Answer:
-√17/4
Step-by-step explanation:
Because both the x- and the y-coordinates of (-4, -1) are negative, the angle, theta, is in Quadrant III.
tan theta = opp/adj = vertical side / horizontal side = 4/1, or just 4.
The two coordinates are the legs (both shorter than the hypotenuse) of the triangle formed by this terminal side / point.
The length of the hypotenuse is found using the Pythagorean Theorem and is:
√[ (1)² + (4)² = √17.
Again remembering that our terminal side is in Quadrant III,
sin Ф = opp/hyp = -1/√17
cos Ф = adj/hyp = -4/√17
tan Ф = opp/adj = 4 (see discussion above)
The instructions are to "find sec(theta)." The sec function is the inverse of the cos function. Here cos Ф = -4/√17, and so the secant of this angle is
the inverse (reciprocal) of the cosine, and is thus -√17/4
The value of sec(theta) is found by first determining the radius using the Pythagorean theorem and then calculating the reciprocal of the cosine function, which in this case is -√17/4.
Explanation:To find the secant of angle theta (sec(θ)) when given a point (-4,-1) on its terminal side, we first need to understand that sec(θ) = 1/cos(θ). Since cos(θ) is the x-coordinate of the point on the unit circle divided by the radius, we need to find the radius of the circle that would pass through the point (-4, -1). This radius can be found using the Pythagorean theorem.
Let's calculate the radius (r):
r = √((-4)^2 + (-1)^2)
r = √(16 + 1)
r = √17
Now, since the x-coordinate is -4, cos(θ) = -4/r. Plugging in the value of r, we get:
cos(θ) = -4/√17.
Therefore, sec(θ) is the reciprocal of cos(θ):
sec(θ) = -√17/4.
PLEASE HELP ME FAST!!!!!!!
Answer:
I think it is (5, -2)
I hope it helps.
Step-by-step explanation:
What is the longest side of a right triangle called?
Answer:
Step-by-step explanation:
hypotenuse
Which of the following is the quotient of the rational expressions shown here?
For this case we must find the quotient of the following expression:
[tex]\frac {\frac {x} {x-1}} {\frac {1} {x + 1}}[/tex]
Applying double C we have the following expression:
[tex]\frac {x (x + 1)} {x-1} =[/tex]
Applying distributive property to the terms within the parentheses of the numerator we have:
[tex]\frac {x ^ 2 + x} {x-1}[/tex]
Thus, the quotient is given by option A
Answer:
Option A
Answer:
The answer is option A. (x^2 + x)/(x-1)
Step-by-step explanation:
To solve this problem, we must first understand how to divide fractions. When dividing fractions, the first fraction is unchanged and is multiplied by the reciprocal of the second fraction. If we apply this knowledge to this problem, we get:
x/x-1 * x+1/1
When we multiply fractions, we simply multiply both of the numerators together and both of the denominators together to create a single fraction.
In this case we get:
x(x+1)/x-1
When we simplify this single fraction by using the distributive property, we get the following:
(x^2 + x)/(x-1)
Therefore, your answer is option A.
Hope this helps!
1 Point
What is the remainder for the synthetic division problem below?
Answer:
A. 3
Step-by-step explanation:
see attached for the tableau
___
As you know, the number on the bottom row is multiplied by the divisor to get the next middle-row number to the right. Top and middle rows are added to get the bottom row.
Need help with a math question
Answer:
x=13°
Step-by-step explanation:
If BE is an angle bisector, then it divides the angle into two equal angles. This means that
∠ABE=∠EBC
Since ∠ABE=2x+20 and ∠EBC=4x-6, we have
2x+20=4x-6
2x-4x=-6-20
-2x=-26
2x=26
x=13°
Can someone check this for me? Thanks!
Answer:
two or zero positive real roots, one or zero negative real roots
Step-by-step explanation:
f(x) = 9x³ − 2x² − x + 5
There are 2 sign changes, so the number of positive real zeros is 2 or an even number less than that. So there are two or zero positive real roots.
f(-x) = 9(-x)³ − 2(-x)² − (-x) + 5
f(-x) = -9x³ − 2x² + x + 5
There is 1 sign change, so the number of negative real zeros is 1 or an even number less than that. So there is exactly 1 negative real root.
Your answer is correct.
2.
Find the coordinates of the midpoint of the segment whose endpoints are H(8, 13) and K(10, 9).
(9, 11)
(5, 6)
(1, 2)
(2, 4)
Answer:
(9,11)
Step-by-step explanation:
The given points are H(8,13) and K(10,9).
By using mid point formula,
(x, y) =(x1+x2, y1+y2)
2 2
= (8+10)2/, (13+9)/2
= 18/2, 22/2
= (9,11)
Which of the following gives all values of b that satisfy the inequality above?
A) b<-1
B) b>-1
C) b<1
D) b>1
Answer:
A
Step-by-step explanation:
[tex]\frac{1}{5} (7-3b) > 2[/tex]
[tex]=> 7-3b > 10\\=> 7-10 > 3b\\=> -3 > 3b\\=> -1 > b[/tex]
At a party, there are 2 six-packs of regular cola, 1 six-pack of diet cola, 1 six-pack of cherry cola, and 1 six-pack of vanilla cola. If a can of cola is chosen at random, what is the probability it will be a cherry cola or a vanilla cola?
A. 1/5 B. 2/5 C. 1/4 D. 1/2 Please select the best answer from the choices provided
A B C D
Answer:
B.
Step-by-step explanation:
There are 5 total 6-packs of cola. 1 is cherry and the other is vanilla. 2 out of 5 are the flavors. This means you have a 2 in 5 chance of getting a cherry or vanilla cola.
Final answer:
The probability of randomly choosing a cherry cola or vanilla cola from all the cans available is 2/5, since there are 12 such cans out of a total of 30 cans.
Explanation:
To find the probability that a can of cola chosen at random will be either cherry cola or vanilla cola, we first need to count the total number of cans and then count the number of cherry and vanilla cola cans.
There are 2 six-packs of regular cola, which amounts to 12 cans. There is 1 six-pack each of diet cola, cherry cola, and vanilla cola, which adds up to 6 + 6 + 6 = 18 cans. In total, there are 12 + 18 = 30 cans of cola.
Out of these, there are 6 cans of cherry cola and 6 cans of vanilla cola, totalling 12 cans. Thus, the probability of choosing a cherry or vanilla cola is the number of cherry and vanilla cans divided by the total number of cans, which is 12/30.
When we simplify 12/30, we get 2/5. Therefore, the correct answer is B. 2/5.
Company X can install chairs in a theater in 10 hours company Y can install them in 15 hours. How long would the two companies working together need to install the chairs?
Answer: 6 hours
Step-by-step explanation:
Given : The time taken by Company X to install chairs : [tex]t_1=10\text{ hours}[/tex]
The time taken by Company Y to install chairs : [tex]t_2=15\text{ hours}[/tex]
Then , the time taken (T) by both of them to install the chairs if they work together is given by :-
[tex]\dfrac{1}{T}=\dfrac{1}{t_1}+\dfrac{1}{t_2}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{10}{60}\\\\\Rightarrow\ T=6[/tex]
Hence, it will take 6 hours to the two companies if they working together .
Susan invested part of her $15,000 bonus in a find that paid and 11% profit and invested the rest in stock that suffered a 5% loss. Find the amount of each investment if her overall net profit was $850.
Answer:
$10,000 in the 11% fund$5,000 in the stockStep-by-step explanation:
Let f and s represent the amounts invested in the fund and in stocks, respectively. The problem statement gives rise to two equations:
f + s = 15000 . . . . . . . Susan invested a total of 15000
0.11f + (-0.05)s = 850 . . . . . her total return was 850
These can be solved by any of a variety of methods. Using elimination, we can multiply the second equation by 20 and add it to the first:
20(0.11f -0.05s) +(f + s) = 20(850) +15000
3.2f = 32000 . . . . . . . . . simplify
f = 10000
s = 15000 -f = 5000
Susan invested $10,000 in the fund and $5,000 in stock.
The graph below shows a proportional relationship between x and y.
Answer:
4
Step-by-step explanation:
The problem statement tells you the constant of proportionality is y/x. The graph shows y=4 for x=1. Then y/x = 4/1 = 4.
The constant of proportionality is 4.
_____
Caveat
Before you copy this answer, be certain the graph in your problem statement is identical to this graph. If your marked point has different coordinates than (1, 4), your constant of proportionality may be different. It will still be computed as y/x, but you need to use the x and y values of the marked point on your graph (or those of any other point whose coordinates you can read).
What does d = in this equation? d — =21 7
Use the conversion table to convert the following English units into the given metric units. Calculate all problems by hand. Round your answers to two decimal places. 10 in. to millimeters 60 ft. to meters 4.5 in. to millimeters 12 U.S. quarts to liters 25 feet per second to meters per second 100 miles to kilometers
1. 10 in. to millimeters: 254.00 mm
2. 60 ft. to meters: 18.29 m
3. 4.5 in. to millimeters: 114.30 mm
4. 12 U.S. quarts to liters: 11.36 L
5. 25 feet per second to meters per second: 7.62 m/s
6. 100 miles to kilometers: 160.93 km
Explanation:To convert inches to millimeters, we use the conversion factor 1 inch = 25.4 millimeters. Therefore, for 10 inches, the calculation is: [tex]\(10 \, in. \times 25.4 \, \frac{mm}{in.} = 254.00 \, mm.\)[/tex]
For the conversion from feet to meters, the conversion factor is 1 foot = 0.3048 meters. Thus, for 60 feet, the calculation is: [tex]\(60 \, ft. \times 0.3048 \, \frac{m}{ft.} = 18.29 \, m.\)[/tex]
Converting inches to millimeters again, using the same conversion factor, we get [tex]\(4.5 \, in. \times 25.4 \, \frac{mm}{in.} = 114.30 \, mm.\)[/tex]
Moving on to quarts to liters, 1 U.S. quart is approximately 0.94635 liters. For 12 quarts, the conversion is [tex]\(12 \, qts \times 0.94635 \, \frac{L}{qt} = 11.36 \, L.\)[/tex]
For the speed conversion from feet per second to meters per second, we use the conversion factor 1 ft/s = 0.3048 m/s. Thus,[tex]\(25 \, ft/s \times 0.3048 \, \frac{m}{ft} = 7.62 \, m/s.\)[/tex]
Finally, for miles to kilometers, the conversion factor is 1 mile = 1.60934 kilometers. Hence, [tex]\(100 \, miles \times 1.60934 \, \frac{km}{mile} = 160.93 \, km.\)[/tex]
Answer:1. 10 in. to millimeters: 254.00 mm2. 60 ft. to meters: 18.29 m3. 4.5 in. to millimeters: 114.30 mm4. 12 U.S. quarts to liters: 11.36 L5. 25 feet per second to meters per second: 7.62 m/s6. 100 miles to kilometers: 160.93 km
Step-by-step explanation:
What is the maximum number of times a line can cross the x-axis?
I needed help with the answer
Answer:
1 time
Step-by-step explanation:
A line is on straight thing that keeps going straight for ever so there for it can only cross the x axis once
PLS HELP BRAINLIEST WILL BE AWARDED IF ANSWER IS CORRECT
Answer:
AC = 18.1 cm
Step-by-step explanation:
Construct a line from point B perpendicular to the line AD and mark it as E on line AD. Now you have a right triangle ABE with AB = 16 cm and AE = AD - BC
so AE = 11 cm - 4 cm = 7 cm
You can find BE by using Pythagorean theorem
BE^2 = AB^2 - AE^2
BE^2 = 16^2 - 7^2
BE^2 = 256 - 49
BE^2 = 207
BE = 14.4 cm
Draw a line from A to C, you have a right triangle ACD with AD = 11cm and CD = BE = 14.4 cm
Using Pythagorean theorem
AC^2 = AD^2 + CD^2
AC^2 = 11^2 + 207
AC^2 = 121 + 207
AC^2 = 328
AC = 18.1 cm
PLS HELP SHOW ALL YOUR WORKING OUT AND THE CORRECT ANSWER WILL RECIEVE BRAINLIEST
If f(x) = -5x + 1 and g(x) = x3, what is (gºf)(0)?
Enter the correct answer
Answer:
1
Step-by-step explanation:
To evaluate (g ￮ f)(0), substitute x = 0 into f(x) then substitute the value obtained into g(x), that is
f(0) = 5(0) + 1 = 0 + 1 = 1, then
g(1) = 1³ = 1
If the lengths of an object are measured in feet, then the area of the object will be measured in which of the following units of measurement?
feet
square feet
cubic feet
feet to the fourth power
Answer:
square feet
Step-by-step explanation:
Units multiply the same way any variable does:
(x ft)(y ft) = x·y ft·ft = x·y ft² . . . . . . the units of the product are square feet
Answer:
Square feet
Step-by-step explanation:
The area of the object will be measured in square feet.
Hope this helps!
What is the probability that you will select someone from the survey that does not watch ABC?
13/45
16/45
4/9
9/20
Answer:
4/9
Step-by-step explanation:
Will someone please explain step by step how to do this question? Thank you!
Answer:
(1000, 179°)
Step-by-step explanation:
In rectangular coordinates, where east is the +x direction and north is the +y direction, the woman's final position is (1000 yards west, 20 yards north) or (-1000, 20).
This is translated to polar coordinates (r, θ) using ...
r = √(x² +y²)
θ = arctan(y/x) . . . . with attention to quadrant
The magnitude of the distance (r) is ...
r = √((-1000)² +20²) = √1000400 ≈ 1000.2 ≈ 1000
θ = arctan(20/-1000) in quadrant 2, so is 180° -1.15° = 178.85° ≈ 179°
In polar coordinates, the final position is (1000, 179°).
Ryan is trying a low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:
110 < 2x + 10 and 2x + 10 < 310
Solve for x in this inequality, and explain what the answer represents.
x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.
x < 50 and x > 150; Ryan needs to consume less than 50 grams of carbohydrates or more than 150 grams of carbohydrates.
x > 60 and x < 160; Ryan needs to consume more than 60 grams of carbohydrates, but less than 160 grams of carbohydrates.
x < 60 and x > 160; Ryan needs to consume less than 60 grams of carbohydrates or more than 160 grams of carbohydrates.
Answer:
Option A (x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates).
Step-by-step explanation:
There are two inequalities. One is 110 < 2x + 10 and 2x + 10 < 310. x is the amount of carbs consumed in grams, the first inequality is the lower limit, and the second inequality is the upper limit. The question requires to solve the two inequalities.
1)
110 < 2x + 10.
100 < 2x.
50 < x (or x > 50).
2)
2x + 10 < 310.
2x < 300.
x < 150.
Now combining the two inequality gives:
50 < x < 150.
So Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates. Therefore, Option A is the correct answer!!!
Answer:
a
Step-by-step explanation:
On a map the scale in four inches to one mile. The distance on the map from Huntington to Northport is ten inches. How many miles apart are they?
Answer:
yall still in schoo
Step-by-step explanation:
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0 0 cannot be determined 1 2
[tex]\Delta=5^2-4\cdot1\cdot7=25-28=-3[/tex]
[tex]\Delta<0[/tex] so 0 solutions.
Answer:
No Real roots to this Quadratic Equation
Step-by-step explanation:
Our Quadratic equation is given as
[tex]x^2+5x+7=0[/tex]
In order to find that do we have the real roots of a quadratic equation , the Discriminant must be greater or equal to 0. The Discriminant is denoted by D and given by the formula
[tex]D= b^2-4ac[/tex]
Where b is the coefficient of the middle term containing x, a is the coefficient of the term containing [tex]x^{2}[/tex] and the c is the constant term.
Hence we have
a = 1 , b = 5 and c = 7
Calculate D
[tex]D=b^2-4ac\\D=5^2-4*1*7\\D=25-28\\D=-3[/tex]
Hence we see that the Discriminant (D) is less than 0, our answer is no real roots to this quadratic equation.
What are the number for x in 8x-6x=-18
Answer:
8x-6x=-18
8x-6x=2x
2x=-18
-18/2=-9
x=-9
Step-by-step explanation:
Help with this question, please!! I am on a time limit!
Answer:
C)
Explanation:
Movement along a vector is compared by adding, subtracting, multiplying, or dividing the values respectively.
Identify the measure of arc PR.
Arc PR measures 90 degrees because it is a minor arc that intercepts central angle PQR, which measures 90 degrees.
The measure of arc PR is 90 degrees. This can be determined from the given diagram, which shows a circle with arc PR labeled. We also know that central angle PQR measures 90 degrees.
Minor arcs are arcs that intercept central angles less than 180 degrees. Major arcs are arcs that intercept central angles greater than or equal to 180 degrees.
Since arc PR intercepts central angle PQR, which measures 90 degrees, arc PR must be a minor arc. Minor arcs have the same measure as their central angles, so arc PR must also measure 90 degrees.
Here is an alternative way to think about it:
The entire circle can be divided into 360 degrees.
Arc PR is a portion of the circle, so it must have some measure.
Central angle PQR also divides the circle into two portions.
Since arc PR intercepts central angle PQR, it must have the same measure as central angle PQR, which is 90 degrees.
Therefore, the measure of arc PR is 90 degrees.
For more such information on: Arc
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What equation can be written from this sequence -50,-33,-16,1
Answer: [tex]a_n=-50+(n-1)17[/tex]
Step-by-step explanation:
The Arithmetic Sequence Formula is:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
[tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the sequence.
[tex]a_1[/tex] is the first term of the sequence.
[tex]n[/tex] is the term position.
[tex]d[/tex] is the common difference of any pair of consecutive numbers.
We can observe that the first term is:
[tex]a_1=-50[/tex]
Now, we need to find "d". This is:
[tex]d=-16-(-33)\\d=-16+33\\d=17[/tex]
Then, substituting, we get the following equation:
[tex]a_n=-50+(n-1)17[/tex]
Reymonte went hiking last weekend. He started at an elevation of 49 feet below sea level, which can be thought of as an
elevation of -49 feet. At the end of the hike, his elevation was 281 feet higher than where he started. What was his
elevation relative to sea level, in feet, at the end of the hike?
Answer:
232 ft above sea level
Step-by-step explanation:
He started at -49 ft and then he was later 281 ft higher than that... so just do -49+281 or 281-49= 232
Reymonte started his hike 49 feet below sea level, or at an elevation of -49 feet. He then hiked up 281 feet. By adding these two numbers together, we find that Reymonte ended his hike at an elevation of 232 feet above sea level.
Explanation:The subject of this question is Mathematics, and it's specifically related to the topic of integers. In the context of this question, elevation is used to indicate height relative to sea level, with negative indicating below sea level and positive above. Reymonte started at an elevation of -49 feet, or 49 feet below sea level. He then hiked up 281 feet.
To find his final elevation relative to sea level, we add the increase in elevation to his initial elevation. So, we add 281 feet to -49 feet:
-49 feet + 281 feet = 232 feet
So at the end of the hike, Reymonte was at an elevation of 232 feet above sea level.
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Using pie! 3.14 calculate the areas of the circles with diameter of 21 and leave your answer in 2 demical place
If we use 3.14 as pi, the areas of these circles are 415.265 square units (I recommend rounding up to 415.27 unless it says otherwise).
Step-by-step explanation:
To find the area of a circle, square the radius and multiply it by pi. To find the radius, we divide the diameter by 2 to get 11.5. Then, square 11.5 to get 132.25 and multiply by pi, or 3.14, to get 415.265, rounding up to 415.27 square units.