To find all possible values for θ if 0° < θ < 360° and tanθ = -1, we need to determine in which quadrants the tangent function is negative and then find the specific angles in those quadrants where the tangent equals -1.
The tangent function is negative in the second and fourth quadrants. Since tan(45°) = 1, we are looking for angles where the reference angle is 45° and the tangent is negative.
In the second quadrant, the angle that meets these criteria is 180° - 45° = 135°.
In the fourth quadrant, the angle that meets these criteria is 360° - 45° = 315°.
Therefore, the correct values for θ are:
c. 135°
e. 315°
The correct answer is [tex]135^{0}[/tex], [tex]225^{0}[/tex]
To find all possible values of θ if 0° < θ < 360° and tan θ = -1, we need to consider the values of θ in the different quadrants where the tangent function is negative.
In the first quadrant (0° < θ < 90°), the tangent function is positive, so there are no solutions in this range.
In the second quadrant (90° < θ < 180°), the tangent function is negative, and tan(135°) = -1.
In the third quadrant (180° < θ < 270°), the tangent function is also negative, and tan(225°) = -1.
In the fourth quadrant (270° < θ < 360°), the tangent function is positive, so there are no solutions in this range.
Therefore, the possible values of θ satisfying the given conditions are:
[tex]\theta = 135^\circ and \theta = 225^\circ[/tex]
Analyzing the given options:
a. [tex]-225^\circ[/tex] is not a solution, as it lies outside the given range of 0° < θ < 360°.
b. [tex]-45^\circ[/tex] is not a solution, as the tangent function is positive in the fourth quadrant.
c. [tex]135^\circ[/tex] is a solution, as tan(135°) = -1.
d. [tex]225^\circ[/tex] is a solution, as tan(225°) = -1.
e. [tex]315^\circ[/tex] is not a solution, as the tangent function is positive in the fourth quadrant.
Therefore, the correct options are c. 135° and d. 225°.
The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.
The numbers are: ___ ,___ or ____,___
The smaller number is 11 and the larger number is [tex]55 \frac{1}{2}[/tex].
Let's denote the two numbers as x and y, where x is the smaller number. We're given that [tex]y - x = 44 \frac{1}{2}[/tex] and [tex]7x - y = 10 \frac{3}{14}[/tex].
To solve this system of equations, we can use substitution or elimination. Let's use elimination:
1. Multiply the second equation by 2 to clear fractions: [tex]14x - 2y = 20 \frac{6}{14}[/tex].
2. Add the modified second equation to the first equation:
[tex](y - x) + (14x - 2y) = 44 \frac{1}{2} + 20 \frac{6}{14}[/tex]
[tex]13x - y = 64 \frac{11}{14}[/tex]
Now, we have a simpler equation: [tex]13x - y = 64 \frac{11}{14}[/tex].
3. Add this equation to the original second equation to find x:
[tex]7x - y + 13x - y = 10 \frac{3}{14} + 64 \frac{11}{14}[/tex]
[tex]20x - 2y = 75[/tex]
4. Now, we can solve this equation along with the first equation to find x and y.
After solving, we get x = 11 and [tex]y = 55 \frac{1}{2}[/tex].
The smaller number is 11 and the larger number is [tex]55 \frac{1}{2}[/tex].
Thus, the numbers are [tex]{11 \text{ and } 55 \frac{1}{2}}[/tex].
Correct Question:
The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
HELP PLEASE
Find the value of x, if you know the hypotenuse is 10 and 1 of the sides is 5. X is the other side.
1) when to use the median to describe the measure of center of a data set, 2) what measures of spread can we find when using box-plots, 3) what measure of spread is most appropriate to describe symmetrical data sets, 4) how does an outlier affect the mean of data set and give an example,
Answer:
what the dude above me put he wrong
Step-by-step explanation:
What are the zeros of the quadratic function f(x) = 8x2 – 16x – 15? x = –1 – and x = –1 + x = –1 – and x = –1 + x = 1 – and x = 1 + x = 1 – and x = 1 +
To find the zeros of the quadratic function [tex]\( f(x) = 8x^2 - 16x - 15 \)[/tex], you need to solve for [tex]\( x \) when \( f(x) = 0 \)[/tex].
So, you set \( f(x) \) equal to zero:
[tex]\[ 8x^2 - 16x - 15 = 0 \][/tex]
To solve this quadratic equation, you can use the quadratic formula:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \]where \( a = 8 \), \( b = -16 \), and \( c = -15 \).[/tex]
Plugging these values into the quadratic formula:
[tex]\[ x = \frac{{-(-16) \pm \sqrt{{(-16)^2 - 4(8)(-15)}}}}{{2(8)}} \]\[ x = \frac{{16 \pm \sqrt{{256 + 480}}}}{{16}} \]\[ x = \frac{{16 \pm \sqrt{{736}}}}{{16}} \][/tex]
Now, you simplify the expression under the square root:
[tex]\[ \sqrt{736} = \sqrt{16 \times 46} = 4\sqrt{46} \][/tex]
So, the expression becomes:
[tex]\[ x = \frac{{16 \pm 4\sqrt{46}}}{{16}} \][/tex]
Now, you can simplify further:
[tex]\[ x = \frac{{4(4 \pm \sqrt{46})}}{{4 \times 4}} \]\[ x = \frac{{4 \pm \sqrt{46}}}{{4}} \][/tex]
This gives you two solutions:
[tex]\[ x = \frac{{4 + \sqrt{46}}}{{4}} \]\[ x = \frac{{4 - \sqrt{46}}}{{4}} \][/tex]
These are the zeros of the quadratic function [tex]\( f(x) = 8x^2 - 16x - 15 \).[/tex]
Complete question :
What are the zeros of the quadratic function f(x) = 8x2 - 16x - 15?
If a family has three children draw a tree diagram representing the possible outcomes for the genders of the children and then list the sample space
20 POINTS! What is the slope of the line through the points (2, 5) and (6, 13)?
Find the inverse function for the function f(x) = mx + b?
What is another way to write this number 300+70+5/10+8/100
Find m∠A given ΔABC where a=4, b=6, c=3.
John rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 7, given that the first roll is a 1?
one over six
one over three
one over two
five over six
Answer: The correct option is (d) five over six.
Step-by-step explanation: Given that John rolls a number cube twice. We are to find the probability that the sum of the 2 rolls is less than 8 given that he first roll is a 1.
The sample space of an event of rolling a cube is
S = {1, 2, 3, 4, 5, 6}.
That is, n(S) = 6.
Now, let 'A' be the event that the sum of the two rolls is less than 7, then
A = {1, 2, 3, 4, 5}.
That is, n(A) = 5.
So, the probability of happening of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{5}{6}.[/tex]
Thus, the required probability is five over six.
Option (d) is correct.
help please
integral of sqrt (x^2+6x) dx
Find the measure of each angle please?
1. Add or subtract.
a. (x^2 - 4 x + 5) + (7x^2 + 2x + 3)
b. (7x^2 + 4x - 6) - (2x^2 - 3x + 1)
1a.
Answer is 8x² - 2x + 8
(x² - 4x + 5) + (7x² + 2x + 3)
The parentheses can go away since this is all addition (associative property of addition)
x² - 4 x + 5 + 7x² + 2x + 3
Combine like terms.
(x^2 + 7x²) + (-4x + 2x) + (5 + 3) = 8x² - 2x + 8
======
1b.
Answer is 5x^2 + 7x - 7
(7x² + 4x - 6) - (2x² - 3x + 1)
Distribute the negative into the right parentheses.
(7x² + 4x - 6) - (2x² - 3x + 1)
= 7x² + 4x - 6 - 2x² + 3x - 1
= (7x² - 2x²) + (4x + 3x) + (-6 - 1)
= 5x^2 + 7x - 7
Two 6-sided dice are rolled. what is the probability that the sum of the two numbers on the dice will be greater than 9?
HELP:
Whic reformer was not a journalist who investigated corruption in business or government?
(Points : 3)
Ray Stannard Baker
Upton Sinclair
Lincoln Steffens
William Booth
i wend with D
**NEED HELP!!!
Bo’s gross annual income is $45,408. He is paid semimonthly and has 6% deducted from his paychecks for his 403(b). His employer matches his deduction, up to 3%.
How much is deposited into Bo’s 403(b) each payday?
Answer:
170.28
Step-by-step explanation:
I just took the test and am reviewing the correct answers.
why is 5 a rational number?
x/10=2/4?
or x over 10
equals to 2 over 4
Help please on properties of exponents? will give a medal!
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.
a. 3 to the 2 over 3 power inches squared
b. 3 to the 8 over 3 power inches squared
c. 9 inches squared
d.9 to the 2 over 3 power inches squared
2.)Explain how the Quotient of Powers was used to simplify this expression.
2 to the fifth power, over 8 = 2 to the 2nd power
a.By finding the quotient of the bases to be one fourth and cancelling common factors
b. By finding the quotient of the bases to be one fourth and simplifying the expression
c. By simplifying 8 to 23 to make both powers base two and subtracting the exponents
d. By simplifying 8 to 23 to make both powers base two and adding the exponents
3.)the cube root of 2 to the seventh power
a. 2 to the 3 over 7 power
b. 2 to the 7 over 3 power
c. 2^21
d. 2^4,
Ques 1)
Option: C is the correct answer.
c. 9 inches square.
Ques 2)
Option: c
c. By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.
Ques 3)
Option: b
b. 2 to the 7 over 3 power
Step-by-step explanation:Ques 1)
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches.
i.e. let 'l' and 'b' denote the length and width of the rectangle.
i.e.[tex]l=\sqrt[3]{81}\\\\l=(3^4)^{\dfrac{1}{3}}\\\\l=3^{\dfrac{4}{3}[/tex]
since,
[tex](a^m)^n=a^{mn}[/tex]
and
[tex]w=3^{\dfrac{2}{3}}[/tex]
Hence, the area of rectangle is given by:
[tex]Area=l\times w\\\\\\Area=3^{\dfrac{1}{3}}\times3^{\dfrac{4}{3}}\\\\\\Area=3^({\dfrac{1}{3}+\dfrac{4}{3}})\\\\\\Area=3^{\dfrac{6}{3}}\\\\\\Area=3^2\\\\\\Area=9\ square\ inches[/tex]
As we know that:
[tex]a^m\times a^n=a^{m+n}[/tex]
Hence, Area=9 square inches.
Ques 2)
2 to the fifth power, over 8 = 2 to the 2nd power
i.e. we need to prove that:
[tex]\dfrac{2^5}{8}=2^2[/tex]
As we know that:
[tex]\dfrac{2^5}{8}=\dfrac{2^5}{2^3}=2^{5-3}=2^2[/tex]
( since
[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex] )
Hence, the correct answer is: Option: c
Ques 3)
The cube root of 2 to the seventh power.
i.e.
[tex]\sqrt[3]{2^7}\\\\=(2^7)^{\dfrac{1}{3}}\\\\=2^{\dfrac{7}{3}}[/tex]
Since,
[tex]\sqrt[n]{x}=x^{\dfrac{1}{n}}[/tex]
and
[tex](a^m)^n=a^{mn}[/tex]
Hence, the correct answer is: option: b
Solve the inequality
-40 > -10k
Andrew has a coupon for $2.80 puppy treats. One bag of treats usually costs $9.94 and contains 42 of the treats. If Andrew uses his coupon what will be the price per puppy treats
Andrew's price per puppy treat, after using a $2.80 coupon on a $9.94 bag that contains 42 treats, will be $0.17.
Andrew has a coupon that will reduce the price of puppy treats. Without the coupon, one bag of treats costs $9.94 and contains 42 treats. To find the price per treat after using the $2.80 coupon, we first subtract the coupon value from the original price of the bag. This gives us the discounted price of the bag:
Discounted Price = Original Price - Coupon Value = $9.94 - $2.80 = $7.14
Next, we find the price per treat by dividing the discounted price of the bag by the number of treats in the bag:
Price per Treat = Discounted Price ÷ Number of Treats = $7.14 ÷ 42 = $0.17 (rounded to two decimal places)
After using the coupon, the price per puppy treat will be $0.17.
In july in seattle, the grass grows 1/2 inch a day on a sunny day and 1/4 inch a day on a cloudy day. in seattle, in july, 75% of the days are sunny and 25% of the days are cloudy.
a.find the expected value of grass growth for the day
b.find the expected value of grass growth for the month of july ( 31 days ) -- round both to 2 decimal placees
Final answer:
Calculate the expected grass growth in Seattle based on the daily growth rates for sunny and cloudy days, then find the expected growth for the month of July.
Explanation:
a. Expected value of grass growth for the day:
Expected growth = (0.75 x 0.5) + (0.25 x 0.25) = 0.4375 inches
b. Expected value of grass growth for the month of July:
Expected growth for July = 31 days x Expected growth per day = 31 x 0.4375 = 13.56 inches
If AB is a tangent then point b must be the point of tangency true or false
Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters, so the height of the dam is meters. NextReset
Answer:
The height of dam =45.5 m.
Step-by-step explanation:
We are given that Scarlett stands 90 m away from the dam and records the angle of elevation to the top of the dam to be [tex]26^{\circ}p[/tex]
Scarelett's height is 1.65 meters.
We have to find the height of the dam.
Let h be the height of dam
AC=AB+BC
BC=x
h=1.65+x
CD=EB=90 m
In triangle ABE
[tex]\theta=26^{\circ}[/tex]
[tex]tan\theta=\frac{perpendicular\;side}{Base}[/tex]
[tex]tan26^{\circ}=\frac{AB}{90}[/tex]
[tex]0.4877=\frac{x}{90}[/tex]
[tex]x=0.4877\times 90[/tex]
[tex]x=43.893 m[/tex]
Therefore, the height of dam=1.65+43.893=45.543 m
Answer: The height of dam =45.5 m
A population has size 25 at time t = 0, with t measured in years. (a) if the population decreases by 4 people per year, find a function for the population size, p, at time t. enter your answer as an equation with p on the left side, and an expression involving t on the right
90% * x = 50 pounds of money
The area of a rectangular classroom is given by the trinomial 10x^2 + 3x - 4 What are the possible dimensions of the classroom? Use Factoring.
Answer:
(5x + 4) and (2x – 1)
Step-by-step explanation:
Will give brainliest answer!!
a(t) = (t - k)(t - 3)(t - 6)(t + 3) is a polynomial function of t, where k is a constant. Given that a(2) = 0, what is the absolute value of the product of the zeros of a?