In order to find the 7th of the sequence, first let's find the common ratio of the sequence.
To do so, let's divide one term by the term before:
[tex]q=\frac{4}{5}[/tex]Now, we can use the following formula to find the 7th term:
[tex]a_n=a_1\cdot q^{n-1}[/tex]For n = 7, we have:
[tex]\begin{gathered} a_7=5\cdot(\frac{4}{5})^6 \\ a_7=1.311 \end{gathered}[/tex]A hot air balloon descended 3240 feet in an hour. Find the change in altitude per minute?
Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.
Solving the QuestionWe're given:
[tex]\dfrac{3240\hspace{4}feet}{hour}[/tex]
We also know that:
[tex]\dfrac{hour}{60\hspace{4}minutes}[/tex]
Multiply the two to cancel out the hour:
[tex]\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}[/tex]
Simplify:
[tex]=\dfrac{54\hspace{4}feet}{minute}[/tex]
Answer[tex]\dfrac{54\hspace{4}feet}{minute}[/tex]
Solve the triangle. (Do not round until the final answer. Round angles to the nearest degree and side lengths to the nearest tenth of a unit.)C=___∠A=___∠B=___
Explanation
to solve this we need to use the cosine law
Law of cosines says
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ b^2=a^2+c^2-2ac\cdot\cos (B) \\ c^2=a^2+b^2-2ab\cdot\cos (C) \end{gathered}[/tex]then
Step 1
find c
Let
[tex]\begin{gathered} b=8 \\ a=5 \\ \angle C=67 \end{gathered}[/tex]now, let's find c
[tex]\begin{gathered} c^2=a^2+b^2-2bc\cdot\cos (C) \\ \text{replace} \\ c^2=5^2+8^2-2\cdot5\cdot8\cdot\cos (67) \\ c^2=25+64-31.25849028 \\ c^2=57.74 \\ \text{square root in both sides} \\ \sqrt{c^2}=\sqrt{57.74} \\ c=7.598 \\ \text{rounded} \\ c=7.6 \end{gathered}[/tex]Step 2
now,let's find the angle A
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ replace \\ 5^2=8^2+7.6^2-2\cdot8\cdot7.6\cdot\cos (A) \\ 25=64+57.76-121.6\text{ cos(A)} \\ 25=121.76-121.6(\cos A) \\ \text{subtract 121.76 in both sides} \\ 25-121.76=121.76-121.6(\cos A)-121.76 \\ -96.76=-121.6(\cos A) \\ \text{divide both sides by -121.6} \\ \frac{-96.76}{-121.6}=\frac{-121.6(\cos A)}{-121.6} \\ 0.795=\cos \text{ (A)} \\ Inverse\text{ cosine} \\ \cos ^{-1}(0.795)=\cos ^{-1}(\cos \text{ (A))} \\ 37.276=\text{ A} \\ \text{rounded} \\ A=37\~\text{ =A} \end{gathered}[/tex]Step 3
Finally,let's find angle B
we can use the formula as we did in step 2 to find angle A, but also we can use this fact:
the sum of the internal angles in a triangle equals 180 ,so
[tex]\angle A+\angle B+\angle C=180[/tex]replace and solve for angle C
[tex]\begin{gathered} \angle A+\angle B+\angle C=180 \\ 37+\angle B+67=180 \\ 104+\angle B=180 \\ \text{subtract 104 in both sides} \\ 104+\angle B-104=180-104 \\ \angle B=76 \end{gathered}[/tex]What is the value of 1/2 x^2 -10 when x = 6?
If we have the expression:
[tex]\frac{1}{2}x^2-10[/tex]we can find its value when x=6 by replacing x with the value 6 and calculating the result:
[tex]\frac{1}{2}(6)^2-10=\frac{1}{2}\cdot36-10=18-10=8[/tex]Answer: the expression has a value of 8 when x=6.
6)26 A 4 R2 (B) 2 R4 © 4 DE
On red step we multiply 6 by 4 to obtan 24, and subtract with 26, the solution is 2
O green step we add a comma to 4 do add a zero on the last solution (2), now the number is 20 and multiply 6 by 3 to obtan 18 and the solution is 2
As we can see the number two will be repeated forever since 20 divided by 6 is not exact, then the 3 will repeat infinitely
Tamera is using rice paper to make Japanese Lanterns. The expression 2s^2 + 40s represents the surface area of a lantern where the base edges are s inches long. What is the surface area of a lantern when is 9 in?
2s^2 = 2s to the power of two
The surface area of the Japanese Lanterns Tamera made when the sides are 9 inches long will be 522 sq inches.
What is surface area?The Surace area of any 2D or 3D figure is the outer area of the given figure.
Surface areas are of two types they are lateral surface area when we exclude the areas of top and bottom and total surface area is when we include all the sides.
Given that Tamera is using rice paper to make Japanese Lanterns.
The expression 2s² + 40s represents the surface area of a lantern where the base edges are 's' inches long.
Therefore to find The surface area of the Japanese Lanterns when the sides are 9 inches in length we have to substitute 9 into the variable s.
So, 2(9)² + 40(9).
= 2×81 + 360.
= 162 + 360.
= 522 sq inches.
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Each side of a square is lengthened by 5 inches. The area of this new, larger square is 49 square inches. Find the length of
a side of the original square.
Answer:
2 inches
Step-by-step explanation:
Since the area of the larger square is 49 inches, each side of this square is 7 inches, which is 5 inches longer than the original square. So each side of the original square is 2 inches.
how many solutions does 2(x+4)=4(x+2)
lets solve the equation!
[tex]\begin{gathered} 2(x+4)=4(x+2) \\ x+4=\frac{4}{2}(x+2) \\ x+4=2(x+2) \\ x+4=2x+4 \\ 4-4=2x-x \\ x=0 \\ \\ \text{Thus there is only ONE solution, and it is x=0} \end{gathered}[/tex]The drama club is selling tickets to their play to raise money for the show's expenses.Each student ticket sells for $5 and each adult ticket sells for $7.50. The auditoriumcan hold at most 125 people. The drama club must make no less than $790 fromticket sales to cover the show's costs. If 73 adult tickets were sold, determine allpossible values for the number of student tickets that the drama club must sell inorder to meet the show's expenses. Your answer should be a comma separated list ofvalues. If there are no possible solutions, submit an empty answer.
Let
x ------> number of student tickets that the drama club must sell
so
we have
[tex]x+73\leq125[/tex][tex]\begin{gathered} x\leq125-73 \\ x\leq52 \end{gathered}[/tex]and
[tex]5x+7.50\cdot73\ge790[/tex][tex]\begin{gathered} 5x\ge790-547.5 \\ 5x\ge242.5 \\ x\ge48.5 \end{gathered}[/tex]the values of x lie on the interval [48.5,52]
therefore
all possible values for the number of student tickets are on the interval
[49,52]
Integers greater than or equal to 49 and less than or equal to 52possibles values are 49,50,51,52Solve the equation below.
3(x−9)−6=16x−72
3x-27-6=16x-72
3x-33=16x-72
3x-16x= -72+33
-13x=39
x= -3
heyyyy i need help with jumber 2
We are asked to determine whether the given two polygons are similar or not.
Recall that the two polygons are said to be similar if the ratio of their corresponding sides is equal.
The corresponding sides of the two polygons are
side 3 = side 6
side 4 = side 8
side 5.5 = side 11
Let us check if they are in the same ratio
[tex]\begin{gathered} \frac{3}{6}=\frac{4}{8}=\frac{5.5}{11} \\ \frac{1}{2}=\frac{1}{2}=\frac{1}{2} \end{gathered}[/tex]As you can see, the ratio of the corresponding sides is equal.
Therefore, the given pair of polygons is similar.
I need the answer right now please someone help.Use the figure below to complete the following problem.Given:R, S, T are midpoints of AC, AB, and CB. AB||RTRCTC
From the diagram provided, line AB is parallel to line RT
AB | | RT
Edgar has a credit card payment that is increasing each month. The records for his bank payment are shown below. What kind of function can be used to best represent this data? A) Linear B) exponential C) quadratic
Notice that:
[tex]\begin{gathered} 250=250\cdot1.1^0 \\ 275=250\cdot1.1^1 \\ 302.5=250\cdot1.1^2 \\ 332.75=250\cdot1.1^3 \end{gathered}[/tex]Therefore the function that best models the behavior is:
[tex]f(x)=250\cdot1.1^x[/tex]Which is an exponential function.
Please help me solve the pictured problemFind the midline for f(x)=2cos(3x−5π6)−2.
Given the function:
[tex]f(x)=2cos(3x-\frac{5\pi}{6})-2[/tex]You need to remember that the General Equation of the Cosine Function is:
[tex]y=Acos(B(x+C))+D[/tex]Where:
- The Amplitude is:
[tex]|A|[/tex]- The Period is:
[tex]\frac{2\pi}{B}[/tex]- The horizontal shift is "C".
- The Vertical Shift is "D".
- The midlline is:
[tex]y=D[/tex]In this case, you can identify that:
[tex]D=-2[/tex]Therefore, the midline is:
A line passes through the point (-3, -9) and has a slope of -2.
Write an equation in slope-intercept form for this line.
When you add 12 to a number and then divide the sum by 13, you get the same result as when you subtract 13 from the number and then divide the difference by 12. What is the number?
help pleaseeeeee!!!!!!!!!!!!!!!!!!!
Answer:
1. No
2. Yes
3. No
4. No
Step-by-step explanation:
Solve the equation: 3x - 6 = 2(x - 2)no solution0all real numbers0.752
Problem
Solve the equation: 3x - 6 = 2(x - 2)
Solution
For this case we can do the following:
3x -6= 2x -4
And now we can subtract in both sides 2x and we got:
3x- 2x = 6-4
x = 2
And the final solution for this case would be x=2
Substitution method. show work.7.) y=x+2 10.) 2x+y=3 y=3x+4 3x-y=2elimination method. show work.11.) 5x+y=9 12.) -7x+y=-19 10x-7y=18 -2+3y=-19
Solution
7) y= x+2
replacing this in the second equation we got:
x +2 = 3x +4
-2 = 2x
x= -1
And solving for y we got:
y = -1 +2 = 1
10) 2x +y = 3
If we solve for y we got:
y = 3-2x
And replacing into the second equation we got:
3x - 3+2x = 2
5x = 5
x= 1
And solving for y we got:
y = 3 -2*1 = 3-2= 1
11) If we multiply the first equation by -2 and we add to the second one we got:
-10 x -2y = -18
10x -7y = 18
___________
-9y = 0
y=0
x= (9-0)/5 = 9/5
12) If we multiply the first equation by -3 we got:
21x -3y = 57
-2x +3y =-19
_______________
19x = 38
x= 2
y= (-19 + 4)/3= -5
Evaluate. 0⁵= equal
The most important concept to solve this questio
Answer:
0
Step-by-step explanation:
o^5 = 0 x 0 x 0 x 0 x 0 = 0
help or I die,... HELP
Regarding the points on the given line, it is found that:
a) The midpoint is: (3,4.5).
b) The coordinates of C are: C(4,5).
c) The coordinates of the other end of the line are: (4,3).
MidpointThe midpoint between two points is given by the mean of the coordinates of these points.
In this problem, the coordinates of points A and B are given as follows:
A(0,3) and B(6,6).
Hence the coordinates of the midpoint are given as follows:
x-coordinate: (0 + 6)/2 = 3.y-coordinate: (3 + 6)/2 = 4.5.As for point C, we have that C is closer to B then A, hence:
The x-coordinate is greater than 3.The y-coordinate is greater than 4.5.The coordinates are integers, hence it is given as follows:
C(4,5).
As for line AB, it is found that:
The other line is parallel, hence the slope is also of 0.5. (change in y divided by change in x is of 0.5).For the x-coordinate, on line AB, they change by 6, hence in the new line they increase by 2/3 x 6 = 4.For the y-coordinate, on line AB, they change by 3, hence in the new line they increase by 2/3 x 3 = 3.Thus the other endpoint is:
(4,3).
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helpp pleasee List the domain of the following function.(0,1),(9,0), (2,7),(4,3)
Problem
Solution
For this case we want to determine the domain from the following relation:
(0,1), (9,0), (2,7), (4,3)
And if we see the first cooridnate for all the points we have the domain and then the answer we have:
0,2,4,9
6. Work The dollar amount d that Julia earns varies directly as the number of hours !that she works, and d=$116.25 when 1 = 15 h. Find t when d = $178.25.
Answer:
t = 23
Explanation:
If the dollar amount d varies directly as the number of hours, t, the equation that relates these variables is
d = kt
Where k is a constant.
We know that for d = $116.25, t = 15 h, so we can replace these values and solve for k as follows
116.25 = k(15)
116.25/15 = k(15)/15
7.75 = k
Then, the equation that relates d and t is
d = 7.75t
Now, we know that d = $178.25 and we want to calculate t, so replacing d and solving for t, we get
178.25 = 7.75t
178.25/7.75 = 7.75t/7.75
23 = t
Therefore t = 23
7^2 -(3 + 2)^2 + 3^3 *
We want to calculate the following expression
[tex]7^2-(3+2)^2+3^3[/tex]We have an order that we must do the operations. First, we need to solve what is inside of the parenthesis, then, solve the exponentials, and with their results, do the additions and subtractions.
[tex]\begin{gathered} 7^2-(3+2)^2+3^3 \\ =7^2-(5)^2+3^3 \\ =7^2-5^2+3^3 \\ =49-25+9 \\ =33 \end{gathered}[/tex]And this is the solution for our problem.
Work out the value of (-8)2
Answer:
-16
Step-by-step explanation:
2x(-8)=16
Hey there!
Assuming you meant:
(-8)^2
= (-8)(-8)
= 64
Therefore, your answer should be:
64
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Show your work (no explanation just the answer and how you got it) DUE TODAY
The solutions to the absolute value equations are given as follows:
1. k = -8 or k = 8.
2. x = -7 or x = 7.
3. a = -10 or a = 6.
4. a = -2.5 or a = 2.5.
5. m = -4 or m = 22.
6. x = -4 or x = 6.8.
7. x = -16 or x = 9.
8. a = -2.4 or a = 1.2.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.This means that there are two possible solutions for the equation |x| = a, which are:
x = a or x = -a.
Item 1The equation is:
|k| = 8.
Applying the definition of the absolute value function, we have that the possible solutions are:
k = -8 or k = 8.
Item 2The equation is:
|x| = 7.
Applying the definition of the absolute value function, we have that the possible solutions are:
x = -7 or x = 7.
Item 3The equation is:
|a + 2| = 8.
The possible solutions are that the inside term can be equals to either -8 or 8, hence:
a + 2 = -8 -> a = -10.a + 2 = 8 -> a = 6.Item 4The equation is:
|8a|/10 = 2
In standard format, the equation is:
|8a| = 20
Then the solutions are:
8a = -20 -> a = -20/8 = -2.5.8a = 20 -> a = 20/8 = 2.5.Item 5The possible solutions are:
-m + 9 = -13 -> m = 22.-m + 9 = 13 -> m = -4.Item 6The possible solutions are:
7 - 5x = -27 -> 5x = 34 -> x = 6.8.7 - 5x = 27 -> 5x = -20 -> x = -4.Item 7Applying cross multiplication, the expression is:
|2x + 7| = 25
The possible solutions are:
2x + 7 = -25 -> 2x = -32 -> x = -16.2x + 7 = 25 -> 2x = 18 -> x = 9.Item 8Applying cross multiplication, the expression is:
|-3 -5a| = 9.
The possible solutions are:
-3 - 5a = -9 -> 5a = 6 -> a = 1.2.-3 - 5a = 9 -> 5a = -12 -> a = -2.4.More can be learned about absolute value equations at https://brainly.com/question/5012769
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using the elimination method, find x and y: please explain to me, I want an explanation because I don't get this a 100% yet 4x - 3y = 25-3x + 8y = 10
Given the system of equations :
[tex]\begin{gathered} 4x-3y=25 \\ -3x+8y=10 \end{gathered}[/tex]To eliminate y :
multiply the first equation by 8 and the second equation by 3
[tex]\begin{gathered} 8\cdot4x-8\cdot3y=8\cdot25 \\ 3\cdot-3x+3\cdot8y=3\cdot10 \\ ================ \\ 32x-24y=200 \\ -9x+24y=30 \end{gathered}[/tex]Add the equation , we will find the sum of y = 0
[tex]\begin{gathered} (32x-24y)+(-9x+24y)=200+30 \\ 32x-24y-9x+24y=230 \\ (32x-9x)+(-24y+24y)=230 \\ (23x)+(0)=230 \end{gathered}[/tex]So, solve the the result for x
[tex]\begin{gathered} 32x-9x=200+30 \\ 23x=230 \\ \\ x=\frac{230}{23}=10 \end{gathered}[/tex]Then substitute with x at the first equation to find y
[tex]\begin{gathered} 4\cdot10-3y=25 \\ 40-3y=25 \\ -3y=25-40 \\ -3y=-15 \\ \\ y=\frac{-15}{-3}=5 \end{gathered}[/tex]So, the answer of the system of equations :
[tex]\begin{gathered} x=10 \\ y=5 \\ (x,y)=(10,5) \end{gathered}[/tex]
the baseball stadium the price for popcorn is $16.20 for 6 bags. If youwanted to buy 5 bags of popcorn, how much would it cost?
It is given that the cost of 6 bags of popcorn is $16.20
So the cost of 1 bag is:
[tex]\frac{16.20}{6}=2.7\text{ dollars}[/tex]So the cost of 5 bags at $2.70 per bag is:
[tex]2.7\times5=13.5\text{ dollars}[/tex]So the cost of 5 bags of popcorn is $13.5.
4.) Rotate 90° counterclockwise about the origin.Original NewCoordinates: Coordinates:A: (___) A: ()YAON+COB:(_)B': ()2D2CC: (-)C':(___)D: (___)D:(__)
The Solution:
Rule:
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
The original coordinates of the given points are as follows:
[tex]\begin{gathered} A(-4,3)_{} \\ B(2,3) \\ C(2,-1) \\ D(-4,-1) \end{gathered}[/tex]So, the new coordinates of the given points are below:
[tex]A^{\prime}(-3,-4)[/tex][tex]B^{\prime}(-3,2)[/tex][tex]C^{\prime}(1,2)[/tex][tex]D^{\prime}(1,-4)[/tex]Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 28 and 36 miles per gallon is?
The probability that a random vehicle gets between 28 and 36 miles per gallon is 0.3333.
What's probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Given that,
a = 23
b = 47
P(c < x < d) = (d - c) / (b - a)
P(28 < x < 36) = (36 - 28) / (47 - 23) = 0.3333
Probability = 0.3333
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I keep getting the wrong answer for some reason, help please
In order to find the measure of angle A we have the next equation. Remember that the sum of the interior angles of a triangle is 180°
[tex](3x-6)+(8x+4)+(180-130)=180[/tex]Then we sum like terms
[tex]11x+48=180[/tex]Then we isolate the x
[tex]11x=180-48[/tex][tex]11x=132[/tex][tex]x=\frac{132}{11}[/tex][tex]x=12[/tex]For angle A
angle A= 3x-6=3(12)-6=30°
angle A=30°
