Answers
The value of [tex]\sec\theta =\pm\sqrt{\frac{11}{8}}[/tex].
Solution:
Given data:
[tex]$\tan^2\theta=\frac{3}{8}[/tex]
To find the value of [tex]\sec\theta:[/tex]
Using trigonometric identity,
[tex]\sec^2\theta=1+\tan^2\theta[/tex]
Substitute [tex]\tan^2\theta=\frac{3}{8}[/tex] in the identity, we get
[tex]$\Rightarrow \sec^2\theta=1+\frac{3}{8}[/tex]
1 can be written as [tex]\frac{1}{1}[/tex].
[tex]$ =\frac{1}{1} +\frac{3}{8}[/tex]
Do cross multiplication.
[tex]$ =\frac{8}{8} +\frac{3}{8}[/tex]
Denominators are same, so you can add the fractions.
[tex]$ =\frac{8+3}{8}[/tex]
[tex]$\Rightarrow \sec^2\theta =\frac{11}{8}[/tex]
Taking square root on both sides, we get
[tex]$\Rightarrow \sec\theta =\pm\sqrt{\frac{11}{8}}[/tex]
Option B is the correct answer.
Hence the value of [tex]\sec\theta =\pm\sqrt{\frac{11}{8}}[/tex].
Related Questions
Express 2.41 x 10/4 in a standard form.
Answers
The number written in standard form is 24100
Step-by-step explanation:
An object is said to be written in scientific notation when it is written in the following form:
[tex]m\cdot 10^n[/tex]
where
m is the coefficient
n is the exponent of the power of ten
The number can be rewritten in standard form by writing the coefficient and then moving to the right (or to the left) the decimal point by n positions if n is positive (or negative).
In this problem, the number is
[tex]2.41\cdot 10^4[/tex]
So we have
m = 2.41
n = 4
Therefore, we have to write 2.41 and then move the decimal point 4 positions to the right: so we get
[tex]2.41\cdot 10^4 = 24100[/tex]
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I need help finding the values of x and z
Answers
Answer:
z = 73
x = 15
Step-by-step explanation:
Since z and (5x +32) share a straight line, adding them would equal 180.
(5x+32) + z = 180
Since z is 73, we can replace z
(5x + 32) + 73 = 180
(5x + 32) = 107
(5x) = 75
x = 15
The volume, V, of any cube with a side length, s. can be determined using the forma
V=s^3What is the volume, in cubic centimeters, of a cube with a side length
of 23 centimeters?
Answers
The volume of the cube is 12.167cm^3
Volume of a cubeThe formula for calculating the volume of a cube is expressed as:
V = s^3s is the side length of the cube
Given the following
side eof a cube = 2.3cm
Substitute into the formula
V = 2.3^3
V = 12.167cm63
Hence the volume of the cube is 12.167cm^3
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Answer:
dogs
Step-by-step explanation:
first you got a multiply the then you got to multiply the and then multiply me beautiful
Express the product in simplest form.
8/2x+8*x^2-16/4
A. (x + 4)
B. 2(x − 4)
C. (x − 4)
D. (x + 4)(x − 4)
Answers
The product in simplest form is (x - 4)
Solution:
Given expression is:
[tex]\frac{8}{2x+8} \times \frac{x^2-16}{4}[/tex]
We have to find the product in simplest form
In the given expression,
2x + 8 = 2(x+ 4)
We know that,
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Therefore,
[tex]x^2-16 = x^2-4^2 =(x+4)(x-4)[/tex]
Substitute these in given expression
[tex]\frac{8}{2(x+4)} \times \frac{(x+4)(x-4)}{4}[/tex]
Cancel the common factors,
[tex]\frac{8}{2(x+4)} \times \frac{(x+4)(x-4)}{4} = x - 4[/tex]
Thus the product in simplest form is (x - 4)
$8000 principal earning 5% compounded annually, after 6 years
Answers
Answer:
The final balance is $10,792.14.
The total compound interest is $2,792.14.
Step-by-step explanation:
Final answer:
Explanation on calculating the amount of $8000 principal at 5% compounded annually after 6 years using compound interest formula.
Explanation:
The question: $8000 principal earning 5% compounded annually after 6 years.
Step-by-step explanation:
Use the compound interest formula: A = P(1 + r/n)^(nt) where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.
Plug in the values: P = $8000, r = 0.05, n = 1 (compounded annually), t = 6.
Calculate: A = $8000(1 + 0.05/1)^(1*6)
A = $10,720.77.
suppose you flip a coin twice. what is the probability that you get tails on the first flip and tail on the second flip?
Answers
Probability of getting tails on the first flip: 1/2 (because it's one of two possible outcomes).
Probability of getting tails on two consecutive flips: 1/4 (because it's one out of four possible outcomes- tails tails, tails heads, heads tails, heads heads)
A simpler way of thinking about it is 1/2*1/2, because you already have 1/2 for getting tails the first time, and if getting tails the second time were an independent event then the probability would be 1/3, but since it's getting tails twice you multiply the probabilities.
Either way, the answer is 1/4 (or 25%)
If you flip a coin twice the probability that you get tails on the first flip and tails on the second flip is 1/4.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that you flip a coin twice, the probability getting tails on the first flip we have to find the probability that you get tails on the first flip and tails on the second flip.
The probability of getting tails on the first flip is
P(T) = 1/2
When two coins get flipped the total possible outcomes are,
(T, H)(T,T)(H,H)(H,T)
Probability of getting tails on two consecutive flips,
P(T) =1/4
The probability that you get tails on the first flip and tails on the second flip
Thus, if you flip a coin twice the probability that you get tails on the first flip and tails on the second flip is 1/4.
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First: State the degree and tell which monomial (term) you determined to be the one as the greatest degree. Second: Classify each of the 2 polynomials. If it is NOT a polynomial, explain why you think it is not a polynomial. For example you may say: Polynomial # 4. has degree of 5 and is classified as a quintic polynomial of 4 terms. We covered this in class (see below). Explain in sentences how you determined degree and "name" or why it is NOT a polynomial: 1. 7x4 + 5x2 + x − 92. 7x6 − 4x3 + 1x
Answers
Step-by-step explanation:
The relationship between monomial, degree and polynomial
A monomial is basically an individual term. A polynomial is the sum of monomials. Any monomial (term) which contains the highest power of the variable would be considered as the degree of a polynomial. For example, [tex]2x^{2} + 3x + 1[/tex] is a polynomial of degree 3, as the first monomial (term) has the highest power (degree) of the variable x.Now, lets analyze the given algebraic expressions
Examining the first polynomial
Considering the first polynomial
[tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex]
Carefully notice that the first term [tex]7x^{4}[/tex] which is also called a monomial does have the highest exponent or power of a variable x, which is 4. Thus, it can be determined that the degree of [tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex] will be 4.Here is the summary of the classification of the first polynomial [tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex].
[tex]7x^4\:+\:5x^2\:+\:x\:-\:9[/tex] is a polynomial of 4 terms.Its degree is 4.It can also be named as 'quintic' because its degree is 4Examining the second polynomial
Considering the expression
[tex]7x^6\:-\:4x^3\:+\:1/x[/tex]
It is easy to figure out that [tex]7x^6\:-\:4x^3\:+\:1/x[/tex] is not a polynomial as it does not fulfill the criteria to be a polynomial as its last term is [tex]\frac{1}{x}[/tex] has the variable x in the denominator.
Here are some important things that need to be fulfilled for any expression to be a polynomial.
The polynomial can not contain any variable having fractional or negative powers. For example, any expression containing [tex]2v^{-5}[/tex] in any of its terms can not be a polynomial as the variable v has a negative power of exponent. Similarly, the polynomial can not contain any square root of variables. For example, any algebraic expression with the term [tex]2\sqrt{v}[/tex] can not be a polynomial as the variable v is right inside the radical symbol.The polynomial can not have any variable in the denominator. For example, any expression that contains the term [tex]\frac{7}{v}[/tex] would not be treated as the polynomial as the variable v is in the denominator.Therefore, from the above discussion we can safely say that the expression [tex]7x^6\:-\:4x^3\:+\:1/x[/tex] can not be treated as as a Polynomial as its last term [tex]\frac{1}{x}[/tex] contains the variable x which is in the denominator.
Keywords: matrimonial, polynomial, exponent, degree
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1. Annual sales for a fast food restaurant are $650.000 and are increasing at a rate of 4% per year.
Use an exponential function to find the annual sales after 7 years.
Help pls
Answers
The annual sales after 7 years is $ 855.3556
Solution:
The growth function is given as:
[tex]y = a(1+r)^t[/tex]
Where,
y is the future value
a is the initial value
r is the growth rate
t is the number of years
From given,
a = 650
t = 7
[tex]r = 4 \% = \frac{4}{100} = 0.04[/tex]
Therefore,
[tex]y = 650(1 + 0.04)^7\\\\y = 650(1.04)^7\\\\y = 650 \times 1.315931\\\\y = 855.3556[/tex]
Thus the annual sales after 7 years is $ 855.3556
carrie picked 7 red apples and 7 green apples
Answers
Answer:
she has 14 apples altogether
50× 3/8 how to reduce answer to lowest te
Answers
The lowest term is [tex]\frac{75}{4}[/tex].
Solution:
Given expression is [tex]50\times\frac{3}{8}[/tex]
To reduce this term to the lowest term:
[tex]$50\times\frac{3}{8}=\frac{50}{1}\times\frac{3}{8}[/tex]
Multiply the numerator and denominator.
[tex]$50\times\frac{3}{8}=\frac{150}{8}[/tex]
Now, divide the numerator and denominator by the greatest common factor.
Here 150 and 8 both have common factor 2.
So, divide numerator and denominator by 2.
[tex]$=\frac{150\div2}{8\div2}[/tex]
[tex]$=\frac{75}{4}[/tex]
[tex]$50\times\frac{3}{8}=\frac{75}{4}[/tex]
Hence the lowest term is [tex]\frac{75}{4}[/tex].
the store offers a 20% discount. the discount price of a hat is 18$. what is the regular price?
The discount price for t-shirt is 16.40
The discount price in dollars is 3.28
Answers
The regular price of the hat is $22.5
Explanation:
We know that the discount price of a hat is $18, so we need to find the regular price of the hat.
Let:
x: Regular price
So:
[tex]\\ \\ Regular \ price \ - \ percentage \ discount \times Regular \ price =discount \ price \\ \\ x-20\%(x)=18 \\ \\ x-0.20x=18 \\ \\ 0.8x=18 \\ \\ x=\frac{18}{0.8} \\ \\ x=22.5[/tex]
Finally, the regular price of the hat is $22.5
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if x equals 10 what 5x-10
Answers
Answer:
40
Step-by-step explanation:
x = 10
Substitute 10 for x
5 (10) -10
Multiply 5 by 10
50 - 10
= 40
Mark Brainliest
Answer:40
Step-by-step explanation:
PLEASE HELP ! Trying to make honor roll !
Which point represents the solution to the system of equations below ?
Answers
Answer:
Point C
Step-by-step explanation:
When you graph the two equations, they meet at point c, which is the solution
Answer:
Point C
Step-by-step explanation:
You know the x so you can substitute that into the point:
(4, y)
You don't know y but you can substitute in the x and solve the equation. You would get -3. So the point would be:
(4, -3)
Find that point on the graph and it's Point C.
What is the difference of the polynomials?
(8r⁶s³-9r⁵s⁴+3r⁴s⁵)-(2r⁴s⁵-5r³s⁶-4r⁵s⁴)
Answers
Answer:
8r⁶s³ - 5r⁵s⁴ + r⁴s⁵ + 5r³s⁶
Step-by-step explanation:
(8r⁶s³-9r⁵s⁴+3r⁴s⁵)-(2r⁴s⁵-5r³s⁶-4r⁵s⁴)
We need to combine like terms, take care the exponents of r and s
(8r⁶s³-9r⁵s⁴+3r⁴s⁵)-(2r⁴s⁵-5r³s⁶-4r⁵s⁴)
multiply the second parenthesis by -1
= 8r⁶s³-9r⁵s⁴+3r⁴s⁵-2r⁴s⁵+5r³s⁶+4r⁵s⁴
= 8r⁶s³ + (-9r⁵s⁴ + 4r⁵s⁴) + (3r⁴s⁵-2r⁴s⁵) + 5r³s⁶
= 8r⁶s³ - 5r⁵s⁴ + r⁴s⁵ + 5r³s⁶
Note: r⁶s³ is not like r³s⁶
(PLEASE HELP WILL GIVE BRAINLIEST)
What is the equation of this trend line?
Enter your answers by filling in the boxes.
K = _ J + _
Answers
Answer:
K=2J+28
Step-by-step explanation:
Y intercept is 28
Slope is 2
Given the graph of the function F(x) below, what happens to F(x) when x is a negative number with a large absolute value?
Answers
Answer:F(x) is a negative number with a small absolute value
Step-by-step explanation:
The true statement about the graph of f(x) is (a) f(x) is a negative number with a small absolute value
How to interpret the function?From the given graph, we have the following highlights:
As the absolute value of x increases in the positive axis, the value of f(x) decreasesAs the absolute value of x decreases in the negative axis, the value of f(x) decreasesThe above means that, when x is a negative number with a large absolute value, then the absolute value of x is a very large positive number.
And so the value of f(x) would be a small absolute value negative number
Hence, the correct option is (a) f(x) is a negative number with a small absolute value
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Find the measure of angle 5. Will someone please help me. I have to answer this one question before I can move on to another one. Please help
Answers
The measure of angle 5 is 75°.
Step-by-step explanation:
Properties of intersecting lines :
The angles formed opposite to each other at the point of intersection are called vertically opposite angles. These vertically opposite angles are congruent (same).step 1 :
From the figure, the angle (-9x-12) and angle (6x+183) are vertically opposite and are equal.
-9x-12 = 6x+183
⇒ -9x-6x = 183+12
⇒ -15x = 195
⇒ x = -(195/15) = -13
step 2 :
Substitute x= -13 in the angle (-9x-12)
⇒ (-9x-12) = -9(-13)-12
⇒ 117 - 12 = 105°
step 3 :
The measure of angle in a line is supplementary (180°).
Let angle 5 be unknown value "a".
Then, angle (-9x-12) + angle a = 180°
⇒ 105° + a = 180°
⇒ a = 180 - 105
⇒ a = 75°
∴ The measure of angle 5 is 75°
the cost of producing x laser printers is given by C(x)=325x + 2,300,000. Each printer can be sold for $450
Answers
Answer:
C(450)=2,446,250
Step-by-step explanation:
C(450)=325(450)+ 2,300,000
C(450)=146,250+2,300,000
C(450)=2,446,250
The profit from producing and selling x laser printers is given by the equation P(x) = 125x - 2300000.
Explanation:The question is about the calculation of profit in a business scenario. The calculation of profit involves finding the difference between the cost of production and the revenue obtained from selling the products. In this case, the cost function C(x) = 325x + 2300000 defines the cost of producing x laser printers. Each printer is sold for $450, which means the revenue function R(x) can be represented as R(x) = 450x.
To find the profit, we subtract the cost from the revenue. This gives us the profit function P(x) = R(x) - C(x) = 450x - (325x + 2300000). Simplifying this, we get P(x) = 125x - 2300000. This equation tells us the profit made from producing and selling x laser printers.
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pls help thx
A bag contains 1 red, 2 blue, and 3 green marbles. Two marbles are drawn from the bag without replacement.
Based on the tree diagram, what is the probability that a GREEN marble and then a RED marble is drawn? (in simplest fraction form)
A)
1
5
B)
1
10
C)
3
10
D)
4
11
Answers
Answer:
Step-by-step explanation:
so you have 1 red, 2 blue, and 3 red. Together that would be 6 marbles. However it apears that with each draw you gain two marbles. therefore there are 12 possibilities. The likely hood that you will get a green marble then a red marble should be 2/12. In simplified form it is 1/6.
Answer:the answer is 1/5 the other guy got it wrong
Step-by-step explanation:
a 9-kilogram bag of sugar cost $27.54. what is the unit price ?
Answers
Answer:
The answer is 3.06
Step-by-step explanation:
In order to find unit price. You divide the cost per how many units you have.
In this case, you divide 27.54 to 9.
This gives you the answer (3.06)
What is the unit price ?
$27.54 : 9 = $3.06
what is the surface area of the pyramid in square inches? 17in 15in 16in
Answers
Answer:
so its gonna be
Step-by-step explanation:
2=2
the basketball team scored 24 points. Uriah scored 7 of those points. About what percent of the points did he score?
Answers
Joanne and Betty have a combined age of 60 years. If Joanne is 18 years old,
how old is Betty?
Answers
Answer:
42
Step-by-step explanation:
Answer:
42
Step-by-step explanation:
Let Joanne age be x
let betty age by y
. ° . x + y = 60
if joanne is 18
y = 18
x + 18 = 60
x = 60 - 18
x = 42
. ° . betty = 42
A ruler is 12 inches long. What is the of this ruler
Answers
Can you please clarify what you want to ask? Thanks!
Which of the following fractions is not equivalent to the others 24/36 8/12 12/16 4/6
Answers
Answer:
12/16
Step-by-step explanation:
because he 6 in 4/6 cant go into 16 and 16 from 12/16 c 36 so that is why the answer is 12/16
After simplifying each fraction to its lowest terms, it's clear that 12/16, which simplifies to 3/4, is not equivalent to the others since they all simplify to 2/3.
The question asks which of the following fractions is not equivalent to the others: 24/36, 8/12, 12/16, 4/6. To determine this, we need to simplify these fractions to their lowest terms.
24/36 simplifies to 2/3, by dividing both numerator and denominator by 12.
8/12 simplifies to 2/3, by dividing both numerator and denominator by 4.
12/16 simplifies to 3/4, by dividing both numerator and denominator by 4.
4/6 simplifies to 2/3, by dividing both numerator and denominator by 2.
Therefore, the fraction 12/16 is not equivalent to the others since it simplifies to 3/4, while the others simplify to 2/3.
The current rates for an 80/20 mortgage are 4.25% for the first mortgage and
9.75% for the second mortgage. On a $100,000 30-year mortgage, what is the
actual rate?
Answers
The actual rate of the mortgage is 5.27%.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Since, we're taking two mortgages for a total of $100,000 for 30 years,
Now, we can find the actual rate of the mortgage by finding the weighted average of the two rates.
Hence, The weights in this case will be the proportion of loan taken at each rate;
We have
Rates Weights Rates × Weights
4.15 0.80 4.15 x 0.80 = 3.32
9.75 0.20 9.75 x 0.20 = 1.95
Hence, The actual rate of the mortgage is,
⇒ 3.32 + 1.95
⇒ 5.27%.
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Answer:
mine was 5.45$
Step-by-step explanation:
Which sum will be neither positive nor negative. a. 3+2 b. -4+(-4) c. -6+6 d. 7+(-6)
Answers
Answer:
c
Step-by-step explanation:
Jeff bought a bottle of water for $2. He also
bought some hot dogs for $3 each. Jeff did
not spend more than $14 on the hot dogs
and the bottle of water. Write an inequality
statement that can be used to find h, the
number of hot dogs that Jeff could have
bought.
Answers
Final answer:
The inequality to determine the number of hot dogs Jeff could have bought is 3h + 2 ≤ 14, representing the cost of hot dogs and the bottle of water not exceeding the total amount of $14.
Explanation:
To find h, the number of hot dogs that Jeff could have bought, we can write an inequality statement based on the maximum amount Jeff can spend and the cost of the hot dogs and water. Jeff bought one bottle of water for $2 and some hot dogs for $3 each. Given that he did not spend more than $14 on everything, the inequality to represent this scenario can be written as:
Cost of water + Cost of hot dogs ≤ Total amount Jeff can spend
2 + 3h ≤ 14
This inequality suggests that when we multiply the number of hot dogs Jeff bought (h) by $3 and add the cost of the water ($2), it should not exceed $14. So the inequality demonstrating the number of hot dogs Jeff could have bought without spending more than $14, including the water, is 3h + 2 ≤ 14.
-1/3 +5e =3/7
find e
Answers
Answer:
0.1523
Step-by-step explanation:
-1/3 + 5e = 3/7
5e = 3/7 + 1/3
By Elysium
5e = (9 + 7)/21
5e = 16/21
5e = 0.7619
e = 0.7619/5
0.1523
What is the solution to the equation x−23=−13 ? Enter your answer in the box.
Answers
Answer:
Step-by-step explanation: so u are going to put it like this x- -6 =5
Next u subtract -6 from both sides
x=11
Answer:
x=10
Step-by-step explanation: