Graph 1 contains the two angles in the domain 0 ≤ θ ≤ 360º that have cosine given by cos(θ) = -3/5.
Where is the cosine of angle negative?The sine and the cosine of an angle are represented in the unit circle, in which:
The x-axis is composed by the cosine of the angle.The y-axis is composed by the sine of the angle.Hence the cosine of the angle is negative when the x-axis is negative, which happens in these following quadrants:
Second quadrant.Third quadrant.The only equation that can be solved in the context of this problem is:
cos(θ) = -3/5.
The solution is composed by two angles, one in the second quadrant and one in the third quadrant, hence Graph 1 shows the correct solution.
The exact angles are found applying the inverse cosine function as follows:
θ = arccos(-3/5) = 126.9º = 233.1º.
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Which sequence shows the numbers in order from least to greatest?
A. |-8.23| < 8 1/5 < 8.3
B. 8 1/5 > 8.3 > |-8.23|
C. 8 1/5 < |-8.23| < 8.3
D. 8.3 < |-8.23| < 8 1/5
The sequence that shows the numbers in order from least to greatest is A. |-8.23| < 8 1/5 < 8.3
How to illustrate the information?It's important to note that arranging numbers from the least to the greatest simply means ascending order.
In this case, it's vital to note that the negative value is the smallest. Then 8 1/5 is 8.2. This conea after. The greatest number is 8.3 since it's the biggest.
In conclusion, the correct option is A.
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Find the value of x for which the lines p and q are parallel.
Question 17 options:
A) 6
B) 8
C) 9
D) 7
Answer:
D
Step-by-step explanation:
(14x + 18) and 116 are corresponding angles and are congruent, then
14x + 18 = 116 ( subtract 18 from both sides )
14x = 98 ( divide both sides by 14 )
x = 7
How to solve Y=2x-1 2x+y=3 in solving systems using substitution
Answer:
x = 1, y = 1
Step-by-step explanation:
This Question involves the concept of Solving Simulteanous Equations.
Simulteanous EquationsSimulteanous Equations are 2 sets of equation with 2 unknownes to solve. Methods used are Substitution and Elimination methods, use either to solve unless question specify a method.
Example:
2x + 4y = 67
3x + 9y = 90
ApplicationWe are given the 2 equations:
y = 2x - 1 (Equation 1)
2x + y = 3 (Equation 2)
We are asked to use the Substitution Method.
We first substitute Equation 1 to Equation 2 to find the value of x.
2x + (2x - 1) = 3
2x + 2x - 1 = 3
4x - 1 = 3
4x = 3 + 1
4x = 4
x = 4 ÷ 4 = 1
Now we can substitute x into Equation 1 to find the value of y.
y = 2(1) - 1
y = 2 - 1 = 1
gary gets an average of 15 text messages during his 8 hour work day. in order to find the probability that gary will get exactly 3 text messages in a 2 hour portion of his work day using the poisson distribution, what is the time interval of interest?
The probability that Gary will get exactly 3 text messages in a 2-hour portion of his work day using the Poisson distribution, what is the time interval of interest: 2 hours
Gary will get calls according to Poisson distribution with an average # of calls per hour = 15.
Let x be the Poisson random Variable Such that X ~Poisson (15).
We need to find P(x≤3) in 2 hours.
Thus, the time interval of interest is 2 hours.
What is probability ?
Probability is the likelihood of an event occurring. It can range from an impossible event to a probability to an absolute certainty. In mathematics, probability is on a scale of 0-1. Zero means the event is impossible, like rolling seven dice with only the numbers 1-6. One is an event that will happen, that's for sure. An example of a specific event is tomorrow is Friday if today is Thursday. It will definitely happen. The median is 0.5 or half and these events are equally likely. A good example of half probability is tossing a coin. It gets straight heads or tails.
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PLEASE HELP ASAP! What is the rate of change (slope) and the initial value (y-axis) for this table?
Answer: m = 24
Step-by-step explanation:
The right side of the table is the x value, and the left side is the y value.
Pick two points, I will pick (1,35) and (3,83).
Once you pick the points, input them in the rise over run formula:
y2-y1/x2-x1
83-35/3-1 = 48/2 = 24
HELP ASAP PLSSSPLSPSLPSLPLSS
Given f(x) = 3x − 4 and g(x) = f(2x), which table represents g(x)?
The values of g(x) at x = 1, 2 and 3 are 2, 8 and 14 respectively.
Which table contains the values of g(x)?
Since f(x) = 3x - 4 and g(x) = f(2x)
so, in f(x) = 3x - 4, we can replace x with 2x:
g(x) = f(2x) = 3(2x) - 4 = 6x - 4
when x = 1:
g(x) = 6(1) - 4
= 6 - 4 = 2
when x = 2:
g(x) = 6(2) - 4
= 12 - 4 = 8
when x = 3:
g(x) = 6(3) - 4
= 18 - 4 = 14
Therefore, when x = 1, 2 and 3, their corresponding values of g(x) are 2, 8 and 14. So 4th table contains the values of g(x).
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Answer: D
Step-by-step explanation: I Chose D and got it right for my quiz.
In the diagram shown, lines MN and PQ intersect at R. If ZNRS is a right angle and the measure of ZMRQ is 1420, then what is the measure of ZPRS? Show or explain how you arrive at your answer.
The measure of the angle PRS is given as follows:
m<PRS = 45º.
Measure of angle PRSAs stated in this problem, these following angles are given:
<MRQ = 142º.m<NRS = 90º.MRQ and and QRN form a ray, hence they are supplementary angles.
For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:
142 + x = 180
x = 180 - 142
x = 38º.
The entire diagram forms an angle of 360º, hence:
142 + 38 + 90 + m<MRS = 360º.
270 + m<MRS = 360º
m<MRS = 90º.
The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:
The diagram is given by the image at the end of the answer.
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solve 2/3x + 4 = 5/6x by eliminating the fraction.
The value of x in the given equation is 24.
Given equation:
(2/3)x + 4 = (5/6)x
We have to find the value of x by eliminating the fraction.
Fraction
Fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator.
LCM (3,6) = 6
Multiplying the whole equation by 6, we get:-
(2/3)x*6 + 4*6 = (5/6)x*6
4x + 24 = 5x
5x - 4x = 24
x = 24
Hence, the value of x is 24.
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Complete the equation of the line through (4, -8) and (8,5).
I WILL FIND THE GRADIENT FIRST
[tex]m = \frac{y2 - y1}{x2 - x1} \\ = \frac{5 - ( - 8)}{8 - 4} \\ m = \frac{5 + 8}{4} \\ m = \frac{13}{4} [/tex]
THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c
I will use the point (8,5)
to find the value of c
[tex]5 = \frac{13}{4} (8) + c \\ 5 = \frac{104}{4} + c \\ c = 5 - \frac{104}{4} \\ c = - \frac{84}{4} \\ c = -21[/tex]
THE EQUATION IS
[tex]y = \frac{13}{4} x - 21[/tex]
Are the following Parallel, Perpendicular, or neither: y = 2x - 5 and -x + 2y = -5
two lines are parallel if their slope is equal
equation of line is
y=mx+c
where m=slope
for y=2x-5
m=2
for -x+2y=-5
2y=-5+x
y=-5/2+x/2
m=1/2
lines are nor parallel becuase m (slope) is not equal
now we will test for perpendicularity
perpendicular lines have slopes that are reciprocal of each other
first line , m=2
second line, m=1/2
2 and 1/2 are reciprocals
therefore, the lines are perpendicular
how many 1/5 inch pieces can be cut from a piece of ribbon 7/20 of an inch long.
1) Gathering the data
1/5 inch
7/20 inches long
2) Let's them divide, 7/20 by 1/5 inches
When divide fractions, we multiply the reciprocal of the second fraction
and if possible we can simplify
9th grade math HHhH HHhH
Answer:y=-x+3
Step-by-step explanation:
please help thank you
462 people get on an empty train at a station. At the first stop, 234 more people get on the train, and 95 people get off. There are no more stops until the train reaches it final destination, where everybody gets off the train. How many people get off the train at the final destination?
Answer:
wow your so goood
Step-by-step explanation:
Solve 4h = 92 for h.h = ___
Answer:
23
Step-by-step explanation:
4h = 92
Divide both sides by 4 to get h by itself
h = 23
X^2+8x-35=0 which number would be added to complete the square
Answer:
x =(8-√204)/2=4-√ 51 = -3.141
x =(8+√204)/2=4+√ 51 = 11.141
Step-by-step explanation:
Factoring x2-8x-35
The first term is, x2 its coefficient is 1 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is -35
Step-1 : Multiply the coefficient of the first term by the constant 1 • -35 = -35
Step-2 : Find two factors of -35 whose sum equals the coefficient of the middle term, which is -8 .
-35 + 1 = -34
-7 + 5 = -2
-5 + 7 = 2
-1 + 35 = 34
Traci planted a tree in her backyard.She made this graph to show the tree growth over 5 years. 100 POINTS IF YOU HELP!!!!
A. The slope of the function = 1.5.
a = 15; b = 3; c = 3; d = 1.5
B. y-intercept (b) = 7.5
C. The equation of the function is: y = 1.5x + 7.5.
The height in 10 years is approximately 17.5 feet.
How to Write the Equation of a Linear Function?The equation of a function can be expressed as y = mx + b, if we know the value of the slope, m, and the value of the y-intercept, b.
Part A:
Using the two points on the graph, we can find the slope of the function as shown below:
The two points are (3, 12) and (5, 15):
Slope of the function = (15 - 12)/(5 - 3)
= 3/2
Slope (m) = 1.5.
Thus, the values that represents each letters would be:
a = 15; b = 3; c = 3; d = 1.5
Part B: The y-intercept of the function
The y-intercept of the function can be defined as the initial tree height which is the point where the line intercepts the y-axis of the graph.
Substitute m = 1.5 and (x, y) = (3, 12) into y = mx + b to find the y-intercept (b) of the function:
12 = 1.5(3) + b
12 = 4.5 + b
12 - 4.5 = b
7.5 = b
b = 7.5
y-intercept (b) = 7.5
Part C: To write the equation of the function, substitute m = 1.5 and b = 7.5 into y = mx + b:
y = 1.5x + 7.5.
Therefore, the initiate tree height is 7.5 feet, and it increases at a rate of 1.5 feet per year.
To find the height in 10 years, substitute x = 10 into the equation of the function, y = 1.5x + 7.5:
y = 1.5(10) + 7.5
y = 10 + 7.5
y = 17.5 feet
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Last night, the two dinner specials at Rhianna's favorite restaurant were salmon filet and steak. The restaurant served 52 specials in all, 25% of which were salmon filets. How many salmon filets did the restaurant serve?
There were 13 salmon fillets that the restaurant served.
How do we calculate how many salmon fillets the restaurant served?The solution to this math problem involves fractions, especially percentage. A percentage is a fraction of a hundred. The literal meaning of percentage is "per 100". Percentage is often referred to as percent. The symbol or sign for percentage is %. The number beside the symbol/sign is the numerator, so for example, 10% can also be written as 10/100.
We're given that 25% of the dinner specials served by the restaurant were salmon fillets. In order to find out how many salmon fillets were served, we only need to multiply 52 by 25%.
52 × 25% =
52 × 25/100 =
(52 × 25)/100 =
1,300/100 = 13
There were indeed thirteen salmon fillets served by the restaurant.
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What is the midpoint of A B if A = (−2, 2) and B = (3, −1)? Enter your answer in the boxes below. Midpoint of A B = ( , )
The coordinate of the midpoint AB is (1/2, 1/2)
How to determine the midpoint?From the question, the coordinates of the points are given as
A = (-2, 2)
B = (3, -1)
The midpoint of a line or points is then calculated using the following midpoint formula
Midpoint = 1/2 * (x₂ + x₁, y₂ + y₁)
Where x and y are the coordinates of A and B
Substitute the known values in the above equation
So, we have the following equation
AB = 1/2 * (-2 + 3, 2 - 1)
Evaluate the sum
AB = 1/2 * (1, 1)
Evaluate the products
AB = (1/2, 1/2)
Hence, the midpoint is (1/2, 1/2)
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Sigma notation for 22, 28, 34, 40, 46
The sigma notation for the sequence 22, 28, 34, 40, 46 is as follows:
[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]
How to represent a notation in sigma notation?A sequence is represented in sigma notation according to the following rule:
[tex]\sum_{n = 0}^{n = N-1} a + bn[/tex]
In which the parameters are described as follows:
N is the number of terms in the sequence.a is the first term of the sequence.b is the common difference between the terms of the sequence.In the context of this problem, the sequence is:
22, 28, 34, 40, 46.
Hence the values of these parameters are given as follows:
N = 5, as there are 5 terms in the sequence.a = 22, which is the first term of the sequence.b = 6, as the difference between each term of the sequence is.Hence the sigma notation of the sequence is given by:
[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]
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Find the reminder when 2 to the 100th power is divided by 5 explain your work
The remainder when 2 to the 100th power is divided by 5 is 8.
What is the remainder when 2 to the 100th power is divided by 5?The remainder when 2 to the 100th power is divided by 5 is 8. We can achieve the accurate result by using the exponential formula where:
a^mn = a^m(n)
So, applying this here, we will have
2^10 (10)/5
Recall that multiplying 10 by 10 will give us 100. What was done in this case is simply splitting the figures up to make the division simpler. The exponential law was applied here.
Now, 2^10/5
204.8
The remainder as we can see from this result is 8. Thus we arrive at the answer 8.
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3a. Sketch the line that goes through the points A(4,3) and B( 8, 1)Find the slope and the equation of line AB3b. Find the length of segment AB3c. Find the midpoint of segment AB
Hello! First, let's remember:
We can write a point as a cartesian coordinate (x, y).
The exercise has given two points, A(4,3) and B(8,1).
a. Slope:To calculate the slope of a line, we can use the formula below:
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's consider A equal to the first point (4, 3) = (x1, y1), and B will be the second point (8, 1) = (x2, y2). Replacing these values in the formula:
[tex]\text{Slope}=\frac{1_{}-(3)_{}}{8-(4)}=\frac{-2}{4}=-\frac{1}{2}[/tex]b. Lenght of segment AB:To find this length, we have to use another formula. Now we will calculate the distance between two points:
[tex]\text{Distance}=\sqrt[]{(x_2-x_1)^2+(y_2_{}-y_1_{})^2}[/tex]Still considering A (4, 3) = (x1, y1), and B (8, 1) = (x2, y2), let's replace the values in the formula:
[tex]\begin{gathered} \text{Distance}=\sqrt[]{(8_{}-4_{})^2+(1-3_{})^2} \\ \text{Distance}=\sqrt[]{(4_{})^2+(-2_{})^2} \\ \text{Distance}=\sqrt[]{(16^{}+4)^{}} \\ \text{Distance}=\sqrt[]{20} \\ \text{Distance}=2\sqrt[]{5} \end{gathered}[/tex]c. Midpoint of segment AB:This value will be the medium point. To calculate it, we'll use another formula:
[tex]x_m=(\frac{x_1+x_2}{2}+\frac{y_1+y_2_{}_{}}{2})[/tex]Still considering the same values for (x1, y1) and (x2, y2), let's replace them:
[tex]\begin{gathered} x_m=(\frac{8+4_{}}{2},\frac{3+1_{}}{2}) \\ \\ x_m=(\frac{12_{}}{2},\frac{4_{}}{2}) \\ \\ x_m=(6,2) \end{gathered}[/tex]The midpoint of segment AB will be at point X (6, 2).
You can see this line represented in a cartesian plan below:
Question 2 of 10
Use the quadratic formula to find the solution to the quadratic equation given
below.
9
ײ − 3x + 9/4 =0
PLEASE HELP
Answer:
using the quadratic formula
Step-by-step explanation:
x= 3/2
Judy is 12 years old and is 8 years old mukta is 16 years old which of the following ratios best expresses the relationship between the ages 4 ratio 3 ratio to 2 ratio 3 ratio 4:3 ratio 2 ratio 4:3 ratio 4 ratio 2 ratio 4 ratio 3
Age of Judy = 12 yrs old
Age of x = 8 yrs old
Age of Mukta= 16 yrs old
Ratio between the 3 ages = 12 : 8 : 16
Since all the three numbers are divisible by 4
Therefore the ratio comes out to be 3 : 2 : 4 or 3 ratio 2 ratio 4
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Answer:
= 12 : 8 : 16
all the three numbers are divisible by 4
the ratio is 3 : 2 : 4
12. Find the value of x.
+f
(7x+4) +(10x-11)=180 mid segment
The value of x is 11.
What is an equation?
Equations are mathematical statements which contains two algebraic expressions on both sides of an equal to '=' sign. it represents the relationship of equality among the expressions.
We are given an equation (7x+4)+(10x-11)=180
We open brackets and simplify the equation by adding similar values we get
17x-7=180
17x=187
on dividing both sides by 17 we get
x=11
Hence the value of x is 11
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A box has a width of 12 cm and a length of 9 cm. the volume of the box is decreasing at a rate of 541 cubic cm per second, with the width and length being held constant. what is the rate of change of the height, in cm per second, when the height is 6 cm?
With the width and length being held constant, the height of the box decreases at rate 5 cm/s
Let:
l = length
w = wide
h = height
Then, the volume of the box is given by:
V = l . w. h
The length and the width are assumed to be constant. Hence, the derivative with respect to time is:
dV/dt = l . w dh/dt
Parameters given:
dV/dt = - 541 cm³/dt
l = 9 cm
w = 12 cm
Plug these parameters into the formula:
-541 = 12 . 9 . dh/dt
dh/dt = 5 cm/s
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The ratios in an equivalent ratio and 3:12 , 4:16 and 5:20 if frost number is 10 what is the second number ?
Rewrite the following equation as a function of x.
1+ 3y - 29 = 0
O A. f(x)
f(x) = 9,2808 2
OB. f(x) = -9,280 +
O c. f(x) = -9,280 + 20
O D. f(x) = 9,280
1
20x
15yards to 18 yard increase or decrease
Answer:
Increase
Step-by-step explanation:
You start at 15 yards then proceed to MOVE UP(Increase) 3 more yards getting you to 18.
Answer:
increase
Step-by-step explanation:
because your going 3 more yards on a number line you would travel right
Please help I answered all the questions that I could but this one I don’t understand! If someone couple please help that would be amazing!
Given the function:
Find the following values.
g(x)=-2-2.5x
a) g(4)
g(4) =
b) g(0)
g(0) =
c) g(-4)
g(-4)=
Wherever you see the letter [tex]x[/tex] in the equation, you write [tex]4[/tex], [tex]0[/tex] or [tex]-4[/tex] and perform arithmetic operations. Good luck!