Given the first four terms of this sequence:
[tex](5120,1280,320,80,\ldots)[/tex]We can see a pattern. To analize this pattern, let's first check the difference between those terms.
[tex]\begin{gathered} 5120-1280=3840 \\ 1280-320=960 \\ 320-80=240 \end{gathered}[/tex]From those differences, we can verify the following equations:
[tex]\begin{gathered} 3840=4(960) \\ 960=4(240) \end{gathered}[/tex]From this, we can write the general rule for this sequence:
[tex]a_n=\frac{5120}{4^{n-1}}[/tex]This sequence gives us:
[tex]\begin{gathered} a_1=5120 \\ a_2=1280 \\ a_3=320 \\ a_4=80 \\ a_5=20 \\ a_6=5 \\ a_7=1.25 \end{gathered}[/tex]Then, we have the following 3 terms. (20, 5, 1.25)
Back | Next Question 2 Indicate the answer choice that best completes the statement or answers the question. Determine if the two figures are congruent by using transformations. Explain your reasonin a. congruent; a rotation followed by a reflection Ob. congruent; a reflection followed by another reflection Oc. congruent; a reflection followed by translation O d. not congruent
b. congruent; a reflection followed by another reflection
If grey shape is reflected across the x-axis and then the y-axis, or viceversa, white shape is obtained.
Write the series using sigma notation to find the sum of the termsDrag the tiles to the correct location is not a tiles will be used
The number over the sigma sign is 5
Explanation:
5 represent the finale value
For each ordered pair, determine whether it is a solution to the system of equations -5x+4y=2. 3x-5y=4 solution? (x, y) (6,8) it is a solution yes or no. (-4,-4) it is a solutions yes or no. (-7,0) it is a solution yes or no. (3,1) it is a solution yes or no
Check the solutions
(6,8)
(-4,-4)
(-7,0)
(3,1)
To check if the pair is a solution to teh system of equations you must replace x and y on both of the equations and see if the equation is fulfilled
(6,8) Is not a solution to the system of a solutions
[tex]\begin{gathered} \begin{aligned}-5(6)+4(8)=2 \\ 3(6)-5(8)=4\end{aligned} \\ \\ -30+32=2\longrightarrow2=2 \\ 18-40=4\longrightarrow-22\ne4 \end{gathered}[/tex](-4,-4) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(-4)+4(-4)=2 \\ 3(-4)-5(-4)=4\end{aligned} \\ \\ 20-16=2\longrightarrow4\ne2 \\ -12+16=4\longrightarrow4=4 \end{gathered}[/tex](-7,0) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(-7)+4(0)=2 \\ 3(-7)-5(0)=4\end{aligned} \\ \\ 35+0=2\longrightarrow35\ne2 \\ -21-0=4-21\ne4 \end{gathered}[/tex](3,1) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(3)+4(1)=2 \\ 3(3)-5(1)=4\end{aligned} \\ \\ -15+4=2\longrightarrow-11\ne2 \\ 9-5=4\longrightarrow4=4 \end{gathered}[/tex]When planning a cruise, you have a choice of 2 destinations: Cozumel (C) or Jamaica (J); a choice of 4 types of rooms: balcony (B), inside view (I), ocean view (O), or suite (S); and a choice of 2 types of excursions: water sports (W) or horseback riding (H). If you are choosing only one of each, list the sample space in regard to the vacations (combinations of destinations, rooms, and excursions) you could pick from.
Given
There are 2 options for a destination: Cozumel (C) or Jamaica (J)
There are 4 types of rooms : Balcony (B), Inside View (I), Ocean View (O), Suite (S)
There are two types of excursions : Water sports (W) or Horseback (H)
The sample space is a combination of all the available options and can be calculated using the formula:
[tex]\begin{gathered} Sample\text{ space = Number of options for A }\times\text{ Number of options for B }\times \\ Number\text{ of options C} \end{gathered}[/tex]Applying the formula:
[tex]\begin{gathered} Sample\text{ space = 2 }\times\text{ 4 }\times\text{ 2} \\ =\text{ 16 } \end{gathered}[/tex]The list of the combinations is shown below:
CBW, CBH, CIW, CIH , COW, COH, CSW, CSH, JBW, JBH, JIW, JIH, JOW, JOH, JSW, JSH
write a linear equation that has m=4 and has an x intercept of (5,0)
the equation is of the form y = mx + b, then
for b:
[tex]\begin{gathered} 0=4(5)+b \\ 0=20+b \\ 0-20=20+b-20 \\ b=-20 \end{gathered}[/tex]the equation is:
[tex]y=4x-20[/tex]Can you please me with the question on the picture
Solution
[tex]\begin{gathered} \text{Total marbles= 6+}5+4_{} \\ \text{Total marbles =15 marbles} \end{gathered}[/tex]6blue marbles
5 red marbles
4 white marbles
Part A
Formula
Not white means it blue or 5 = 11
[tex]P(\text{Blue given not white)}=\frac{P(B\text{ n W)}}{P(W)}=\frac{\frac{6}{15}\times\frac{6}{15}}{\frac{11}{15}}=\frac{6}{15}[/tex]Part B
A figure has an area of 100 units `2 what will the new area be after dilation with a scale factor of 2\5
16 u²
1) If a figure has an area and it's been dilated of k= 2/5
2) Then we can sketch that situation, concerning to areas:
So, we can state this dilated figure is going to have an area of 16 u².
Hence, the answer is 16 u²
What is the length of the hypotenuse of the right triangle with coordinates:(-2, -1), (-6,5), and (4, 3)?
ANSWER:
10.2 units
STEP-BY-STEP EXPLANATION:
The first thing is to make a sketch of the triangle formed in the Cartesian plane, like this:
The hypotenuse is the side opposite the right angle, therefore, it would be the side from the point (-6, 5) to the point (4, 3).
We calculate the distance between these two points using the following formula:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]We replace and calculate the length of the hypotenuse:
[tex]\begin{gathered} d=\sqrt{\left(4-\left(-6\right)\right)^2+\left(3-5\right)^2} \\ d=\sqrt[]{(4+6)^2+(3-5)^2} \\ d=\sqrt[]{(10)^2+(-2)^2} \\ d=\sqrt[]{100+4} \\ d=\sqrt[]{104} \\ d\cong10.2 \end{gathered}[/tex]The length of the hypotenuse is 10.2 units.
Use substitution to solve.Solve the first equation for y and substitute it into the second equation. The resulting equati
The first equation is given as,
[tex]\begin{gathered} 2X^2\text{ = 5 +Y} \\ Y\text{ = }2X^2\text{ - 5\_\_\_\_\_\_\_(1)} \end{gathered}[/tex]The second equation is given as,
[tex]4Y\text{ = }-20\text{ }+8X^2_{_{_{_{}}}}\text{ \_\_\_\_\_\_\_\_\_(2)}[/tex]Substituting equation ( 1 ) in equation (2),
[tex]4(\text{ }2X^2\text{ - 5) = }-20\text{ }+8X^2_{_{_{_{}}}}\text{ }[/tex]Simplifying further,
[tex]8X^2-20\text{ = -20 + }8X^2[/tex]Thus the required answer is
[tex]8X^2-20\text{ = -20 + }8X^2[/tex]I need help with a math assignment i linked the picture below with the question
Answer:
[tex]P\text{ = 29x+5}[/tex]Explanation:
Here, we want to get the perimeter of the rectangle
Mathematically, that is:
[tex]P\text{ = 2(L + B)}[/tex]Where L is the length of the rectangle, given as 6.5x + 9 ft and B is the width of the rectangle which is 8x-6.5
Substituting these values into the formula, we have the perimeter of the rectangle as follows:
[tex]\begin{gathered} P=2(6.5x\text{ + 9 +8x-6.5)} \\ P\text{ = 2(14.5x+2.5)} \\ P\text{ = 29x+5} \end{gathered}[/tex]what property do we use to check that our factored form is equivalent to the standard form
Lets solve an example:
[tex]\begin{gathered} y=x^2+6x+8 \\ \end{gathered}[/tex]this quadratic polynomial is in standard form. We can write the same polynomial in factored form as
[tex]y=(x+4)(x+2)[/tex]In the case of quadratic polynomials, a fast check is
that is, 4 plus 2 must be equal to 6 in the term 6x and
4 times 2 must be 8 in the constant term, which is 8.
A If mzABD 61, and mzDBC = 59, then mABC = [ ?P
Write each ratio in simplest form1- 300:1082- 5280:8003- 42:1204- 20:965- 24:16
Given:
1) 300:108
[tex]\begin{gathered} \frac{300}{108} \\ \text{Greatest common factor of 300 and 108 is 12.} \\ \frac{300}{108}=\frac{25\cdot12}{9\cdot12}=\frac{25}{9}\Rightarrow25\colon9 \end{gathered}[/tex]2) 5280:800
[tex]\begin{gathered} \frac{5280}{800} \\ \text{Greatest common factor of 5280 and 800 is 160.} \\ \frac{5280}{800}=\frac{33\cdot160}{5\cdot160}=\frac{33}{5}\Rightarrow33\colon5 \end{gathered}[/tex]3) 42:120
[tex]\begin{gathered} \frac{42}{120} \\ \text{Greatest common factor of 42 and 120 is 6.} \\ \frac{42}{120}=\frac{7\cdot6}{20\cdot6}=\frac{7}{20}\Rightarrow7\colon20 \end{gathered}[/tex]4) 20:96
[tex]\begin{gathered} \frac{20}{96} \\ \text{Greatest common factor of 20 and 96 is 4.} \\ \frac{20}{96}=\frac{4\cdot5}{4\cdot24}=\frac{5}{24}\Rightarrow5\colon24 \end{gathered}[/tex]5)
[tex]\begin{gathered} \frac{24}{16} \\ \text{Greatest common factor of 24 and 16 is 8.} \\ \frac{24}{16}=\frac{3\cdot8}{2\cdot8}=\frac{3}{2}\Rightarrow3\colon2 \end{gathered}[/tex]What is 5,421 rounded to the nearest hundred?A.4,000B.5,000C.5,4000D.5,200
We have the following number:
[tex]5,421[/tex]By rounding down this number to the nearest hundred, we get
[tex]5,400[/tex]which corespond to option C
i need some help on this word problem please do it for me (12)
The first thing we need to do is identify the important values, our variables, and our equations that model or describe our problem.
• A total of 560 tickets were sold.
• Tickets can be ,A,dult or ,S,tudent
[tex]A+S=560\to(1)[/tex]• The total of tickets sold $3166
,• The value of the Adult ticket is $8
,• The value of the Student ticket is $3.5
[tex]8A+3.5S=3166\to(2)[/tex]We can see that A and S correspond to the number of Adult or Student tickets sold. We solve the equations to find our numbers.
[tex]A=560-S\to\text{(1)}[/tex][tex]\begin{gathered} 8(560-S)+3.5S=3166 \\ 8\times560-8S+3.5S=3166 \\ S(3.5-8)=3166-4480 \\ -4.5S=-1314 \\ S=\frac{-1314}{-4.5} \\ S=292 \end{gathered}[/tex][tex]\begin{gathered} A=560-292 \\ A=268 \end{gathered}[/tex]In total, 292 Student tickets and 268 Adult tickets were sold.I need the answer as fast as you can give it to me
Explanation
Given
[tex](256x^{16})^{\frac{1}{4}}[/tex]We can simplify the expression below;
[tex]\begin{gathered} =256^{\frac{1}{4}}\times x^{16\times\frac{1}{4}} \\ =\sqrt[4]{256}\times x^{\frac{16}{4}} \\ =4x^4 \end{gathered}[/tex]Answer:
An archer hits a bullseye 64% of the time. What is the probability the archer hitsthe bullseye exactly 4 times during 10 total attempts?a. 242b. .365C..077d. 168
If the probability of hitting the bullseye is 64% (P(H) = 0.64), then the probability of not hitting the bullseye (P(H_bar)) is:
[tex]P(\bar{H})=1-P(H)=1-0.64=0.36[/tex]Now, if we have 10 attempts, and the archer hits 4 times, then he misses 6 times.
So we have 4 cases of hitting (P(H)) and 6 cases of not hitting(P(H_bar)), and the probability is the product of the probabilities of each case:
[tex]P=P(H)^4\cdot P(\bar{H})^6=(0.64)^4\cdot(0.36)^6=0.16777\cdot0,0021767=0\text{.}0003652[/tex]We also need to multiply this probability by a combination of 10 choose 4, because the 4 hits among the 10 attempts can be any of the 10, in any order:
[tex]C(10,4)=\frac{10!}{4!(10-4)!}=\frac{10!}{4!6!}=\frac{10\cdot9\cdot8\cdot7}{4\cdot3\cdot2}=210[/tex]So the final probability is:
[tex]P^{\prime}=P\cdot C(10,4)=0.0003652\cdot210=0.077[/tex]So the answer is C.
can you please help me
We have two types of crust, each of them with a different type of sauce and choice of toppings. The answer would be 54 single topping pizzas because we have two types of crust for 3 types of sauce 2*3 = 6
and 9 choices of toppings for each of them 6*9 = 54
If possible, find the area of the triangle defined by the following: a = 7, b = 4, y = 43°9.5 square units19.3 square units14 square units16.8 square units
So C = 180 - 23.7 - 35
= 121.3°
[tex]\begin{gathered} \text{ }\frac{C\text{ }}{\sin\text{ C}}\text{ = }\frac{B}{\sin \text{ B}} \\ \frac{C}{\sin\text{ 121.3}}\text{ = }\frac{100}{\sin \text{ 35}} \\ \text{ C = }\frac{100\sin \text{ 121.3}}{\sin \text{ 35}} \\ C\text{ = }\frac{85.44}{0.57} \\ C\text{ = 150 mi} \end{gathered}[/tex]3x=4 1/2 I need help to solve for x
We need to solve the equation:
[tex]3x=4\frac{1}{2}[/tex]First, notice that the mixed number 4 1/2 can be written as:
[tex]4\frac{1}{2}=4+\frac{1}{2}[/tex]Now, we can solve the equation for x by dividing both sides of the equation by 3. We obtain:
[tex]\begin{gathered} \frac{3x}{3}=\frac{\mleft(4+\frac{1}{2}\mright)}{3} \\ \\ x=\mleft(4+\frac{1}{2}\mright)\cdot\frac{1}{3} \\ \\ x=4\cdot\frac{1}{3}+\frac{1}{2}\cdot\frac{1}{3} \\ \\ x=\frac{4}{3}+\frac{1}{6} \\ \\ x=\frac{8}{6}+\frac{1}{6} \\ \\ x=\frac{9}{6} \\ \\ x=\frac{3}{2} \\ \\ x=1\frac{1}{2} \end{gathered}[/tex]Therefore, the solution is:
[tex]\mathbf{x=1\frac{1}{2}}[/tex]Answer:
Exact form:
x = 3/2
decimal form:
x = 1.5
mixed number form:
x = 1
1/2
Step-by-step explanation:
What is the volume of the solid?8 cm12 cm12 cm16 cm2 cmWe talenteΟ Α112 cubic cmОв192 cubic cmОс224 cubic cmOD304 cubic cm
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
diagram:
solid
Step 02:
geometry:
volume:
we must analyze the figure to find the solution.
volume solid 1:
rectangle:
V = l * w * h
V1 = 12 cm * (16 cm - 12 cm) * 2 cm = 12 cm * 4 cm * 2 cm = 96 cm³
volume solid 2:
rectangle:
V = l * w * h
V2 = 12 cm * 2 cm * (16 cm - 8 cm) = 12 cm * 2 cm * 8 cm = 192 cm³
Total volume:
VT = V1 + V2 = "96 cm + ³192 cm = ³
Use the specified row transformation to change the given matrix.6R_1+R_2
ANSWER:
[tex]6\cdot R_1+R_2=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}[/tex]STEP-BY-STEP EXPLANATION:
We have the following matrix:
[tex]\begin{bmatrix}{1} & 5 & {4} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{cases}R_1 \\ R_2 \\ R_3\end{cases}[/tex]Now, we apply the following changes
[tex]\begin{gathered} 6\cdot R_1+R_2 \\ 6\cdot R_1=\begin{bmatrix}{6\cdot1} & 6\cdot5 & 6\cdot{4} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{bmatrix}{6} & 30 & {24} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \\ 6\cdot R_1+R_2=\begin{bmatrix}{6+(-6)} & 30+9 & {24+(-1)} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \\ 6\cdot R_1+R_2=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \end{gathered}[/tex]I need some help on finding the surface area. i don't know how to solve with a triangular base?
The surface area(A) of a triangular pyramid can be found using the formula:
[tex]A\text{ = }\frac{1}{2}\text{ }\times\text{ a }\times\text{ b + }\frac{3}{2}\text{ }\times b\text{ }\times\text{ s}[/tex]Given the triangular prism:
Hence, we have:
a = 3.5 m
b = 4m
s = 11.1 m
Substituting the values into the formula:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times3.5\text{ }\times4\text{ + }\frac{3}{2}\text{ }\times\text{ 4 }\times\text{ 11.1} \\ =\text{ 7 + 66.6} \\ =\text{ 73.6 m}^2 \end{gathered}[/tex]Hence, the surface area of the pyramid is 73.6 square meter
Find the area of the semicircle. Round to the nearest tenih. Use 3.14 for 3.8 yda. 22.7 yd²b. 23.9 yd²c. 45.3 yd²d. 11.9 yd²
Answer:
[tex]A[/tex]Explanation:
Here, we want to calculate the area of the semi-circle
To get this, we have to calculate the area of the circle and divide by 2
Mathematically, we have that as follows:
[tex]A\text{ = }\frac{\pi r^2}{2}[/tex]where pi is 3.14 and r which is the radius of the circle is 3.8 yd
Mathematically, we calculate the area as follows:
[tex]A\text{ = }\frac{3.14\times3.8^2}{2}\text{ = 22.7 yd}^2[/tex]Hi i have uploaded the question in the image. Equation no. 2 (ii).
Let's determine if g(x) is a factor of f(x).
[tex]\text{ f(x) }=\text{ }x^3\text{ }-3x^2+4x-4[/tex][tex]\text{ g(x) = }x\text{ - 2}[/tex]Given that g(x) = x - 2, at x = 2, let's check the value of f(x) at x = 2, If f(x) = 0, then g(x) is a factor, otherwise, g(x) is not a factor of f(x).
We get,
At x = 2,
[tex]\begin{gathered} \text{ f(x) }=\text{ }x^3\text{ }-3x^2+4x-4 \\ \text{ f(2) = (2)}^3-3(2)^2\text{ + 4(2) - }4 \\ \text{ f(2) = 8 - 12 + 8 - }4 \\ \text{ f(2) = 16 - 1}6 \\ \text{ f(2) = 0} \end{gathered}[/tex]Therefore, g(x) is a factor of f(x).
please solve this for me
The equation of the line in slope intercept form is y = -x + 6
How to write equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptThe slope of the line can be found as follows:
using (6, 0) and (5, 1)
m = slope = 1 - 0 / 5 - 6
slope = 1 / -1
slope = -1
Therefore, let's find the y-intercept of the line using (0, 6).
y = -x + b
6 = -(0) + b
b = 6
Therefore, the equation of the line is y = -x + 6
learn more on equation of a line here: brainly.com/question/28883396
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Ezra is finding the perimeter of different-sized regular pentagons. There is a proportional relationship between the side length of the regular pentagon in inches, x, and the perimeter of the regular pentagon in inches, y. The equation that models this relationship is y=5x. What is the perimeter of a regular pentagon with a side length of 2 inches? Write your answer as a whole number or decimal.
The perimeter of the regular pentagon Ezra is finding is 10m inches
How to find the perimeter of a regular pentagon with a side length of 2 inchesPerimeter refers to the total outside length of an object,
The equation given in the problem is
y = 5x
where
the side length of the regular pentagon in inches, x,
the perimeter of the regular pentagon in inches, y
if the side length is 5, we plug in 2 into the equation above
y = 5x
y = 5 * 2
y = 10 inches
Learn more about perimeter here:
https://brainly.com/question/397857
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LMNO is a rhombus find at 3s + 12 5x - 2y -6
In this case the answer is very simple. .
To find the solution to the exercise we'll have to carry out several steps.
(3x + 12) = (5x -2)
12 + 2 = 5x - 3x
14 = 2x
14 /2 = x
7 = x
The answer is:
x = 7
Write an inequality for each of the following Mrs. Champlin needs to make at least 28 costumes for the school play
ok
x = number of costumes
The inequality is:
[tex]\text{ x }\ge\text{ 28}[/tex]where "x" is the number of costumes
In the sentence given, they use the terms "at least", that means that the number must be equal or greater than 28.
In maths, there are five symbol that we can use in inequalities.
= means equal
< means less than
> means greater than
[tex]\begin{gathered} \ge\text{ means greater or equal than} \\ \leq\text{ means less or equal than} \end{gathered}[/tex]
In the sentence given, as they use at least, we must use greater or equal, it means it could be 28 or a greater number.
891 to which closer to hundred
891 is closer to 900.
Consider the following:
800, 820, 840, 860, 880, 900
891 is found between 880 and 900
Thus, the hundred 891 is closer to is 900