By applying fundamental and derivate trigonometric expressions it is to be concluded that the secant of the line segment whose terminal side is (3, - 2) is approximately 1.202.
How to apply trigonometric expressions
Trigonometric expressions are trascendent expressions derived from relationships between sides of the triangle contained in a goniometrical diagram.
There are at least six trigonometric expressions: sine, cosine, tangent, cotangent, secant, cosecant. The first two expressions are fundamental, whereas the rest are derived from them.
We can derive an expression for the secant of the angle by applying trigonometric expressions:
[tex]\sec \theta = \frac{1}{\cos \theta} = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex] (1)
If we know that x = 3 and y = - 2, then the secant of the angle is:
[tex]\sec \theta = \frac{\sqrt{3^{2}+(-2)^{2}}}{3}[/tex]
sec θ ≈ 1.202
By applying fundamental and derivate trigonometric expressions it is to be concluded that the secant of the line segment whose terminal side is (3, - 2) is approximately 1.202.
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11 by 12 minus 7 by 15
27
using bodmas rule:
[tex]\sf b - bracket, o - order, d - division, m - multiplication, a - addtion, s - subtraction[/tex]
=================
Solve:
11 x 12 - 7 x 15 (carry out multiplication first)
132 - 105 (subtract)
27 (final answer)
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{11}{12}-\dfrac{7}{15}[/tex]
Take LCM (60}[tex]\\ \rm\Rrightarrow \dfrac{11(5)-7(4)}{60}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{55-28}{60}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{27}{60}[/tex]
simplify 1/2 / 5/8 + 1/4
Answer: 1 1/20
Step-by-step explanation:
1/2 / 5/8 + 1/4
=8/10 +1/4
=21/20
=1 1/20
The graph shows the distance, y in miles, of a moving train from a station for a certain period of time, x, in hours: A graph titled Distance Vs Time is shown with Time in hours labeled on x-axis and Distance from Station in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 50, 100, 150, 200, 250, 300, 350, 400. The graph shows a straight line joining the ordered pairs 0, 100, and 1, 150, and 2, 200, and 3, 250, and 4, 300. What is the speed (in miles per hour) of the train?
Answer:
50
Step-by-step explanation:
I just did it with my friend.
WHY IS NOBODY HELP ME I GOT 2 OTHER QUESTIONS POSTED AND NOBODY ANSWERED ME
Answer:
B. F(0) = 4
Step-by-step explanation:
Im unsure about the C tho.
Can yall pls help me its due im 1 hour
Answer:
option 1 is correct
Mathematics question :)
How would I graph this?
Answer:g(x) = f(x) + 1.5
Step-by-step explanation: The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?
The vertex of the graph of g is 1.5 units to the left of
the vertex of the graph of f.
B
The y-intercept of the graph of g is 1.5 units above the
y-intercept of the graph of f.
The graph of g is a reflection of the graph of f across
the y-axis.
The graph of g is a reflection of the graph of f across
the x-axis.
can someone help me please?? :))
====================================================
How I got that answer:
The interval 0 < t < 30 has the midpoint of 15 since (0+30)/2 = 15
The interval 30 < t < 60 has the midpoint 45 because (30+60)/2 = 45
We add up the endpoints and then divide by 2 to get the midpoint.
Repeat this for each of the intervals mentioned.
From top to bottom, the midpoints are:
154575105Notice we add 30 to each midpoint to get the next one. This is directly due to the fact that each interval is 30 units wide (eg: 90-60 = 30).
Multiply each midpoint by the corresponding frequency for a given row.
15*7 = 10545*27 = 121575*12 = 900105*4 = 420Then add up those products.
105+1215+900+420 = 2640
Lastly, we divide this over the sum of the frequencies 7+27+12+4 = 50 to get 2640/50 = 52.8
The average time spent on homework is estimated to be about 52.8 minutes
Note that the majority of the the students (27) are in the 30 < t < 60 interval, so the mean of 52.8 fits this interval perfectly. It's closer to the right endpoint of the interval due to the fact the other 12+4 = 16 students are above this, and they make up the second most majority compared to the 27.
The reason why 52.8 is an estimate rather than the actual mean is because we are estimating each interval by picking out the midpoint each time. The midpoint is at the direct center, so it's the best guess we can do.
What is 0.75 written as a fraction?
A-1/75
B-10/75
C-75/100
D-7/5
E-75-10
Answer:
[C] 75/100
Step-by-step explanation:
0.75 as a fraction is 75/100.
Steps:
0.75 over 1
0.75/1
Multiply both the numerator and denominator by 100
75/100
Hence, the answer is [C] 75/100
[RevyBreeze]
Answer:
[C] 75/100
Step-by-step explanation:
Given:
What is 0.75 written as a fraction?
Solution:
0.75 = Decimal
Rewriting the decimal number as a fraction with 1 in the denominator
[tex]0.75=\frac{0.75}1[/tex]
Now, multiply to remove the 2 decimal places. So, you multiply top and bottom by 10² = 100
10² is the same thing as 100 because 10² = 10 × 10 and 10 × 10 = 100
[tex]\frac{0.75}{1}\times\frac{100}{100}=\frac{75}{100}[/tex]
Thus, the answer is [C] 75/100
Kavinsky
Help! Urgent! its due in 2 hours
Answer:
diameter-- last picture on right side
radius-second last picture on right side
πd=2πr
2r=d/2
Step-by-step explanation:
diameter is a line segment that goes through the center of a circle
this will match to the last image on the right side
radius is half of the diameter or from a point on the outer edge of the circle to the center
this will match to the second one on the right side
πd-- d=2*radius
2πr
2r=d/2
because radius is half of the diameter
The length of one of the sides of a regular hexagon is 7.8cm, find the perimeter of this polygon
Answer:
46.8 cm
Step-by-step explanation:
A hexagon has six sides. If it is a regular hexagon, then it is equilateral, meaning that each side is the same length. If one side is 7.8cm, then all sides will be 7.8cm. You can find the perimeter by adding 7.8 six times, or multiplying 7.8 by six.
7.8 · 6 = 46.8
hope this helps!
Applications of Differential Equations : Mass-spring system
The motion of a certain mass in a spring is described by:
[tex]\sf x''+2x'+2x=5sin(t)[/tex]
a) What is the amplitude of the resulting constant periodic oscillations?
b) Suppose the mass is initially at rest, that is, x(0)=0 and x′(0)=0, find the position function x(t).
Answer:
Step-by-step explanation:
The motion of a certain mass in a spring is described by:
I am currently learning about converting to log. However, My teacher did not explain converting to log with multiple variables.
Ex: 12^3 = (x^4)*(y^3)*(z^6)
Can anyone explain how to make that a logarithmic equation?
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\\\ \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]12^3~~ = ~~x^4 y^3 z^6\implies \log_{12}(x^4 y^3 z^6)=3 \\\\\\ \log_{12}(x^4)~~ + ~~\log_{12}(y^3)~~ + ~~\log_{12}(z^6)~~ = ~~3 \\\\\\ 4\log_{12}(x)~~ + ~~3\log_{12}(y)~~ + ~~6\log_{12}(z)~~ = ~~3[/tex]
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 28 ft/s. The ball's height h (in feet) after 1 seconds is given by the following:
h = 3 +28t-16t^2
Find all values of 1 for which the ball's height is 11 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
1 seconds
DO
х
?
initial
height
ground
The value of t at a height of 11 feet is 0.36 sec when the ball is going upwards and 1.39 seconds when the ball is coming downwards.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
Given that the height of the ball at time t is given by the function,
[tex]h(t) = 3+ 28t -16t^2[/tex]
where t is in seconds and h is in feet.
Now, the height of the ball is given to be 11 feet, therefore, substituting the value of h in the function as 11,
[tex]h(t) = 3+ 28t -16t^2\\\\11 = 3+ 28t -16t^2\\\\-16t^2 + 28t +3 -11 = 0\\\\-16t^2 + 28t -8 = 0[/tex]
Now, solving the given quadratic equation, we will get,
[tex]x= \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t = \dfrac{-(28)\pm \sqrt{(28)^2-4(-16)(-8)}}{2(-16)}\\\\t= 0.36\ or\ 1.39[/tex]
Hence, the value of t at a height of 11 feet is 0.36 sec when the ball is going upwards and 1.39 seconds when the ball is coming downwards.
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Matthew collected data about the ages of the actors in two different community theater groups. He drew a box plot for one of the sets of data and made a table of the other set of data.Ages of Actors is the Southside Players
For the Northside players, the median is 36, the range is 32 and the IQR is 18. For the southside Players : the median is 26, the range is 12 and the IQR is 12.
What is median?The median is regarded as the middle number among a series of sorted numbers that are placed in ascending or descending order.
Note that from the image attached, the northside ages are 22, 25, 28, 29, 29, 36, 36, 41, 49, 49, 54.
The median northside ages therefore is 36
For Range = Highest number - Lowest number
54-22 = 32
IQR = Q₃ - Q₁
Note that first quartile Q1 is said to be the median of the n lowest values and third quartile Q3 is the median of the n highest values.
Lowest value is 22 + 25/2 = 28.5.
Highest value is 49 + 44/ 2= 46.5.
Therefore, IQR = Q₃ - Q₁
46.5 - 28.5 =
IQR = 36
Note, for Southside Players;
If the Ages of Actors is the Southside Players are 20 22 24 26 28 30 32 34.
Then the median is = 26
Range is = 34-22 = 12
IQR = Q₃ - Q₁
Lowest = 20 + 22/ 2 = 21
Highest is 32 + 34 / 2 = 33
33 - 21
IQR = 12
Therefore, for the Northside players, the median is 36, the range is 32 and the IQR is 18. For the southside Players : the median is 26, the range is 12 and the IQR is 12.
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The diameter of a circle is 11 cm. Find its circumference in terms of .
Answer:
C= 34.56 cm
Step-by-step explanation:
Using the formulas
C=2πr
d=2r
Solving for C
C= πd = π·11 ≈ 34.55752cm
What is the solution to the equation -3(h + 5) + 2 = 4(h + 6) - 9
Answer:
The solution would be h=-4
Step-by-step explanation:
By distributing, we are able to find this answer.
01. Se tienen los angulos consecutivos AOB, BOC y COD. se cumple m& AOC=125° m
La diferencia entre los ángulos AOB y COD del sistema de tres ángulos consecutivos es igual a 25°.
La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°.
Cómo analizar tres ángulos consecutivos
Por la geometría Euclídea conocemos que un conjunto de ángulos cuando comparten entre cada par de ángulos vecinos comparten el mismo vértice y la misma semirrecta.
De acuerdo con el enunciado, tenemos las siguientes condiciones:
∠AOB + ∠BOC = 125° (1)
∠BOC + ∠COD = 100° (2)
Por (1) y (2) tenemos las siguiente identidad:
∠AOB - 25° = ∠COD
∠AOB - ∠COD = 25°
La diferencia entre los ángulos AOB y COD del sistema de tres ángulos consecutivos es igual a 25°. [tex]\blacksquare[/tex]
En el segundo caso, tenemos el siguiente sistema:
∠AOB = ∠BOC + ∠COD (3)
∠AOB + ∠BOC - ∠COD = 40° (4)
Por (3) y (4) tenemos la siguiente identidad:
2 · ∠BOC = 40°
∠BOC = 20°
La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°. [tex]\blacksquare[/tex]
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If a_1=4a 1 =4 and a_{n+1}=3a_n-3a n+1 =3a n −3 then find the value of a_3a 3
Answer:
Step-by-step explanation:
Apples were sold at 9 for $5. Carol bought a total of 27 apples. If Carol paid the cashier using two $10 bills, how much change did she recive?
Answer:
She received $5 back
Step-by-step explanation:
Answer:
170
Step-by-step
Add 5 27 times count by 5s and you will get the answer.
A game lasts 5/8 hours. Rachel played 4 of these games. For how long did she play in total? Write your answer in the simplest form.
Answer:
5/2 or 2 1/2 hours
Step-by-step explanation:
Multiply 5/8 by 4, which is 20/8, then you simply from there so 5/2=2 1/2
Describe a set of transformations that would map Red Triangle to the Blue Triangle.
PLEASE ANSWER FAST I NEED HELP
Part D
? Question
Suppose Coach Bennet selects one senior and one junior as the first two players. The coach then randomly selects
the third player from either group.
Taylor and Jamie are both juniors on the team. If Taylor is selected as one of the first two players, what is the
probability that Jamie will be selected as the third player?
Type in the correct answer in the box. Use numerals instead of words. If necessary, round your answer to the
nearest tenth.
The probability that Jamie will be selected as the third player, given that Taylor is selected as one of the
The question is an illustration of conditional probability, and the value of the conditional probability P(A|B) is 0.38
How to determine the value of the probability expression?The question is incomplete, as the required parameters are not given.
So, I will give a general explanation.
The question is an illustration of conditional probability
What is a conditional probability?The conditional probability is used to determine the probability of an event, given that another independent event has already occurred.
The conditional probability is calculated using:
P(A|B) = n(A and B)/n(B)
Assume the following parameters
n(A and B) = 9
n(B) = 24
The equation to calculate the probability expression is represented as:
P(A|B) = n(A and B)/n(B)
Substitute the assumed values
P(A|B) = 9/24
Evaluate the expression
P(A|B) = 0.38
Hence, the value of the conditional probability P(A|B) is 0.38
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How can you find a unit rate from a graph?
Answer:
To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate. So in this case, divide the numerator and denominator of 70/5 by 5, to get 14/1, or 14 students per class, which is the unit rate.
Also, what are unit rates? A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.
Step-by-step explanation:
1. You live in New York and travel by express subway to work 4 times a week for a cost of $15.00 each day. You can get an unlimited week pass for $34. How much can you save by buying the pass?
Answer:
$26
Step-by-step explanation:
4 times a week, $15 a day
It means that he have to pay $60 a week for travelling
$60-$34 = $26
By buying the pass I can save $26 a week
Answer:26 DOLLARS saved
Step-by-step explanation:
A square garden plot has an area of 24 ft2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot.
Answer:
4.9 ft
Step-by-step explanation:
Area of square = side squared
S² = A
Sub in 24 for A, then take square root of each side to find S.
S² = 24
S = sqrt (24)
= sqrt (4×6) - factorize
= 2(sqrt (6)) ft
≈ 4.9 ft
What is the area of a circle with a radius of 4 meters? Use ≈ 3.14.
Answer: A≈50.27m²
The area of a circle with a radius o 4 meters is A≈50.27m²
Step-by-step explanation:
What is an equation of the line perpendicular to 5x−4y=10 that passes through the point (−1,−6) ?
Answer:
y = -4/5x-34/5
Step-by-step explanation:
1. Put into slope-intercept form: 5x-4y = 10 ⇒ 4y = 5x-10 ⇒ y = 5/4x - 5/2
2. A perpendicular slope is the negative reciprocal of the original slope. ⇒ m = -4/5
3. Make a general solution using the new slope: y = -4/5x + b
4. Plug in the point (-1,-6) and solve for b: -6 = -4/5(-1) + b ⇒ -6-(4/5) = b ⇒
b = -34/5
5. Put b in the general solution to find the particular solution: y = -4/5x-34/5
Question 3 of 10
Which expression is the simplest form of 5(22–3)-3(x+4)?
9
O A. 7x - 3
-
O B. 134-27
9
O c.
72-3
9
Answer:
(D)
Step-by-step explanation:
[tex]\frac{5(2x-3) -3(x+4)}{9}[/tex] = [tex]\frac{10x-15-3x-12}{9}[/tex] = [tex]\frac{7x-27}{9}[/tex]
what is the product of the mixed number 5 x 1 1/6?
5 5/6
5 x 1 1/6 = 5 5/6
Answer:
The answer is 5 5/6. Hope this helps!