Prove that (1+cosα)(1-secα)=-sinα tanα
We need to prove
(1 + cos a)(1 - sec a) = -sin a tan a
LHS
= (1 + cos a)(1 - sec a)
= 1 -sec a + cos a - cos a sec a
= 1 - sec a + cos a - cos a (1/cos a)
= 1 - sec a + cos a - 1
= cos a - sec a
= cos a - 1/cos a
= [tex]\frac{cos^{2}a - 1}{cos a}[/tex]
We know that [tex]sin^{2}a+ cos^{2}a = 1[/tex],
Then [tex]1 - cos^{2}a = sin^{2} a[/tex]
[tex]cos^{2}a - 1 = -sin^{2}a[/tex]
= [tex]-\frac{sin^2a}{cos a}[/tex]
= [tex]-\frac{(sina)(sina)}{cosa}[/tex]
=[tex]- (sin a)(\frac{sin a}{cosa} )[/tex]
We know that tan a = sin a / cos a
= - sin a tan a
= RHS
LHS = RHS
Hence Proved
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Write the function whose graph is the graph of y=x^2, but is translated 3 units to the left
Answer:
[tex]f(x) = x^2 + 6x+9[/tex]
Step-by-step explanation:
[tex]y=(x+3)^2 = x^2 + 6x+9[/tex]
Use the Distributive Property to rewrite each of the following products
and then calculate the value, as shown in the example below.
Example: 4(307)= 4(300)+4(7)=1200+28 = 1228
9(410)
6(592)
a.
b.
as sums,
i will give a lot of points
Answer: I hope this helps.
Step-by-step explanation:
Susan has two jobs and can work no more than 28 total hours per week. If she earns
$8.50 per hour as a cashier and $10.00 per hour as a florist and she needs to earn at
least $160 for the week, how many hours does she need to work at each job? Write a
system of inequalities that could represent this situation.
The system of inequalities is,
The total hours will be X+Y≤4.
The total amount she can earn 8.5X + 10Y ≤ 22.85.
First let us assume that she work 7 days in the week.
If she works for 28 hours a week, Then the hours of work done by her in a day will be,
28hours/7days
Per day working hours are 4 hours per day.
now, if she has to earn at least 160$ a week. Then, the amount she has to earn in one day will be 160$/7days,
Amount needed to be earned in one day is 22.85$,
Now, if she work for X hours as cashier, then she can work Y hours as florist.
The total hours for which she can can be represented by,
X+Y≤4
The amount she will earn in one day can be represented by the inequality,
8.5X + 10Y ≤ 22.85.
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Find the missing number so that the equation has no solutions.
x+1=
–
2x–6
The missing number so that the equation has no solutions is -7/3.
How to calculate the equation?The equation given is represented by:
x+1 = -2x–6
It should be noted that we just have to find the value of x. This will be
x+1 = -2x–6
x + 2x = -6 - 1
3x = -7
x = -7/3
Therefore, the value of x is -7/3.
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Can someone help me with this question?
Answer:
1. 740 students
2. 4 years
3. 185 students per year
4. 357 students
5. 185t+357
6. 3132 students
Work:
1. 1837 - 1097 = 740
2. 2008 - 2004 = 4
3. (1837 - 1097) / (2008 - 2004) = 185
4. 185(0) + 357 = 357
5. 185t + 357
6. 185(15) + 357 = 3132
three less than the sum of x and y
Answer:
X+Y-3
Step-by-step explanation:
I don’t know what X/Y is, but “three less than” means you need to subtract 3 from the sum of X+Y
Explain a method to find the area of triangle QRS given that RT is perpendicular QS. Then find the area. Show your work.
Applying the distance formula to find the base and height of the triangle, the area of the triangle is calculated as: 17.85 units².
How to Find the Area of a Triangle?Area of triangle = 1/2(base)(height).
The base of triangle QRS is QS.
The height of triangle QRS is RT.
Use the distance formula [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex] to find the length of QS and RT:
Q(2, 4) = (x1, y1)
S(8, -2) = (x2, y2)
QS = √[(8−2)² + (−2−4)²]
QS = √72
QS ≈ 8.5 units
R(6, 6) = (x1, y1)
T(3, 3) = (x2, y2)
RT = √[(3−6)² + (3−6)²]
RT = √18
RT ≈ 4.2 units
Area of triangle QRS = 1/2(8.5)(4.2)
Area of triangle QRS = 1/2(35.7)
The area of triangle QRS = 17.85 units²
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Please help me out here!!
The equation, in point-slope form, that represents the distance of Byron from home is: A. y - 4 = -6(x - 1/2).
How to Write an Equation in Point-slope Form?An equation can be written in point-slope form, where m represents the slope and (a, b) represents a point on the line, as: y - b = m(x - a).
From the given information describing Bray's distance from home after some time, we have the following parameters:
x = hours (time)y = distance (miles)Slope (m) = -6A point = (1/2, 4)Substitute m = -6 and (a, b) = (1/2, 4) into y - b = m(x - a):
y - 4 = -6(x - 1/2)
Therefore, the equation, in point-slope form, that represents the distance of Byron from home is: A. y - 4 = -6(x - 1/2).
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Bella needs to order some new supplies for the restaurant where she works. The restaurant needs at least 503 glasses. There are currently 295 glasses. If each set on sale contains 10 glasses, which inequality can be used to determine ss, the minimum number of sets of glasses Bella should buy?
The inequality that can be used to determine the minimum number of sets of glasses Bella bought is x ≥ 20.8.
How to use inequality to represent a situation?She needs to order some new supplies for the restaurant where she works.
The restaurant needs at least 503 glasses.
Each set on sale contains 10 glasses.
The inequality that can be used to determine the minimum number of sets of glasses Bella bought is as follows:
Therefore,
x = number of sets
Hence,
295 + 10x ≥ 503
10x ≥ 503 - 295
10x ≥ 208
x ≥ 208 / 10
x ≥ 20.8
Therefore, the inequality that can be used to determine the minimum number of sets of glasses Bella bought is x ≥ 20.8.
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NJNOLMKNJOLMKJOKJKJKPPKLKPOO
Answer:
NJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOONJNOLMKNJOLMKJOKJKJKPPKLKPOO
PLSSS HELPPP ME WITH THISSSS THERES A PHOTO IM IN CLASS
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!
The equation of the linear least-squares regression line is given by:
[tex]\sqrt[3]{\text{Volume}} = -0.006 + 0.64(\text{Time})[/tex]
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, we have that:
The input is the time.The output is the cube root of the volume.From the table, we get that:
The intercept is the constant, of -0.006.The slope is the coefficient of 0.64.Water is being poured into the cone, hence the volume is increasing and the slope is positive. The equation will be given by:
[tex]\sqrt[3]{\text{Volume}} = -0.006 + 0.64(\text{Time})[/tex]
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what two numbers are 1/16 away from - 1/5
The two numbers that are (1/16) away from -(1/5) are -(11/80) and -(21/80).
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The two numbers that are 1/16 away form -(1/5) can be found by adding 1/16 to -(1/5) and subtracting 1/16 from -(1/5). Therefore, we can write,
-(1/5) + (1/16) = -(11/80)
-(1/5) - (1/16) = -(21/80)
Hence, the two numbers that are (1/16) away from -(1/5) are -(11/80) and -(21/80).
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What is the sum of the first six terms of the geometric series?
2 – 6 + 18 – 54 +
Answer:
S₆ = - 364
Step-by-step explanation:
the sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then
S₆ = [tex]\frac{2((-3)^{6}-1) }{-3-1}[/tex]
= [tex]\frac{2(729-1)}{-4}[/tex]
= [tex]\frac{2(728)}{-4}[/tex]
= [tex]\frac{1456}{-4}[/tex]
= - 364
Which of the following represents a function?
x -10 -9 0 5
y 19 17 25 19
A value 0 in x corresponds to 7 in y, and 52 in y. A value 1 in x corresponds to 4 in y. A value 2 in x corresponds to 16 in y. A value 3 in x corresponds to 7 in y.
{(0,0), (-4,3), (7,1), (-4,5), (3,2)}
A graph plots the points (negative 3, 4), (negative 3, negative 4), (negative 2, 3), (negative 2, negative 3), (negative 1, 0), (1, 0), (2, 3), (2, negative 3), (3, 4) and (3, negative 4) on the x y coordinate plane.
Addison worked at three part-time jobs last week. At one job, she worked 11 hours at a salary of $21 per hour, at another she worked 11 hours at $19 per hour,
and at the third she worked 17 hours at $18 per hour. What was her mean hourly wage?
11*21+11*19+17*18/3=746/3=248.3
PLEASE HELP
the length of a rectangle is three more than double the width. if the perimeter is 126 inches, find the dimensions.
Answer:
Length of the rectangle = 43 inches
Width of the rectangle= 20 inches
Step-by-step explanation:
Let the width (w) of the rectangle be = x inches-> Length (l) of the rectangle will be = (2x + 3) inches.Perimeter of the rectangle = 126 inches-> 2(l + w) = 126-> l + w = 126/2-> l + w = 63 -> x + (2x + 3) = 63-> 3x = 63 - 3-> 3x = 60-> x = 60/3-> x = 20 -> 2x + 3 = 2(20) + 3 = 43 Thus, Length of the rectangle = 43 inchesWidth of the rectangle= 20 inches7. The supply and demand curves for a new widget are shown in the
graph. Notice there are two demand curves. The original demand
curve is d. Months after the product was introduced, there was
a possible health concern over use of the product, and demand
dropped to the new demand cürve, d. The movement of the
demand curve is called a shift
Based on the demand curves and the movement of the demand curve, the equilibrium price before the demand shift is b and the equilibrium quantity before the demand shift was e.
What was the equilibrum price?The equilibrium price refers to the price at the point where the supply and demand curves meet on the graph.
Before the shift in demand, the equilibrium price was at Price b which was the intersection between demand curve d1 and the Supply curve.
The equilibrium quantity was the quantity at this equilibrium price and this was Quantity e.
Rest of the question is:
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what is negative 8 = x over 2.5 minus 6
The value of x in the given expression 8 = x over 2.5 minus 6 is (-1/8)^(2/7)
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
given expression is :
-8 = x^(2.5-6)
Now, solving for x by transferring power of x to -1/8 that will become -8 to the power (2/7) :
-8 = x^(-3.5)
-8 = 1/x^(3.5)
x^(3.5) = -1/8
x^(7/2) = -1/8
x = (-1/8)^(2/7)
Therefore, the value of x in the given expression is (-1/8)^(2/7)
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please help Use the following statement to answer ALL three parts of the question. Statement: If two angles are supplementary, then the angles are a linear pair
Step-by-step explanation:
supplementary angles are two angles that are together 180°.
they don't have to be adjacent, but the fact that the 2 angles can be placed "randomly" in a scenario is rarely used, except maybe for intersection angles of a line with parallel lines.
a linear pair are 2 angles that are truly adjacent (neighbors, touching each other) that are together 180°.
so, our original statement is
if 2 angles are supplementary, then the angles are a linear pair.
that by itself is (as described) not true in all cases. angles can be non-adjacent (and therefore not a linear pair) and still be supplementary.
so the original statement is false.
(a)
the inverse is
if 2 angles are not supplementary, then the angles are not a linear pair.
that is true.
as per the definition, linear pair angles are a true subset of supplementary angles (every linear pair is a pair of supplementary angles, but not every pair of supplementary angles is a linear pair).
so, if they are not a member of the set of supplementary angles, they cannot be a member of a subset either.
(b)
the converse is
if 2 angles are a linear pair, then the angles are supplementary.
that is true.
because linear pair angles are a true subset of supplementary angles. if something is a member of a subset, it is also a member of any superset.
(c)
the contrapositive is
if 2 angles are not a linear pair, then the angles are not supplementary.
that is false.
as described, linear angles are a true subset of supplementary angles. so, an element can be outside a subset but still inside a superset.
like in the original example, 2 angles across intersected parallel lines can be supplementary, but they are not a linear pair.
Which personal expense did the Penders spend more on than they had budgeted? Refer to Figure 3.4 on page 165 of the ebook or at the back of the packet. Figure 3.4.pdf Download Figure 3.4.pdf
Group of answer choices
Credit Cards & Clothing
Clothing
Clothing & Pocket Money
Credit Cards & Pocket Money
The personal expense that the Penders spent more on than they had budgeted is:
Credit Cards & Pocket Money to the tune of $ 23.75 (Option C)
What is a budget?A budget is an estimate of revenue and costs for a given period of time that is generally created and re-evaluated on a regular basis. Budgets may be created for an individual, a group of individuals, a company, a government, or almost anything else that generates and spends money.
What is the justification for the above answer?The budgeted amount for Credit Card was $50. Total amount spent was $60. Hence the excess amount spent is $10.
The budgeted amount for Pocket money was $80. Total amount spent was $93.75. Hence the excess amount spent is $13.75.
Hence total amount spend over budget is $23.75
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Norm's electric bill for December 2013 was $149.32. In 2014 the electric bill was $194.31. Next year Norm expects the bill to be the 2013 amount plus $25.00 more than the difference between 2013 and 2014. What is the new bill expected to be?
A): 2013 = 149.32
Find difference of: 194.31
2014 = 194.31 149.32
= 44.99
2015 Total Will Be:
B):
149.32 + 25 = 174.32
(2013)
174.32 + 44.99 = 219.31(B) (A)
Gabriela plans to save at least $5,600 to buy a car. She already has $2,500 saved and plans to save $500 each month.
Which inequality represents how many months (m) it will take Gabriela to save at least $5,600?
m < 6
m > 6
m ≤ 6
m ≥ 6
Inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.
As given in the question,
Amount Gabriela plans to save to buy a car = at least $5,600
Amount she already has = $2500
Amount she needs to save at least = $(5600 -2500)
=$3100
Plans to save each month =$500
Inequality to represents the number of months to save at least $5600
m ≥ 3100/500
⇒ m ≥ 6
Therefore, inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.
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Solve the linear inequality and express the solution in set-builder notation.
4(3-2x) + 3x < 6(4 + 2x)
...
The solution in set-builder notation is {x|
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Answer:
Step-by-step explanation:
Of the 30 champions of the National Spelling Bee from 1974 to 2003, 16 are boys. Find the ratio of the number of champions who are girls to the number who are boys.
Answer:
14/16 or 7/8.
Step-by-step explanation:
We know the total champions is 30. There are 16 boys, so to find the number of girls we can do 30-16. This gives us 14. Now we know that there are 16 boys and 14 girls, and the question is asking for the ratio of champions who are girls to the number who are boys. This means the ratio would simply be 14 to 16, for every 14 girls there are 16 boys. You can simply this ratio to 7 to 8, meaning for every 7 girls there are 8 boys.
Carol brought 4 pies to a party. Each serving of pie is 1/8 of an entire pie. How many servings of pie did Carol bring to the party?
Answer:
32
Step-by-step explanation:
do 4 divided by 1/8
if you flip the fraction it will become 4/1 × 8/1 = 32
micheal launches a rocket straight up into the air. the table below gives the height H(t) of the rocket (in meters) at a few times t (in seconds) during its flight.
(a) The average rate of change for the height from 0 seconds to 4.6 seconds is 30 meters per second.
(b) The average rate of change for the height from 9.2 seconds to 11.5 seconds is -10 meters per second.
The height at 0 seconds is 0 meters.The height at 2.3 seconds is 92 meters.The height at 4.6 seconds is 138 meters.The height at 9.2 seconds is 23 meters.The height at 11.5 seconds is 0 meters.(a) The average rate of change for the height from 0 seconds to 4.6 seconds is equal to the ratio of the change in height for the given time and the time difference.The average rate of change for the height from 0 seconds to 4.6 seconds is (138-0)/(4.6-0).The average rate of change for the height from 0 seconds to 4.6 seconds is 30 meters per second.(b) The average rate of change for the height from 9.2 seconds to 11.5 seconds is equal to the ratio of the change in height for the given time and the time difference.The average rate of change for the height from 9.2 seconds to 11.5 seconds is (0-23)/(11.5-9.2).The average rate of change for the height from 9.2 seconds to 11.5 seconds is -10 meters per second.To learn more about average, visit :
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Select the best answer to the question.
ہے
Percent Sold
40%
30%
20%
10%
0%
O Line Graph
O Pie Chart
Trucks
What type of graph is this example?
O Bar Graph
O Table
Vehicle Sales
Cars
SUVS
Vehicle Types
Motorcycles
Answer:
all the correct answers are the correct answers of
Step-by-step explanation:
step by step explanation no needed because answer already answered okay there answer needed.
What is the coefficient of the x2-term of the algebraic expression 2 x 4 + x squared minus x + 7?
The Coefficient of x^2 in algebraic Expression 2x^4 + x^2 -x +7 will be 1.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Given algebraic Expression is :
2x^4 + x^2 -x +7
Now,
The coefficient is the constant term multiplied with the variable.
Therefore, here the Coefficient of of x^2 will be 1.
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