Answers
To find Q, we use the SSS (side-side-side) theorem.
The law of cosine formula:
a^2 = b^2 + c^2 - 2bcCosA
using the letters in the diagram and since we looking for Q, it becomes:
q^2 = p^2 + r^2 -2prCosQ
Making Cos Q, the subject of formula:
q² - p² - r² = -2prCosQ
(q² - p² - r²)/-2pr = -2prCosQ/-2pr
(q² - p² - r²)/-2pr = CosQ
Cos Q = -(q² - p² - r²)/2pr
q =
Related Questions
which equation , together with y=-1.5x+3 , makes a system with just on solution.y = -1.5x+6y = -1.5x2y = -3x+62y + 3x = 6y = -2x + 3
Answers
EXPLANATION
Given the equation y= -1.5x + 3
In order to get a system with just one solution, the viable options are those that allow both lines to intersect in just one point.
Those equations are:
y= -1.5x
y=-2x + 3
The system of equations y=-1.5x+3 and y=-1.5x+6 has no solution because subtracting both expressions give us the result 3=0
The system y=-1.5x+3 and 2y = -3x+6, or in the same way the system y=-1.5x+3 and 2y + 3x = 6 has no solution because they have the same expression.
i need help simplifying 1/3(3n+9)
Answers
Answer:
n+3
Explanation:
Given the expression:
[tex]\frac{1}{3}(3n+9)[/tex]To simplify, we first open the bracket.
[tex]=\frac{1}{3}(3n)+\frac{1}{3}(9)[/tex]We can then divide common factors:
[tex]\begin{gathered} =\frac{3n}{3}+\frac{9}{3} \\ =n+3 \end{gathered}[/tex]The simplified form is: n+3
what is the slope - intercept form of a line that passes through points(2,12) and (4,17) ?
Answers
A line pass through points (2, 11) and (4, 17);
The slope-intercept form of a line is given as;
[tex]\begin{gathered} y=mx+c \\ \text{Where m = slope} \\ c=\text{ y-intercept} \\ \\ \text{But slope m=}\frac{y_2-y_1}{x_2-x_1} \\ \text{Where x}_1=2 \\ x_2=4 \\ y_1=11 \\ y_2=17 \\ m=\frac{17-11}{4-2}=\frac{6}{2} \\ m=3 \end{gathered}[/tex]Also, for the y-intercept c;
[tex]\begin{gathered} \text{But when x=2, y=11} \\ \text{let's use this point to get the c} \\ 11=3(2)+c \\ c=11-6 \\ c=5 \\ \end{gathered}[/tex]Thus, the slope intercept equation of the line is;
y = 3x + 5
A 5000-seat theater has tickets for sale at $25 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $149,000? The number of tickets for sale at $25 should be ____ The number of tickets for sale at $40 should be ____
Answers
Let us call x the number of $25 seats and y $40 seats, then we know that there are in total 5000 seats in a theatre; therefore, we have the equation
[tex]x+y=5000[/tex]Also, after selling this many tickets the total revenue should be $149, 000; therefore, we get the equation
[tex]25x+40y=149,0000[/tex]Hence, we have a system of equations with two equations and two unknowns.
We solve this system by substitution.
First, we solve for x in the first equation to get
[tex]x=5000-y[/tex]we then put this into the second equation to get
[tex]25(5000-y)+40y=149,000[/tex][tex]\rightarrow125,000-25y+40y=149,000[/tex][tex]\rightarrow125,000+15y=149,000[/tex][tex]\rightarrow15y=24,000[/tex][tex]\therefore y=1600.[/tex]Now that we have y, we now solve for x to get:
[tex]x=5000-1600[/tex][tex]x=3400.[/tex]Hence x = 3400 and y = 1600 and the correct statements are as follows.
The number of tickets for sale at $25 should be 3400.
The number of tickets for sale at $40 should be 1600.
Find the coordinates of the midpoint between (8, 1) and (0, - 9). F. (4, -5) G. (4, -4) H. (8, -5) J. (8, -8)
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(4, -4)
ExplanationIn order to find the midpoint between two points we have to obtain the midpoint horizontally and vertically.
In this case, we have:
help me with this question please
Answers
So,
From the graph, we can clearly state that:
In 2 mins, there were 0 calls.
In 3 mins, there was 1 call.
In 4 mins, there were 4 calls.
In 5 mins, there were 6 calls.
In 6 mins, there were 4 calls.
Then, the number of calls that were answered to in 6 mins or less were 0+1+4+6+4 = 15
Part B: select the box or boxes under the coordinate pairs the represent solutions for the system.
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The given system of inequalities is
[tex]\begin{gathered} y>\frac{3}{2}x-2 \\ y\leq-3x-4 \end{gathered}[/tex]The area of the solution is the area shaded by the 2 colors
Let us check the points
(-2, -5) it lies on the red dashed line
Since the line is dashed, then the points lie on it do not belong to the solution, then
(-2, -5) does not belong to the solution
(-2, -5) is not a solution
(-2, 2) it lies on the blue line
Since the line is solid, then the points that lie on it belong to the solution, then
(-2, 2) is a solution
(0, -4) it is out of the area of both colors, then
(0, -4) is not a solution
(-3, -1) it lies in the area of the common colors, then
(-3, -1) is a solution
(-1, 4) it is out the area of both colors, then
(-1, 4) is not a solution
(-20, 15) is in the area of the common colors, then
(-20, 15) is a solution
(15, 20) it is out the area of both colors, then
(15, 20) is not a solution
Then the solutions of the system are:
(-2, 2), (-3, -1), (-20, 15)
What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21
The answer I need begins with y =
Please do not answer if your solution doesn't end that way, thank you.
Answers
The linear equation that is perpendicular to the line x+3y=21 is:
y = 3*x - 6
How to find the equation of the line?A general line in the slope-intercept form is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two linear equations are perpendicular if the product between the two slopes is equal to -1.
Rewriting the given line we can get:
x +3y = 21
3y = 21 - x
y = 21/3 - x/3
y = (-1/3)*x + 21/3
Then the slope is (-1/3), if our line is perpendicular to this one, then:
m*(-1/3) = -1
m = 3
our line is:
y = 3*x + b
To find the value of b, we use the fact that our line passes through (1, - 3)
-3 = 3*1 + b
-3 - 3 = b
-6 = b
The line is y = 3*x - 6
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Find the side of a square whose diagonal is of the given measure.Given = ft.
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see the figure below to better understand the problem
In the given square ABCD
Apply the Pythagorean Theoren in the right triangle BDC
[tex]\begin{gathered} D^2=a^2+a^2 \\ D^2=2a^2 \\ we\text{ have} \\ D=12\sqrt{10}\text{ ft} \end{gathered}[/tex]Substitute given value
[tex]\begin{gathered} (12\sqrt{10})^2=2a^2 \\ 144(10)=2a^2 \\ 2a^2=1,440 \\ a^2=720 \\ a=\sqrt{720}\text{ ft} \end{gathered}[/tex]Simplify
[tex]a=12\sqrt{5}\text{ ft}[/tex]The sum of two consecutive integers is 17. Which equations could be used to find the twoconsecutive integers? Select all that are correct.A.X+X+1=17B.X+x=17C.2x=17D.2x+2=17E.X+X+2=17F.2x+1=17
Answers
hello
the answer to the question is option A
to solve a problem like this, let x represent the first number
x + (x + 1) = 17
x = first number
x + 1 = successive number
which point is located at (0,8)
Answers
The point (0, 8) simply means the x axis is 0 while the y axis is 8. The answer is C.
Find 5x3 + 2y2 - 9, where x = 4 and y = 2
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The equation can be solved when we substitute the value of x and y accordingly .
[tex]\begin{gathered} 5(4)^3+2(2)^2\text{ - 9} \\ 5\text{ }\times\text{ 64 + 2 }\times\text{ 4 - 9} \\ 320\text{ + 8 - 9} \\ =319 \end{gathered}[/tex]There are 1300 people over the age over the age of 12 in the small town. If the same rate of cell phone usage continues , how many yrs will it takes for 1300 people have a cell phone.
Answers
We have to find how many years it will take for the 1300 people to have a cellphone.
This means we have to find x for f(x) = 1300, that is "the number of people using cellphones at time x is 1300".
Then, we can write:
[tex]\begin{gathered} f(x)=1300 \\ 880(1.03)^x=1300 \\ 1.03^x=\frac{1300}{880} \\ 1.03^x\approx1.477 \\ x\cdot\ln (1.03)=\ln (1.477) \\ x=\frac{\ln (1.477)}{\ln (1.03)} \\ x\approx\frac{0.39}{0.03} \\ x\approx13.2 \end{gathered}[/tex]Answer: it will take 13.2 years for the 1300 people to have a cellphone.
Zacaria's kayaks store annual rent and fixed cost are $ 15,600. The variable cost each kayak old is $315 and the price of each kayak is $425.e. What is the number of kayaks that must be sold to obtain $ 50,000 in the profits?
Answers
The profit function can be gotten using the formula below:
[tex]P(x)=R(x)-C(x)[/tex]where R(x) is the revenue function and C(x) is the cost function.
As previously calculated, the revenue and cost functions are given to be:
[tex]\begin{gathered} R(x)=425x \\ C(x)=315x+15600 \end{gathered}[/tex]Therefore, the profit function is:
[tex]\begin{gathered} P(x)=425x-(315x+15600) \\ P(x)=425x-315x-15600 \\ P(x)=110x-15600 \end{gathered}[/tex]The profit to be made is $50,000. Equating the profit function to this amount, we can get the number of kayaks required. This is shown below:
[tex]\begin{gathered} 50000=110x-15600 \\ 110x=50000+15600 \\ 110x=65600 \\ x=\frac{65600}{110} \\ x=596.4 \end{gathered}[/tex]Therefore, the number of kayaks that must be sold is approximately 597 kayaks to make $50,000 in profits.
Harold cut 18 1/2 inches off a rope that was 60 inches long. How is the length of the remaining rope written in decimals?
Answers
Substract 18 1/2 from 60 to determine the length of remaining rope.
[tex]\begin{gathered} 60-18\frac{1}{2}=60-\frac{37}{2} \\ =\frac{120-37}{2} \\ =\frac{83}{2} \\ =41.5 \end{gathered}[/tex]So length of remaining rope is 41.5 inches.
Perform (3x3 – 2x2 + 3x – 4) ÷ (x – 3) to find the value of the remainder.Question 3 options:A) 98B) 88C) 68D) 78
Answers
The remainder of the division can be found below
The answer is definitely C.
Solve the inequality AND graph the solution set. 7(4y - 8) < -5(y-2)
Answers
A solution to the given inequality is y < 2, which is represented by the graph shown in the image attached below.
What is a graph?In Mathematics, a graph simply refers a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate or a number line.
Next, we would solve the given inequality by simplifying it as follows:
7(4y - 8) < -5(y - 2)
Opening the bracket, we have the following:
28y - 56 < -5y + 10
Rearranging the inequality by collecting like terms, we have the following:
28y + 5y < 10 + 56
33y < 66
Dividing both sides of the inequality by 33, we have the following:
y < 66/33
y < 2
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=O GRAPHINGFinding the next terms of an arithmetic sequence with integersThe first three terms of an arithmetic sequence are as follows.-5, -8, -11Find the next two terms of this sequence.5.-8.-11.008 OBx 6
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Solution:
Given the first three terms of an arithmetic sequence as;
[tex]-5,-8,-11[/tex]An arithmetic sequence is a sequence with a common difference d, The common difference is the difference between two consecutive terms. Where;
[tex]\begin{gathered} d=a_2-a_1 \\ \text{Where;} \\ a_2=\text{ second term;} \\ a_1=\text{first term} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} d=-8-(-5) \\ d=-8+5 \\ d=-3 \end{gathered}[/tex]Also, the next term of the sequence can be known by adding the common difference to the previous term.
Hence, the next two terms are;
[tex]\begin{gathered} =-11+(-3) \\ =-11-3 \\ =-14 \\ \text{and } \\ =-14+(-3) \\ =-14-3 \\ =-17 \end{gathered}[/tex]FINAL ANSWER:
[tex]-14,-17[/tex]Runner A averages 5 miles per hour, and Runner B averages 6 miles per hour. At these rates, how much longer does it take Runner A than Runner B to run 15
miles?
1 hour
Shour
2.5 hours
1.5 hours
3 hours
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If Runner A averages 5 miles per hour, and Runner B averages 6 miles per hour. At these rates, then it took 3 hours for runner A.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Runner A averages 5 miles per hour, and
Runner B averages 6 miles per hour.
The time required for A to complete 15 miles is
15/5=Time
3 hrs
Hence Runner A needs 3 hours to run 15 miles.
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neeed double chedking on this
Answers
The area will be the area of the blue part minus the area of the white part:
9(8)-5(3)=72-15= 57 square centimeters
6. 5.6% of 283 is what number?7. 55% sign of 104 is what number?
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To solve the exercise you can use a rule of three:
[tex]\begin{gathered} 283\rightarrow100\text{\%} \\ x\rightarrow5.6\text{\%} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{5.6\text{\%}\cdot283}{100\text{\%}} \\ x=\frac{5.6\cdot283}{100} \\ x=\frac{1584.8}{100} \\ x=15.848 \end{gathered}[/tex]Therefore, 5.6% of 283 is 15.848.
what is 19,593 in expanded form?
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The extended form of the given number is:
[tex]10000+9000+500+90+3[/tex]Each table represents a proportional relationship. For each, find theconstant of proportionality, k, and write an equation that represents therelationship. Write k as a simplified proper or improper fraction and use thegiven variables.
Answers
**For the first table:
*We determine the value of k, as follows:
[tex]30=k(18)\Rightarrow k=\frac{5}{3}[/tex]The equation that represents the table is:
[tex]f=\frac{5}{3}d[/tex]**For the second table:
*We determine the value of k, as follows:
[tex]18=k(30)\Rightarrow k=\frac{3}{5}[/tex]The equation that represents the table is:
[tex]d=\frac{3}{5}f[/tex]Sketch the graphs of each of the following functions showing all steps on the same set of axe
Answers
Part D
we have the function
[tex]\begin{gathered} y=\frac{4}{-(x+1)}+3=\frac{4-3(x+1)}{-(x+1)}=\frac{4-3x-3}{-(x+1)}=\frac{1-3x}{-(x+1)}=\frac{3x-1}{x+1} \\ \\ y=\frac{3x-1}{x+1} \end{gathered}[/tex]In this rational function
Remember that
The denominator cannot be equal to zero
so
The value of x cannot be equal to x=-1
At x=-1 there is a vertical asymptote
Find out a horizontal asymptote
Degree on Top is Equal to the Bottom
so
the horizontal asymptote is at y=3/1=3
Find out the intercepts
y-intercept (value of y when the value of x=0)
For x=0
[tex]y=\frac{3(0)-1}{0+1}=-1[/tex]The y-intercept is (0,-1)
Find out the x-intercept (value of x when the value of y=0)
For y=0
[tex]\begin{gathered} 0=\frac{3x-1}{x+1} \\ \\ 3x-1=0 \\ 3x=1 \\ x=\frac{1}{3} \end{gathered}[/tex]The x-intercept is (0.33,0)
With the given information
Graph the function
using a graphing tool
see the figure below
An airplane pilot over the Pacific sights an atoll at the angle of depressionof 5º. At this time, the horizontal distance from the airplane to the atoll is4,535 meters. What is the height of the plane to the nearest meter?
Answers
Answer:
397 meters
Explanation:
Let us draw a diagram to understand the situation better.
Where H is the height of the plane.
Now the tan ratio for 5° gives
[tex]\tan 5^o=\frac{opposite}{\text{adjacent}}[/tex]Since opposite = H and adjacent = 4535 meters, the above gives
[tex]\tan (5^o)=\frac{H}{4535}[/tex]Multiplying both sides by 4535 gives
[tex]\tan (5^o)\times4535=H[/tex]Since tan(5°) =0.0875.., ( just used a calculator to find out) the above becomes
[tex]0.0875\times4535=H[/tex][tex]H=396.8125[/tex]rounding to the nearest meter gives
[tex]\boxed{H=397.}[/tex]Simplify: (3x-8)+(4x-17)
Answers
Answer:
7x-25
Explanation:
Given the expression:
[tex]\mleft(3x-8\mright)+\mleft(4x-17\mright)[/tex]First, we open the brackets
[tex]=3x-8+4x-17[/tex]Next, we rearrange bringing like terms together.
[tex]\begin{gathered} =3x+4x-8-17 \\ =7x-25 \end{gathered}[/tex][the ending was select all that apply ] can somebody help me with this with an explanation on how to do it?
Answers
Answer: the goal is to isolate the variable so the answer is 12
Step-by-step explanation:
8. An elephant weighs 74,416 ounces. How many tons does it weigh?
Answers
To know how many tons does the elephant weigh, we have to do a convertion:
1 ounce=3.125x10^-5 ton
[tex]74.416ounces\times\frac{3.125\times10^{-5}}{1\text{ ounce}}=2.3255\times10^{-3}[/tex]The elephant weighs 2.3255x10^-3 tons
A store is having a 20% off sale on all merchandise if my buys one item and see if $13 what was the original price of a purchase
Answers
Since all merchandise has 20% off, so the original price is multiplied by 0.8 (80%).
Let's use the variable x to represent the original price. So we can write the following equation and solve it for x:
[tex]\begin{gathered} 0.8\cdot x=13 \\ x=\frac{13}{0.8} \\ x=16.25 \end{gathered}[/tex]Therefore the original price is $16.25.
If anyone to solve this problem it will be greatly appreciated and I will be sure to give the best possible rating
Answers
Step 1
Graph the points from the table and make a plot that can help determine the possible line of best fit.
Hence, the equation of the line of best fit with values to the nearest hundredths will be;
[tex]y=0.06x+2.57[/tex]