Answer:
-1280
Step-by-step explanation:
So, as we can see just by loooing at this geometric sequence, the factor is -2. Let's double check this.
10 * -2 = -20 * -2 = 40
We can just keep multiplying to find the 8th term!
40 * -2 = -80 * -2 = 160 *-2 = -320 * -2 = 640 * -2 = -1280
Sometimes with a short sequence, it is better to just multiply it out. You could also do it like this, though:
[tex]a_{n}=a_{1} *r^{n-1}[/tex]
Here, r = -2. We are looking for the 8th term, which would be 8
Plug in our values:
[tex]a_{8}=10*-2^{7}[/tex]
[tex]-2^{7}=-128\\[/tex]
[tex]10*-128=-1280[/tex]
That is the same answer we got before. I would suggest doing it mathematically if you have a long sequence (15, 100, 300 terms)
Hope this helped!
soving equations variable on both sides 3x=2x+50
Answer:
x = 50
Step-by-step explanation:
Solve the equation:3x = 2x + 50
Subtract 2x from both sides,
3x - 2x = 2x -2x + 50
x = 50
I need help with this and I need it explained to me how to do it
Answer:
14.42 feet
Explanation:
In the figure, we can see that the pole form a right triangle with legs equal to 12 feet and 8 feet, where 8 ft is half the wide or 16 ft/2 = 8 ft.
Then, by the Pythagorean theorem, the length of the slanted pole square is equal to the sum of the square of the legs, so
[tex]x^2=12^2+8^2[/tex]Where x is the minimum length of the slanted pole. Therefore, x is equal to
[tex]\begin{gathered} x^2=144+64 \\ x^2=208 \\ x=\sqrt[]{208} \\ x=14.42 \end{gathered}[/tex]Therefore, the answer is 14.42 feet.
Which of the following notations correctly describe the end behavior of the polynomial graph below?
The end behaviour of the polynomial graph is (b) x ⇒ +∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ -∝
How to determine the end behaviour of the polynomial graph?The polynomial graph represents the given parameter
This polynomial graph is a quadratic function opened downwards
Polynomial function of this form have the following end behaviour:
As x increases, f(x) decreasesAs x decreases, f(x) decreasesThis is represented as
x ⇒ +∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ -∝
Hence, the end behaviour is (b)
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the lenght, l , of a rectangle is twice its width, w and the premiter is p
which mathematical relationship(s) this senerio
select all that apply
A L=W-P
B2L=W
C 2W=L
D 2(L+2W)=P
E 2(L+W)=P
F p=6W
The perimeter for the length L and width W that is 2L will be 2W=L as the definition of perimeter says, "The total length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges".
What is perimeter?The total length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The perimeter of a shape is the space surrounding its edge. A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. We must add up the lengths of the rectangle's four sides in order to determine its perimeter. Since there are two of each side length, it is easy to accomplish this by simply adding the length and width and multiplying the result by two. The perimeter formula is defined as perimeter=2(length + width).
Here,
Perimeter=2(length + width)
Length=L
Width=W=2L
2(L+W)=P
In accordance with the definition of perimeter, the perimeter for a length L and a width W that is equal to 2L will be 2W=L "In geometry, a shape's perimeter is referred to as its overall length. The perimeter of a shape is determined by adding all of its sides' and edges' lengths ".
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х1451°Find the value of x. Round to the nearest tenth.x=
To solve this question, we employ the sine relation;
[tex]\begin{gathered} \frac{14}{x}=\sin 51 \\ \end{gathered}[/tex]Rearranging the equation, we obtain ;
[tex]x=\frac{14}{\sin 51}=20.88\approx20.9[/tex]Therefore, x = 20.9
3. (02.02 MC)
The beginning mean bi-weekly wage in a certain industry is $2,498.00. If the mean bi-weekly wage grows by 3.25%, what is the new mean annual wage? (4 points)
$62,903.63
$64,948.00
$67,058.81
$69,079.13
If the mean bi-weekly wage grows by 3.25%, the new mean annual wage is: C. $67,058.81.
What is annual wage?Annual wage can simply be defined as the amount a person is paid annually as wages . Wages can be paid daily or weekly.
Using this formula to find the new mean annual wage
New mean annual wage = [Beginning mean bi-weekly wage × ( 1+ mean bi-weekly wage ) ]× Number of weeks per year /2
Let plug in the formula
New mean annual wage = [$2,498.00 × (1+ 0.0325)] × 52 weeks /2
New mean annual wage = [$2,498.00 × (1.0325)] × 26 weeks
New mean annual wage = $2,579.185 × 26 weeks
New mean annual wage = $67,058.81
Therefore the correct option is C.
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How much interest will Harley earn in 3 years if she deposits $1,200 into a savings account that pays 6% simple interest?
Ruben bought 6 comic books for $21 Each comic book was the same price.
What was the cost for 1 comic book?
Solve the system of linear equations using matrices.4y-z=-5X+ 5y +z=-32x-y + 3z =13
The given system expressed as a matrix would be
0 4 -1 -5
1 5 1 -3
2 -1 3 13
To solve this, first, we have to change the first row for the second
1 5 1 -3
0 4 -1 -5
2 -1 3 13
Now, we multiply the first row by 2, then subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 -11 1 19
Then, we multiple the second row with -11/4 to subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 0 -7/4 21/4
The resulting system would be
[tex]\mleft\{\begin{aligned}x+5y+z=-3 \\ 4y-z=-5 \\ -\frac{7}{4}z=\frac{21}{4}\end{aligned}\mright.[/tex]We solve for z
[tex]\begin{gathered} \frac{-7}{4}z=\frac{21}{4} \\ z=\frac{21}{-7}=-3 \end{gathered}[/tex]Therefore, z is equal to -3.
We use z to find y in the second equation.
[tex]\begin{gathered} 4y-(-3)=-5 \\ 4y+3=-5 \\ 4y=-5-3 \\ 4y=-8 \\ y=\frac{-8}{4}=-2 \end{gathered}[/tex]Therefore, y is equal to -2.
We use y and z to find x in the first equation.
[tex]\begin{gathered} x+5(-2)+(-3)=-3 \\ x-10-3=-3 \\ x=-3+10+3=10 \end{gathered}[/tex]Therefore, x is equal to 10.
guys can u help me with this question, please
The cross marked at the points (-2.5 , -5) and (0 , -1.5) is shown below .
The x and y coordinate helps in identifying a point in the coordinate axis and it is written as a ordered pair (x,y) .
where x represents the position of point with reference to the x-axis
and y represents the position of point with reference to the y axis .
In the question ,
points are given , we have to plot them and mark a cross .
Part(a)
point is (-2.5 , -5)
So , the x coordinate is -2.5
means the point is 2.5 units left from the origin ,
and y coordinate is -5 .
means the point is 2.5 units down from the origin .
the cross mark on the point is shown below .
Part(b)
point is (0 , -1.5)
So , the x coordinate is -2.5
means the point is 0 units units from the origin ,
and y coordinate is -1.5 ,
means the point is 1.5 units down from the origin .
the cross mark on the point is shown below .
Therefore , The cross marked at the points (-2.5 , -5) and (0 , -1.5) is shown below .
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7/10 3/10 solve complex fraction
The value of the complex fraction 7/10/3/10 is
2 1/3
What is a complex fraction?A fraction is made up of two parts, a numerator and a denominator; the number above the line is the numerator and the number below the line is the denominator. The line or slash in that separates the numerator and the denominator in a fraction represents division.
A complex fraction can be defined as a fraction in which the denominator and numerator or both contain fractions. For example( 5/2)/(6/4).
Therefore the fraction (7/10)/(3/10) can be simplified as 7/10÷3/10= 7/10×10/3 = 7/3= 2 1/3
Therefore the simplified value of the complex fraction is 2 1/3.
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the basketball game had 600 people in attendance if the ratio of hawk fans to cyclone fans is 2:10 how many more cyclone fans were there
Variables:
x: hawk fans
y: cyclone fans
The basketball game had 600 people in attendance means:
x + y = 600
The ratio of hawk fans to cyclone fans is 2:10 means
[tex]\begin{gathered} \frac{x}{y}=\frac{2}{10} \\ 10x=2y \\ \frac{10x}{2}=y \\ 5x=y \end{gathered}[/tex]Substituting the last equation into the first equation, we get:
x + 5x = 600
6x = 600
x = 600/6
x = 100
And the value of y is:
y = 5*100
y = 500
There were 500 - 100 = 400 more cyclone fans
There are 348 identical plastic chips numbered 1 through 348 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 213? Express your answer as a simplified fraction or a decimal rounded to four decimal places
We have to find the probability of randomly drawing a chip number that is smaller than 213.
As the chips are numbered from 1 to 348,this probability will be equal to the proportion of chips that have a number that is less than 213.
We have 212 chips in the bag that have a number less than 213, so we can calculate the probability P as:
[tex]P=\frac{X}{N}=\frac{212}{348}=\frac{53}{87}\approx0.6092[/tex]Answer: the probability is 53/87 or approximately 0.6092.
find the area of this parallelogram in unit9yd13 yd10 yd
Given: A parallelogram with the dimension below
[tex]\begin{gathered} b=\text{base}=13yd \\ h=\text{height}=9yd \\ a=\text{slant side=10yd} \end{gathered}[/tex]To Determine: The area of the given parallelogram
The area of a paralleogram is given by the formula
[tex]A_{\text{PARALLELOGRAM}}=\text{base}\times height[/tex]Substitute the base and the height into the formula
[tex]\begin{gathered} A_{\text{PARALLELOGRAM}}=13yd\times9yd \\ A_{\text{PARALLELOGRAM}}=117yd^2 \end{gathered}[/tex]Hence, the area of the given parallelogram is 117yd²
The circumference of a circle is 24π in. What is the area, in square inches? Express your answer in terms of π.
Given
[tex]circumference\text{ of circle = 24}\pi\text{ in}[/tex]Recall that the formula for the circumference of a circle C is:
[tex]C\text{ = 2}\pi r[/tex]Using the formula, we can find the radius of the circle as shown:
[tex]\begin{gathered} 2\pi r\text{ = 24}\pi \\ Divide\text{ both sides by 2}\pi \\ r\text{ = }\frac{24\pi}{2\pi} \\ r\text{ = 12 in} \end{gathered}[/tex]The area A of a circle can be found using the formula:
[tex]A\text{ = }\pi r^2[/tex]Substituting the value obtained:
[tex]\begin{gathered} A\text{ = }\pi\text{ }\times\text{ 12}^2 \\ =\text{ 144}\pi\text{ in}^2 \end{gathered}[/tex]The area is 144π square in
Find the distance between the two points.|(1,4)✓ [?](-2,-3)Enter the number thatgoes beneath theradical symbol.Enter
The distance between two points is given as;
[tex]D=\sqrt[]{(y_2-y_{1_{}})^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} \text{Where x}_1=-2 \\ y_1=-3 \\ x_2=1 \\ y_2=4 \end{gathered}[/tex][tex]\begin{gathered} D=\sqrt[]{(4-(-3)^2+(1-(-2)^2} \\ D=\sqrt[]{7^2+3^2} \\ D=\sqrt[]{49+9} \\ D=\sqrt[]{58} \end{gathered}[/tex]The number beneath the radical symbol is 58.
Combined gas law
Please reply with the steps, I'm confused
Answer:
V₂ = 1.0 L
Step-by-step explanation:
Combined Gas Law
[tex]\sf \dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}[/tex]
where:
P₁ is the initial pressure.V₁ is the initial volume.T₁ is the initial temperature.P₂ is the final pressure.V₂ is the final volume.T₂ is the final temperature.Temperature must be in kelvins (K).
To convert Celsius to kelvins, add 273.15.
Volume can be in any unit.
Given values:
P₁ = 5 atmV₁ = 1 LT₁ = 300 KP₂ = 10 atmT₂ = 600 KRearrange the equation to isolate V₂:
[tex]\implies \sf V_2=\dfrac{P_1V_1T_2}{P_2T_1}[/tex]
Substitute the given values into the equation:
[tex]\sf \implies V_2=\dfrac{5 \cdot 1 \cdot 600}{10 \cdot 300}[/tex]
[tex]\sf \implies V_2=\dfrac{3000}{3000}[/tex]
[tex]\sf \implies V_2=1.0\;L[/tex]
Therefore, the volume of V₂ is 1.0 L.
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Can someone help me on this I’m confused
Step-by-step explanation:
if the goal is to have both numbers with denominator 6, then the first one is totally simple :
3 1/6 = 3 1/6
what else could it be ... ?
and the second, well, how many thirds are in a whole ?
right, 3, that's why we call them "thirds".
how many 6ths are in a whole ?
right, 6.
do you notice something ? it is easy to get from 3 to 6 by multiplying 3 by 2.
in order to keep the overall value of a fraction unchanged, when we multiply one part of the fraction by something we need to multiply the other part by the same number too.
so,
5 2/3 = 5 2/2×2/3 = 5 4/6
in short : yes, every third contains 2 6ths.
therefore, 2/3 = 4/6
What is the difference between, obtuse, right, and scalene angles?
Answer:
Obtuse angles are angles with a measure over 90 degrees.
Right angles are angles with a measure of exactly 90 degrees.
A scalene triangle can be defined as a triangle whose all three sides have different lengths, and all three angles are of different measures. The angles of a scalene triangle follow the angle sum property and always add up to 180.
Step-by-step explanation:
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
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Answer:
Diagonal = 9m
Step-by-step explanation:
area of a rectangle=L×W.-----------(I)
L=2W---------------(ii)
from (1)
32=2W×W
32=2W²
W²=32/2
W²=16
W=√16
W=4
from (ii)
length(L)=2W=2(4)=8m
Width(W)=4m
ii)Diagonal of a rectangle involves the use of Pythagoras theorem
Hyp²=opp²+Adj²
Hyp²=8²+4²
Hyp²=64+16
Hyp²=80
Hyp=√80
Hyp=8.94427191
Hyp=9m
:-The diagonal =9m
Which number lines have a point that is equal to point
P? Check all that apply.
←
H
-
-60
-60
-60
-60
0
0
0
0
0
Answer:
Step-by-step explanation:
-60 -60 -60 0 0
1/3b+11/18 when b=1/6
To answer this question, we have that the expression is:
[tex]\frac{1}{3}b+\frac{1}{18}[/tex]Answer:
Solve for b by simplifying both sides of the equation, then isolating the variable. Exact Form:
b = 3/17 Decimal Form: b=0.17647058
Step-by-step explanation:
14 08.08LCChoose the brand of chips with the lowest price per ounce.Brand A 20 ounces for $2.50Brand 6 32 ounces for $3.25 (1 point)O Brand ABrandBoth brands have the same price per ounce.Not enough information is given
Brand 6
1) In this problem, we need to find the unit rate. So let's do it and then compare for both brands
2) Brand A
[tex]\begin{gathered} 20oz----2.5 \\ 1oz-----x \\ 20x=2.5 \\ \frac{20x}{20}=\frac{2.5}{20} \\ x=\$0.125 \end{gathered}[/tex]So for Brand A, 1 oz is approximately 13 cents ( rounding up to the nearest hundredth)
3) Brand 6
We can write out another proportion:
[tex]\begin{gathered} 32oz----3.25 \\ 1oz----y \\ 32y=3.25 \\ \frac{32y}{32}=\frac{3.25}{32} \\ y=\$0.101 \end{gathered}[/tex]So brand 6, 1 oz is approximately 10 cents.
I need help with this check the picture
The numbers 7 in the domain and 10 in the range don't belong there.
Describe the domain and range of a function.The domain is the set of values over which the provided function is defined. The range is the set of all values that the function that is provided can return.
How are intervals in numbers understood?[a,b] refers to all values between a and b as well as a and b themselves.
With the exception of b, all values between a and b are referred to as (a,b).
We cannot write about them since we cannot include infinity or negative infinity since they are symbols for arbitrary enormous or tiny numbers, respectively.
Another thing to keep in mind is that when we plot functions, the inputs are typically on the x-axis and the outputs are typically on the vertical axis (y-axis).
Given : (2,7). (8, 12). (5,9). (10.15)
Domain: The initial value of numbers will always apply; 2, 8, 5, 10
Range: Numbers will always have a second value; 7, 12, 9, 15.
What you have here is :
Domain: (2,5, 7, 8, 10)
Range: (7.9. 10. 12. 15)
The problem is that 10 is in the range but 7 is in the domain. They shouldn't be there, those two. There is also an additional number there that you have. Only 4 digits should be in the Domain and Range. Given that there are four sets or pairs of values.
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26,862 divided by 407
Answer:
66
Step-by-step explanation:
it is 66
can someone help me with this assignment
Answer:
6
Step-by-step explanation:
On the coordinate plane, it shows that the y axis is 6. Therefore, (16, 6)
Answer:
5
Step-by-step explanation:
Find the measure of the angle between the two vectors.
7) u = (6,-2)
v = (8,-8)
9) u =(2, 6)
v = (-5, -8)
8) u = (-2, 3)
v = (4, -6)
10) u = (-9, 4)
v = (-7, -1)
Answer:
780
Step-by-step explanation:
graph the function, not by plotting points, but by starting from the graph of y=e^x in the figure below.
the function is: y= e^-x -1
?? I need help finding the asymptote??
The given function has a horizontal asymptote and the equation of the horizontal asymptote is y = -1.
What is an asymptote of a function?
An asymptote is a line that a function's graph approaches as x or y approaches positive or negative infinity. Asymptotes are classified into three types: vertical, horizontal, and oblique. That is, the function approaches positive or negative infinity as approached from either the positive or negative side.
The given function is [tex]y=e^{-x}-1[/tex]
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y = -1
Horizontal Asymptote: y = -1.
The graph of the function [tex]y=e^{-x}-1[/tex] can be drawn as
Hence, the given function has a horizontal asymptote and the equation of the horizontal asymptote is y = -1.
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A science teacher prepares an activity for her class. She cuts 3/4 yard of ribbon into 6 pieces of equal size. Write and solve an equation to find the length of each piece of ribbon.
The equation that represents the given situation will be (x=3/4÷6) and the length of each piece of ribbon will be 1/8 yards.
What is an equation?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, the equation that recipients the given situation:
The ribbon is 3/4 yards.Cuts into 6 equal pieces.Then, the equation will be:
x = 3/4 ÷ 6Now, calculate the equation for x as follows:
x = 3/4 ÷ 6x = 3/4 × 1/6x = 1/4 × 1/2x = 1/8
Therefore, the equation that represents the given situation will be (x=3/4÷6) and the length of each piece of ribbon will be 1/8 yard.
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The rectangle below has an perimeter of 50 units.2x - 2What is the length, in units, of the shorter side?
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
From the diagram,
length = 2x - 2
width = x
Perimeter = 50
Thus,
50 = 2(2x - 2 + x)
Dividing both sides of the equation by 2, it becomes
50/2 = 2x + x - 2
25 = 3x - 2
3x = 25 + 2 = 27
x = 27/3
x = 9
The length of the shorter side is 9