The first four terms of the sequence are 6, -24, 96 and -384
How to determine the first four terms?
The sequence is given as:
an=6(-4)^n-1
When n = 1, we have:
a(1)=6(-4)^(1-1)
This gives
a(1) = 6
When n = 2, we have:
a(2)=6(-4)^(2-1)
This gives
a(2) = -24
When n = 3, we have:
a(3)=6(-4)^(3-1)
This gives
a(3)=96
When n = 4, we have:
a(4)=6(-4)^(4-1)
This gives
a(4)=-384
Hence, the first four terms of the sequence are 6, -24, 96 and -384
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I WILL MARK BRAINLIEST PLEASE HELP !! Determine whether the two triangles are similar.
The two triangles are similar by SSA similarity. Option B is correct.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
If the ratio of the sides are same as well as the one angle is common between the two triangles then in that condition there will be SSA similarity.
From the triangle ABC and DEC
The ratio of the sides is;
[tex]\rm \frac{10}{12}= \frac{8}{9.6} \\\\ \frac{5}{6}= \frac{5}{6}[/tex]
One angle c is common in the two triangles.
The two triangles are similar by SSA similarity.
Hence, option B is correct.
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A distance travaled by train in three hours with a constant speed of r miles per hour
The distance travelled by the train with constant speed of r miles will be 3r.
What is Speed?The most crucial scientific notion is measurement. Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance. Let's explore speed in-depth in this session. The pace at which an object's location changes in any direction. When an object travels the same distance in the same amount of time, it is said to be moving at a uniform speed. When an object travels a different distance at regular intervals, it is said to have variable speed.We know the formula of distance linking the speed and the time.
Distance = speed × time
Substituting the given values to get:
Distance = r × 3
Distance = 3r
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A(n) Blank______ is a data characteristic that stands for a value that changes or varies over time. Multiple choice question. information fact variable
Variable is a data characteristic that stands for a value that changes or varies over time.
A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.
Information is that portion of the content of a signal or message which conveys meaning. (so this is the wrong option)
A fact is a quantitative piece of information - such as a sale or a download. (so this is also the wrong option)
Hence, a Variable is a data characteristic that stands for a value that changes or varies over time.
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Medians: Using the methods previously described, the medians of each group were found to be:
Answer:
Medians: Using the methods previously described, the medians of each
group were found to be: Low: ( , ) Medium: ( . ) High: ( . ) Use these points to find the equation of the median fit regression line. Slope: What is the slope of the median regression line? m = Jig—y" = (Round to the nearest H—xL hundredth.) Y-lntercept: What is the y-intercept of the median regression line? kW _ 3 b _ (33—(—U.01)(2300))+(27—(—0.01)(3350))+(19—(—U.01)(4400)) _ 3 m (Round to the nearest hundredth.) Regression Line: The equation of the median regression line isy= x+
What is the measure of RCD?
Find length CD first, which is the hypotenuse of the triangle.
PD = opposite
Opposite & hypotenuse = SOH or sin
Sin(27) = 15/H
x h, then ÷ sin(27)
H = 15/sin(27)
H = 33.04....
Move to triangle CDR:
15 is length opposite the angle we're after.
So far, we've got the hypotenuse (which we just found to be 33.04....) & the opposite of our triangle
Hypotenuse & opposite = SOH
Sin(x) = 15/33.04... but, to find the angle we do inverse of sin
sin-1(15/33.04...) = x
x = 27
(33.04... means I used the full numbers displayed on my calculator)
Thus, RCD is 27 degrees
Hope this helps!
Call a number quasi-prime if it is composite but not divisible by 2, 7, or 11. For instance, the five smallest quasi-prime numbers are 5, 9, 15, 25, 27, and 39. There are 95 prime numbers less than 500. How many quasi-prime numbers are there less than 500
The number of quasi-prime numbers that are less than 500 = 92
What are quasi-prime numbers?Quasi-prime numbers are those numbers that are also known as semi prime numbers which can not be divided by 2,7 or 11.
They are often derived from prime numbers which are 95 in number from 2 - 499. ( less than 500).
The 95 prime numbers - 3 numbers( such as 2,7 or 11) = 92
Therefore, the number of quasi-prime numbers that are less than 500 = 92
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An arithmetic sequence has this recursive formula:
a1= 5
an= an-1-4
The explicit formula for the sequence is an = 5 + (n - 1)(-4)
Explicit rule of a sequenceThe formula for calculating the nth term of an arithmetic sequence is expressed as:
an = a + (n - 1)d
where
a is the first term
d is the common difference
n is the number of terms
From the given data
a = 5
a2 = a1 - 4
a2 = 5 - 4
a2. = 1
d = a2 - a
d = 1 - 5
d = -4
Substitute
an = 5 + (n - 1)(-4)
Hence the explicit formula for the sequence is an = 5 + (n - 1)(-4)
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Mikal is proving that AE ≅ CE .
Triangles A B E and C D E are connected at point E. Angles A B E and E D C are right angles. The lengths of A C and D C are congruent.
Which reason does the ♣ represent in Mikal’s proof?
SAS
SSS
ASA
AAS
The reason that this represent in Mikal’s proof regarding the triangle is SAS.
How to illustrate the triangle?It should be noted that a triangle is a shape that has three sides and angles.
The SAS implies the side angle side. It shows that any two sides and angles that are included between the sides of an angle are equal to the other two sides.
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Answer:
AAS
Step-by-step explanation:
2022 edge
IJ=
Help me please thanks
Answer: 11
Step-by-step explanation:
By the secant-secant theorem,
[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]
4= 3/7(3x+14)
Solve for x in simplest form.
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On the number line above, point L (not
shown) is located on line segment JK so that
JL = LK. What is the position of point L?
The position of point L is halfway between points K and L
How to determine the position?The line segment is given as:
JK
This means that the endpoints of the line are:
J and K
Also, we have:
JL = LK
So, we have:
JK = JL + LK
Substitute JL = LK
JK = JL + JL
This gives
JK = 2JL
Divide by 2
JL = 1/2 JK
Hence, the position of point L is halfway between points K and L
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The value of an investment portfolio decreased by 8 % in 2010. In 2011, its value increased by 5% of
its value in 2010. Given that the value of the portfolio at the end of 2011 was $ 61 824, find its
original value.
Answer:
$63422.42
Step-by-step explanation:
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Can someone help me out on this problem and show work
Step-by-step explanation:
1. multiply by 8
2. divide by 2
Answer:
4096, 125
Step-by-step explanation:
In the first sequence, notice that each term increases by a factor of 8 (multiplied by 8 each time). Therefore, the fourth term would be 64*8 = 512, so the fifth term is 512*8 = 4096.
In the second sequence, each term decreases by a factor of 2 (divided by 2 each time). The fourth term would be 500/2 = 250, so the fifth term is 250/2 = 125.
A sports league has 10 teams. Each team must send at least one player to the league's annual meeting, but may send as many as 5 if space is available based on the cost of the meeting. Holding the meeting costs the league $600 for the facility, plus $50 per player for food and materials. The league cannot spend more than $1900 on the meeting. Which inequality shows the number of players, n, who could be at the meeting?
can I get your number personally
I am not able to solve this question
First, we multiply the numbers : 10 x 5 = 50
Now, we multiply r squared to r^6. To do this, we add the index numbers together : r^2 x r^6 = r^(2+6) = r^8
So, the answer is 50r^8, or b.
To join a new fitness center, there is a $40 initiation fee. It costs an additional $10 for every spinning class you attend. What is the average cost per class if you take 10 classes in the first month of joining the fitness center
the average cost per class is $14.
Think of this as an algebraic equation, which would be expressed as 40+10s=total cost
The (s) would be the number of spinning classes you decide to take.
Therefore to find the average cost of the class, you would plug in 10 classes for s.
This brings the total cost to $140 dollars.
To find the average you must divide this cost by the number of classes you took.
This will be the price per class, which is $14.
Statement of the equality of two expressions formulated by way of making use of a set of variables the algebraic operations, particularly, addition, subtraction, multiplication, department, elevating to energy, and extraction of a root.
In arithmetic, an algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some area, regularly the field of rational numbers.
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help me please i dont understand
Answer:
96 ft^2.
Step-by-step explanation:
Area of shaded region = area of the original rectangle - area of the one removed
= 8 * 16 - 8*4
= 128 - 32
= 96
A can of soup has a height of 10 cm. If the volume of the can is 363 cubic cm, what is its radius?
The radius of the circular cross-section of the can of soup is; 3.4cm.
What is the radius of the can of soup?Since, the can has a height of 10cm and the volume of the can is 363cm³, it follows that the area of the circular cross-section can be evaluated as;
A = 363/10 = 36.3cm²
Hence, it follows that the radius can be evaluated as follows;
36.3 = 3.14 × r²
r² = 36.3/3.14
r² = 11.56
r = 3.4cm
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could you show me what sin D is?
Answer:
sin D = 28/53
Step-by-step explanation:
sin D = opp/hyp
For angle D, the opposite leg is FE with length 28.
The hypotenuse is DE with length 53.
sin D = 28/53
Answer: sinD=28/53.
Step-by-step explanation:
[tex]sinD=\frac{FE}{DE} =\frac{28}{53} .[/tex]
Determine the length of the missing sides for each special right triangle. Leave answer in exact (reduced radical) form. Geometry!! pls help!!
Answer:
[tex]a = 18 \sqrt{3} [/tex]
[tex]c = 36[/tex]
look at images........
Answer:
[tex] \pink{ \rule{1pt}{3000000pt}}[/tex][tex] \red{ \rule{1pt}{3000000pt}}[/tex][tex] \purple{ \rule{1pt}{3000000pt}}[/tex]
Find the vertex of the function given below.
y= 2x² + 8x+1
A. (-2,-7)
B. (-2,-1)
OC. (3,-4)
D. (1,7)
Answer:
A
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c (a ≠ 0 ) then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 2x² + 8x + 1 ← is in standard form
with a = 2 , b = 8 , then
x = - [tex]\frac{8}{4}[/tex] = - 2
substitute x = - 2 into the equation for corresponding y- coordinate
y = 2(- 2)² + 8(- 2) + 1 = 2(4) - 16 + 1 = 8 - 16 + 1 = - 7
vertex = (- 2, - 7 )
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x -and y-axes. A polygon ABCD has A at ordered pair 1, 3, B at ordered pair 3, 4, C at ordered pair 2, 1, D at ordered pair 1, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 3, 3, B prime at ordered pair negative 5, 4, C prime at ordered pair negative 4, 1, D prime at ordered pair negative 3, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Reflection over the x-axis followed by a translation to the right by 2 units
Reflection over the y-axis followed by a translation to the left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 2 units
The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'
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Use the following set of data: 78, 78, 83, 85, 89, 91, 95, 98 what is the median for the set of data? (a) 85 (b) 89 (c) 87 (d) 98 please help!!!!!!!!!!!!!1
Find two numbers such that one number is 3 less than twice as big as the other number and the two numbers sum to 21.
Answer:
The two numbers are:
8 and 13
Step-by-step explanation:
a = 2b - 3 Eq. 1
a + b = 21 Eq. 2
Replacing Eq. 1 in Eq. 2:
(2b-3) + b = 21
3b - 3 = 21
3b = 21 + 3
3b = 24
b = 24/3
b = 8
from Eq. 1
a = 2*8 - 3
a = 16 - 3
a = 13
Check:
From Eq. 2:
a + b = 21
13 + 8 = 21
The graph shows the heights, y (in centimeters), of a plant after a certain number of weeks, x. Donna drew the line of best fit on the graph.
A graph titled Plant Height shows Number of Weeks on x axis and Height of Plant in cm on y axis. The scales on both x and y axes are shown from 0 to 5 at increments of 5. The graph shows dots at the ordered pairs 0, 1 and 0.5, 1.5 and 1, 2 and 1.5, 2.5 and 2, 2.8 and 2.5, 3 and 3, 3.4 and 3.5, 3.5 and 4, 4 and 4.5,4.5 and 5, 5. A straight line joins the ordered pairs 0, 1 and 5, 5
What would most likely be the approximate height of the plant after 8 weeks?
11.0 centimeters
9.25 centimeters
8.8 centimeters
7.4 centimeters
(Please show your work)
Thank you!
Using the given linear function of best-fit, the most likely approximate height of the plant after 8 weeks would be of 7.4 centimeters.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line of best-fit goes through points (0,1) and (5,5). Point (0,1) means that the y-intercept is of b = 1. The slope is given as follows:
m = (5 - 1)/(5 - 0) = 4/5 = 0.8.
Hence the equation that gives the approximate height after x weeks is:
y = 0.8x + 1.
After 8 weeks, the expected height is:
y = 0.8 x 8 + 1 = 6.4 + 1 = 7.4 centimeters.
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The coordinates of C are (4,4), and the midpoint of CD is at M(-2,-6), what are the coordinates of point D?
The coordinates of D is (-8 , -16 )
What are Coordinates ?Coordinates are the location of a point on the x-y plane.
It is given that the coordinates of C are (4,4)
the midpoint of CD is at M(-2,-6)
The distance between D to the midpoint is equal to distance between C and the mid point M .
The distance between C and M is
( -2 - 4 , -6 -4 )
( -6 , -10)
Adding this to the mid point will give the location of D
(-2 -6 , -6 , -10 )
(-8 , -16 )
Therefore the coordinates of D is (-8 , -16 ).
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Answer:
-8, -16
Step-by-step explanation:
got it right on the est.
Solve the equation f(x)=x3+2x2+4x+8 given that one of its roots is x=−2.
Okay, first you need to understand that function of x, (or f(x)) is y.
We now plug in x.
f(-2) or y=-2(3)+(2•2)+4(-2)+8
f(-2)=-6+4+-8+8
f(-2)=-2
When x=-2, y=-2. Lets plug it back in to see if its true.
-2=-2(3) + (2x2) + (4(-2)) + 8
-2 = -6 + 4 + -8 + 8
-2 = -2.
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The slope of the line below is -3. Which of the following is the point-slope form of the line?
Answer:
Step-by-step explanation:
Is there a graph or more information?
Write down a multiple of 9 that is between 60 and 80
Answer:
72
Step-by-step explanation:
9×8 = 72 which means that 72 is a multiple of 9 lying between 60 and 80.
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