.Folding the paper and orienting marks which are visible through the paper.Drawing the line segments.Thus, the techniques used in geometric constructions with paper folding are marking points and folding the paper and aligning marks seen through the paper.
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Answer:
Drawing line segments
Marking Points
Folding the paper and aligning marks seen through the paper
Write 90 cents to $1.30 a fully simplified ratio by first converting to the same units, and then simplifying.(plz answer I will put brainliest)
Answers
Answer:
9:13.
Step-by-step explanation:
$1.30 = 130 cents
So the ratio is 90:130
= 9:13.
What is the recursive formula for this sequence? 14,18,22,26,30...
Answers
Answer:
an = an-1 +4
a1 = 14
Step-by-step explanation:
The recursive formula is
an = an-1 +d where d is the common difference
a1 = initial term
a1 = 14
d = the difference between the terms
Take the second term and subtract the first term
18-4 = 4
That is the common difference
an = an-1 +4
a1 = 14
If we will analyze this sequence, we will notice that:
The sequence started by 14. So, the first term ([tex]a_1[/tex]) is 14. From 14 to 18 we add 4. From 18 to 22 we add 4. This standard repeats itself infinitely. The next term is equals the last term plus 4.So,
[tex]\boxed{\left \{ {{a_1=14} \atop {a_n=a_{n-1}+4}} \right.}[/tex]
Therefore, the correct option is letter C.
Bert’s cab company charges $1.00 plus an additional $3.00 per mile for a ride. Madeline’s cab company charges $3.00 plus an additional $2.00 per mile for a ride. Write a system of linear equations that shows the cost in dollars, y, for a cab ride of x miles for each cab driver. Bert’s _____________________________________ Madeline’s ________________________________
Answers
Answer:
3*m+1 and 3+2*m
Step-by-step explanation:
$600.99
Step-by-step explanation:
Because the cab company is located in New York. In New York, cab drivers basically rob you.
this is an easy question, and i'm giving all my points, so if y'all want that, answer the following questions
Answers
Answer:
Step-by-step explanation:
a)180 degrees
b)parallel
c)90 degrees
d)supplementary and adiacent
e)right
f)supplementary
Answer:
a) 180°
b) parallel
c) 90°
d) adjacent
e) right angled
f) supplementary
The diagram shows a solid shape.
The volume of the cone is 270 cm.
Work out the volume of the solid shape.
Give your answer in terms of pi
Answers
Answer:
[tex]756\pi[/tex]
Solution,
Volume of cone=270 pi cm^3
[tex] \frac{1}{3} \pi \: {r}^{2} = 270\pi \\ or \: {r}^{2} \times 10 = 270 \times 3 \\ or \: {r}^{2} \times 10 = 810 \\ or \: {r}^{2} = \frac{810}{10} \\ or \: {r}^{2} = 81 \\ or \: r = \sqrt{81} \\ or \: r = \sqrt{ {9}^{2} } \\ r = 9 \: cm[/tex]
Volume of semisphere:
[tex] \frac{2}{3} \pi {r}^{3} \\ = \: \frac{2}{3} \times \pi \times 9 \times 9 \times 9 \\ = 486\pi[/tex]
Total:
[tex]270\pi + 486\pi \\ = 756\pi[/tex]
hope this helps...
Good luck on your assignment..
Easy enough!!! BRAINLIEST AWARDED IF YOU GET IT RIGHT! Solve the problems:
Answers
Answer:
line PQ and line SR are parallel and line PS and line QR are parallel. And we can amuse QS as the transversal.
answers to pairs of angles:
7. opposite interior angles
8. opposite interior angles
9. adjacent interior angles
10. corresponding angles
11. opposite interior angles
Hope it helps
Step-by-step explanation:
If there are 50 cups of rice for a group of five people who have a combined weight of 880 pounds, determine how many cups each person should get per 100 pounds. Round to the nearest tenth of a cup.
Answers
Answer:
28.4 cups
Step-by-step explanation:
If 5 people have a combined weight of 880 pounds, each person sould have a weight of 880/5 = 176 pounds.
Now, we can set up a proportion:
[tex]\frac{176}{50} =\frac{100}{x}[/tex]
Cross Multiply:
176x = 5000
x = 5000/176 = 28.4 cups
The required number of cups that each person has 5.6 cups per 100 pounds.
There are 50 cups of rice and group of 5 combined weight of 880 pounds. To determine how many cups each person should get per 100 pounds.
Fraction is defined as the number of composition constitute the whole.
average wait of people = 880/5 = 176 pounds
Each person can have cup beside the 100 pound weight = 50/5 = 10(max)
Number of cups per 100 pounds = 50/880*100
= 5.6 cups per 100 pound
Thus, the required number of cups that each person has 5.6 cups per 100 pounds.
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Helpppp me plz answer this for me plz
Answers
Answer:
0.1
Step-by-step explanation:
There are 10 letters and only 1 of them is a G so the chance of drawing a G is 1/10 = 0.1.
Answer:
0.1 is the right answer
What’s the answer? It’s a ratio and proportion assignment.
Answers
Answer:
G
Step-by-step explanation:
168/14=12*13.72=164.64
._.