Answers
The nth term of a geometric sequence is expressed as:
[tex]a_n=ar^{n-1}[/tex]were:
• a is the first term
,• r is the common ratio
,• n is the number of terms
If the 2nd term a₂ = 28, then;
[tex]\begin{gathered} 28=ar^{2-1} \\ ar=28 \end{gathered}[/tex]If the 5th term a₅ = 1792, then;
[tex]\begin{gathered} 1792=ar^{5-1} \\ ar^4=1792 \end{gathered}[/tex]Take the ratio of both equations to have:
[tex]\begin{gathered} \frac{ar^4}{ar}=\frac{1792}{28} \\ r^3=64 \\ r=\sqrt[3]{64} \\ r=4 \end{gathered}[/tex]Substitute r = 4 into any of the equations to have:
[tex]\begin{gathered} ar=28 \\ 4a=28 \\ a=\frac{28}{4} \\ a=7 \end{gathered}[/tex]Determine the rule for the nth term of the geometric sequence. Recall that;
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7(4)^{n-1} \end{gathered}[/tex]This gives the nth term of the geometric sequence
Related Questions
determine the type and key parts of the graph of the second equation
Answers
ANSWER
[tex]\begin{gathered} \left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6 \\ major\text{ axis;vertical} \\ minoraxis;horizontal \end{gathered}[/tex]EXPLANATION
The second equation;
[tex]\frac{x^2}{9}+\frac{y^2}{36}=1[/tex]It is an Elipse.
Ellipse standard equation;
[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]Rewrite the given equation in the form of the standard equation;
Hence, we have;
[tex]\frac{\left(x-0\right)^2}{3^2}+\frac{\left(y-0\right)^2}{6^2}=1[/tex]Therefore the ellipse properties are;
[tex]\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6[/tex]Major axis is;
[tex]\begin{gathered} 2a \\ =2\times6=12 \end{gathered}[/tex]Minor axis is;
[tex]\begin{gathered} 2b \\ =2\times3=6 \end{gathered}[/tex]Find the better buy:14 oz of doritos for $2.50 or 22 oz of doritos for $3.99.Make sure you round everything up to the nearest cent
Answers
Answer:
Both
Explanation:
To determine the better buy, find the unit price for each of the purchase:
[tex]\begin{gathered} \text{14 oz of doritos }\cos ts\text{ \$}2.5 \\ \text{Unit Price=}\frac{\text{2.5}}{14} \\ =\$0.179\text{ per oz} \\ \approx\$0.18\text{ per oz} \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \text{22 oz of doritos }\cos ts\text{ \$}3.99 \\ \text{Unit Price=}\frac{\text{3}.99}{22} \\ =\$0.181\text{ per oz} \\ \approx\$0.18\text{ per oz} \end{gathered}[/tex]Therefore, to the nearest cent, both are equal buys since they have the same value.
When Ruby works out, she spends 2 minutes stretching for every 15 minutes of exercise. If Ruby spends 15 minutes stretching, how long did she spend exercising?
Answers
The ratio of time spend for stretching to time spend for exercise remain same.
Equate the ratio of time spend for stretching to time spend for exercise in both cases.
[tex]\begin{gathered} \frac{2}{15}=\frac{15}{x} \\ x=\frac{15\cdot15}{2} \\ =112.5 \end{gathered}[/tex]So Ruby spend 112 and a half minute to spend 15 minutes in stretching.
So answer is 112.5 min or
[tex]112\frac{1}{2}[/tex]19.) A.) use the idea of walking and turning around a shape to determine the sum of the exterior angles of the quadrilateral and figured 10.93. In other words, determine e + f + g + h. Measure with a protractor m to check that your formula is correct for this quadrilateral. B.) Will there be a similar formula for the sum of the exterior angles of Pentagon ‘s, hexagons, heptagon ‘s, octagons, and so on? Explain.C.) using your for your formula for the sum of the exterior angles of a quadrilateral, reduce the sum of the interior angles of the quadrilateral.in other words, find a+b+c+d, as pictured in figure 10.93. Explain your reasoning. Measure with a protractor to verify that your formula is correct for this quadrilateral.D.) based on your work, what formula would you expect to be true for the sum of the interior angles of a pentagon? what about for a hexagon? What about for a polygon with 10 sides? Explain briefly
Answers
A) To find the external angles of the quadrilateral we will walk around the shape measuring every turn we take. We will start on the A point, rotate clock-wise and move in the direction of point "B", when we get there we will rotate clock-wise again and walk to the direction of point "C". When we do get to the point C we will notice that we rotated 180 degrees in relation to the initial position we had in point A. Moving forwars we will now rotate clockwise and go to the poind D, rotate clock-wise again when we get there, performing all the rotations needed. We will notice that we have the same orientation from the beginning, this means that we rotated 360 degrees. In other words the sum of the external angles of the quadrilateral is 360 degrees.
B) Yes, any regular polygon will have the sum of its external angles equal to 360 degrees.
C) The internal and external angles are suplementary. This means that the sum of these angles must be equal to 180 degrees, therefore:
[tex]\begin{gathered} external\text{ = 180-internal} \\ e+f+g+h=360 \\ (180-a)+(180-b)+(180-c)+(180-d)=360 \\ a+b+c+d=180+180+180+180-360 \\ a+b+c+d=4\cdot180-2\cdot180 \\ a+b+c+d=(4-2)\cdot180 \\ a+b+c+d=2\cdot180=360 \end{gathered}[/tex]Since each external angle is the same as "180 degrees" minus the internal angle that is close to it we can represent the sum of the external angles as 360 degrees and use the mentioned relation to convert them into internal angles. If we isolate them as a sum we will find the value of the sum of the internal angles.
D) If we look at the fith line from the solution above we will notice that the sum of internal angles is represented by "(4-2)*180", the polygon had "4" sides. This means that for one that is 5 sides we should expect that it would be "(5-2)*180" and so on. So the formula is:
[tex]\text{internal = (n-2)}\cdot180[/tex]Where "n" is the number of sides of the polygon.
need to show 1,242 ÷ 23 = and 732 x 268 = show answers on graph
Answers
1,242 ÷ 23 = 54
and
732 x 268 = 196, 176
Graph each line given the slope and y-intercept.Label each one
Answers
A)
Equation:
[tex]y=\frac{1}{3}x-3[/tex]B)
Equation:
[tex]y=0.5x+1.5[/tex]C)
Equation:
[tex]y=-2x-5[/tex]D)
Equation:
[tex]y=\frac{3}{2}x+2[/tex]Which quadrant includes every points with a negative x-coordinate and a negative y-coordinateA) Quadrant IVB) Quadrant IC) Quadrant IID) Quadrant III
Answers
Hello!
Let's analyze the points from each quadrant:
Quadrant I:
x > 0 and y > 0
Quadrant II:
x < 0 and y > 0
Quadrant III:
x < 0 and y < 0
Quadrant IV:
x > 0 and y < 0
So, the answer is:
Alternative D) Quadrant III.
Write an equation for a line perpendicular to y=-5x-3 and passing through the point (15,4)
Answers
1) We need to consider the fact that perpendicular lines described by linear functions have opposite and reciprocal slopes when compared to the original linear function.
2) So we can state that the perpendicular line to y=-5x-3 has a slope of :
[tex]m=\frac{1}{5}[/tex]3) Now, the next step is to plug into the Slope-intercept form the following point (15,4) and then find the y-intercept:
[tex]\begin{gathered} y=mx+b \\ 4=\frac{1}{5}(15)+b \\ 4=3+b \\ 4-3=b \\ b=1 \end{gathered}[/tex]4) Thus, the equation of a perpendicular line to the line described by the linear function y=-5x-3 is:
[tex]y=\frac{1}{5}x+1[/tex]
Use the Pythagorean theorem to find the length of this segment.
Answers
To find the length of the segment use the Pythagoras theorem below:
[tex]AC^2=AB^2+BC^2[/tex]From the graph, we have:
AB = 15 - 3 = 12
BC = 7 - 2 = 5
Let's solve for the length of the segment AC:
[tex]\begin{gathered} AC^2=12^2+5^2 \\ \\ AC^2=144+25 \\ \\ AC^2=169 \end{gathered}[/tex]Take the square-root of both sides:
[tex]\begin{gathered} \sqrt[]{AC^2}=\sqrt[]{169} \\ \\ AC\text{ = 13} \end{gathered}[/tex]Therefore, the length of this segment is 13
ANSWER:
13
what is 1 plus 1?help me
Answers
Answer:
it's 2
Step-by-step explanation:
don't forget to follow rate like
Preform the indicated Operation g(n)=2n^2-4nh(n)=n-1find g(h(1-b))
Answers
GIven:
The expressions are given as,
[tex]\begin{gathered} g(n)=-2n^2-4n \\ h(n)=n-1 \end{gathered}[/tex]The objective is to find g(h(-1-b)).
Explanation:
To find h(-1-b):
The value of h(-1-b) can be calculated by replacing the n with (-1-b) in the expression of h(n).
[tex]\begin{gathered} h(n)=n-1 \\ h(-1-b)=-1-b-1 \\ h(-1-b)=-2-b\text{ . . . . . . (1)} \end{gathered}[/tex]To find g(h(-1-b)):
The value of g(h(-1-b)) can be calculated by replacing the n with h(-1-b) in the expression g(n).
[tex]\begin{gathered} g(n)=-2n^2-4n \\ g(h(-1-b))=-2(-2-b)^2-4(-2-b)\text{ . . . . (2)} \end{gathered}[/tex]On further solving the equation (2),
[tex]undefined[/tex]The pollution of Linton is 12 times as great as a pollution of Ellmore. The combine population of both sounds is 9,646 people. What is the population of Linton?
Answers
Explanation
[tex]\begin{gathered} 12x+x=9646 \\ 13x=9646 \\ x=\frac{9646}{13} \\ x=742 \end{gathered}[/tex]The population of Linton is 742*12=8904
Answer
8904
What E is. if E=2 when W=15, find E when W=10
Answers
Since the elongation E varies directly with the weight W, they are related as follows
[tex]E=kW[/tex]where k is the constant of proportionality. In order to find k, we can substitute the given values, that is, when E=2, W=15, then we have
[tex]2=k\cdot15[/tex]Then, k is given as
[tex]k=\frac{2}{15}[/tex]Therefore, our formula for any E and W is
[tex]E=\frac{2}{15}W[/tex]Now, in order to find E in the second case, by replacing W=10, we get
[tex]E=\frac{2}{15}(10)[/tex]which yields
[tex]E=\frac{20}{15}=\frac{4}{3}[/tex]Therefore, the answer is
[tex]E=\frac{4}{3}[/tex]I will show you a pic
Answers
Answer
The red line represents y = x + 1
The blue line represents y = 2x - 7
We can see that the two lines and equation intersect at (8, 9)
Solution
x = 8
y = 9
Explanation
The two equations are
y = x + 1
y = 2x - 7
To solve this graphically, we will plot the two equations on the same graph and the solution will exist at the point where the two lines meet.
To plot the lines for each of these equations, we will use intercepts to obtain two points on each line and then connect the two points to get each of the lines.
y = x + 1
when x = 0
y = x + 1
y = 0 + 1
y = 1
First point on the line is (0, 1)
when y = 0
y = x + 1
0 = x + 1
x = -1
Second point on the line is (-1, 0)
The two points are (0, 1) and (-1, 0)
y = 2x - 7
when x = 0
y = 2x - 7
y = 2(0) - 7
y = 0 - 7
y = -7
First point on the line is (0, -7)
when y = 0
y = 2x - 7
0 = 2x - 7
2x = - 7
Divide both sides by 2
(2x/2) = (-7/2)
x = -3.5
Second point on the line is (-3.5, 0)
The two points are (0, -7) and (-3.5, 0)
The graph of this question will now be presented under answer and the point of intersection will bw evident.
Hope this Helps!!!
A linear function contains the following points.
X
y
What are the slope and y-intercept of this function?
A. The slope is 4.
The y-intercept is (0, -1).
5
B. The slope is.
The y-intercept is (0, -1).
C. The slope is.
The y-intercept is (-1,0).
D. The slope is.
0
-1
The y-intercept is (0, -1).
5
3
Answers
The slope will be 4/5.
And, The y - intercept will be (0, - 1)
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The points are,
(0, - 1) and (5, 3)
Now,
Since, The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is;
m = (y₂ - y₁) / (x₂ - x₁)
So, The slope of the line passing through the points (0, - 1) and (5, 3) is;
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-1)) / (5 - 0)
m = (3 + 1) / 5
m = 4/5
And, The y - intercept is at x = 0
Thus, The slope will be 4/5.
And, The y - intercept will be (0, - 1)
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What is the yintercept of O A. (0,0) O B. (0,1) O C. (1,0) OD (9)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y-intercept = ?
f(x) = (1/2) ^ x
Step 02:
y-intercept :
x = 0
[tex]\begin{gathered} y\text{ = (}\frac{1}{2})^0=1 \\ \end{gathered}[/tex]The answer is:
y-intercept
(0 , 1)
7. Find the value of x in the figure below. Justify your answer. 4 pts 20° (x - 15)° X = Reason:
Answers
Answer
x = 85°
Explanation
The image of this question shows that the two angles 20° and (x - 15)° both sum up to give a right angle (90°). So,
20° + (x - 15)° = 90°
20° + x - 15° = 90°
x° + 20° - 15° = 90°
x + 5° = 90°
x = 90° - 5°
x = 85°
Hope this Helps!!!
Which values are solutions to the inequality below? Check all that apply. x^2
Answers
Answer:
11, 7, and -8
At the end of the winter, coats are on sale for 75% off. Question: a. If a heavy coat was priced at $ 160, then how much money will you save since it is on sale?
Answers
$120
Explanation
remember
[tex]75\text{ \% =}\frac{75}{100}=0.75[/tex]it means you can find 75 % of any value, just by doing th product of the number and 0.75
[tex]\begin{gathered} 160\cdot0.75=120 \\ \end{gathered}[/tex]Hence, 75% is $120 ,
the discount is 120,the new price is 40
the money you save is the difference, it is 120
I hope this helps you
What is the approximate percentage of huskies that weigh less than Jason's dog
Answers
step 1
Find the z-score
z=(49-52)/7
z=-0.43
using the tables
P=33.36%
therefore
answer is 33%How to find the inverse of the matrix Question number 19
Answers
Okay, here we have this:
We need to find the inverse of the matrix, let's do it:
[tex]\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {1} & {-1} \\ {1} & {4} & {0}\end{bmatrix}[/tex]For that we are going to make the augmented form with the identity matrix and convert the original matrix into the identity:
[tex]\begin{gathered} \begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ -1 & 1 & -1 & | & 0 & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix} \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix}\text{ }R_2\leftarrow R_2+\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 2 & -\frac{1}{2} & | & -\frac{1}{2} & 0 & 1\end{pmatrix}\text{ }R_3\leftarrow R_3-\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -\frac{1}{6} & | & -\frac{5}{6} & -\frac{2}{3} & 1\end{pmatrix}R_3\leftarrow R_3-2/3R_2 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_3\leftarrow-6R_3 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow R_2+\frac{1}{2}R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow\frac{1}{3}R_2 \\ =\begin{pmatrix}2 & 0 & 0 & | & -8 & -8 & 10 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-4R_2 \\ =\begin{pmatrix}1 & 0 & 0 & | & -4 & -4 & 5 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow\frac{1}{2}R_1 \end{gathered}[/tex]Finally the inverse is on the right side of the augmented matrix:
[tex]=\begin{pmatrix}-4 & -4 & 5 \\ 1 & 1 & -1 \\ 5 & 4 & -6\end{pmatrix}[/tex]Hi, can you help me answer this question please, thank you!
Answers
We are asked to determine the test statistic for two populations. To do that we will use the following formula:
[tex]z=\frac{\bar{x_2}-\bar{x_1}}{\sqrt[]{\frac{SD^2_2}{n_2}+\frac{SD^2_1}{n_1}}}[/tex]Where:
[tex]\begin{gathered} \bar{x_1},\bar{x_2}=\text{ population means} \\ SD_1,SD_2=\text{ standard deviations} \\ n_1,n_2=\text{ population sizes} \end{gathered}[/tex]Substituting the values we get:
[tex]z=\frac{83.3_{}-75.4}{\sqrt[]{\frac{(17.8)^2_{}}{19}+\frac{(9.7)^2_{}}{12}}}[/tex]Solving the operations we get:
[tex]z=1.596[/tex]Therefore, the test statistic is 1.596.
To determine the P-value we will determine the probability that the test statistic is less than the value we determined. This is:
[tex]p-\text{value}=P(z<1.596)[/tex]The value of the probability we find it in the z-table using the value z = 1.596, we get:
[tex]p-\text{value}=0.9441[/tex]Therefore, the p-value is 0.9441.
3(t - 24) = 8t - 4(t + 15)
Answers
We need to solve the equation:
[tex]3(t-24)=8t-4(t+15)[/tex]Then:
[tex]\begin{gathered} 3(t-24)=8t-4(t+15) \\ 3t-72=8t-4t-60 \\ 3t-72=4t-60 \\ 3t-4t=-60+72 \\ -t=12 \\ t=-12 \end{gathered}[/tex]Therefore, t=-12.
The expression(Toys =)equalsy"zsztwhere1, the exponent of y, is:s, the exponent of %, is:t, the exponent of X, is:Next Question
Answers
The given expression can be simplified as follows:
[tex]\frac{(x^4y^5z^5)^6}{(x^5y^5z)^5}=\frac{x^{24}y^{30}z^{30}}{x^{25}y^{25}z^5}=x^{-1}y^5z^{25}=\frac{y^5z^{25}}{x}[/tex]Compare with the given term as follows:
[tex]\frac{y^5z^{25}}{x}=\frac{y^rz^s}{x^t}[/tex]Therefore r, the exponent of y is 5
s, the exponent of z is 25
t, the exponent of x is 1.
between 1993 and 1996 there where 6545 injured horses find the ratio of injuries per year
Answers
First, we have to know the total number of years between 1993 and 1996. If we subtract, we find the there are 3 years in between.
Now, we divide the total number of injured horses by the total numbers of years.
[tex]r=\frac{6545}{3}=2,181.7[/tex]However, we can't round to 2,182 because horses are not incomplete.
Therefore, the total number of injured horses per year is 2,181.1) The expression 5p represents the total price of buying 5 movie tickets. • What do the parts of the expression 5p represent? ) The variable p represents the ticket price The number 5 represents the number of tickets Today there is a discount of $10 off a purchase of 5 or more movie tickets. Which expression can you use to find the total price of 5 movie tickets after the discount? 10p + 5 5p - 10 10p - 5 5p + 10
Answers
Solution
The expression 5p represents the total price of buying 5 movie tickets. • What do the parts of the expression 5p represent?
The variable p represents the ticket price The number 5 represents the number of tickets
For this case the correct answer would be:
5p -10
The coefficient 5 represents the price of 1 ticket
for the next part the answer would be:
7 +3x
And the last part
2/3 y -6
List the values at which X has a local Minimum or no minimum. What is the local minima, if one exist?
Answers
Looking at the graph
we have that
The local minimum is at
x=-4 and x=1The values of the local minimum are
For x=-4 ------> y=-1
For x=1 -----> y=-1
The values of the local minimum are equal to -1Tools - Question 4 The coordinate planle below shows the location of segment QR. 109Y 5 Q1-4,3) 70-9-8-7-6-5-4-3-3 2 3 4 5 6 7 8 9 TU R(8,-6) What is the unit distance between the two endpoints of the segment? Illuminate Education TM, Inc.
Answers
Apply the distance between 2 points formula:
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]We have the points:
(x1,y1) = (-4,3)
(x2,y2) = (8,-6)
[tex]D=\sqrt[]{(8-(-4))^2+(-6-3)^2}=\sqrt[]{(8+4)^2+(-9)^2}=\sqrt[]{144+81}=\sqrt[]{225}=15[/tex]Distance = 15
Find the zeros of each function by using a graph and a table. f(x)=x^2+2x–24.
Answers
Explanation
Step 1
[tex]f(x)=x^2+2x-24[/tex]Zeros
A(-6,0) B(4,0)
because
[tex]\begin{gathered} f(x)=x^2+2x-24 \\ f(-6)=(-6)^2+2(-6)-24=36-12-24=0 \\ f(4)=4^2+2\cdot4-24=16+8-24=0 \end{gathered}[/tex]Step 2
table
[tex]\begin{gathered} (-6,0) \\ (4,0) \\ f(-1)=-1^2+2\cdot-1-24=1-2-24=-25 \\ (1,-25) \\ \end{gathered}[/tex]I hope this helps you
What is the answer
(3t/t^5)^-5
Answers
The resultant answer of the given expression (3t/t⁵)⁻⁵ is t²⁰/243.
What exactly are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.To evaluate an algebraic expression, you must substitute a number for each variable and perform the arithmetic operations.The previous example's variable x is equivalent to 6 because 6 plus 6 = 12.If we know the values of our variables, we can replace the original variables with those values before evaluating the expression.So, solve the expression as follows: (3t/t^5)^-5
Apply exponent rule:
(3t/t^5)^-51/((3t/t^5)^5)Simplify as shown:
(3t/t^5)^5: 243/t²⁰1/243/t²⁰Apply function rule:
t²⁰/243Therefore, the resultant answer of the given expression (3t/t⁵)⁻⁵ is t²⁰/243.
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