The threes solutions to the given equation sec²x - secx = 2 are:
[tex]x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ; \ x_3=\pi[/tex]What exactly are equations?An equation is a statement composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To solve: sec²x - secx = 2 on interval [0,2[tex]\pi[/tex])
When we set t = sec x, we get the quadratic equation:
[tex]t^2-t-2=0[/tex]Which has the solutions: [tex]t_1=2 ; \quad t_2=-1[/tex]As a result, we must seek solutions to the equations:
[tex][1] \sec x=2: \quad \cos x=\frac{1}{2} \rightarrow x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ;$\\\text { [2] } \sec x=-1: \quad \cos x=-1 \rightarrow x_3=\pi ;[/tex]
Therefore, the three solutions are:
[tex]x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ; \ x_3=\pi[/tex]Know more about equations here:
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The correct question is given below:
solve the equation sec²x - secx = 2 on interval [0,2[tex]\pi[/tex])
Solve the inequality and express your answer in interval notation. x^2-12x+3<0
Solution:
B.) [tex](6-\sqrt{33}, 6+\sqrt{33})[/tex]
Hope this helps! If so, please lmk! Thanks and good luck!
Rochelle needs to pack a picture frame that measures 7611 inches on each side. Will it fit into a box that measures 7.52 inches on each side? Explain.
No, the picture frame will not fit into a box that measures 7.5 inches on each side because the side of the frame will be greater than it that is 7.54 inches.
Length of picture frame is given as:
= 7 (6 / 11)
= 7.54 inches
The length of Box is given as = 7.5 inches
From the above, we can see that the length of the box is smaller than the length of the picture frame.
So, the picture frame will not be able to fit in the box.
Therefore, we get that, the picture frame will not be able to fit into a box that measures 7.5 inches on each side because the side of the frame will be greater than it that is 7.54 inches.
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Your question was incomplete. Please refer the content below:
Rochelle needs to pack a picture frame that measures 7 6/11 (fraction 6 over 11) inches
on each side. Will it fit into a box that measures 7.5 inches on each
side?
Please help me
Thank you
Answer: 3 gallons per hour
Step-by-step explanation: 14-(3x) =5 14-5=9 9/3=3
E= 1R solve for R pls help me I don’t understand
Answer:
r = e or 2.718282
Step-by-step explanation:
a) simplify both sides of the equation
2.718282 = r
b) flip the equation
r = 2.718282
Sid makes a living baking cakes. For each cake, he uses 1 3/4 cups of sugar, 4 1/5 cups
of flour, and 3/10 of a cup of milk. How many cups of ingredients will Sid need to
make 4 cakes? Please I need the answer
By adding the number of cups needed for each cake, we conclude that you will need 25 cups of ingredients to make the 4 cakes.
How many cups of ingredients sill Sid need for 4 cakes?We know that the recipe calls for:
(1 + 3/4 ) cups of sugar.(4 + 1/5) cups of flour.3/10 of a coup of milk.That is for a single cake, so in a single cake you need a total of cups given by the sum of the above quantities, this gives:
(1 + 3/4) + (4 + 1/5) + 3/10 = (1 + 4) + (3/4 + 1/5 + 3/10)
= 5 + (3/4 + 2/10 + 3/10) = 5 + (3/4 + 5/10) = 5 + (3/4 + 1/2) = 5 + 5/4
= 5 + 4/4 + 1/4 = 6 + 1/4
Each cake needs (6 + 1/4) cups of ingredients, so 4 cakes will need:
4* (6 + 1/4) = 24 + 4/4 = 25
You will need 25 cups of ingredients to make the 4 cakes.
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how many unique straight lines in parallelogram
Answer:
4 lines
Step-by-step explanation:
We know that a parallelogram is constructed using two parallel lines intersecting other pairs of parallel lines so basically we require 4 lines to construct a parallelogram.
Answer:4
Step-by-step explanation:
All flowers need water
Some trees need water
Some flowers are trees
Valud or Invalid
valid . some trees grow flowers i belive
Michael Wittry has been investing in his Roth IRA retirement account for 21 years. Two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. What is the current value of his Roth IRA
If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.
Current valueFirst step is to calculate the value loss
Value loss=1/3× original value
Value loss= 1/3× $215,613
Value loss= $71,871
Second step is to calculate the new value
New value=$215,613-$71,871
New value= $143,742
Third step is to calculate the value gained
Value gained= 1/2× new value
Valued gained=1/2× $143,742
Valued gained=$71,871
Fourth step is to calculate the current value
Current value= $143,742+$71,871
Current value=$$215,613
Therefore If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.
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3)
Chicken cost $7.19 per pound. You buy 0.82 pounds at the supermarket.
How much did you spend?
Answer:
$5.90
Step-by-step explanation:
(7.19)(.82) Put these numbers in your calculator and multiply them together.
5.8958 Round to the nearest cent
$5.90
Assistant Manager Clyde works as a part-time assistant manager for the Barkley Coffeehouse to earn money to help pay for his college expenses. He makes $11.50 per hour. The coffeehouse sells whole bean coffee, mugs, and other coffee products. Clyde earns $0.50 for each of these items he sells. Last week he worked 30 hours and earned $364. How many coffee products did he sell last week?
The number of coffee product he sells is 38.
How to find the number of coffee products he sells?He makes $11.50 per hour.
He earns $0.50 for each of these items he sells.
Last week he worked 30 hours and earned $364.
Therefore, the number of coffee product he sells last week can be calculated as follows:
let
x = number of coffee product he sells.
364 = 11.50(30) + 0.50(x)
364 = 345 + 0.50x
364 - 345 = 0.50x
19 = 0.5x
divide both sides by 0.5
x = 19 / 0.5
x = 38
Therefore, the number of coffee product he sells is 38.
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Two boy scouts were selling popcorn for a fundraiser at a local grocery store and made $640. They sold twice the amount of kettle corn as butter popcorn, and 6 more bags of cheddar popcorn than kettle corn. If kettle corn cost $15 a bag, butter popcorn cost $8 per bag, and cheddar popcorn cost $10 per bag, how much of each type of popcorn did they sell? Write an equation to solve the problem.
They sold 10 bags of butter popcorn, 20 bags of kettle corn and 26 bags of cheddar cheese.
Here, we are given that two boy scouts were selling popcorn for a fundraiser.
Their total revenue = $640
Let the bags of butter popcorn be x
then, the bags of kettle corn sold = 2x
and the bags of cheddar popcorn sold = 2x + 6
Cost of kettle corn = $15/ bag
Cost of butter popcorn = $8/ bag
Cost of cheddar popcorn = $10/ bag
Thus, the total revenue from from kettle corn = $30x
total revenue from from butter popcorn = $8x
total revenue from from cheddar popcorn = $10(2x + 6)x
Thus, we will get the following equation-
30x + 8x + 10(2x + 6) = 640
38x + 20x + 60 = 640
58x + 60 = 640
58x = 580
x = 580/ 58
x = 10
Thus, 2x = 20 and 2x + 6 = 26
Hence, they sold 10 bags of butter popcorn, 20 bags of kettle corn and 26 bags of cheddar cheese.
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given z (x)=15x-x^2+3
Answer:
○ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]
Step-by-step explanation:
We are told that:
[tex]z(x)= 15x - x^2 + 3[/tex],
and told to find an expression for [tex]z(x - 1)[/tex].
In order to find [tex]z(x - 1)[/tex], we have to replace [tex]x[/tex] in the definition of [tex]z(x)[/tex] with [tex](x-1)[/tex]:
[tex]z(x - 1) = 15(x -1) - (x - 1)^2 + 3[/tex]
Now we can simplify:
⇒ [tex]z(x-1) = 15x - 15 - (x - 1)^2 + 3[/tex] [Distributing 15 into the first brakets]
⇒ [tex]z(x-1) = 15x - 15 - (x^2 - 2x + 1) + 3[/tex]
⇒ [tex]z(x-1) = 15x - 15 - x^2 + 2x - 1 + 3[/tex] [Distributing the minus sign]
⇒ [tex]z(x - 1) = 17x - x^2 -13[/tex] [Combining like terms]
⇒ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]
Therefore, the first option is the correct one.
1. The last time Jerry took a math quiz he got a score of 1.5 (out of 4) because he didn't study.
When he retook the quiz a week later he got a score of 4. By what percent did his score
increase by?
Answer:
6 is my final answer
Step-by-step explanation:
set as brainliest
Find the population mean or sample mean as indicated. 17, 10, 3, 5, 25
12 is the population mean or sample mean of given data.
Given that
The collected data
17, 10, 3, 5, 25
To find
The population mean or sample mean
So, according to the question
we have,
The collected data
17, 10, 3, 5, 25
For calculate the the population mean or sample mean, We have to find out the total of data, and total number of data.
Total of data = 17+ 10 +3 + 5+ 25
Total of data = 60
Total number of data (n) = 5,
So, we know that
Sample mean = [tex]\frac{total\;of\;data}{n\;number\;of\;data}[/tex]
Now, putting the all values,
We will get,
Sample mean = 60/5
= 12
The Sample mean of given data is 12.
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Multiple choice: Which of the following steps below would be a good first step when solving the equation 2x+5=11
Divide both sides by 2
Add 5 to both sides of the equation
Subtract 5 from both sides of the equation
Add 11 to both sides of the equation
Answer:
easy
Step-by-step explanation:
How to solve a system of equations by elimination.
Write both equations in standard form.
Make the coefficients of one variable opposites.
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
What is a two step problem with variables on each side equal 19? (Please help)
The equation of the two-step problem is 2x = x + 19
How to determine the two-step problem?The conditions are given as
Variable on both sidesSolution = 19Let the variable in the equation be x
So, a possible equation is as follows
2x = x + 19
The solution to the equation is as follows
2x = x + 19
Subtract x from both sides
x = 19
Hence, the equation of the two-step problem is 2x = x + 19
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Solve.
3x+2y−z=8
2x+2z=−4
x+3y=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
How to resolve a system of linear equations
In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:
x = 4 - 3 · y
Second, substitute x in the first two equations:
3 · (4 - 3 · y) + 2 · y - z = 8
12 - 9 · y + 2 · y - z = 8
- 7 · y - z = - 4
2 · (4 - 3 · y) + 2 · z = - 4
8 - 6 · y + 2 · z = - 4
- 6 · y + 2 · z = - 12
Third, clear z in the first equation derived in the previous step:
z = 4 - 7 · y
Fourth, substitute z in the second equation derived in the second step:
- 6 · y + 2 · (4 - 7 · y) = - 12
- 6 · y + 8 - 14 · y = - 12
- 20 · y = - 20
y = 1
Fifth, calculate y and x:
z = 4 - 7 · 1
z = - 3
x = 4 - 3 · 1
x = 1
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
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219 +485 = 348 + please
Answer: please=356
Step-by-step explanation:
219 +485 = 348 + please
704=348 + please
please=356
Jessica earns $10.35/hour at her part-time job. Usually she works 24 hours a week. If she can only put aside 30% of her earnings, about how many weeks will she need to work in
order to save money for a new cell phone at $399?
Select one:
A. 3
B. 6
C. 5
D. 4
Answer:
B. 6
Step-by-step explanation:
$10.35 × 24 = 248.4 per week
248.4 × 30% = 74.52 {30% of her earnings}
$74.52 × 6 weeks = $447.12
∴ She needs to work for 6 weeks in order to save up to $399
Georgia has 17 songs in her playlist, while Scarlet has 36 songs in her playlist. Which statement correctly compares the number
of songs in the two playlists?
O 17 < 36
O 17 > 36
O 17 = 36
36 < 17
The statement that correctly compares the number of songs on Georgia and Scarlet's playlists are is 17 < 36.
How to know the correct statement?Georgia has 17 songs on her playlist while Scarlet has 36 songs on her playlist.
In the number line, the number 36 comes after the number 17. This means that 36 is greater than 17.
The statement that therefore correctly compares the number of songs in the playlist is:
17 < 36
In conclusion, the statement that correctly compares the songs in the two playlists is 17 < 36.
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How do you solve this??
Answer:
0.234
Step-by-step explanation:
The total number of people in the age range from 30-49 is 7282 (3752 + 3530 the totals at the bottom of the column. The total number of people out of that group that have completed high school is 1704 (787 + 917 the number of people in that column that have finished high school).
[tex]\frac{1704}{7282}[/tex] = .23400164789 Rounded to the nearest thousandths place is .234
What are the coordinates of point A?
Answer:
It's coordinates are (1,-2)
Taylor is curious to know how different types of music will impact how long it takes someone to finish their homework. She gathers a group of 12 year olds and breaks them into groups of 3. The first group listens to nothing. The 2nd group listens to classical, the 3rd listens to pop music, and the 4th listens to heavy metal. Each group needs to read 20 pages of the same book and answer the same set of 20 math questions. She times each group and compares.
a) Find the Independent Variable
b) Find the dependent variable
c) Find the Control Group
d) Find the experimental group
e) Find 3 constants
Please help
Find the equation of the line then write it in the form y=mx+b
Y= ?
Answer:
y=1/5x
y=0
Step-by-step explanation:
Cosx-1=0[tex]Cos(x)-1=0[/tex]
The solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.
What is the solution of the given trigonometric equation as in the task content?It follows from the task content that the solution to the given trigonometric equation is to be determined.
Given;
Cos(x) - 1 = 0
Add 1 to both sides of the equation;
Cos (x) = 1
Therefore, the value of x can be determined by evaluating the cos inverse of (-1).
Hence,
x = Cos-¹(1)
x = nπ (where n is any integer real number value).
Ultimately, the solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.
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Can someone please explain this to me? Thank youuu:)
Answer:
B: 3x+(4x+2)=180
Step-by-step explanation:
Supplementary angles are those angles that sum up to 180 degrees. The question gives you the two angles that compose the 180 degree angle thus you get the equation:
Angle 1 + Angle 2 = Supplementary Angle
In this case we see that these two angles are Angles B and C and a supplementary angle is 180 degrees thus:
(4x+2)+3x = 180
Furthermore this also allows you to find x.
PLEASE HELP! Triangle BCD has the following side lengths: BC = 60, CD = 50
Triangle RST has the following side lengths: RS = 11x-4, ST = 70
What is the value of x? (put just the number in the first box)
What is the length of side RS? (put just the number in the second box)
The value of x is 11 units and the length of side RS = 11x-4 is 117 units.
with measurement BC = 60, CD = 50.
Triangle RST : RS = 11x-4, ST = 70
What is similarity?Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.
Given:
BC = 60 and CD = 50
RS = 11x - 4 and ST = 70
Now, considering
BC : CD = RS : ST
60 : 50 = 11x - 4 : 70
60/50 = (11x - 4)/70
50 * (11x - 4) = 70 * 60
11x - 4 = 84
11x = 88
x = 11
So, RS = 11x - 4
RS = 11 x 11 - 4
RS = 117
Hence, the value of x is 11 and the length of side RS is 117
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Question 6 of 10
A triangle has two sides of lengths 4 and 7. What value could the length of
the third side be? Check all that apply.
DA7
B. 17
C. 9
D. 3
E 11
F. 5
all that sides which can be applicable in the given side of triangle are:
F.5
A.7
C.9
WHICH THEOREM IS APPLICABLE FOR FINDING THE THIRD SIDE OF TRIANGLE ?Third Side of a Right Angle Triangle Pythagorean Theorem. The length of the hypotenuse in a right triangle can be determined using the Pythagorean Theorem. You can determine the length of the missing side using algebra and square roots as long as you are only given two lengths.
CALCULATIONa,b and c are the sides of a triangle if it satisfies:
a<b+c , b<a+c and c<b+a
Here, a=4 and b=7
We have to find c
i.e. all those c which satisfies:
4<7+c , 7<4+c and c<4+7=11
D.3 it is not true since it doesn't satisfies second inequality
F.5 it is true
A.7 it is true
C.9 it is true
E.11 This is clearly false, since it doesn't satisfies inequality third
F.5 This is clearly false, since it doesn't satisfies inequality third
Hence, correct options are:
F.5
A.7
C.9
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A and B are vertical angles.
If m/A = (2x +29)° and m B (3x - 17)°, then find the measure of B.
=
The required measure of the angle m∠B is 121°.
Given that,
Angle A and B are two vertical equal angles.
m∠B = 3x - 17
m∠A = 2x + 29
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
m∠A = m∠B
2x + 29 = 3x - 17
-x = - 46
x = 46
Now,
m∠B = 3 *46 - 17
m∠B = 138 - 17
m∠B = 121°
Thus, the required measure of the angle m∠B is 121°.
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The terminal side of an angle theta in standard position passes through the point -6(-4,). Use the figure to find the following value. r
Answer is - 2 [tex]\sqrt{3}[/tex] / 13
Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position
cosθ = cos (π + d) (d is the inner angle of the tringle)
= - cos 2
= - 4 / - [tex]\sqrt{(- 6^{2} + (- 4^{2} )[/tex]
= - 4 / - [tex]\sqrt{36 + 16 }[/tex]
= - 4 / -[tex]\sqrt{52}[/tex]
= - 4 / 2[tex]\sqrt{13}[/tex]
= - 2 / [tex]\sqrt{13}[/tex]
multiply by [tex]\sqrt{13}[/tex]
we get,
= - [tex]\frac{2 \sqrt{13} }{13}[/tex]
Formulae :
Arc cosecant y = arcs(x) = csc-1(x). Another way to write x = csc(y).
Arccosine y = arcos(x) = cos-1(x). Another way to write x = cos(y).
Arc cotangent y = arcos(x) = cot-1(x). Another way to write x = cot(y).
Arc secant y = arcsec(x) = sec-1(x). Another way to write x = sec(y).
Arcsine y = arcsine(x) = sin-1(x). Another way to write x = sin(y).
Arctangent y = arctan(x) = tan-1(x). Another way to write x = tan(y).
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