The value of sec(θ) given [tex]\tan^2(\theta) = \frac{3}{8}[/tex] is [tex]\frac{\sqrt{22}}{4}[/tex]. Using the identity [tex]\tan^2(\theta) + 1 = \sec^2(\theta)[/tex], we find [tex]\sec(\theta) = \frac{\sqrt{22}}{4}[/tex].
To find the value of sec(θ) given that [tex]\tan^2(\theta) = \frac{3}{8}[/tex], we'll use the trigonometric identity:
[tex]\[ \tan^2(\theta) + 1 = \sec^2(\theta) \][/tex]
Given that [tex]\(\tan^2(\theta) = \frac{3}{8}\)[/tex], we can plug this into the identity:
[tex]\[ \frac{3}{8} + 1 = \sec^2(\theta) \][/tex]
[tex]\[ \frac{3}{8} + \frac{8}{8} = \sec^2(\theta) \][/tex]
[tex]\[ \frac{11}{8} = \sec^2(\theta) \][/tex]
To find [tex]\(\sec(\theta)\)[/tex], we take the square root of both sides, but since sec(θ) is always positive, we'll take the positive square root:
[tex]\[ \sec(\theta) = \sqrt{\frac{11}{8}} \][/tex]
[tex]\[ \sec(\theta) = \sqrt{\frac{11}{8}} \times \frac{\sqrt{8}}{\sqrt{8}} \][/tex]
[tex]\[ \sec(\theta) = \sqrt{\frac{88}{64}} \][/tex]
[tex]\[ \sec(\theta) = \frac{\sqrt{88}}{\sqrt{64}} \][/tex]
[tex]\[ \sec(\theta) = \frac{\sqrt{88}}{8} \][/tex]
[tex]\[ \sec(\theta) = \frac{2\sqrt{22}}{8} \][/tex]
[tex]\[ \sec(\theta) = \frac{\sqrt{22}}{4} \][/tex]
So, the value of [tex]\(\sec(\theta)\)[/tex] given [tex]\(\tan^2(\theta) = \frac{3}{8}\)[/tex]is [tex]\(\frac{\sqrt{22}}{4}\)[/tex].
Complete Question:
Given that tan²(θ) = 3/8, what is the value of sec(θ)?
The value of sec(θ) given that tan²(θ) = 3/8 is (1/4)√22.
To find the value of sec(θ) given that tan²(θ) = 3/8, we first need to recall the relationship between tangent (tan) and secant (sec) functions.
The relationship is as follows:
[tex]\[ \tan^2(\theta) + 1 = \sec^2(\theta) \][/tex]
Given that [tex]\( \tan^2(\theta) = \frac{3}{8} \),[/tex] we can substitute this value into the equation above:
[tex]\[ \left(\frac{3}{8}\right) + 1 = \sec^2(\theta) \][/tex]
Now, let's simplify the expression:
[tex]\[ \frac{3}{8} + 1 = \frac{3}{8} + \frac{8}{8} = \frac{3 + 8}{8} = \frac{11}{8} \][/tex]
So, [tex]\( \sec^2(\theta) = \frac{11}{8} \).[/tex]
Now, to find the value of sec(θ), we take the square root of both sides:
[tex]\[ \sec(\theta) = \sqrt{\frac{11}{8}} \][/tex]
To rationalize the denominator, we multiply both the numerator and the denominator by [tex]\( \sqrt{8} \):[/tex]
[tex]\[ \sec(\theta) = \frac{\sqrt{11 \times 8}}{\sqrt{8 \times 8}} = \frac{\sqrt{88}}{8} \][/tex]
Now, we can simplify the expression under the square root:
[tex]\[ \sqrt{88} = \sqrt{4 \times 22} = 2 \sqrt{22} \][/tex]
So, the final expression for sec(θ) is:
[tex]\[ \sec(\theta) = \frac{2 \sqrt{22}}{8} \][/tex]
And if we simplify it further, we get:
[tex]\[ \sec(\theta) = \frac{\sqrt{22}}{4} \][/tex]
This is the final answer for the value of sec(θ) in terms of the given information.
The Complete Question:
Given that tan²(θ) = 3/8, what is the value of sec(θ)?
The hypotenuse of a right triangle is 17. The lengths of the two legs are whole numbers. What are they?
Answer:
The legs would be 15 & 8
Step-by-step explanation:
According to the Pythagorean theorem:
17² = a² + b²
289 = a² + b²
289 = 225 + 64
289 = 15² + 8²
The lengths of the two legs are 15 and 8.
The area of a square poster is 50 in.2. Find the length of one side of the poster to the neare
tenth of an inch.
The length of one side of the poster is in.
(Round to the nearest tenth as needed.)
Answer: (rounded) 7.1 inches.
For this problem, you have to find the square root of 50, since in a square all sides are equal. When you find the square root, you get 7.071067...., but rounded this would be 7.1 .
Answer:
the answer is sevenm point one
Step-by-step explanation:
10. Find the sum -18 + (-36).
Answer: -54
All you need to do is add the two together
Answer:
Step-by-step explanation:
-18 + (-36) = -18-36 = -54
Simplify the square root of 5 times the cube root of 5.
five to the five sixths power
five to the one sixth power
five to the two thirds power
five to the seven sixths power
Answer:
Option 3 - five to the two thirds power
Step-by-step explanation:
Given : Expression 'the square root of 5 times the cube root of 5'.
To find : Simplify the expression ?
Solution :
Writing expression in numeric form,
The cube root of 5 means [tex]\sqrt[3]{5}[/tex]
The square root of 5 times the cube root of 5 means [tex]\sqrt{5\sqrt[3]{5}}[/tex]
Now, simplify the expression
[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{5\times (5)^{\frac{1}{3}}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{1+\frac{1}{3}}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{\frac{4}{3}}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=((5)^{\frac{4}{3}})^{\frac{1}{2}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=(5)^{\frac{4}{3}\times \frac{1}{2}}[/tex]
[tex]\sqrt{5\sqrt[3]{5}}=(5)^{\frac{2}{3}}[/tex]
The expression is five to the two thirds power.
Therefore, Option 3 is correct.
The correct option is d. To simplify [tex]\(\sqrt{5} \cdot \sqrt[3]{5}\)[/tex], we get [tex]\(5^{5/6}\)[/tex]. Therefore, the correct answer is five to the seven sixths power.
To simplify [tex]\( \sqrt{5} \times \sqrt[3]{5} \)[/tex], we combine the radicals:
[tex]\[ \sqrt{5} \times \sqrt[3]{5} = 5^{1/2} \times 5^{1/3} \][/tex]
Using the property of exponents [tex]\( a^m \times a^n = a^{m+n} \)[/tex]:
[tex]\[ 5^{1/2} \times 5^{1/3} = 5^{1/2 + 1/3} \][/tex]
Now, find a common denominator for the exponents:
[tex]\[ \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \][/tex]
Therefore,
[tex]\[ 5^{1/2} \times 5^{1/3} = 5^{5/6} \][/tex]
So, the simplified expression is [tex]\( {5^{5/6}} \).[/tex]
This corresponds to option (d) in your choices: five to the seven sixths power.
The complete question is- Simplify the square root of 5 times the cube root of 5.
a. five to the five sixths power
b. five to the one sixth power
c. five to the two thirds power
d. five to the seven sixths power
2=2 x 7 -22=? too what
Answer:
0
Step-by-step explanation:
clearly this page is not in need of in answer it does not seem like a real equation you need help with.
Your grades on four exams are 78, 85, 97, and 92
What grade do you need on the next exam to have an
average of 90 on the five exams?
Let g = grade needed
(78 + 85 + 92 + 97 + g)/5 = 90
Solve for g.
At the grand opening, every 8th customer received a free coffee mug, and every 12th customer received a free baseball cap. How many of the first 100 customers received both a mug and a cap?
8 people received a Baseball Cap
12 people received a Coffee Mug
Hope this helped!
Look at the following numbers:
-4, -1,0,4
Which pair of numbers has a sum of 0?
Answer:
-4 + 4
Step-by-step explanation:
because when you add a negative number with a positive number the sum will always equal 0
I am joyus to assist :)
Answer:
-4+4
Step-by-step explanation:
1/8 is called a terminating decimal
Explain
Answer:
Step-by-step explanation:
Maybe if we defined a non terminating fraction first, a terminating one would make more sense to you.
non terminating means that it goes on forever.
1/3 = 0.3333333333333333333333333333333....333333333333333333...333
I/3 never really ends.
1/8 on the other hand had
1/8 = 0.125 as a value and that's all there is. We're done.
So a terminating decimal ends.
8x-4y=-12;x=-3,-1,1 do not know how to the assignment
Answer:
y= -3,1,5
Step-by-step explanation:
actually the question is what are the values of y when x = -3,-1,1
Answer: -1=-1 ,1=1
You just need to plug it in to the graph.
what 1/8 of 12 in simplest form
Answer:
1½
Step-by-step explanation:
[tex] \frac{1}{8}(12) = \frac{12}{8} = 1 \frac{4}{8} = 1 \frac{1}{2} [/tex]
I am joyous to assist you anytime.
The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph?
Answer:
The coordinates of the vertex of the graph are (-2, -9).
Step-by-step explanation:
The quadratic function is described by the standard equation The graph of a quadratic function is called a parabola.
We have the quadratic function
We identify the coefficients a, b, and c. For this equation,
The axis of symmetry is , i.e., Thus, the statement in the question for the symmetry axis x = -2 is correct.
The vertex (or turning point) is where or
The parabola opens upward because a > 0, resulting in a vertex that is a minimum.
Finding the minimum value is as follows:
Therefore, the coordinates of the vertex of the graph are (h, k), i.e.,
Other components:
The y-intercept of the quadratic function f(x) = x² + 4x - 5 is (0, c), i.e., the point
The factorization of f (x) = x² + 4x - 5 becomes f(x) = (x + 5)(x - 1). Then we get the x-intercepts at
Learn more
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Keywords: the axis of symmetry, for a function, f(x) = x² + 4x − 5, x = −2, which is the graph of f(x) = (x - 1)(x + 4), what, the coordinates of the vertex of the graph, the x-intercept, quadratic function, a standard equation, the y-intercept, parabola, upward, the minimum value
Answer:
the vertex of the graph is (-2, -9)
Step-by-step explanation:
The given function is:
[tex]f(x)=x^2+4x-5[/tex]
Given x = -2 is the axis of symmetry and because we know that the vertex of the graph lies on its axis of symmetry
=> coordinate of vertex is (-2, y)
When x= -2 we have
[tex]f(-2) =(-2)^2+4(-2)-5\\<=> y=4-8-5\\<=> y=-9[/tex]
So the vertex of the graph is (-2,-9)
Evaluate B^2for B=9.
Answer:
81
Step-by-step explanation:
since b is 9
do 9x9 which is 81
What sequence of events explains why Anderson did not make any money from her patent?
Anderson was unable to capitalize on her invention, and other companies were able to profit from her invention without paying her.
The sequence of events that explains why Anderson did not make any money from her patent is as follows:
Anderson invented the windshield wiper in 1903.She patented her invention in 1905.She tried to sell her patent to a Canadian company, but they refused to buy it.She tried to sell her patent to other companies, but none of them were interested.Anderson did not have enough money to market and manufacture her invention herself.Other companies began to make and sell windshield wipers without her permission.Anderson could not afford to sue the companies for patent infringement.Anderson's patent expired in 1920.Anderson never made any money from her invention.The image of Mary Anderson and the First Windshield Wipers confirms this sequence of events. The image shows Anderson with a model of her windshield wiper invention. The text below the image states that Anderson "failed to sell her patent to any manufacturer" and that "her patent expired in 1920 without her making any money from her invention."
In addition to the information in the image, we can also infer that Anderson did not make any money from her patent because she did not have the business acumen or resources to bring her invention to market. She was a single woman with no business experience. She also did not have the financial resources to manufacture and market her invention on her own.
are 5(8y - 8) and 40y - 40 equal?
Answer:
Step-by-step explanation:
5 * 8y = 40y
8 * 5 = 40
40y - 40 IS equal to 40y - 40
Answer: no they are not
Step-by-step explanation: since the expression is in the parentheses you have to distribute the 8 amount 5y and 8 basically multiply 8 by he two numbers inside the parentheses 8(5y-8)
40y-64 is not equal to 40y -40
The local pharmacy has a coupon for two-in-one shampoo and conditioner. The original cost of one bottle is $6.99, and the coupon is for $1.75
off. How much does one bottle cost when the coupon is applied?
$6.99
$5.24
$5.00
$1.75
Answer:
5.24
Step-by-step explanation:
6.99-1.75 is 5.24.
Answer:
$5.24
Step-by-step explanation:
[tex]\begin{array}{rcr}\text{Original cost} & = & 6.99\\\text{Less coupon} & = & -1.75\\\text{Net cost} & = & \mathbf{5.24}\\\end{array}[/tex]
7. A city has a population of 2,549,786 people.
Estimate this population to the nearest million.
Express your answer as the product of a single
digit and a power of 10.
Rounded to the nearest million, the population
is about
Written as the product of a single digit and
a power of ten, this number is
x 10
Answer:
1) [tex]2,549,786\ people \approx3,000,000\ people[/tex]
2) [tex]3*10^6[/tex]
Step-by-step explanation:
1) To round a number to the nearest million, you must look at the digit located in the hundred thousands place. If this is greater than or equal to 5 you must round up, and if this is less than 5, you must round down.
In this case you know that the city has a population of [tex]2,549,786\ people[/tex].
You can notice that the digit located in the hundred thousands place is 5, therefore, you must round up:
[tex]2,549,786\ people \approx3,000,000\ people[/tex]
2) Scientific notation has the following form:
[tex]a*10^n[/tex]
Where "a" must be a number from 1 to 10 but not including 10 and "n" must be an integer.
To express [tex]3,000,000[/tex] in Scientific notation, the decimal point must be moved 6 places to the left; therefore, the exponent will be positive.
Then:
[tex]=3*10^6[/tex]
Jada says: “If you multiply a number by 0.001, the decimal point of the number moves three places to the left.” Do you agree with her statement? Explain your reasoning.
pls help
Step-by-step explanation:
Yes, I agree with her. If you multiply a number by .001 youll move the decimal point to the left 3 times. For example let's say 480. multiplied by .001. it will then become .480 or .48
Yes I agree I just did this in class
If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
Answer:
Roots are complex numbers
Step-by-step explanation:
we know that
In a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex]
The discriminant is equal to [tex]b^{2} -4ac[/tex]
If [tex]b^{2} -4ac=0[/tex] -----> The equation has only one real root
If [tex]b^{2} -4ac>0[/tex] -----> The equation has two real roots
If [tex]b^{2} -4ac<0[/tex] -----> The equation has complex roots
In this problem the discriminant is -8
so
-8 < 0
therefore
Roots are complex numbers
Answer:
A) There are two complex roots
Step-by-step explanation:
took the test
Given that y=3(4x - 3)+5, find the value of x when y=-2.
Answer:
x=-2
Step-by-step explanation:
Distribute the 3 with the parenthesis to make the new equation -2=12x-9+5.
Combine like terms. -2=12x-4.
Move -4 to other side. -6=12x.
Divide by -6. x=-2
28.9-32.5
i will be fine i just forget the steps
Answer:
-3.6
Step-by-step explanation:
Since 32.5 is greater than 28.9, you just subtract 32.5 from 28.9 then add an equal sign. 32.5-28.9=3.6. With the negative, it would be -3.6
The value obtained by making the subtraction operation is -3.6
Subtracting ValuesTo perform the subtraction operation, the right hand side value is taken away from left hand side value .
Here , we have;
28.9 - 32.5 = -3.6We obtained a negative value because the right hand value is greater than the left hand value.
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The following shows the floorplan for a room that is being added on to your house. If the scale factor is 2.5” = 3 ft, what is the area of the room in the real world?
Answer:
9 ft
Step-by-step explanation:
you multiply side a by side b
so 3x3 = 9 ft
Suppose the function h(t) gives the heart rate of a runner at various points in time, t, during a 10 mile run. Select an appropriate domain for this function. Assume that the runner completed the 10 mile run in 112 minutes.
Write the domain of this function using interval notation.
The domain of the heart rate function h(t) for a runner who completed a 10-mile run in 112 minutes is [0, 112] in interval notation.
Explanation:In this scenario, the domain of the function h(t) is the time duration during which the runner is running. Thus, since the runner completed the 10-mile run in 112 minutes, the domain is from 0 (the start of the run) to 112 (the end of the run). We represent this in interval notation as [0, 112]. The square brackets indicate that the endpoints are included in the domain. So, the domain of the function h(t) in this context is [0, 112].
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Mary is n years old. What expression represents her age 5 years from now? 5 years ago?
Answer:
After 5 years : ( n + 5 ) years !
Before 5 years : ( n - 5 )
Step-by-step explanation:
Given the age of Mary is n years old
After 5 years , She must be 5 years more from now so,
Her age will be ( n + 5 ) years after 5 years from now !
Also, 5 years ago she must be 5 years less than from now ,
So, her age 5 years ago was ( n - 5 ) years !
To represent Mary's age 5 years from now, the expression 'n + 5' is used. To represent her age 5 years ago, the expression 'n - 5' is used.
Explanation:To represent Mary's age 5 years from now, we can use the expression n + 5. This is because we add 5 to her current age, represented by 'n', to find her age in the future.
To represent Mary's age 5 years ago, we can use the expression n - 5. This is because we subtract 5 from her current age, represented by 'n', to find her age in the past.
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263 grams dental stone powder
80 milliliters of water
If you use 70 grams of stone, how many milliliters of water are needed?
Answer:
21.29 milliliters
Step-by-step explanation:
First find how much water is need for 1 gram of stone by dividing both numbers by 263. Then multiplying both numbers by 70.
Grams : Milliliters
263 80
1 : 0.3042 (Rounded to 4 decimal places)
70 : 21.29 (Rounded to 2 decimal places)
The amount of water needed when using 70 grams of dental stone powder is approximately 21.29 milliliters. This is based on the ratio of stone powder to water in the original mixture.
Explanation:The question is asking for the calculation of the amount of water needed if 70 grams of dental stone powder is used. This can be resolved by determining the ratio of water to dental stone powder in the initial mixture, and then applying this ratio to the lesser quantity of 70 grams. In the original mixture, there are 263 grams of dental stone powder to 80 milliliters of water which simplifies to approximately 1 gram to 0.3042 milliliters of water. Therefore, if you use 70 grams of stone powder, you multiply 70 grams by 0.3042 milliliters/g, which equates to approximately 21.29 milliliters of water.
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How do I do ( +7 ) - ( -2 ) = ?
Answer:
=9
Step-by-step explanation:
7−(−2)
=7−(−2)
=7+2
=9
what is 1 plus 5.00
A. 5.01
B.1
C. 12345678
D. 501
Answer:
Step-by-step explanation:
501
Help with number 1 plz
Yes, it will! It will be the same because of the Commutative property. Hope this gives you your whole answer!
Help find the distance between two points?
Answer:
4
Step-by-step explanation:
Calculate the distance using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = B(0, 0) and (x₂, y₂ ) = ([tex]\frac{\sqrt{6} }{2}[/tex], [tex]\frac{\sqrt{58} }{2}[/tex] )
AB = [tex]\sqrt{((\frac{\sqrt{6} }{2})^2 }[/tex] + [tex]\{(\frac{\sqrt{58} }{2})^2 }[/tex]
= [tex]\sqrt{\frac{6}{4} }[/tex] + [tex]\frac{58}{4}[/tex]
= [tex]\sqrt{\frac{64}{4} }[/tex]
= [tex]\sqrt{16}[/tex]
= 4
find the coordinates of the midpoint of the segment with the given endpoints. Y(-13,8) and Z (2,-10)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Y(\stackrel{x_1}{-13}~,~\stackrel{y_1}{8})\qquad Z(\stackrel{x_2}{2}~,~\stackrel{y_2}{-10}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2-13}{2}~~,~~\cfrac{-10+8}{2} \right)\implies \left( \cfrac{-11}{2}~,~\cfrac{-2}{2} \right)\implies \left(-5\frac{1}{2}~,~-1 \right)[/tex]