Thus L.H.S = R.H.S that is [tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex] = [tex]sec(\frac{\pi }{6-x} )[/tex] is proved
According to the question we have been given that
[tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex] = [tex]sec(\frac{\pi }{6-x} )[/tex]
And we need to prove that left hand side is equal to the right hand side.
To prove this we will solve the right-hand side of the equation first with the help of trigonometry identity. The right hand side of the equation is :
R.H.S = [tex]sec(\frac{\pi }{6-x} )[/tex]
= [tex]\frac{1}{cos(\frac{\pi }{6-x} )}[/tex]
[As secƟ = 1/cosƟ)
= [tex]\frac{1}{\frac{cos\pi }{6cosx} + \frac{sin\pi }{6sinx} }[/tex]
[As cos (X-Y) = cosXcosY + sinXsinY , which is a trigonometry identity where X = Π/6 and Y = x]
[tex]=\frac{1}{\frac{\sqrt{3} }{2}cosx + \frac{1}{2}sinx } \\= \frac{1}{\frac{\sqrt{3}cosx + sinx }{2} }\\=\frac{2}{\sqrt{3}cosx + sinx}[/tex]
R.H.S = L.H.S
or L.H.S = R.H.S
Hence [tex]\frac{2}{\sqrt{3} cosx + sinx } = sec(\frac{\pi }{6-x})[/tex] is proved
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Y= 1/2x -2
y= 3/4x +3
Anna is going to save pennies each week according to a sequence she learned.
. She has saved 3 Pennie’s to start on week 0.
. Each week after that, she will save twice the total number of Pennie’s she has saved from the previous week, minus 1.
Which recursive formula can be used to determine the number of pennies Anna will save during the nth week?
Whoever answers correctly will get Brainliest!
Answer:
I think that the answer is D.
Step-by-step explanation:
someone PLEASE help me with this asap.
The description and definition and values of the sequence are;
a. Each term of sequence A is produced from the previous term by multiplying the previous term by 2
b. Each term of sequence B is produced from the previous term by adding 10 to the previous term
c. [tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]
d. B(n) = 2 + (n-1) × 10
e. B(9) > A(9)
What is a sequence of numbers?A sequence is series of objects that follow each other in a particular order.
a. The terms of sequence A are;
1/4, 1/2, 1, 2, 4
Therefore, each term is produced from the previous term by multiplying the previous term by 2 as follows;
1/4 × 2 = 1/2,
1/2 × 2 = 1
1 × 2 = 2
2 × 2 = 4
b. The values in sequence B are;
2, 12, 22, 32, and 42
Therefore, each term is produced from the previous term by adding 10 to the previous term as follows;
2 + 10 = 1212 + 10 = 2222 + 10 = 3232 + 10 = 42c. The definition of the nth term of sequence A is found using the formula for a geometric progression as follows;
nth term of a GP is; A(n) = a•r^(n-1)
Where;
a = The first term = 1/4
r = The common ratio = 1/2/(1/4) = 2
The nth term of sequence A is therefore;
[tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]d. The definition of the nth term of sequence B is found using the formula for a arithmetic progression as follows;
nth term of a AP is; B(n) = a + (n-1)•d
Where;
a = The first term = 2
d = The common difference = 12 - 2 = 10
The nth term is therefore
B(n) = 2 + (n-1) × 10
e. The value of A(9) is therefore;
[tex] A(9) = \frac{1}{2} \times 2^{(9-1)} = 64 [/tex]
Which gives; A(9) = 64
The value of B(9) = 2 + (9-1) × 10 = 82
B(9) = 82
Which gives;
B(9) = 82 > A(9) = 64
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Her teacher asked her to write the correct equation or inequality that matches the
graph. Laurie wrote the following: y ≤ 2x - 4. Her teacher marked her answer
incorrect. Explain the error that Laurie made and then write the correct solution.
The correct solution of Laurie's inequality expression is y ≥ 2x – 4
Given,
The inequality expression wrote by Laurie = y > 2x - 4
The graph of the inequality expression that completes this question is added as an attachment
From the attached graph, we can see that the line of the inequality is a thick or closed line
Thick and closed line are represented by the inequality signs ≤ and ≥
Since the upper region is shaded, we make use of ≥ inequality sign
Hence, the correct solution of Laurie's inequality expression is y ≥ 2x - 4
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Solve: -5(15)
I’m so confused
Answer:
- 75
Step-by-step explanation:
- 5(15) means - 5 × 15 = - 75
an isosceles triangle has an angle that measures 40 what measures are possible for the other two angles
The measures are possible for the other two angles are 70 degrees respectively
Isosceles triangleAn isosceles triangle is a triangle that has 2 of its sides and angles to be equal.
Let the measure of the other possible angles be x and y such that x = y
Since the sum of angle in a triangle is 180 degrees, hence;
x+y +40 = 180
x+x+40=180
2x+40=180
2x=180-40
2x = 140
x = 70
x = y = 70 degrees
Hence the measures are possible for the other two angles are 70 degrees respectively
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Triangle LMK has vertices L(-6, 0), M(0, -6), and K(-6, -6) and triangle XYW has vertices X(0, 6), Y(8, 6), and W(4, 2). Using the definition of congruence, decide whether the two triangles are congruent. Explain your answer. Give coordinate notation for the transformations you use.
Using the distance between two points formula to calculate the side lengths, it is found that the figures are not congruent.
What are congruent figures?Congruent figures are figures that have the same outer side lengths.
We are given the vertices for this problem, hence we use the distance between two points formula to calculate the lengths.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.
For Triangle LMK, the side lengths are given as follows:
[tex]LM = \sqrt{(0 - (-6))^2+(-6 - 0)^2} = 6\sqrt{2}[/tex][tex]KM = \sqrt{(-6 - (-6))^2+(-6 - 0)^2} = 6[/tex][tex]LK = \sqrt{(-6 - (-6))^2+(-6 - 0)^2} = 6[/tex]For Triangle XYW, the side lengths are given as follows:
[tex]XY = \sqrt{(8 - 0)^2+(6 - 6)^2} = 8[/tex][tex]WY = \sqrt{(8 - 4)^2+(6 - 2)^2} = 4\sqrt{2}[/tex][tex]XW= \sqrt{(4 - 0)^2+(6 - 2)^2} = 4\sqrt{2}[/tex]Due to different side lengths, the figures are not congruent, and nothing can be stated about the transformations that were used.
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Juilan divided his savings equally between two charities. If its Julian's savings, evaluate the expression when s=$125
The expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
WE have been given that Juilan divided his savings equally between two charities. then Julian's savings as 's' =$125
First, we will write the expression;
s/2
Second, substitute the value 125 in for the variable s.
Then simplify by dividing 125 and 2.
=$125 / 2
= $62.50
Hence the expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.
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Which of the following intervals is equivalent to -2
A. [-2, 3]
B. [-2, 3)
C. (-2, 3]
D. (-2, 3)
Answer:
the answer is A
what is the simplest form of 14/27 divided by 7/1
Answer:
2/27
Step-by-step explanation:
i think this is the answer.
Solve 6 + a = 3 for a.
Answer:
subtract 6 from 3 and a is -3
Step-by-step explanation:
Answer:
a= -3
Step-by-step explanation:
a=3-6
a=-3
Which is the graph of g(x) = (two-thirds) Superscript x – 2?
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)
the correct option is:
"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"
Which is the graph of the given function?
Here we have the exponential function:
g(x) = (2/3)^x - 2
Now, remember that for any real number different than zero, we have that:
x^0 = 1
So if we evaluate our function in x= 0 we will get:
g(0) = (2/3)^0 - 2 = 1 - 2 = -1
Then the function passes through the point (0, -1)
With this in mind, we conclude that the correct option is:
"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"
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Answer:
C: The third graph
Step-by-step explanation:
on edge
Reflection over the line y=x of the point (7,2)
Answer:
2,7
Step-by-step explanation:
when y=x similary x= y
The first step in solving 7 + 3(x - 2) = 2x + 10 is to
Answer:
x=9
Step-by-step explanation:
Simplify 7+3x−67+3x−6 to 3x+13x+1.
Subtract 11 from both sides
Simplify 2x+10−12x+10−1 to 2x+92x+9.
Subtract 2x2x from both sides.
Simplify 3x−2x3x−2x to xx.
Answer: x=9
Step-by-step explanation:
7+3(x-2)=2x+10
7+3x-6=2x+10
1+3x=2x+10
1+3x-2x=2x-2x+10
1+1x=10
1x=9
x=9
write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3, 4), (−13, −14)
The standard equation of the circle will be (x+5)²+(y+5)²= 145
The center of the circle, which is the midpoint between those two locations, may be found first since you know the diameter endpoints.
formula for the midpoint
= ((x1+x2)/2, (y1+y2)/2)
Given points are - (3, 4), (−13, −14)
The circle's center is at (-5,-5)
Therefore, the circle's equation will take the form (x+5)²+(y+5)²=R², where R is the circle's radius.
The distance between a point on the circle and the circle's center in order to get the radius.
Therefore, let's calculate the distance between (-5, -5) and (-13,-14)
Radius R = √((-13+5)²+(-14+5)²) using the distance formula.
= 12.04
equation will be -
(x+5)²+(y+5)²= 145
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PLEASE HELP!! 80 PTS!! You research the cost of a gallon of gasoline over several years to look for a trend. The table shows your data. What is the equation for a line of best fit? How much would you expect to pay for a tank of gas in the year 2019? Let x be the number of years after 1998.
Answer: Because the initial value is $26.40, the line must pass through this when x is 0. Thus, the answer is either the first or the second equation.
Next, we calculate the difference between the year 2019 and 1998 and substitute it into the value of x.
2019 - 1998 = 21.
Substituting this into the equation:
y = 1.006(21) + 26.40
y = $47.52
Thus, the first option is correct.
Verify whether x = -1/√3 is a zero of the polynomial 3x²-1.
Answer:
Below.
Step-by-step explanation:
3x² - 1 = 0
3x² = 1
x² = 1/3
x = ±√(1/3)
= -1/√3, 1/√3.
So, -1/√3 is a zero of 3x² - 1 .
Yes, x = -1/√3 is a zero of the polynomial 3x² - 1 because substituting the value results in zero, confirming its solution to the equation.
To verify whether x = -1/√3 is a zero of the polynomial 3x² - 1, we need to substitute this value into the polynomial and check if it results in zero.
Given polynomial: 3x² - 1
Now, substitute x = -1/√3 into the polynomial:
3(-1/√3)² - 1
Now, simplify:
3(1/3) - 1
1 - 1
The result is zero. Since the expression evaluates to zero when x = -1/√3, this means that x = -1/√3 is indeed a zero of the polynomial 3x² - 1.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer: 3/4
Step-by-step explanation:
please solve this equation for me its algebra
solve
-4b=48
Answer:-12
Step-by-step explanation: -4b=48 b=48/-4 b=-12
hope it helps
The cost for decorations and the disc jockey for the homecoming dance was $1,800. The class members sold 279 tickets and made a profit of $3,450. If x represents the price of each ticket sold, which equation could be used to find x?.
What is another way to write the absolute value inequality |p|<12
Another way to write the absolute value inequality |p|<12 is
-12 < p < 12
What is absolute values?
This is a term in mathematics that refers to numbers considered regardless of the sign. The concept of absolute values is well appreciated in a number line. In a case where the signs helps on to position the number but do not have influence in the magnitude or size of the number.
Since absolute values considers the magnitude of the number and not the sign. We can see the equation given to represent values from zero to a point just less than 12 as this will have same magnitude to the point from zero to a point just less than negative 12. The sign just gives the direction.
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Simplify
√5 x √12 x √50
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3} \times \sqrt{2 \times {5}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 5 \times 2 \sqrt{5 \times 3 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 10 \sqrt{30} [/tex]
Alex has twice the number of hats that Joey has, plus 2 more. The number
of hats Alex has is also 4 times the difference of the number of hats and 5
that Joey has. Find how hats many each of them has.
From the given Alex and Joey hats equation we got Alex has 24 hats Joey has 11 hats.
Given that,
Joey only has 2 times more hats than Alex, who has 2 more. The difference between the amount of hats Alex has and the 5 that Joey has is also 4 times the number of hats Alex has.
We have to discover how many hats each one of them has.
Let Alex has x hats Joey has y hats.
From the given
We get
x=2y+2 ------> equation (1)
x=4(y-5) --------> equation (2)
Equating equation (1) and equation (2)
2y+2=4(y-5)
2y+2=4y-20
2y-4y=-20-2
-2y=-22
y=-22/-2
y=11
Take y=11 in equation (1)
x=2(11)+2
x=22+2
x=24
Therefore, Alex has 24 hats Joey has 11 hats.
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daisy is making solid spikes for her halloween costume. the spikes are shaped like right circular cones with base radius of 2222 inches and height of 6666 inches. if daisy has 360360360360 cubic inches of material for making the spikes, what is the maximum number of spikes she can make?
Question :- Daisy is making solid spikes for her Halloween costume. the spikes are shaped like right circular cones with base radius of 2 inches and height of 6 inches. if daisy has 360 cubic inches of material for making the spikes, what is the maximum number of spikes she can make ?
Answer:- She can only create a maximum of 14 spikes.
Step-by-step explanation:
Given that :-
Daisy is making solid spikes for her Halloween costume.The spikes have a base radius of 2 inches and a height of 6 inches. They are formed like right circular cones.For creating the spikes, Daisy has 360 cubic inches of material.To find :-
maximum number of spikes made by her.According to Question,
We have,
base radius of the spikes = 2 inchheight of the spikes = 6 inchFor finding the maximum number of spikes,
We have to divide the volume of the material by the volume of the cone, for producing a maximum number of spikes.
So,
Maximum spikes = Volume of the material / volume of the cone
Now,
Volume of the material = 360 cubic inches
Volume of the cone = [tex]\frac{1}{3}[/tex] πr²h
Where:
r = radius = 2 in
h = height = 6 in
π = pi = 22/7
= [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × [tex]2^{2}[/tex] ×6
= 3.14 × 4 × 2
= 25.12
So,
Maximum spikes = Volume of the material / volume of the cone
= [tex]\frac{360}{25.12}[/tex]
= 14.33
∴ The number of spikes must be an integer.
∵ Maximum spikes = 14.
Answer:- She can only create a maximum of 14 spikes.
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2a-18 in algebraic form
Answer: 2(a-9)
Step-by-step explanation:
2a-18
then factor
which leads to 2(a-9)
Answer: 2(a-9)
Step-by-step explanation: Factor out 2 from the expression 2(a-9)
Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
Answer:
2 and 12
Step-by-step explanation:
2x3=6
12 x 6=72
6 and 72 is 78
Answer:
2 and 12
Step-by-step explanation:
Find the product. Simplify your answer. (3f–1)(4f+1)
definition of differentiation in mathematics
Answer:
This is also known as "Derivative"." in mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus."! hope this helps!
Solve the system of inequalities by graphing.
y < 2x +3
2x y ≤ 5
Step-by-step explanation:
To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
HELP ME PLEASE I need this now
question 1 first picture is to this question
As x decreases without bound, f(x) increases without bound.
As x increases without bound, f(x) approaches the line y = - 4.
As x decreases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches the line y = 4.
question 2 the second picture to this question
As x decreases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) increases without bound.
As x decreases without bound, f(x) increases without bound.
Answer:
Question 1:
As x decreases without bound, f(x) increases without bound. TRUEAs x increases without bound, f(x) approaches the line y = - 4. TRUEAs x decreases without bound, f(x) approaches zero. FALSEAs x decreases without bound, f(x) approaches the line y = 4. FALSEQuestion 2:
As x decreases without bound, f(x) approaches the line y = 6. TRUEAs x increases without bound, f(x) approaches the line y = 6. FALSEAs x increases without bound, f(x) increases without bound. TRUEAs x decreases without bound, f(x) increases without bound. FALSEAs x decreases without bound, f(x) approaches the line y = 6.Step-by-step explanation:
Question 1:
options
As x decreases without bound, f(x) increases without bound.As x increases without bound, f(x) approaches the line y = - 4.As x decreases without bound, f(x) approaches zero.As x decreases without bound, f(x) approaches the line y = 4.Solving notes:
As x decreases without bound, f(x) does NOT approach zero.
As x decreases without bound, f(x) does NOT approaches the line y = 4.
_________________________________________________
Question 2:
options
As x decreases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) increases without bound.As x decreases without bound, f(x) increases without bound.Solving notes:
As x increases without bound, f(x) does NOT approach the line y = 6.
As x decreases without bound, f(x) does NOT increase without bound.