Answer:
−3(1.5n−1)−3(1.5n−1)
Step-by-step explanation:
To factor the expression −4.5n+3−4.5n+3, find the GCF between each term. Using the GCF 3, divide each term by 3 and rewrite it as −3(1.5n−1)−3(1.5n−1).
The other options are not the factors because they give the wrong signs of at least one term in the expression.
−1.5(−3n+2)−1.5(−3n+2) = 4.5n -3 + 4.5n - 3
−1.5(3n+2)−1.5(3n+2) = -4.5n - 3 - 4.5n - 3
−3(1.5n+1) = -4.5n - 3
Solve the system by using a matrix equation
Answer:
Option A is correct (17,11).
Step-by-step explanation:
6x - 9y = 3
3x - 4y =7
it can be represented in matrix form as[tex]\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right][/tex]
A= [tex]\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] [/tex]
X= [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex]
B= [tex] \left[\begin{array}{c}3\\7\end{array}\right][/tex]
i.e, AX=B
or X= A⁻¹ B
A⁻¹ = 1/|A| * Adj A
determinant of A = |A|= (6*-4) - (-9*3)
= (-24)-(-27)
= (-24) + 27 = 3
so, |A| = 3
Adj A= [tex]\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right] [/tex]
A⁻¹ = [tex]\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right] [/tex]/3
A⁻¹ = [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] [/tex]
X= A⁻¹ B
X= [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}-4+21\\-3+14\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}17\\11\end{array}\right][/tex]
x= 17, y= 11
solution set= (17,11).
Answer:
a. (17,11)
Step-by-step explanation:
The given system is ;
[tex]6x-9y=3[/tex]
[tex]3x-4y=7[/tex]
The augmented matrices is
[tex]\left[\begin{array}{ccc}6&-9&|3\\3&-4&|7\end{array}\right][/tex]
Divide Row 1 by 6
[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\3&-4&|7\end{array}\right][/tex]
Subtract 3 times Row 1 from Row 2
[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&\frac{1}{2}&|\frac{11}{2}\end{array}\right][/tex]
Divide Row 2 by [tex]\frac{1}{2}[/tex]
[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&1}&|11\end{array}\right][/tex]
Add [tex]\frac{3}{2}[/tex] times Row 2 to Row 1
[tex]\left[\begin{array}{ccc}1&0&|17\\0&1}&|11\end{array}\right][/tex]
Hence the solution is (17,11)
There are 139 students and 10 adults on a field trip to the museum. The museum conducts tours in groups of 8. How many groups are needed for everyone to go on the tour.
Answer:
Step-by-step explanation:
139 +10 = 149
149 / 8 = 18.625
round to nearest hundredth = 18
the sum of two numbers is 61 and the difference is 19. what are the numbers?
Larger number:
Smaller number:
Answer:
the solution is (40, 21)
Step-by-step explanation:
Let the two numbers be x and y.
Then x + y = the sum = 61, and
x - y = the difference = 19.
Solve the system of linear equations
x + y = 61
x - y = 19
Combining these two equations:
x + y = 61
x - y = 19
---------------
2x = 80, so x must be 40.
Substituting 40 for x in the first equation, we get 40 + y = 61.
Combining the constants, we get y = 21.
Then the solution is (40, 21).
The numbers whose sum is 61 and difference 19 are 40 and 21. This is obtained by using algebraic expression for the given condition.
Find the algebraic expression for the question:Given that sum of numbers is 61 and difference is 19.
Let the larger number be x and smaller number be y.
Then we can write that, x+y=61 (sum) and x-y=19 (difference)
Calculate the numbers:By solving the algebraic equations we can find the numbers.
From second equation we can write, x = 19+y Substitute this in first equation,(19+y) + y = 61
19+2y = 61
2y = 61 - 19 = 42
y=42/2=21 ⇒ y=21 is the smaller number
x = 19+y = 19+21 =40 ⇒ x=40 is the larger number
Hence the numbers whose sum is 61 and difference 19 are 40 and 21.
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What is the surface area of the cone below?
For this case we have that by definition, the surface area of a cone is given by:
[tex]SA = \pi * r * S + \pi * r ^ 2[/tex]
Where:
SA: It is the surface area
A: It's the radio
S: It's slant height
Then, replacing the values of the figure in the formula we have:
[tex]SA = \pi * 6 * 15 + \pi * 6 ^ 2\\SA = 90 \pi + 36 \pi\\SA = 126 \pi \ units ^ 2[/tex]
ANswer:
Option A
What is the measure of ∠PQR ? Enter your answer in the box. ° A triangle with one angle measuring 80 degrees and one angle measuring 70 degrees.
Answer:
∠PQR=30°
Step-by-step explanation:
I assuming that the measure of angle PQR is the third internal angle of the triangle
Remember that
The sum of the internal angles of a triangle must be equal to 180 degrees
80°+70°+∠PQR=180°
150°+∠PQR=180°
∠PQR=180°-150°
∠PQR=30°
Answer:
The answer is 30 degrees
Step-by-step explanation:
(80+70) - 180 = 30
because all the angles should add up to 180 degrees so to double check your answer you do 30+70+80=180
You drink a beverage with 100 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%.
a. after 5 hours, how many caffeine left in your system.
b. How long until you have 50mg of caffeine?
Answer:
a. The amount of caffeine left is 52.77 mg
b. It will take about 5.42 hours
Step-by-step explanation:
* Lets solve it as an exponential decay
- Exponential decay: If a quantity decrease by a fixed percent at
regular intervals, the pattern can be depicted by this functions
y = a(1 - r)^x
# a = initial value (the amount before measuring growth or decay)
# r = growth or decay rate (most often represented as a percentage
and expressed as a decimal)
# x = number of time intervals that have passed
* Now lets solve the problem
∵ The initial amount of caffeine is 100 mg
∴ a = 100 mg
∵ The caffeine decreases by about 12% each hour
∴ r = 12/100 = 0.12
* Lets solve a.
a. ∵ x = 5 ⇒ the time interval
∵ The amount of caffeine left = a(1 - r)^x
∴ The amount of caffeine left = 100(1 - 0.12)^5
∴ The amount of caffeine left = 100(0.88)^5= 52.77 mg
* To find the time x use the linear logarithmic function
b. ∵ The amount of caffeine is 50 mg
∴ 50 = 100(1 - 0.12)^x ⇒ divide both sides by 100
∴ 50/100 = (0.88)^x
∴ 0.5 = (0.88)^x ⇒ take ln for each side
∴ ln(0.5) = ln(0.88)^x
∵ ln(a)^n = n ln(a)
∴ ln(0.5) = x ln(0.88) ⇒ divide both sides by ln(0.88)
∴ x = ln(0.5)/ln(0.88) = 5.4 years
* It will take about 5.42 hours
After 5 hours, approximately 54.47 mg of caffeine would remain in your system. It would take approximately 3.72 hours for the caffeine level to reach 50 mg.
Explanation:To find the remaining amount of caffeine after 5 hours, we need to calculate the decreasing amount of caffeine each hour. The decrease in caffeine can be calculated by multiplying the previous amount of caffeine by 0.88 (1 - 0.12). So, after 5 hours, the remaining caffeine can be found using the formula:
Initial amount of caffeine: 100 mgRemaining caffeine after 5 hours: 100 mg * (0.88)5 = 54.47 mgTo find the time it takes to have 50 mg of caffeine remaining, we can set up an equation and solve for time:
Initial amount of caffeine: 100 mgRemaining caffeine: 50 mgDecay rate: 0.88 (1 - 0.12)Equation: 100 mg * (0.88)t = 50 mgSolving for t, we get:t = log0.88(50/100) ≈ 3.72 hoursTherefore, after 5 hours, approximately 54.47 mg of caffeine would remain in your system. It would take approximately 3.72 hours for the caffeine level to reach 50 mg.
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Please please help me out please
Answer:
CD = 9.2 cm
Step-by-step explanation:
The arc of any circle is calculated as
arc = circumference × fraction of circle
= 2πr × [tex]\frac{66.4}{360}[/tex]
= 2π × 7.9 × [tex]\frac{66.4}{360}[/tex]
= [tex]\frac{2(7.9)(66.4)\pi }{360}[/tex] ≈ 9.2
arc CD is approximately 9.2 cm
Use the change of variables s=x+3y, t=y to find the area of the ellipse x2+6xy+10y2≤1.
The change in variables s=x+3y, t=y to find the area of the ellipse x²+6xy+10y²≤1 yields; s² +t²≤ 1.
Substitution of variablesIt follows from the equations given that;
s = x +3y, x = s -3yt = yHence, it follows from substitution that;
(s-3t)² +6(s-3t)t +10t² ≤ 1s² -6st +9t² +6st-18t² +10t² ≤ 1s²+t² ≤ 1Read more on substitution;
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By applying a change of variables to the ellipse equation x2+6xy+10y2≤1, this simplifies to the standard ellipse equation from which the area, π*sqrt(10), can be determined using the standard formula for the area of an ellipse.
Explanation:To find the area of the ellipse defined by the equation x2+6xy+10y2≤1, we can begin by using the provided change of variables, s = x + 3y and t = y. This transformation simplifies the equation of the ellipse to: (s^2) / 10 + (t^2) ≤ 1.
Now the expression looks like the standard equation of an ellipse, where 'a' (the radius on the x-axis) is sqrt(10) and 'b' (the radius on the y-axis) is 1. The area 'A' of an ellipse is given by 'A=πab'. Substituting 'a' and 'b' into the formula gives us 'A = π*sqrt(10)*1 = π*sqrt(10)'
This indicates that the area of the ellipse with the change of variables s=x+3y, t=y for the equation x2+6xy+10y2≤1 is π*sqrt(10).
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What is the leading coefficient of this polynomial?
[tex]f(x)=3x^2-0.2x^5+7x^3[/tex]
The leading coefficient is the number in front of the variable with the highest degree(exponent)
The highest degree (exponent) is 5, so the leading coefficient = -0.2
ANSWER
The leading coefficient of the given polynomial is -0.2
EXPLANATION
The given polynomial function is
[tex]f(x)=3x^2-0.2x^5+7x^3[/tex]
We rewrite in standard form to obtain,
[tex]f(x)=-0.2x^5+7x^3+3x^2[/tex]
Note that writing in standard form means writing in descending powers of x.
The coefficient of the leading term is -0.2.
American cars maker produce 5650000 cars each year in Europe that Americans make 6 million 550 cars the mistake did Ben make how can he fix it
Answer:
Ben has mixed up the digit for millions and hundred thousands: he wrote 5 in the place for millions and 6 in the place for hundred thousands, but it should be the other way. I think that he should exchange those two digits in the faulty report.
What are the domain and range of the exponential function below?
[tex]F(x) = 5^x+6[/tex]
Answer:
B
Step-by-step explanation:
The domain is the set of x values for which the function is defined.
The range is the set of y values for which the function is defined.
Attached is the graph of the exponential function.
It is the basic graph of exponential function of y = 5^x which is shifted 6 units above (because of +6 at the end).
Looking at the graph, the domain is the set of all x values.
The range is anything above 6.
Correct answer is B.
Answer: b
Step-by-step explanation:
A P E X
Craig stops at a gas station to fill his tank. He must choose between full-service and self-service and between regular, mid grade and premium gasoline. How many possible combinations are there?
Answer:
6
Step-by-step explanation:
There are 2 service choices and 3 grade choices for each, a total of 2×3 = 6 choices.
Two hikers are walking along the Appalachian Trail. The first hiker is 2 miles ahead of the second hiker. Both hikers are traveling in the same direction at the same speed, 1 mile per hour. Let x represent the distance traveled by the first hiker after a certain time period.
Several students wrote equations for this situation. Which student is correct?
A.
Alex said, “The equation y = 2x + 1 represents the total distance traveled by both hikers.”
B.
Brenda said, “The equation y = 3x represents the total distance traveled by both hikers.”
C.
Chris said, “The equation y = x – 2 represents the distance traveled by the second hiker.”
D.
Drake said, “The equation y = x + 2 represents the distance traveled by the second hiker.”
Answer:
Chris is correct. (Choice letter C)
Step-by-step explanation:
We can eliminate choices A and B from the get-go because the problem stated that both hikers are traveling at 1mi/hr. This means that the slope of the equation would equate to 1, so just x.
That leaves us with C and D. The two equations both have a slope of 1, but C has a y-intercept of -2 and D has a y-intercept of 2, which represents the starting location of the second hiker. The first hiker is the one who is ahead by 2 miles, so it can't be D. This leaves us with choice C. Chris is correct.
Answer:
C. Chris said, “The equation y = x – 2 represents the distance traveled by the second hiker.”
Step-by-step explanation:
find the angle between vector u=i+sqrt 7 j and vector v=-i-4j to the nearest degree.
a. 173 degrees
b. 145 degrees
c. 115 degrees
d. 97 degrees
hence angle between vectors is option a ,173 degree
What is Vector Equation?When an equation has both direction as well as magnitude it refers to vector equation.
How to calculate angle between two vectors?Formula used [tex]\alpha =cos^{-1} (\frac{u.v}{|u||v|})[/tex]
u.v=1*(-1)+[tex]\sqrt{7} *(-4)[/tex]
|u|=[tex]\sqrt{ 1^{2} +\sqrt{7} ^{2}}[/tex]=[tex]2\sqrt{2}[/tex]
|v|=[tex]\sqrt{ (-1^{2}) +(-4^{2})[/tex]=[tex]\sqrt{17}[/tex]
[tex]\alpha =cos^{-1} (\frac{-1-4\sqrt{7} }{|2\sqrt{2} ||\sqrt{17} |})[/tex]
[tex]\alpha =cos^{-1} (\frac{-1-10.58}{2.82*4.12})[/tex]
[tex]\alpha =cos^{-1} (\frac{-11.58}{11.61})[/tex]
[tex]\alpha =cos^{-1} (-0.99)[/tex]
hence option a 173 degree is correct
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Type the correct answer in the box. If necessary, use / for the fraction bar. A fair coin is tossed 5 times in a row. The exact probability of the coin landing heads exactly 2 times is .
Answer:
The probability is [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
Given is that a fair coin is tossed 5 times in a row.
This gives total number of outcomes as = [tex]2\times2\times2\times2\times2=32[/tex]
As its needed that heads comes exactly 2 times, so favorable outcomes are = 5C2
[tex]\frac{5!}{2!(5-2)!}[/tex]
Solving this we get 10
Therefore, the probability of getting heads exactly 2 times is =
[tex]\frac{10}{32}=\frac{5}{16}[/tex]
Answer:
5/16
Step-by-step explanation:
Use the equation below to identify the value fo each variable for the circle.
Standard form equation of a Circle
[tex](x-h)^2+(y-v)^2=r^2[/tex]
(h,v) = center
r = radius
h= ???
v = ???
r = ???
Then, write the standard form equation of the circle.
Answer:
The equation of the circle in standard form is: (x - 2)² + (y - 4)² = 9
Step-by-step explanation:
* Lets revise the standard form of the equation of the circle
- If the center of the circle is point (h , v) and the radius of the
circle is r, then the standard form of the equation of the circle
is (x - h)² + (y - v)² = r²
- (x , y) a general point on the circle
* Lets look to the picture
- The center of the circle is point (2 , 4)
- The highest point on the circle is (2 , 7) and the lowest point
on the circle is (2 , 1)
∴ The diameter of the circle = 7 - 1 = 6
∵ The radius = 1/2 the diameter
∴ The radius of the circle = 1/2 × 6 = 3
* Now we can write the equation of the circle
∵ h = 2 and v = 4
∵ r = 3
∴ (x - 2)² + (y - 4)² = 3²
∴ The equation of the circle in standard form is:
(x - 2)² + (y - 4)² = 9
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A spinner is divided into 4 sections. The spinner is spun 100 times.
The probability distribution shows the results.
What is P(2 ≤ x ≤ 4) ?
Enter your answer, as a decimal, in the box.
Answer: 0.80
Step-by-step explanation:
P (2 ≤ x ≤ 4) is: P(X = 2) + P(X = 3) + P(X = 4)
= 0.36 + 0.12 + 0.32
= 0.48 + 0.32
= 0.80
It can also be calculated as: 1 - P(X = 1)
= 1 - 0.20
= 0.80
A life scientist worksheet has the names of 36 animals of these 18 fed on seeds 15 feed on insects and 6 feed on both seed and insects a student randomly selects one animal for a study What is the probability that the chosen animal feeds on seeds or insects or both
Answer:
11/12
Step-by-step explanation:
18/36 + 15/36= 33/36 = 11/12
The probability that the chosen animal feeds on seeds or insects or both is:
[tex]\dfrac{3}{4}[/tex]
Step-by-step explanation:Let A denote the event that the animal feed on seeds.
B denote the event that the animal feed on insects
and A∩B denote the event that the animal feed on both seed and insects.
and A∪B denote the event that the animal feeds on seeds or insects or both.
Let P denote the probability of an event.
Now, based on the information from the question we have:
[tex]P(A)=\dfrac{18}{36}\\\\P(B)=\dfrac{15}{36}\\\\P(A\bigcap B)=\dfrac{6}{36}[/tex]
Now, we know that:
[tex]P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B)[/tex]
Hence, on putting the values we have:
[tex]P(A\bigcup B)=\dfrac{18}{36}+\dfrac{15}{36}-\dfrac{6}{36}\\\\\\P(A\bigcup B)=\dfrac{18+15-6}{36}\\\\\\P(A\bigcup B)=\dfrac{27}{36}=\dfrac{3}{4}[/tex]
90 POINTS WILL GIVE BRAINLIEST for which value of theta is cot theta equal to cos theta
The answer is 2pi but how so?
Answer:
...so cos t = cot t can only happen when cos t is 0 or sin t is 1. (But sin t = 1 only happens when cos t = 0, so cos t = 0 is enough.)
arccos(0) is pi/2, plus or minus any multiple of pi.
Step-by-step explanation:
cotθ = cosθ
cosθ/sinθ = cosθ
sinθ = 1
θ = π/2
pi also = to 3.14 etc.
Answer:
Step-by-step explanation:
[tex]cot \theta = cos \theta\\ \frac {cos \theta}{sin \theta} = cos \theta[/tex]
An easy solution is if [tex]cos \theta = 0[/tex], or [tex]\theta = \frac \pi 2[/tex], plus or minus any number of half circles.
Ten times the sum of four and three
the answer is
10 × (4+3) = 70
PLEASE ANSWER
A farmer is trying to determine the number of plantain plants in a farm that covers 24 acres. He marks off three acre plots at randomly selected locations in the farm. The first plot contains 291 plants, the second plot contains 327 plants, and the third plot contains 286 plants.
Part A: Using this data, determine which of the following quantities represent an estimate of the number of plantain plants in the entire farm.
A 151
B 301
C 3,616
D 7,232
Part B: Suppose that a plantain plant bears a single bunch on a single stem. An average bunch will have 8 hands of 15 plantains. The farmer determines that around 85% of the total acreage is ready to harvest and sell. If the value at farm level is around $140.00 per thousand of fruits units for plantain, determine the total value at farm level for this farmer after harvesting and selling all the plantains in his farm.
The total value is ____________.
Answer:
C
Step-by-step explanation:
Answer:
option c is the answer
hope it helps
and ur welcm
Let a[0 . . . n] be an array of n + 1 natural numbers not exceeding n. let k < n be an integer such that the values of any two successive entries of a differ at most by k, i.e., |a[j] − a[j + 1]| ≤ k for all j ∈ {0, . . . , n − 1}. 1. prove that there exist an index j such that |a[j] − j| ≤ (k + 1)/2. 2. given the number k, find an o(log n) divide and conquer algorithm that finds such an index.
Answer:
i really have no clue but if i put this i get points so good luck on your test
What is the difference between an observational study and an experiment? Choose the correct answer below. A. In an experiment, a treatment is applied to an entire population and responses are observed. In an observational study, a researcher measures characteristics of interest of an entire population but does not change existing conditions. B. In an experiment, a researcher measures characteristics of interest of a part of a population but does not change existing conditions. In an observational study, a treatment is applied to part of a population and responses are observed. C. In an experiment, a researcher measures characteristics of interest of an entire population but does not change existing conditions. In an observational study, a treatment is applied to an entire population and responses are observed. D. In an experiment, a treatment is applied to part of a population and responses are observed. In an observational study, a researcher measures characteristics of interest of a part of a population but does not change existing conditions.
Answer: “A”
Step-by-step explanation: Your Answer Would Be “A”
Answer:
A
Step-by-step explanation:
THAT IS THE BEST ANWSER OPTION
You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes longer than your brother reads. Write an equation for the number of minutes you read, y, when your brother reads x number of minutes. How many minutes will you read if your brother reads for 15minutes?
the equation would be y = 30 + x and if your brother will read for 15 minutes then you'll read for 45 minutes i believe.
The equation for the number of minutes you read, y, when your brother reads x number of minutes is y = x + 30. Therefore, if your brother reads for 15 minutes, you will read for 45 minutes.
To write an equation for the number of minutes you read, y, when your brother reads x number of minutes and you decide to read 30 minutes longer than him, you can represent this relationship as y = x + 30. This equation signifies that your reading time (y) is equal to your brother's reading time (x) plus an additional 30 minutes.
If your brother reads for 15 minutes (x=15), you can determine how many minutes you will read by substituting 15 into the equation for x, obtaining y = 15 + 30 = 45 minutes. Therefore, if your brother reads for 15 minutes, you will read for 45 minutes to stay ahead.
Please show all of your work! I will mark the brainliest nd gve thanks!
1.Find the standard equation of a circle with its center at (2, 8) and a radius of 10.
2. Find the standard equation of a parabola with its vertex at (2, 2) and a focus at (2, 5).
3. Find the standard equation of a parabola with its vertex at (5, 2) and a directrix x =3.
Answer:
Step-by-step explanation:
1. Equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
If (h, k) is (2, 8) and r = 10:
(x - 2)² + (y - 8)² = 100
2. The vertex and focus have the same x-coordinate, so this is a vertical parabola. Equation of a vertical parabola is:
y = 1/(4p) (x - h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
If (h, k) is (2, 2) and p = 5-2 = 3:
y = 1/12 (x - 2)² + 2
3. The directrix is a vertical line, so this is a horizontal parabola. Equation of a horizontal parabola is:
x = 1/(4p) (y - k)² + h
The distance between the directrix and the vertex is the same as p.
If (h, k) is (5, 2) and p = 5-3 = 2:
x = 1/8 (y - 2)² + 5
A bag contains 8 blue marbles, 6 green marbles, 12 yellow marbles and 10 orange marbles. A marble is drawn from at randm of the bag, what is the probibilty that the marble will not be blue?
8+6+12+10 = 36
6+12+10 = 28
28/36
7/9
Hope this helps ❤️
1) Which method is most efficient method to use to solve 2x^2+4x-3=0
2) Which method is most efficient method to use to solve x^2+5x-6=0
3) Which method is most efficient method to use to solve 2x^2+4x-7=0
A. Factoring
B. Isolating the x^2 term and finding the square root of both sides
C. Using the quadratic formula
D. All three methods would be
(The answer choices are the same for all the problems)
Answer:
1. C
2. A
3. C
Step-by-step explanation:
1. The equation is most easily solved through the quadratic formula since it’s a term is greater than 1.
2. The equation is most easily factored since it’s a term is 1.
3. The equation is most easily solved by the quadratic formula since it’s a term is greater than 1.
Find the exact value of the following expression (without using a calculator): tan(Sin^-1 x/2)
Answer:
tan(Sin^-1 x/2)= [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]
Step-by-step explanation:
Let sin^-1 x/2= θ
then sinθ= x/2
on the basis of unit circle, we have a triangle with hypotenuse of length 1, one side of length x/2 and opposite angle of θ.
tan(Sin^-1 x/2) = tanθ
tanθ= sinθ/cosθ
as per trigonometric identities cosθ= √(1-sin^2θ)
tanθ= sinθ/ √(1-sin^2θ)
substituting the value sinθ=x/2 in the above equation
tanθ= [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]
now substituting the value sin^-1 x/2= θ in above equation
tan(sin^-1 x/2) = [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]
!
Maurice bought 3 sodas and 4 candy bars for $10.17. Larry bought 2 sodas and 5 candy bars for $10.28. How much does a candy bar cost?
Answer:
The cost of a candy bar is [tex]\$1.5[/tex]
Step-by-step explanation:
Let
x----> the cost of a soda
y----> the cost of a candy bar
we know that
[tex]3x+4y=10.17[/tex]-----> equation A
[tex]2x+5y=10.28[/tex]-----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point [tex](1.39,1.5)[/tex]
see the attached figure
therefore
The cost of a soda is [tex]\$1.39[/tex]
The cost of a candy bar is [tex]\$1.5[/tex]
Jenna used the recipe shown below to make punch for a party orange juice 4 cups pineapple 4 cups red tropical 8 cups ginger ale 16 cups if jenna made half a recipe of punch how many quarts of fruit punch did she make
Answer:
4 quarts
Step-by-step explanation: