[tex]\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}[/tex]
From Left side:
[tex]\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)[/tex]
[tex]\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}[/tex]
NOTE: sin²θ + cos²θ = 1
[tex]\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{2}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}[/tex]
[tex]\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}[/tex]
[tex]\dfrac{2sec^2\theta}{tan^2\theta-1}[/tex]
Left side = Right side so proof is complete
Answer:
\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}
From Left side:
\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)
\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}
NOTE: sin²θ + cos²θ = 1
\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}
\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}
\dfrac{2}{sin^2\theta-cos^2\theta}
\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}
\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}
\dfrac{2sec^2\theta}{tan^2\theta-1}
Left side = Right side so proof is complete
Step-by-step explanation:
Suppose you earn $6 an hour at you part time job. What will you new hourly rate be after a 2.5% raise. Explain. Please Help me with this one!!
Answer:
$6.15 an hour
Step-by-step explanation:
To find how much money our raise is, we can multiply the percent times our salary
6 * .025 = .15
Our raise is 15 cents an hour
Take what we were making plus our raise
6+.15
$6.15
This is what we will be making per hour.
Mr.Steve drove 92 miles using 4 gallons of gasoline. Find the unit rate of miles driven per gallon.
Answer:23
Step-by-step explanation:
92/4
Write an equation in slope-intercept form for the line that passes through (-3,2) and is perpendicular to the line y=3/2+4
Answer: the equation is slope-intercept form y = -2/3x
Chris plants 40 pumpkin seeds in five equal how many seats does Chris Plant in each row? Make an array to represent the problem?
a factory makes parts for toys in different quantities,as shown in the table. how much would 11 part cost?
Answer can you show use the graph then i would be able to answer it
What is the slope of the line from point (-4,2) to (-2,2)?
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-4, 2) and (-2, 2). Substitute:
[tex]m=\dfrac{2-2}{-2-(-4)}=\dfrac{0}{-2+4}=0[/tex]
Answer: The slope is equal 0 (it's a horizontal line y = 2).an equation and the steps to solve it are shown below: 3x-1/5(10x+5)=6
[tex]3x-\dfrac{1}{5}(10x+5)=6\qquad\text{use distributive property}\\\\3x-\left(\dfrac{1}{5}\right)(10x)-\left(\dfrac{1}{5}\right)(5)=6\\\\3x-2x-1=6\qquad\text{add 1 to both sides}\\\\\boxed{x=7}[/tex]
how to rewrite
[tex]5 {?}^{ - 2} [/tex]
Answer:
[tex]\frac{1}{25}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex], then
[tex]5^{-2}[/tex] = [tex]\frac{1}{5^{2} }[/tex] = [tex]\frac{1}{25}[/tex]
Blockbuster is a store that used to rent videotapes to customers. They charged a $20 membership fee to open a new account. Then, they charged $3 per movie. Your parents had a goft card for $50. How many movies, m could they afford??? What’s the equation plzzz I will give you 100 points
Hello There,
The answer is:
10 movies
Hope this helps have a great day :)
how do I graph y=−2x?
Answer:
Use the slope-intercept form to find the slope and y-intercept.Slope:
2
Y-Intercept:
0
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.x
y
0
0
1
2
Graph the line using the slope and the y-intercept, or the points.
Slope:
2
Y-Intercept:
0
x
y
0
0
1
2
Step-by-step explanation:
Ms Campbell bought 2 table lamps for $42 with tax included .if each lamp costs $20 before tax was added, what tax rate did she pay on the two lamps
Answer:5%
Step-by-step explanation:
Given, cost of two table lamps including tax = $42
Therefore, cost of one table lamp including tax =[tex]\frac{42}{2}[/tex]=21$
Given, cost of one table lamp before tax = $20
Hence tax amount on each lamp = $21 - $20 = $1
Hence tax rate payed[tex]=\frac{\text {tax amount}}{\text {Sale Price}}\times 100[/tex]
[tex]=\frac{1}{20}\times {100}=5\%[/tex]
sole for y
y-5=1/3(x-12)
Answer:
y = 1/3 x +1
Step-by-step explanation:
y-5=1/3(x-12)
Distribute the 1/3
y-5 = 1/3x -1/3 *12
y-5 = 1/3 x -4
Add 5 to each side
y-5+5 = 1/3 x-4+5
y = 1/3 x +1
Lee likes to water ski on his brother's boat and plans to ski for two days in a row. The boat takes two gallons of gas each hour to run. if the price of gas is $5 per gallon, how much money will he spend on gas just ski for 6 hours each day?
Answer:
120 dollars
Step-by-step explanation:
6 hours per day, for 2 days, leads to a total of 12 hours (2*6 = 12)
If it takes 2 gallons of gas to run the boat for 1 hour, then it will take 24 gallons to run for 12 hours. We can see this if we have the ratio below
2 gallons: 1 hour
12*(2 gallons): 12*(1 hour) .... multiply both sides by 12
24 gallons: 12 hours
Now multiply this gallon count (24) by the cost per gallon ($5) and we get to 5*24 = 120
A sandwich costs $0.75 more than a container of milk. A customer buys 4 sandwiches and 4 containers of milk. The customer pays $7.00. What is the cost of a sandwich? Enter your answer in the box.
Answer:
Assume that the cost of the milk is x.
We are given that a sandwich costs 0.75$ more than the cost of milk. This means that:
cost of sandwich = cost of milk + 0.75
cost of sandwich = x + 0.75
Now, the customer bought 4 sandwiches and 4 containers of milk at the cost of 7$.
We will transform this into an equation as follows:
total cost = cost of 4 sandwiches + cost of 4 containers of milk
7 = 4(x+0.75) + 4(x)
Solve the above equation to get x as follows:
7 = 4x + 3 + 4x
7-3 = 8x
8x = 4
x = 0.5
Therefore:
cost of milk = x = $0.5
cost of sandwich = x+0.75 = 0.5+0.75 = $1.25
Answer:
$1.25
Step-by-step explanation:
How do you convert 68.75% to a decimal and fraction in lowest terms
Answer:
11/16
Step-by-step explanation:
68.75 / 100 is the percentage value. You can divide both top and bottom of the fraction by 2568.75 / 25 = 2.75100/25 = 42.75/4 is one fractional answer. if you want whole numbers on the numerator and denominator, multiply the top and bottom by 42.75 * 4 = 114 * 4 = 16So the actual answer is 11/16Answer:
Decimal: 0.6875 Fraction: 2.75/4
Step-by-step explanation:
To convert percent into a decimal you move the decimal point two places to the left. So 68.75% is equal to 0.6875.
To find the fraction form we know that 68.75% is 68.75/100 because percent is of one hundred. We can simply 68.75/100 by dividing the numerator and denominator by 25 and we get 2.75/4. So 68.75% as a fraction is 2.75/4.
what is the formula of median?
Answer:
Step-by-step explanation: Arrange your numbers in numerical order.
Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
Final answer:
The formula for finding the median depends on whether the total number of data values is odd or even. If it is odd, the median is the middle value when the data is ordered from least to greatest. If it is even, the median is the average of the two middle values when the data is ordered.
Explanation:
The formula for finding the median depends on whether the total number of data values is odd or even. If it is odd, the median is the middle value when the data is ordered from least to greatest. If it is even, the median is the average of the two middle values when the data is ordered. For example, if you have the data set 2, 4, 6, 8, 10, the median would be 6 because it is the middle value. But if you have the data set 2, 4, 6, 8, the median would be (4+6)/2 = 5 because it is the average of the two middle values.
Every minute,
2.2
gallons of water flows from a shower. A family of
5
people showers for an average of
9
minutes per person every morning.
Answer:
Step-by-step explanation: If you are trying to figure out how many gallons the whole family uses, the answer is 99 gallons.The reason is is because it says 2.2 gallons a minute and it takes 9 minutes for a shower. So you multiply 9 by 2.2 which would give you 19.8. Then you multiply it by 5 isnce it says 5 people take a shower.
Answer:
99 gallons
Step-by-step explanation:
Let as assume we need to find how many gallons of water does the family use for showering every morning.
It is given that every minute 2.2 gallons of water flows from a shower.
Total number of family members = 5
Average time of shower = 9 minutes per person every morning.
Total time of shower = [tex]9\times 5=45[/tex] minutes
1 minute = 2.2 gallons
45 minute = 2.2 × 45 gallons
45 minute = 99 gallons
Therefore, in every morning 99 gallons of water was used by the family
Isabel is making bead necklaces.she wants to use thirty eight beads to make four necklaces.if she wants each necklace to have the same number of beads,how many beads will she have left over?
Answer:
Step-by-step explanation:
Make circles. 4 circles. Then divide the beads to your circles. The one's you have leftover is your remainder. Hope that helps.
The coordinate points below show part of the data collected by the cell phone company, where x is age in years and y is texting speed in words per minute.
(12, 16), (13, 18), (13, 10), (14, 16), (15, 9), (15, 8), (16, 17), (17, 23)
If this data was plotted on a scatterplot, would there be a relationship between the variables? If yes, explain the relationship.
Yes, there is a relationship. As age increases, texting speed also increases.
Yes, there is a relationship. As age increases, texting speed decreases.
Yes, there is a relationship. As texting speed decreases, age also decreases.
No, there is no clear relationship between age and texting speed.
Answer:
Correct choice is D
Step-by-step explanation:
Plot points (12, 16), (13, 18), (13, 10), (14, 16), (15, 9), (15, 8), (16, 17), (17, 23) on the coordinate plane. On this coordinate plane x represents age in years and y represents texting speed in words per minute.
Option A is false. Consider points A(12,16) and C(13,10). For these points x-coordinates increases, but y-coordinates decreases. Therefore, as age increases, texting speed doesn't increase.
Option B is false. Consider points A(12,16) and B(13,18). For these points both x-coordinates and y-coordinates increases. Therefore, as age increases, texting speed increases too.
Option C is false. Consider points C(13,10) and F(15,8). For these points y-coordinates decreases, but x-coordinates increases. Therefore, as texting speed decreases, age increases.
Option D is true, there is no clear relationship between age and texting speed.
Answer:
The Answer is D. No, there is no clear relationship between age and texting speed.
Step-by-step explanation:
What is the slope-intercept form of the function that contains the point (8, 12) and has a slope of −2? y = x +
Answer:
y = -2x+28
Step-by-step explanation:
We have the slope and a point, so we can use the point slope form to make a line
y-y1 = m(x-x1)
y-12 = -2(x-8)
Distribute the -2
y-12 = -2x+16
Add 12 to each side
y-12+12 = -2x+16+12
y = -2x+28
This is the slope intercept form of the line
Jack is 5 times younger than her mother. In 6 years, Jack will be three times younger than her mother. How old is each now?
Answer:
Jack is 6 and Mom is 30
Step-by-step explanation:
J = Jacks age
M = Mom's age
5J = M
In 6 years, so add 6 to the age
3(J+6) = (M+6)
We have a system of 2 equations and 2 unknowns
Lets simplify the 2nd equation
3(J+6) = (M+6)
3J + 18 = M+6
Substituting M =5J
3J + 18 = 5J +6
Subtract 3J from each side
3J-3J + 18 = 5J-3J +6
18 = 2J+6
Subtract 6 from each side
18-6 = 2J+6-6
12 = 2J
Divide each side by 2
12/2 = 2J/2
6=J
Jack is 6
We still need to find Mom's age
M = 5J
= 5*6
=30
Mom is 30
Which equation does not represent a linear function?
a. y = 2
b. y = x^2 + 9
c. y = x
d. y = -8x + 1
Is the following relation a function?
Answer: No
Step-by-step explanation:
A function has exactly one y output for each x input, and since the input -1 has two outputs, -1 and 2, it is not a function.
Hi there,
The Answer is no
To solve This we need to Remember That a relation can only be a Function if one number from X goes to Y.
In This instance, -1 goes to 2 and -1, While 6 goes to 3 and 4 to 3
Keep In mind that All the number given are points
Hope this Has Helped
|~Adan |
A basketball player made 44 out of 100 attempted free throws. What percent of free throws was made?
Answer:
How much is 44 out of 100 written as a percentage? Convert fraction (ratio) 44 / 100 Answer: 44%
Step-by-step explanation:
44% of the total free throws are made.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have a basketball player made 44 out of 100 attempted free throws.
Assume the percent of free throws be [x]%. We can write -
[x] = (44/100) x 100
[x] = 44%
Therefore, 44% of the total free throws are made.
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7.2 cw homework help
Answer:
31. Yes (Y)
WXYZ ~ DABC
S.F.=4
32. Yes (Y)
GHIJ ~ KLMN
S.F.=2/3
33. Missing length: 16
34. Missing length: 30
35. x=7
36. x=10
Step-by-step explanation:
31. The polygons are similar if:
WX/DA=XY/AB
Then:
WX/DA=24/6→WX/DA=4
XY/AB=16/4→XY/AB=4
Like WX/DA=4=XY/AB, the polygons WXYZ and DABC are similar
Scale Factor: S.F.=XY/DA=XY/AB→S.F.=4
32. The polygons are similar if:
GH/KL=HI/LM=IJ/MN=GJ/KN
Then:
GH/KL=6/9=(6/3)/(9/3)→GH/KL=2/3
HI/LM=4/6=(4/2)/(6/2)→HI/LM=2/3
IJ/MN=4/6=(4/2)/(6/2)→IJ/MN=2/3
GJ/KN=4/6=(4/2)/(6/2)→GJ/KN=2/3
Like GH/KL=HI/LM=IJ/MN=GJ/KN=4, the polygons GHIJ and KLMN are similar
Scale Factor: S.F.=GH/KL=HI/LM=IJ/MN=GJ/KN→S.F.=2/3
33. If the polygons are similar, their sides must be proportional, then:
x/24=10/15
Simplifying the fraction on the right sides of the equation, dividing the numerator ans denominator by 5:
x/24=(10/5)/(15/5)
Dividing:
x/24=2/3
Solving for x: Multiplying both sides of the equation by 24:
24(x/24)=24(2/3)
Multiplying:
x=8(2)
x=16
34. If the polygons are similar, their sides must be proportional, then:
54/63=(54/9)/(63/9)→54/63=6/7
48/56=(48/8)/(56/8)→48/56=6/7
x/35=6/7
Solving for x: Multiplying both sides of the equation by 35:
35(x/35)=35(6/7)
Multiplying:
x=5(6)
x=30
36. (8x-2)/63=42/49
Simplifying the fraction on the right sides of the equation, dividing the numerator ans denominator by 7:
(8x-2)/63=(42/7)/(49/7)
Dividing:
(8x-2)/63=6/7
Solving for x: Multiplying both sides of the equation by 63:
63(8x-2)63=63(6/7)
Multiplying:
8x-2=9(6)
8x-2=54
Adding 2 both sides of the equation:
8x-2+2=54+2
Adding:
8x=56
Dividing both sides of the equation by 8:
8x/8=56/8
Dividing:
x=7
37. (6x-6)/63=42/49=30/35
Simplifying the fractions
(6x-6)/63=(42/7)/(49/7)=(30/5)/(35/5)
Dividing:
(6x-6)/63=6/7
Solving for x: Multiplying both sides of the equation by 63:
63(6x-6)63=63(6/7)
Multiplying:
6x-6=9(6)
6x-6=54
Adding 6 both sides of the equation:
6x-6+6=54+6
Adding:
6x=60
Dividing both sides of the equation by 6:
6x/6=60/6
Dividing:
x=10
NEED HELPP
Indicate the domain of the following fractions: 5x/3x(x+12)
Answer:
x≠-12; x≠0
Step-by-step explanation:
A fraction denominator cannot be 0.
3x(x+12)≠0
if you multiply a number by zero, the product is also zero
3x≠0
x≠0
x+12≠0
x≠-12
if 10×5=50 then 10×50=500 right
Answer:
yes
Step-by-step explanation:
one way to help is to just do 1x5=5 and add on the two zeros to get 500
Answer:
True
Step-by-step explanation:
10 * 5 = 50
If we ad a zero to one of the numbers, we add a zero to the answer
100 * 5 = 500
10 * 50 = 500
To the nearest whole degree, what angle measure has a sine of 0.9123
Answer:
66° has a sine of 0.9123.Step-by-step explanation:
We are given value of sine trigonometric ratio = 0.9123.
We need to find the angle in degrees whose measure has a sine of 0.9123.
So, we need to find the value of [tex]sin^{-1}(0.9123)[/tex].
On plugging [tex]sin^{-1}(0.9123)[/tex] in calculator, we get
65.82°.
Now, we need to round it to the nearest whole degree.
Therefore, 65.82°≈ 66°.
Therefore, 66° has a sine of 0.9123.cheese production in a country is currently growing at a rate of 4% per year. the equation y=8.3(1.04)^× models the cheese production in the country from 2003 to 2009. In this equation l, y is the amount of cheese produced in billions of pounds and x represents the number of years after 2003.
a. Estimate the total cheese production in the country in 2006
b. assuming this equation continues to be valid in the future use the equation to predict the total amount of cheese produced in the country in 2017.
Answer:
a. 9.34 billions of pounds.
b. 14.37 billions of pounds.
Step-by-step explanation:
We have been given that cheese production in a country is currently growing at a rate of 4% per year. the equation [tex]y=8.3*(1.04)^{x}[/tex] models the cheese production in the country from 2003 to 2009. In this equation l, y is the amount of cheese produced in billions of pounds and x represents the number of years after 2003.
a. To find the total cheese production in the country in 2006 we will substitute x= 3 in our given equation as 2006-2003=3.
[tex]y=8.3*(1.04)^{3}[/tex]
[tex]y=8.3*1.124864[/tex]
[tex]y=9.3363712[/tex]
Therefore, the cheese production in year 2006 will be 9.34 billions of pounds.
b. To find the total cheese production in the country in 2017 we will substitute x= 14 in our given equation as 2017-2003=14.
[tex]y=8.3*(1.04)^{14}[/tex]
[tex]y=8.3*1.7316764476028035[/tex]
[tex]y=14.37291451510326905[/tex]
Therefore, the cheese production in year 2017 will be 14.37 billions of pounds.
Answer:
Given the equation: [tex]y = 8.3(1.04)^x[/tex] ......[1]
where
y is the amount of cheese produced in billions of pounds and
x represents the number of years after 2003
Since, this equation models the cheese production in the country from 2003 to 2009.
(a)
we have to find the total cheese production in the country in 2006.
Substitute x = 3 years(i.e, 2003 -2006) in [1] to solve for y;
[tex]y = 8.3(1.04)^{3}[/tex]
Simplify:
y = $9.3363712
Therefore, the total cheese production in the country in 2006 is, $9.34.
(b)
we use the equation to predict the total amount of cheese produced in the country in 2017.
We have x = 14 years.
Substitute in [1] we get;
[tex]y = 8.3(1.04)^{14}[/tex]
Simplify:
y = $14.3729145151
Therefore, the estimate total amount of cheese produced in the country in 2017 is, $14.37
congruent by identifying all congruent corresponding parts
Answer:
Corresponding Parts of Congruent Figures. The word corresponding refers to parts that match between two congruent triangles. You can identify corresponding angles and corresponding sides. First, name the corresponding angles.
Step-by-step explanation:
In geometry, two figures are congruent if they have the same size and shape. To verify congruence, all corresponding sides and angles of two figures must match in size and measure. For instance, given two triangles ABC and DEF, they would be congruent if their corresponding sides and angles were equal.
Explanation:In geometric terms, two figures are congruent if they have the same size and shape. This means all corresponding sides and angles of the two figures are equal. In order to determine if two shapes are congruent, you need to match each part of one shape with a corresponding part on the other and see if they are of the same size and angle.
For instance, if you have two triangles ABC and DEF, these triangles would be congruent (often written as △ABC≅△DEF) if the sides AB=DE, BC=EF, and AC=DF and angles ∠A=∠D, ∠B=∠E and ∠C=∠F. This is the principle of corresponding parts of congruent figures being congruent.
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