Answer:
-3
Step-by-step explanation:
I'm not sure what the 0s are all about, but I can help with the equation;
To do this, we can do substitution. By equaling x-4 to 3x+2, we get
x-4=3x+2
By isolating the x, we get
-2x=6
x=-3
Hope this helped!
Suppose H is an ntimesn matrix. If the equation Hxequalsc is inconsistent for some c in set of real numbers R Superscript n, what can you say about the equation Hxequals0? Why?
Answer:
The answer is explained below
Step-by-step explanation:
Given that, the equation H*x = c is inconsistent for some c in R^n, we can say that the equation A*x = b has at least one solution for each b in R^n of IMT (Inverse Matrix Theorem) is not fulfilled.
Thanks to this we can say that by equivalence of theorem statement, the equation H*x = 0 will not have only the trivial solution. It will have non-trivial solutions too.
Which statement best interprets the factor (r+7) in this context?
Answer:
the height of the cylinder is 7 units greater than the radius
Step-by-step explanation:
When you match the forms of the equations ...
[tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]
you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...
the height of the cylinder is 7 units greater than the radius.
Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice. Set A Set B The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 42.8 with standard deviation of about 1.86. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set A’s low temperatures have a greater variability than Set B temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set B is about 41.56 with standard deviation of about 6.07. The mean for Set A is about 43.8 with standard deviation of about 14.8. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set A means that Set A’s low temperatures have a greater variability than Set B temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.4. The mean for Set B is about 41.5 with standard deviation of about 6.7. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set B’s low temperatures have a greater variability than Set A temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 43.8 with standard deviation of about 14.8. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set B’s low temperatures have a greater variability than Set A temperatures.
Answer:
Explained below.
Step-by-step explanation:
The question is:
Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.
Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}
Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}
The five-number summary is:
MinimumFirst Quartile Median Third Quartile MaximumThe five-number summary for set A is:
Variable Minimum Q₁ Median Q₃ Maximum
Set A 36.00 38.25 44.00 50.75 54.00
The five-number summary for set B is:
Variable Minimum Q₁ Median Q₃ Maximum
Set B 22.00 28.75 48.00 58.50 65.00
Compute the mean for both the data as follows:
[tex]Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6[/tex]
Both the distribution has the same mean.Compare mean and median for the two data:
[tex]Mean_{A}>Median_{A}\\\\Mean_{B}>Median_{B}[/tex]
This implies that set A is positively skewed whereas set B is negatively skewed.Compute the standard deviation for both the set as follows:
[tex]SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6[/tex]
The set B has a greater standard deviation that set A. Implying set B has a greater variability that set B.Lee watches TV for 2 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
Answer:
$1.08
Step-by-step explanation:
30 days × (2 hrs/day) × (150 W) × (1 kW / 1000 W) × (0.12 $/kWh) = $1.08
PLEASE HELP!!! A LOT OF POINTS AND BRAINLIEST TO CORRECT ANSWERS!!!
1. Find the area of the region enclosed by the graph of [tex]$x^2 + y^2 = 2x - 6y + 6$[/tex].
2. The line [tex]x=4[/tex] is an axis of symmetry of the graph of [tex]$y = ax^2 + bx + c.$[/tex] Find [tex]$\frac{b}{a}$.[/tex].
3. The graph of [tex]$y = ax^2 + bx + c$[/tex] is shown below. Find [tex]$a \cdot b \cdot c$[/tex]. (The distance between the grid lines is one unit, picture of graph attached.)
4. Geometrically speaking, a parabola is defined as the set of points that are the same distance from a given point and a given line. The point is called the focus of the parabola and the line is called the directrix of the parabola. Suppose [tex]$\mathcal{P}$[/tex] is a parabola with focus [tex]$(4,3)$[/tex] and directrix [tex]$y=1$[/tex]. The point [tex]$(8,6)$[/tex] is on [tex]$\mathcal{P}$[/tex] because [tex]$(8,6)$[/tex] is 5 units away from both the focus and the directrix. If we write the equation whose graph is [tex]$\mathcal{P}$[/tex] in the form [tex]$y=ax^2 + bx + c$[/tex], then what is [tex]$a+b+c$[/tex]?
5. (This is a Writing Problem - please please please explain and answer the question thoroughly!) A quadratic of the form [tex]$-2x^2 + bx + c$[/tex] has roots of [tex]$x = 3 + \sqrt{5}$[/tex] and [tex]$x = 3 - \sqrt{5}.$[/tex] The graph of [tex]$y = -2x^2 + bx + c$[/tex] is a parabola. Find the vertex of this parabola.
If you do manage to answer every single one of these correctly, THANK YOU SO MUCH and please know you are very much appreciated! :)
Answer:
1. [tex]Area=16\,\pi=50.265[/tex]
2.- [tex]\frac{b}{a} =-8[/tex]
3. [tex]y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]
4. [tex]a+b+c=\frac{17}{4}[/tex]
5. the vertex is located at: (3, 10)
Step-by-step explanation:
1. If we rewrite the formula of the conic given by completing squares, we can find what conic we are dealing with:
[tex](x^2-2x)+(y^2+6y)=6\\\,\,\,\,\,\,+1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+9\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+10\\(x-1)^2+(y+3)^2=16\\(x-1)^2+(y+3)^2=4^2[/tex]
which corresponds to a circle of radius 4, and we know what the formula is for a circle of radius R, then:
[tex]Area=\pi\,R^2=\pi\,4^2=16\,\pi=50.265[/tex]
2.
If x=4 is the axis of symmetry of the parabola
[tex]y=ax^2+bx+c[/tex]
then recall the formula to obtain the position of the x-value of the vertex:
[tex]x_{vertex}=-\frac{b}{2a} \\4=-\frac{b}{2a}\\4\,(-2)=\frac{b}{a} \\\frac{b}{a} =-8[/tex]
3.
From the graph attached, we see that the vertex of the parabola is at the point: (-3, -2) on the plane, so we can write the general formula for a parabola in vertex form:
[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-(-2)=a\,(x-(-3))^2\\y+2=a(x+3)^2[/tex]
and now find the value of the parameter "a" by requesting the parabola to go through another obvious point, let's say the zero given by (-1, 0) at the crossing of the x-axis:
[tex]y+2=a\,(x+3)^2\\0+2=a(-1+3)^2\\2=a\,2^2\\a=\frac{1}{2}[/tex]
So the equation of the parabola becomes:
[tex]y+2=\frac{1}{2} (x+3)^2\\y+2=\frac{1}{2} (x^2+6x+9)\\y+2=\frac{1}{2} x^2+3x+\frac{9}{2} \\y=\frac{1}{2} x^2+3x+\frac{9}{2} -2\\y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]
4.
From the location of the focus of the parabola as (4, 3) and the directrix as y=1, we conclude that we have a parabola with dominant vertical axis of symmetry, displaced from the origin of coordinates, and responding to the following type of formula:
[tex](x-h)^2=4\,p\,(y-k)[/tex]
with focus at: [tex](h,k+p)[/tex]
directrix given by the horizontal line [tex]y=k-p[/tex]
and symmetry axis given by the vertical line [tex]x=h[/tex]
Since we are given that the focus is at (4, 3), we know that [tex]h=4[/tex], and that [tex]k+p=3[/tex]
Now given that the directrix is: y = 1, then:
[tex]y=k-p\\1=k-p[/tex]
Now combining both equations with these unknowns:
[tex]k+p=3\\k=3-p[/tex]
[tex]1=k-p\\k=1+p[/tex]
then :
[tex]1+p=3-p\\2p=3-1\\2p=2\\p=1[/tex]
and we now can solve for k:
[tex]k=1+p=1+1=2[/tex]
Then we have the three parameters needed to write the equation for this parabola:
[tex](x-h)^2=4\,p\,(y-k)\\(x-4)^2=4\,(1)\,(y-2)\\x^2-8x+16=4y-8\\4y=x^2-8x+16+8\\4y=x^2-8x+24\\y=\frac{1}{4} x^2-2x+6[/tex]
therefore: [tex]a=\frac{1}{4} , \,\,\,b=-2,\,\,and\,\,\,c=6[/tex]
Then [tex]a+b+c=\frac{17}{4}[/tex]
5.
The vertex of a parabola can easily found because they give you the roots of the quadratic function, which are located equidistant from the symmetry axis. So we know that is one root is at [tex]x=3+\sqrt{5}[/tex]and the other root is at [tex]x=3-\sqrt{5}[/tex]
then the x position of the vertex must be located at x = 3 (equidistant from and in the middle of both solutions. Then we can use the formula for the x of the vertex to find b:
[tex]x_{vertex}=-\frac{b}{2a}\\3=-\frac{b}{2\,(-2)}\\ b=12[/tex]
Now, all we need is to find c, which we can do by using the rest of the quadratic formula for the solutions [tex]x=3+\sqrt{5}[/tex] and [tex]x=3-\sqrt{5}[/tex] :
[tex]x=-\frac{b}{2a} +/-\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex]
Therefore the amount [tex]\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex], should give us [tex]\sqrt{5}[/tex]
which means that:
[tex]\sqrt{5}=\frac{\sqrt{b^2-4\,a\,c} }{2\,a} \\5=\frac{b^2-4ac}{4 a^2} \\5\,(4\,(-2)^2)=(12)^2-4\,(-2)\,c\\80=144+8\,c\\8\,c=80-144\\8\,c=-64\\c=-8[/tex]
Ten the quadratic expression is:
[tex]y=-2x^2+12\,x-8[/tex]
and the y value for the vertex is:
[tex]y=-2(3)^2+12\,(3)-8=-18+36-8=10[/tex]
so the vertex is located at: (3, 10)
Determine the intercepts of the line. -5x+9y=-18−5x+9y=−18minus, 5, x, plus, 9, y, equals, minus, 18 xxx-intercept: \Big((left parenthesis ,,comma \Big))right parenthesis yyy-intercept: \Big((left parenthesis ,,comma \Big))
Answer:
(3.6, 0), (0, -2)
Step-by-step explanation:
To find the y-intercept, set x=0:
-5·0 +9y = -18
y = -18/9 = -2
To find the x-intercept, set y=0:
-5x +9·0 = -18
x = -18/-5 = 3.6
The intercepts are ...
x-intercept: 3.6
y-intercept: -2
Which of the following is false? Correlation coefficient and the slope always have the same sign (positive or negative). If the correlation coefficient is 1, then the slope must be 1 as well. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation measures the strength of linear association between two numerical variables.
Answer:
If the correlation coefficient is 1, then the slope must be 1 as well.
Step-by-step explanation:
Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.
If the correlation coefficient is 1, then the slope must be 1 as well.
The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.
Correlation coefficient and the slope both quantify the direction and strength of the relationship between two numeric variables. When the correlation (r) is negative, the regression slope (b) will be negative. When the correlation is positive, the regression slope will be positive.If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them.
So, the false statement is:
If the correlation coefficient is 1, then the slope must be 1 as well.
Learn more:https://brainly.com/question/16557696
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides.
The heights of the pyramids are the same.
The volume of pyramid Als
y the volume of pyramid B. If the helght of pyramid B increases to twice that of pyramid A, the
new volume of pyramid B is
the volume of pyramid A.
Answer:
a. The volume of Pyramid A is double that of Pyramid B.
b. The new volume of B is equal to the volume of A.
Step-by-step explanation:
The base of pyramid A is a rectangle with length 10 meters and width 20 meters.
The base of pyramid B is a square of side length 10 meter.
Both pyramids have the same height, h.
The volume of a pyramid is given as:
V = lwh / 3
where l = length
w = width
h = height
The volume of Pyramid A is:
V = (10 * 20 * h) / 3 = 66.7h cubic metres
The volume of Pyramid B is:
V = (10 * 10 * h) / 3 = 33.3h cubic metres
By comparing their values, the volume of Pyramid A is double that of Pyramid B.
If the height of B increases to 2h, its new volume is:
V = (10 * 10 * 2h) / 3 = 66.7h cubic metres
The new volume of B is equal to the volume of A.
true or false? the circumcenter of a triangle is the center of the only circle that can be inscribed about it
Answer:
TRUE
Step-by-step explanation:
The circumcenter of a triangle is the center of the only circle that can be circumscribed about it
Answer:
False
Step-by-step explanation:
Last winter Armand had StartFraction 5 Over 6 EndFraction of a row of stacked logs. At the end of the winter he had StartFraction 8 Over 15 EndFraction of the same row left. How much wood did he burn over the winter?
Answer:
3/10
Step-by-step explanation:
We have that the Armans last winter had 5/6 of a row of stacked logs and at the end of the winter he had 8/15 of the same row left, therefore:
Ambitious
First we have to do is that the denominator is the same.
in the case of 5/6 it would be 25/30
and for 8/15 it would be 16/30
Now if we can do the subtraction and it would be:
25/30 - 16/30 = 9/30 or what equals 3/10
3/10 was the amount of wood he burned in the winter
Answer:
D) 3/10 row
Step-by-step explanation:
which inequality represents the statement? the number of new cars(C) a ship carries cant exceed 975.
A. c<975
B. c>975
C. c<(—under<)975
D. c>(—under>)975
"can't exceed 975" means this is the largest value possible for C. So we could have C = 975 or smaller. We write this as [tex]C \le 975[/tex] which is read as "C is less than or equal to 975".
Answer: Choice C. [tex]C \le 975[/tex]Answer:
5
Step-by-step explanation:
Q12.
A woman applies for a new job that pays £8.50 a week more (after tax).
She will work 5 days a week and drive to work, as she does in her job now.
The new job is 6 miles further from her house.
Her car travels 8.5 miles per litre of petrol
Petrol costs £1.26 per litre
Will the woman be better off with the new job after she takes the petrol into consideration?
Explain your answer. Include calculations to support your decision.
Decision (yes/no)
8.5x1.295.70
Explanation and supporting calculations
CA
Answer:
Step-by-step explanation:
1l ........8.5 miles
x l .......6 miles
-----------------------
x=6*1/8.5
x=0.70 l
2*0.7=1.4 l petrol/day ( to work and come back home)
5*1.4=7 l/week ( 5 days works in a week)
7*1.26=8.82 L /week
8.82>8.5
The petrol costs more
So the answer is NO
Find [g ° h](x) and [h ° g](x) , if they exist. g(x)=x+6 and h(x)=3x2 YALL PLEASE I NEED HELP :((
Answer:
a) [g ° h](x) = 3x² +6
b) [h ° g](x) =3 x²+36x+108
Step-by-step explanation:
Explanation:-
a)
Given g(x) = x+6 and h(x) = 3x²
Given [g ° h](x) = g(h(x))
= g(3x²) (∵ h(x) =3x²)
= (3x²)+6 (∵ g(x) =x+6)
∴ [g ° h](x) = 3x² +6
b)
Given [h ° g](x) = h (g(x))
= h(x+6) (∵ g(x) =x+6)
= 3 (x+6)² (∵ h(x) =3x²)
= 3 (x²+2(6)x+36) (∵ (a + b)² = a²+2ab+b²)
= 3 (x²+12x+36)
= 3 x²+36x+108)
∴ [h ° g](x) =3 x²+36x+108
–735 = 15(m + 929) m = _______
Answer:
-978
Step-by-step explanation:
1.) Use Distributive property (by multiplying 15 by the values in parentheses): -735=15m + 13935
2.) Subtract 13,935 on both sides, to move that value to the left side, to further isolate the variable m.
-735-13935=15m + 13935 - 13935
3.)-Simplify/Combine Like Terms
-14,670=15m
4.) Divide both sides by 15 to isolate and solve for m
-14,670/15=15m/15
5.) Simplify
-978=m
6.) Rearrange so m is on left side and value is on right side
m=-978
What is the m ZACB?
10°
50°
90°
180°
Answer:
50 deg
Step-by-step explanation:
In an right triangle, the acute angles are complementary. That means their measures have a sum of 90 deg.
m<C + m<B = 90
7x - 20 + 4x = 90
11x = 110
x = 10
m<ACB= 7x - 20
m<ACB = 7(10) - 20
m<ACB = 70 - 20
m<ACB = 50
Answer: m<ACB = 50 deg
The function h(x)=12/x-1 is one to one. Algebraically find it’s inverse, h^-1(x).
Answer:
Step-by-step explanation:
hello,
I assume that you mean
[tex]h(x)=\dfrac{12}{x-1}[/tex]
so first of all let's take x real different from 1 , as this is not allowed to divide by 0
[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]
and this is defined for x real different from 0
hope this helps
If f(x) = 5x – 2 and g(x) = 2x + 1, find (f - g)(x).
A. 3 - 3x
B. 3x-3
C. 7x-1
D. 7x-3
Answer:
The difference of the functions is (f-g)(x) = 3x - 3
Step-by-step explanation:
In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).
f(x) = 5x - 2
g(x) = 2x + 1
(f-g)(x) = (5x - 2) - (2x + 1)
Distribute the negative to (2x + 1)
(f-g)(x) = 5x - 2 - 2x - 1
Combine like terms. Make sure your answer is in standard form.
(f-g)(x) = 3x - 3
So, the answer to the equation is (f-g)(x) = 3x - 3
Find the median of: 1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4
Answer:
4
Step-by-step explanation:
1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4
Arrange the numbers from smallest to largest
0,1, 1,2,2, 3,3, 4, 4,4,4,4,4 , 4, 5, 6, 6, 7, 8, 9,
There are 20 numbers
The middle number is between 10 and 11
0,1, 1,2,2, 3,3, 4, 4,4 ,4,4,4 , 4, 5, 6, 6, 7, 8, 9,
The median is 4
Solution,
Arranging the data in ascending order:
0,1,1,2,2,3,3,4,4,4,4,4,4,4,5,6,6,7,8,9
N(total number of items)= 20
Now,
Median:
[tex] (\frac{n + 1}{2)} ) ^{th \: item} \\ = (\frac{20 + 1}{2} ) ^{th \: item} \\ = \frac{21}{2} \\ = 10.5 \: th \: \: item[/tex]
Again,
Median:
[tex] \frac{10 \: th \: item + 11 \: th \: item}{2} \\ = \frac{4 + 4}{2} \\ = \frac{8}{2} \\ = 4[/tex]
How do you calculate the y-intercept of a line written in Standard Form?
Answer:
y-int = C/B
Step-by-step explanation:
Ax + By = C
y-int = C/B
Answer:
I hope this helps.
Step-by-step explanation:
Which feature of a database displays data in a certain sequence, such as alphabetical order? Chart Filter Search Sort
Answer:
data bar
Step-by-step explanation:
Answer:
chart
Step-by-step explanation:
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers that are 6 or even on the cards are 2, 4, and 6.
3 cards out of a total of 6 cards.
3/6 = 1/2
Answer:
1/2 chance
Step-by-step explanation:
There are 3 numbers that fit the rule, 2, 4, and 6. 3/6 chance of picking one or 1/2, simplified.
What is 62 in expanded form?
A. 2 x 2 x 2 x 2 x 2 x 2
B. 6 x 6
C. 12
D. 36
Answer:
I think so you meant to write 62 as 6^2
If this is the question , then the answer is 6 x 6
HOPE THIS HELPS AND PLS MARK AS BRAINLIEST
THNXX :)
Answer:
B. 6 × 6
Step-by-step explanation:
6²
The square of a number means that the number is multiplied by itself.
6 × 6 (expanded form)
Don’t know this one
Answer:
B
Step-by-step explanation:
The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.
B. [tex](-4)^2\neq -16[/tex].
Hope this helps.
Gregoire sold 24 cars to his friend for $71.76. What was the price per car?
a. $47.76
b. $2.99
c. $17.22
d. $3.25
Answer:
2.99
Step-by-step explanation:
Take the total cost and divide by the number of cards
71.76/24 = 2.99
The cost per car is 2.99
Answer:
b. $2.99.
Step-by-step explanation:
To get the price per car, you get the total price divided by the total number of cars.
That would be 71.26 / 24 = 2.969166667, which is most close to b. $2.99. Those are some cheap cars!
Hope this helps!
What is the explicit rule for the geometric sequence?
600, 300, 150, 75, ...
Answer:
Step-by-step explanation:
Hello, this is a geometric sequence so we are looking for a multiplicative factor.
[tex]a_0=600\\\\a_1=a_0 \cdot \boxed{\dfrac{1}{2}} = 300 = 600 \cdot \boxed{\dfrac{1}{2}}\\\\a_2=a_1 \cdot \boxed{\dfrac{1}{2}} = 150= 300 \cdot \boxed{\dfrac{1}{2}}\\\\a_3=a_2 \cdot \boxed{\dfrac{1}{2}} = 75 = 150 \cdot \boxed{\dfrac{1}{2}}[/tex]
So, the explicit formula is for n
[tex]\boxed{a_n=a_0\cdot \left(\dfrac{1}{2}\right)^n=600\cdot \left(\dfrac{1}{2}\right)^n}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The explicit rule is aₙ = a₀(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.
What is geometric series?The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.
The nth term of a geometric progression is expressed as
Tₙ = arⁿ⁻¹
Where a is the first term, r is the common ratio.
We have been given that geometric sequence as:
600, 300, 150, 75, ...
To determine the explicit rule for the geometric sequence, we have to find the common ratio.
Here the first term (a₀) is 600
So the common ratio = 300/600 = 150/300 = 75/150 = 1/2
Thus, the explicit formula for n would be:
aₙ = a(1/2)ⁿ = 600(1/2)ⁿ
Therefore, the explicit rule is aₙ = a(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.
Learn more about the geometric series here:
brainly.com/question/21087466
#SPJ2
I NEED HELP PLEASE, THANKS! :)
please see the attached picture for full solution..
Hope it helps..
Good luck on your assignment...
Which shapes have the same volume as the given rectangular prism?
Find the value of x.
Answer:
[tex]\huge\boxed{x=\sqrt{66}}[/tex]
Step-by-step explanation:
ΔADC and ΔABD are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AD}{AC}=\dfrac{AB}{AD}[/tex]
Substitute
[tex]AD=x;\ AC=6+5=11;\ AB=6[/tex]
[tex]\dfrac{x}{11}=\dfrac{6}{x}[/tex] cross multiply
[tex](x)(x)=(11)(6)\\\\x^2=66\to x=\sqrt{66}[/tex]
How many gallons of fuel costing $1.15 a gallon must be mixed with a fuel costing $0.85 per gallon to get 40
gallons of a fuel that costs $1 per gallon? Formulate an equation and then solve it in order to determine how
many gallons of fuel costing $1.15.
Answer:
multiply 0.85x40
Step-by-step explanation:
If f(x)=8x and g(x)=2x+1, what is (f×g)(x)
Answer:
(f * g)(x) has a final product of 16x² + 8x.
Step-by-step explanation:
When you see (f * g)(x), this means that we are going to be multiply f(x) and g(x) together.
f(x)=8x
g(x)=2x+1
Now, we multiply these terms together.
(8x)(2x + 1)
Use the foil method to multiply.
16x² + 8x
So, the product of these terms is 16x² + 8x.