Verify which of the following are identities. 1) 1 + = 4 sec 2) 15 cos = 15 a. Only the first equation is an identity. b. None of the equations are identities. c. Only the second equation is an identity. d. Both the equations are identities. Please select the best answer from the choices provided A B C D
The correct option regarding which of the sentences represents a trigonometric identity is given as follows:
b. None of the equations are identities.
What is a trigonometric identity?A trigonometric identity is a relation that is true for all possible angle measures of [tex]\theta[/tex]
The first relation is given as follows:
[tex]4\cos{\theta}\tan{\theta}\sec{\theta} = 4[/tex]
The tangent and secant equations are given as follows:
tan(x) = sin(x)/cos(x).sec(x) = 1/cos(x).Hence:
4cos(x)tan(x)sec(x) = 4cos(x) x sin(x)/cos(x) x 1/cos(x)
4cos(x)tan(x)sec(x) = 4sin(x)/cos(x)
4cos(x)tan(x)sec(x) = 4tan(x).
Meaning that the first statement is not an identity.
The second relation is given as follows:
[tex]\frac{9\sec^{2}{\theta}}{\cos^{2}{\theta}} - \frac{\tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]
With a single denominator, we have that:
[tex]\frac{9\sec^{2}{\theta} - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]
The secant identity is given as follows:
[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]
Hence:
[tex]\frac{9\sec^{2}{\theta} - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]
[tex]\frac{9(1 + \tan^2{\theta}) - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]
[tex]\frac{9 + 8\tan^2{\theta}}{\cos^{2}{\theta}} = 2[/tex]
Is also a false statement, hence neither is an identity and option B is correct.
Missing InformationThe statements are given by the image presented at the end of the answer.
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Reba is a hairdresser. Before her lunch break, she gave 3 haircuts and colored the hair of 3
clients in 330 minutes. After lunch, she gave 3 haircuts and colored the hair of 4 clients in
419 minutes. How long does it take for Reba to perform each type of service, assuming the
amount of time doesn't vary from client to client?
Answer:
To color the hair of one client takes 55 minutes
To give a client a haircut takes 72-55 which is 17
Step-by-step explanation:
i hope this helps ;)
Need Help! (No links)
Answer:
Option C, 13.7 cm
Step-by-step explanation:
Cos(31°) = [tex]\frac{x}{15}[/tex]
=> Multiply 15 on both sides of "="
Cos(31°) * 15 = x
13.7 = x
Hope this helps!
PLz answer before 11:59 pm
Answer:
SA = 2520 ft^2
Step-by-step explanation:
a = 21ft
b = 29ft
c = 20ft
h = 30ft
SA = 2[tex]A_{B}[/tex] + (a+b+c)h
[tex]A_{B}[/tex] = s(s﹣a)(s﹣b)(s﹣c)
s = [tex]\frac{a + b + c}{2}[/tex]
SA= ah + bh + ch + [tex]\frac{1}{2}[/tex] [tex]\sqrt{-a^4 + 2(ab)^2 + 2(ac)^2 - b^4 + 2(bc)^2 - c4}[/tex]
SA= (21 * 30) + (29 * 30) + (20 * 30) +
[tex]\frac{1}{2}[/tex] [tex]\sqrt{-(21)^4 + 2(21 * 29)^2 + 2(21 * 20)^2 - (29)^4 + 2(29 * 20)^2 - (20)^4}[/tex]
SA = 2520 ft^2
(20 points)which of these equations doesn’t fit with each other with what we’ve been learning about perpendicular lines explain why for full credit, equations in photo
Answer:
Line D
Step-by-step explanation:
You want to know which line is not parallel or perpendicular to the other given lines:
A: 2y -x = 2
B: 4y = -8x -4
C: y = -2x +4
D: 5y = 10x +15
Standard formWe can write each of these equations in standard form to make it easier to compare them. That form is ...
ax +by = c
where a > 0 and a, b, c are mutually prime.
The equations are ...
A: x -2y = -2
B: 2x +y = -1
C: 2x +y = 4
D: 2x -y = -3
Parallel linesEquations with the same coefficients of x and y will be parallel:
2x +y = -1 and 2x +y = 4 . . . . lines B and C
Perpendicular linesEquations with coefficients that have been swapped, with one negated, will be perpendicular:
x -2y = -2 and 2x +y = -1 . . . . lines A and B
Line A is perpendicular to parallel lines B and C, so line D is the odd one out.
Line D doesn't fit.
Find the area.
A. 156 ft²
B. 126 ft²
C. 80 ft²
D. 39 ft²
Answer:
The answer is A
Step-by-step explanation:
12 x 5 = 60
16 x 6 = 96
60 + 96 =156 ft
Answer:
[tex]6 \times 5 + 6 \times 16 = 6 \times 21 = 126[/tex]
Perry bought one package of strawberries for $3. How many packages of strawberries can Mei buy if she has $9?
Answer:
3 packs
Step-by-step explanation:
1 pack = $3
To see how many she could buy divide the money she has by how much each pack costs
9/3 = 3
$3 for each pack is the same as
3+3+3 = 6+3 = 9
What is the answer to this question
Answer: A)
[tex]A) The ~ low ~ temperature ~ in ~Edmonton ~was\\\~greater ~than~the ~low ~temperature~ in~ fort~ Nelson[/tex]
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hope it helps...
have a great day!!!
sasha needs 3/4 cup of flour to make a batch of muffins and 1 2/3 cups of flour to make loaf of bread. How many cups of flour does sasha need to make both a batch of muffins and a loaf of bread
Using the addition operation, the number of cups of flour Sasha needs to make both a batch of muffins and a loaf of bread is 2⁵/₁₂ cups.
How is the number or quantity determined?We can use the addition operation to determine the quantity of flour that Sasha needs.
We add the cups of flour needed for both items to determine the total quantity.
The quantity of flour for making a batch of muffins = 3/4 cups
The quantity of flour for making a loaf of bread = 1²/₃ cups
The total quantity of flour needed for making a batch of muffins and a loaf of bread = 2⁵/₁₂ cups (³/₄ + 1²/₃)
(³/₄ + 1²/₃)
= ³/₄ + ⁵/₃
= (9 + 20)/12
= 29/12
= 2⁵/₁₂
Thus, to make a batch of muffins and a loaf of bread, Sasha needs 2⁵/₁₂ cups of flour.
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6x-14<-14 or 3x+10>13
Answer:
solution set must contain all numbers less than zero or greater than one
graph H illustrates this solution
Step-by-step explanation:
6x - 14 < -14
6x < 0
x < 0
3x + 10 > 13
3x > 3
x > 1
If 4, x, y, 108 are the consecutive terms of a G.P., find x and y.
Given:
4, x, y, 108 are the consecutive terms of a G.P.
To find:
The x and y.
Solution:
The nth term of a G.P. is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Let us consider 4, x, y, 108 are the first 4 terms of the G.P. Here 4 is the first term of the given G.P.
Suppose r the common ratio, then 4th term of the given G.P. is:
[tex]a_4=4(r)^{4-1}[/tex]
[tex]a_4=4(r)^{3}[/tex]
The 4th term of the G.P. is 108.
[tex]4(r)^{3}=108[/tex]
[tex]r^{3}=\dfrac{108}{4}[/tex]
[tex]r^{3}=27[/tex]
[tex]r^{3}=3^3[/tex]
On comparing both sides, we get
[tex]r=3[/tex]
The common ratio is 3.
The second term of the given G.P. is:
[tex]x=4r[/tex]
[tex]x=4(3)[/tex]
[tex]x=12[/tex]
The third term of the given G.P. is:
[tex]y=xr[/tex]
[tex]y=12(3)[/tex]
[tex]y=36[/tex]
Therefore, the value x is 12 and the value of y is 36.
Hey can I have some help on this I can only give you 10 points though
Why can’t a nose be 12 inches long Worksheet
Find the lateral area of the cylinder to the nearest tenth.
9 cm
19 cm
Not drawn to scale
Оа
2
1046.2 cm
Ob
2
664.4 cm
ос
2
537.2 cm
Od
2
1201.
Answer:
Lateral surface area is 847.8 centimeters^2
Step-by-step explanation:
The formula for determining the lateral surface area of a cylinder is expressed as
Lateral surface area = 2πrh
Where
r = radius of the cylinder
h = the height of the cylinder
From the information given,
r = 9 centimeters
h = 15 centimeters
π = 3.14
Lateral surface area = 2 × 3.14 × 9 × 15 = 847.8 centimeters^2
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1.171875 as a fraction
false
it is a decimal not a fraction
Solve the following equation 3x - 2(x + 3) = 4x - 7
Answer:
3x-2x-6=4x-7
x-6. =4x-7
3x=1
X=1/3
Please help me please I only have a couple hours left and this is taking soooo much time
Answer:
it would be the first answer
Step-by-step explanation:
you can draw the net of the shapes, and count each corner there
3/4 of the children in a school have blue eyes the rest have brown eyes. if 84 children have blue eyes how many have brown eyes?
Answer:
Let the total number of people in the group=x
So total number of men =3x/8
Hence total number of women=5x/8
No. of men having brown eyes=2/3*3x/8=x/4
Total no. of people having brown eyes=3x/4
No.of women having brown eyes
=3x/4 -x/4=2x/4=x/2
No. of women who don't have brown eyes= 5x/8-x/2 = x/8
So the fraction is x/8x= 1/8
Step-by-step explanation:
Answer: 28 children
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.
First, we would need to figure out the total number of students. To do this, we can divide 84 by 3, then add that to the total.
84 ÷ 3 = 28
28 + 84 = 112
This means that there are 112 students in the classroom.
If 3/4 of the children in the school have blue eyes, we know that 1/4 of the children will have brown eyes. We can convert 1/4 into a decimal, or into a percentage, to get the number of children with brown eyes.
1/4 = 0.25 = 25%
To figure out how much 25% of 112 is, we can simply multiply 112 by 0.25.
112 × 0.25 = 28
So, this means that there are 28 children with blue eyes in the school.
1/2k+6=4k-8
Please explain step by step
So on solving the provided question, we can say that the value of k is 4, in this linear equation question.
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
1/2k +6= 4k-8
Multiplying both sides by 2,
k+12= 8k-16
7k=28
Therefore,
k=4
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rachel made 16 out of 20 free throw shots about how many out of next 30 free throw shots would u expect her to miss
Sam made 16 goals in 12 games. How many goals should she make in 36 games?
Answer:
42 goals
Step-by-step explanation:
For the function graphed below, what is the output when x=-2?
Step-by-step explanation:
that is a college level question ? and you don't know the answer ?
that is basic, basic, basic ...
you go on the x-axis to -2.
from there you go either up or down and look at what y-value are you crossing the functional curve.
it is -1.
so, the "output" for x = -2 is y = -1. or simply -1.
Mr Campbell has a jar on his desk that contains 1o0 marbles . At the end of class, each student draws a marble from the jar without looking, notes the color, and then puts it back in the jar. If a student draws the red marble , the student gets a pass on that day's homework. How can the students determine the probability of drawing the red marbles ?
Answer:
noseee
Step-by-step explanation:
Find the limits given based on the graph.
Limits of the functions shown in the graph are limx +f(x) = 0 and limx -f(x) = 0. The link between a group of inputs, each of which has a related output, is known as a function.
what are functions ?The study of mathematics covers a variety of topics, including numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist. An easy way to think of a function is as a relationship between inputs and outputs, where each input leads to a single, distinct result. Each function has a respective domain and a codomain, or scope. Functions are typically represented by the letter f. (x). input is x. The accessible functionalities fall into four categories. based on the following elements: on functions, one-to-one functions, many-to-one functions, and within functions.
given
We first take into account how f(x) behaves as x increases unboundedly for the function in the graph below. As x can always increase because the function has no limit, it can never be zero. However, the function's behavior when x rises.
Similar to how x decreases without bound or how we move leftward on the graph, f(x) also seems to be approaching zero.
So in this case we can write:
limx → +∞f(x) = 0
limx → - ∞f(x) = 0
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what is an irrational number between 4 and 5 is it √12 or √20 or √34 or √80?
Answer:
[tex]\sqrt{20}[/tex]
Step-by-step explanation:
the answer would be between [tex]\sqrt{16}[/tex], which is 4, and [tex]\sqrt{25}[/tex], which is 5.
4.47 i.e., [tex]\sqrt{20}[/tex] is the irrational number between 4 & 5.
What is irrational number?Irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers. For example, there is no number among integers and fractions that equals Square root of [tex]\sqrt{2}[/tex].
Given irrational numbers
[tex]\sqrt{12} = 3.46[/tex]
[tex]\sqrt{20} =4.47[/tex]
[tex]\sqrt{34}=5.83[/tex]
[tex]\sqrt{80} =8.94[/tex]
Therefore, 4.47 i.e., [tex]\sqrt{20}[/tex] is between 4 & 5.
Hence, correct option is B.
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Choose the expression that is equivalent to fraction with 7 raised to the negative tenth power in the numerator and 7 raised to the fourth power times seven raised to the zero power in the denominator.
negative 1 divided by 7 raised to the fourteenth power
−714
1 divided by 7 raised to the fourteenth power
714
Step-by-step explanation:
note that 7⁰ is always 1.
[tex] \frac{ {7}^{ - 10} }{ {7}^{4} } \\ \\ \frac{1}{ {7}^{14} } \\ \\ {7}^{ - 14} [/tex]
the answer is shown above
Answer:
Last option, [tex]\frac{1}{7^{14} }[/tex]
Step-by-step explanation:
[tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex]=>[tex]\frac{7^{-10} }{7^{4+0}}[/tex]=>[tex]\frac{7^{-10} }{7^{4}}[/tex]=>[tex]7^{-10-4}[/tex]=>[tex]7^{-14}[/tex]=>[tex]\frac{1}{7^{14} }[/tex]
What is the formula to find the perimeter of a pentagon
Answer:
For a regular polygon, the perimeter is equal to the product of one side length and the number of sides of the polygon. For example, the perimeter of a regular pentagon whose side length 8 cm, is given by; Perimeter of a regular pentagon = 8 x 5 = 40 cm.
Step-by-step explanation:
I hope I've helped :).
Answer:
perimeter = number of sides x the length of any side.
Step-by-step explanation:
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Part way through painting her room, Sam runs out of paint.
• She estimates that there are about 125 square feet left to paint.
• The purple paint that Sam is using is only available in 1-quart
cans. (Assume she must buy whole cans of paint.)
• Each can of paint covers 40 square feet.
How many cans of paint does Sam need to buy to finish painting her room?
Explain to Sam why she needs this many cans of paint.
Answer:
4
Step-by-step explanation:
You divide 125 by 40 and that will give you 3 1/8. In the question, it says to use whole numbers and you'd have to go up, giving you 4.
It takes you together 6.67 minutes to paint 50 square feet, as you have to consider that the together rate is the sum of the separate rates.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
The together rate is the sum of the separate rates.
In this question:
Sam's rate is 1/10 for 25 square feet, so 1/20 for 50 square feet.
Your's rate is 1/5 for 25 square feet, so 1/10 for 50 square feet.
Together rate:
1/x = 1/20 + 1/10
or, 1/x = 3/20
or, x = 20/3
or, x = 6.67
so, we get,
It takes you together 6.67 minutes to paint 50 square feet, as you have to consider that the together rate is the sum of the separate rates.
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complete question:
Sam and you are going to paint your room together.
Sam takes 10 minutes to paint 25 square feet.
It takes you 5 minutes to paint 25 square feet.
Sam says, "If we paint together, then it will take 15
minutes for us to cover 50 square feet."
Give an explanation to convince Sam that she is
incorrect
Use exponents to rewrite 27.
Answer:
[tex]3^{3}[/tex]
Step-by-step explanation:
The number 27 is written in the form of a base of 3 and the exponent of 3 is given as 3³.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
here, we have,
It is a method for dividing a polynomial into pieces that will be multiplied together.
At this moment, the polynomial's value will be zero.
Rewrite 27 as a base and exponent without using an exponent of 1.
The number 27 can be written as,
27 = 3 x 3 x 3
27 = 3³
Then the number 27 is written in the form of a base of 3 and the exponent of 3 is given as 3³.
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What is the greatest common factor of 3x
Answer:
It is not possible to find the greatest common factor of 3x.
Step-by-step explanation:
The greatest common factor (GCF) of a set of numbers is the largest number that divides into all of the numbers in the set.
In this case, you have provided a variable, 3x, and not a set of numbers. Therefore, it is not possible to find the greatest common factor of 3x.
If you have a set of numbers that you would like to find the greatest common factor of, please let me know and I will be happy to help.