PLEASE HELP ASAP 30 POINTS!!! WILL GIVE BRAINLIEST!!
1. In the first step of proof, the left-handed side of the following identity is factored. Which fundamental identity is used in the second step of the proof?
2. Simplify the expression. csc^2x-1/1+sinx
Answers
1. The factoring step is
sin²θ - cos²θ sin²θ = sin²θ (1 - cos²θ)
Then the Pythagorean identity is invoked:
cos²θ + sin²θ = 1 → 1 - cos²θ = sin²θ
so that
sin²θ - cos²θ sin²θ = sin²θ sin²θ = sin⁴θ
(third option)
2. Recall that a ² - b ² = (a - b) (a + b). The numerator here is such a difference of squares:
csc²x - 1 = (cscx - 1) (cscx + 1)
Then
(csc²x - 1) / (1 + sinx) = ((cscx - 1) (cscx + 1)) / (1 + sinx)
Recall that cscx = 1/sinx, so rewrite this as
… = ((1/sinx - 1) (1/sinx + 1)) / (1 + sinx)
In the numerator, pull out a factor of 1/sinx from both terms:
… = (1/sinx (1 - sinx) × 1/sinx (1 + sinx)) / (1 + sinx)
… = ((1 - sinx) (1 + sinx)) / (sin²x (1 + sinx))
Cancel the common factor of 1 + sinx :
… = (1 - sinx) / sin²x
Expand the fraction and rewrite sin in terms of csc :
… = 1/sin²x - sinx/sin²x
… = 1/sin²x - 1/sinx
… = csc²x - cscx
Factor out cscx to get the second option,
… = cscx (cscx - 1)
Related Questions
Write the equation of the line that passes through the given points. Include your work in your final answer.
(2, 3) and (2, 5)
Answers
Leo is buying a shirt for his grandfather for his upcoming birthday. The shirt cost $34.50 and a 6.5% sales tax is applied. How much is the total cost of the shirt?
Answer choices
A. $32.26
B. $36.82
C.36.74
D.35.00
Answers
4) Does the table show a function?
Yes or no
Answers
Answer:
yes
Step-by-step explanation:
PLEASE HELP ASAP WILL GIVE BRAINLIEST Question 1 of 10
Which point lies on the line described by the equation below?
y + 4 = 4(x-3)
A. (1,-11)
B. (3,-4)
C. (1,11)
D. (0,0)
E. (-2,3)
O F. (2,9)
Answers
Answer:
(3, -4)
Step.
The coordinates of the point which lies on the equation is A ( 3 , -4 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
y + 4 = 4 ( x - 3 ) be equation (1)
when x = 3 and and y = -4
Substituting the values of x and y in the equation , we get
-4 + 4 = 4 ( 3 - 3 )
0 = 4 ( 0 )
0 = 0
Therefore , the point A ( 3 , -4 ) lies in the equation
Hence , the coordinates of the point is A ( 3 , -4 )
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There are 12 girls and 3 boys in the french club. What is the ratio of girls to boys? If you answer this question I'll give your the brainliest
Answers
Answer:
I think ur answer would be
12:3
is girl:boy
3 is a the least common factor
4:1
is girl:boy
hope this helps<3
1. At what price must an article which cost $450 be sold in order to make a profit
of 16.5% on cost?
Answers
Answer:
$450.00 x 16.5% = $74.25
$450.00 + 74.25 = $524.25
Answer $524.25
Step-by-step explanation:
PLEASE HELP 17 POINTS!
1. A slice is being made to a cube. For each slice—
• Describe the two-dimensional figure resulting from the described slice. Use the specific name when possible.
• Determine whether a different slice can produce a congruent two-dimensional figure. If so, describe or sketch an example of the slice. If not, explain why not.
(a) a slice parallel to the base
(b) a slice that contains and
(c) a slice that contains and vertex F
Answers
(a.) A slice parallel to the base would result in two rectangular prisms, as opposed to a cube now. These two rectangular prisms would be congruent to each other as it is a perfect slice through the middle.
(b) A slice that contains and AE and DH will make a slanted cube, meaning it will turn into a cubic pyramid.
(c.) A slice that will contain and vertex F will make the cut the figure in half going slanted. They will technically be congruent, although there is no name for this figure.
What is the volume, in cubic inches, of one cube with an edge length of 1/3inch?
Answers
Answer:
1/27
Step-by-step explanation:
100 points! Mhanifa can you please help? Look at the picture attached. I will mark brainliest!
Answers
Answer:
1 and 2.
Midpoints calculated, plotted and connected to make the triangle DEF, see the attached.
D= (-2, 2), E = (-1, -2), F = (-4, -1)3.
As per definition, midsegment is parallel to a side.
Parallel lines have same slope.
Find slopes of FD and CB and compare.
m(FD) = (2 - (-1))/(-2 -(-4)) = 3/2m(CB) = (1 - (-5))/(1 - (-3)) = 6/4 = 3/2As we see the slopes are sameFind the slopes of FE and AB and compare.
m(FE) = (-2 - (- 1))/(-1 - (-4)) = -1/3m(AB) = (1 - 3)/(1 - (-5)) = -2/6 = -1/3Slopes are sameFind the slopes of DE and AC and compare.
m(DE) = (-2 - 2)/(-1 - (-2)) = -4/1 = -4m(AC) = (-5 - 3)/(-3 - (-5)) = -8/2 = -4Slopes are same4.
As per definition, midsegment is half the parallel side.
We'll show that FD = 1/2CB
FD = [tex]\sqrt{(2+1)^2+(-2+4)^2}[/tex] = [tex]\sqrt{3^2+2^2}[/tex] = [tex]\sqrt{13}[/tex]CB = [tex]\sqrt{(1 + 5)^2+(1+3)^2}[/tex] = [tex]\sqrt{6^2+4^2}[/tex] = 2[tex]\sqrt{13}[/tex]As we see FD = 1/2CBFE = 1/2AB
FE = [tex]\sqrt{(-4+1)^2+(-1+2)^2}[/tex] = [tex]\sqrt{3^2+1^2}[/tex] = [tex]\sqrt{10}[/tex]AB = [tex]\sqrt{(-5 -1)^2+(3-1)^2}[/tex] = [tex]\sqrt{6^2+2^2}[/tex] = 2[tex]\sqrt{10}[/tex]As we see FE = 1/2ABDE = 1/2AC
DE = [tex]\sqrt{(-2+1)^2+(2+2)^2}[/tex] = [tex]\sqrt{1^2+4^2}[/tex] = [tex]\sqrt{17}[/tex]AC = [tex]\sqrt{(-5 +3)^2+(3+5)^2}[/tex] = [tex]\sqrt{2^2+8^2}[/tex] = 2[tex]\sqrt{17}[/tex]As we see DE = 1/2ACHenry has 96 marbles. He is packing containers with 8 marbles in each container. How many containers, c, does Henry need to pack all the marbles?
96 − c = 8
96 = 8 x c
c = 96 + 8
8 ÷ c = 96
Answers
so 96= 8xC
because we know there’s 96 total, and only 8 per c , this would be the setup
REALLY NEED HELP
Graph the line x=4.
Answers
Answer:
X=4 would be right above the 4 on the x axis.
Step-by-step explanation:
So you see where it says x? Graph it on the 4 on that line.
Answer:
Graph it on the 4 on line X
PLEASE HELP ILL GIVE BRAINLIEST!!
WITH WORK PLZ! THANK YOU
The frame around a rectangular picture has a uniform width. The dimensions of the picture are 5 in. by 7 in. If the combined area of the picture and the frame is 80 in.2, what is the width of the frame?
Answers
24 inches hope this helps
Answer:
1.5 in
Step-by-step explanation:
When you combine the like terms -x and -32x,what does that simplify to?
Answers
Answer: 31x
Step-by-step explanation:
( -x + 32x )
( -1 + 32x )
= 31
Please help I need this answer
Answers
Answer:
This is your answer
Step-by-step explanation:
(For the second step I multiplied 6 and 4)
Find < VXW
A.52
B.60
C.68
D.75
PLEASE HELP ME ASAP PLEASE
Answers
the answer is c because
y=60° opposite angles of a parallelogram are congruent.
? = 180-52-60 co- interior
=68°
Miguel measures two sides of a sail: 15 feet and 8 feet. Which could be the measurement of the third side?
A. 6 feet B. 10 feet C. 23 feet D. 30 feet
Answers
Answer:
10
Step-by-step explanation:
6 feet and 10 feet are the possible measurement of the third side.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
To determine the possible measurement of the third side of the sail, we can use the triangle inequality theorem,
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check the answer choices using the triangle inequality theorem:
A. 15 + 8 > 6
23 > 6
This is true, so 6 feet could be a possible measurement of the third side.
B. 15 + 8 > 10
23 > 10
This is true, so 10 feet could be a possible measurement of the third side.
C. 15+8 > 23
23=23
This is false, so 23 feet is not possible measurement of the third sid
D. 15+8 > 30
23>30
This is false, so 30 feet is not possible measurement of the third side
Hence, 6 feet and 10 feet are the possible measurement of the third side.
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4x + 2y = -14 and 7x – y = 16
Answers??
Answers
Answer:
(1,-9)
x=1, y=-9
Step-by-step explanation:
For Halloween Debby and her sister combined the candy they received. Debby had 32 pieces of candy while her sister had 45. If they ate 24 pieces the first night, how many pieces do they have left?
Answers
In triangle RST, the measure of angle T=90°, the measure of angle R=67°, and TR = 94 feet. What is the length of RS to the nearest tenth of a foot?
Answers
Answer:
The answer is 240.6 feet
need an answer please:)
Answers
Answer:230
Step-by-step explanation:
At Fireside Bookshop, you buy a book for $30.00. If the sales tax is 9.5%, what is the total price you pay for the book?
Answers
Answer:
$32.85
Step-by-step explanation: 9.5% of 30 is 2.85
30 + 2.85 = 32.85
Which points lie on a circle that has its center at the origin and contains the point (0, 3)?
Answers
Answer:
(1,2[tex]\sqrt{2}[/tex])
What is the equation of the line in slope-intercept form?
A.) y = x + 8
B.) y = x - 8
C.) y = 8x + 8
D.) y = 8x - 8
Answers
2a.) A(t) is the average high temperature in Aspen, Colorado, "t" months after the
start of the year. M(t) is the average high temperature in Minneapolis, Minnesota,
"t" months after the start of the year. Temperature is measured in degrees
Fahrenheit. Which function had the HIGHER average rate of change between the
beginning of January and middle of March? *
Answers
Answer:
As you didn't add the graph, I will for you.
Step-by-step explanation:
The correct answer is Minneapolis because as you can see Aspen did not change as dramatically as Minneapolis.
The start of January and the middle of March, Minneapolis, or function M(t), had a larger average rate of change. It means that Minneapolis experiences a greater increase in temperature than Aspen does.
What is meant by function?A mathematical formula, rule, or legislation that establishes the link between the independent variable and the dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
In the beginning of January, Aspen's temperature was 35° F, and in the middle of March, it was 48° F. 3.5 months later Minneapolis has lows of 25 degrees Fahrenheit in January and highs of 50 degrees Fahrenheit in the middle of March (at 3.5 months).
So, the average rate of change of temperature of Aspen between the points (1, 35) and (3.5, 48) exists
[tex]$\frac{y_2-y 1}{x_2-x_1}=\frac{48-35}{3.5-1}=5.2$[/tex]
The average rate of change of temperature of Minneapolis between the points (1, 25) and (3.5, 50) is [tex]$\frac{50-25}{3.5-1}=10$[/tex]
Thus, from the start of January and the middle of March, Minneapolis, or function M(t), had a larger average rate of change. It means that Minneapolis experiences a greater increase in temperature than Aspen does.
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On a snowy winters eve two candles are lit at the exact same time. A 18-inch candle and a 21-inch candle are lit at the exact same time. The 18-inch candle burns 2 inches every hour. The 21-inch candle burns 3 inches every hour. Create a system of equations using the information
Answers
Answer:
y=21-3x and y=18-2x
Step-by-step explanation:
Ok, so we have candle A, which is 21 inches and burns 3 inches every hour. in slope-intercept form, the hours would be the x, the 21 is our y intercept. So the first equatio would be y=-3x+21 (negative slope, because the height of the candle is going down). Candle b, which is 18 inches, burns away 2 inches each hour. We can make -2 the slope (negative 2, since the candle is being burned away, not being added to), and the 18 our y intercept. So the two equations would be
y=21-3x
and
y=18-2x
hope this helps!
simplify the answer as much as possible
Answers
Answer:
f(-5)=240
g(-7)=-33
Step-by-step explanation:
1) f(x)=3x^2 - 3x
f(-5)= 3×(-5)^2 - 3×(-5) = -15^2 + 15= 225 + 15=240
2) g(x)=5x + 2
g(-7)= 5×(-7) + 2= -35+2=-33
Which is the graph of y = -(x - 3)2 - 1?
O
6-
у
|
5-
31
2+
1
« Previous
Answers
Answer:
Step-by-step explanation:
y = -½(x-3)²-1
This is the equation of a vertical parabola with vertex at (3,-1). The leading coefficient is negative, so the parabola opens downwards.
Kari plans to attend a 2-year community college. She will receive $4,500 in scholarships and grants each year, and she will earn $1,500 each year through a work study program.
Including her financial aid, what is Kari’s estimated cost per year? $
Kari’s family will contribute $3,000 each year. How much will Kari need to contribute? $
Kari has one year to save enough for her first year’s contributions. Complete each statement to show how much Kari will need to save each month based on her current savings.
If Kari currently has $0 in savings, she will need to save $
each month.
If Kari currently has $1,000 in savings, she will need to save $
each month.
If Kari currently has $2,000 in savings, she will need to save $
each month.
Answers
Answer:
Step-by-step explanation:
4 year Public University
Tuition and fees $ 8500
Room and board $ 6700
Books and supplies $1250
misc expenses $ 700
Total for 1 year
8500+6700+1250+700
= $ 17150
Total for 4 years 4* 17150 = $68600
4 year Private University
Tuition and fees $ 25100
Room and board $ 8000
Books and supplies $ 1300
misc expenses $ 750
Total for 1 year
25100+8000+1300+750
= $ 35150
Total for 4 years 4* 35150 = $ 140600
2 Year Community College
2 Year Community College
Tuition and fees $ 4400
Room and board $ 5000
Books and supplies $ 1100
misc expenses $ 800
Total for 1 year
4400+5000+1100+800
= $ 11300
Total for 2 years 2* 11300 = $ 22600
now given
kari will get $4500 in scholarships and grants yearly and $1500 yearly through work study program
so in total kari will get in financial aid = $6000 yearly
so in 2 years she will get total = 2*6000 = $12000 financial aid
kari's estimated cost per year = total fee of college for 1 year - total financial aid for 1 year
= $11300 - $ 6000 = $5300
Kari's estimated cost per year = $5300
then estimated cost for two years = 2* 5300 = $10600
given Kari's family will contribute $3000 yearly
so for two years Kari will get = 2*3000 = $6000 from family
If kari has 1 year to save for 1st year's contribution then
a) kari has $0 in savings
kari needs to save for year = estimated cos per year - contribution from family per year
= $5300 - $ 3000 = $2300
as kari has $0 savings so kari needs to save $2300 in 1 year
so kari needs to save an amount = 2300/12 = $191.666667 monthly
b) kari has $1000 in saving
then kari needs to save an amount for 1 year = estimated cost per year - contribution from family per year - kari's initial savings
Amount to be saved for 1 year = $5300 - $3000 - $1000
= $1300
so kari needs to save an amount of = 1300/12 = $108.3333333 monthly
c) Kari has $2000 in saving
then kari needs to save an amount for 1 year = estimated cost per year - contribution from family per year - kari's initial savings
Amount to be saved for 1 year = $5300 - $3000 - $2000
= $300
so kari needs to save an amount of = 300/12 = $25 monthly
What is the answer to 153÷1/4=?
Answers
Answer: 38.25
Step-by-step explanation: You divide the whole number by the denominator in the fraction.
153/4 = 38.25
Answer:
612
Step-by-step explanation:
you can always use a calculator if you need help with division : )
Six friends share 8 fruit bars equally. How many fruit bars does each friend get?
Answers
Answer:
0.75 friends per fruit
Hope this helps
Answer:
Each friend get 1 and 1 3rd
Step-by-step explanation: