Remember that the formula for a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]PART A:
With the data given, the formula for the sequence is:
[tex]a_n=11_{}\cdot4^{n-1}[/tex]PART B:
[tex]\begin{gathered} a_1=11\cdot4^{1-1}\rightarrow a_1=11 \\ a_2=11\cdot4^{2-1}\rightarrow a_2=44 \\ a_3=11\cdot4^{3-1}\rightarrow a_3=176 \\ a_4=11\cdot4^{4-1}\rightarrow a_4=704 \\ a_5=11\cdot4^{5-1}\rightarrow a_5=2816 \end{gathered}[/tex]PART C:
For part A, we took the general formula for the geometric sequence and plugged in the first term and the common ratio provided.
For part B, we replaced n for all the numbers from 1 through 5 to get the first 5 terms of the sequence.
In the diagram, GH bisects ∠FGI.Solve for x and find m∠FGH.a. X=b. Find m∠HGI.C. Find m∠FGI.(Simplify your answer.)
Answer:
(a)19 degrees
(b)29 degrees
(c)58 degrees
Explanation:
If GH bisects ∠FGI, it means it divides it into two equal parts ∠FGH and ∠HGI.
[tex]\begin{gathered} m\angle FGH=m\angle\text{HGI} \\ (2x-9)^0=(3x-28)^0 \end{gathered}[/tex](a)We solve the equation above for x.
[tex]\begin{gathered} 3x-2x=-9+28 \\ x=19 \end{gathered}[/tex](b)
[tex]\begin{gathered} m\angle HGI=3x-28 \\ =3(19)-28 \\ =57-28 \\ =29^0 \end{gathered}[/tex](c)
[tex]\begin{gathered} m\angle FGI=2\times m\angle HGI \\ =2\times29^0 \\ =58^0 \end{gathered}[/tex]Find the amount of interest and the monthly payment for the loan described.
Purchase of a living room set for $2,700 at 12% add-on interest for 3 years
The amount of interest is $972 and monthly payment is $102.
What is Simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Given that, a loan described as purchase of a living room set for $2,700 at 12% add-on interest for 3 years
SI = P*R*T/100
SI = 2700*12*3/100 = $972
Amount to be paid = $972+$2,700 = $3672
Amount to be paid monthly = $3672/3*12 = $102
Hence, The amount of interest is $972 and monthly payment is $102.
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The diameter of a circle is 12 meters. What is the area of a sector bounded by a 102° arc?Give the exact answer in simplest form.
Answer:
The area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]Explanation:
The Area of a sector can be calculated using the formula;
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Where:
A = area of the sector
Angle theta = the angle bounding the sector
r = radius
Given:
[tex]\begin{gathered} \theta=102^0 \\ r=\frac{\text{diameter}}{\text{2}}=\frac{12m}{2}=6m \\ r=6m \end{gathered}[/tex]substituting the given values, we have;
[tex]\begin{gathered} A=\frac{102}{360}\times\pi(6^2) \\ A=10.2\pi m^2 \\ A=32.04m^2 \end{gathered}[/tex]Therefore, the area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]
1. Here is an inequality below: Select ALL of the values that are a solutionto the inequality.*72 +62<3r+2X=-3X-2X = -1X=0x= 1x = 2X = 3
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given inequality
[tex]\frac{7x+6}{2}\le3x+2[/tex]STEP 2: Solve for x
[tex]\begin{gathered} \frac{7x+6}{2}\le3x+2 \\ \mathrm{Multiply\: both\: sides\: by\: }2 \\ 7x+6\le2(3x+2) \\ 7x+6\le\: 6x+4 \\ \mathrm{Subtract\: }6\mathrm{\: from\: both\: sides} \\ 7x+6-6\le\: 6x+4-6 \\ \text{By simplification,} \\ 7x\le\: 6x-2 \\ \mathrm{Subtract\: }6x\mathrm{\: from\: both\: sides} \\ 7x-6x\le\: 6x-2-6x \\ x\le\: -2 \end{gathered}[/tex]STEP 3: Select the values that are a solution to the inequality
[tex]\begin{gathered} \text{ Since }x\le-2,\text{ this means that x is less than or equal to -2} \\ \text{This implies that all values less than or equal to 2 are a solution to the inequality} \\ \text{Looking at the options, the values that are less than or equal to 2 are:} \\ x=-3,x=-2 \end{gathered}[/tex]Hence, the values that are a solution to the inequality are:
what is the area of triangle Givenchy height 137 and base 203
the area is calculated according to:
[tex]area=\frac{1}{2}\times203\times137=13,905.5[/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:
A polynomial has one root that equals 2 + i. Name one other root of thispolynomial.
In a polynomial, if it has an imaginary root, then it also has the conjugate of that root. In this case, since 2 + i, is a root then 2 - i, is also a root.
Select the recursive and explicit formula for the Arnold family 2 answer
ANSWER:
[tex]\begin{gathered} A\left(n\right)=a_{n-1}\times 2 \\ A\left(n\right)=0.05\cdot\left(2\right)^{n-1} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the Arnolds family are going to save a nickel on the first day of the month and then double the amount each day.
One nickel is equal to $0.05, therefore, we can make an recursive formula, it is a geometric sequence where the initial value is 0.05 and the ratio is equal to 2, because it doubles every day, therefore:
[tex]A(n)=0.05\cdot(2)^{n-1}[/tex]Now, from the above we can deduce the explicit formula, since the next value will be double the previous value, therefore, the explicit formula would be:
[tex]A(n)=a_{n-1}\times2[/tex]Therefore, the correct answers are the 1st and 4th options.
help me Plss Im begging you
Answer:
2:1
Step-by-step explanation:
No of hydrogen atoms = 4
No of carbon atoms = 2
Ratio of hydrogen atoms to carbon atoms mean that the no of hydrogen atoms need to be divided by the no of Carbon atoms
that is 4/2 = 2/1 = 2 : 1
Perform the indicated operation numbers be sure to express your answer in reduced form
We need to calculate the following sum:
[tex]\frac{8}{15}+\frac{7}{25}[/tex]The first step is to calculate the least common multiplier between the two denominators. This is done below:
[tex]\begin{gathered} 15=3\cdot5 \\ 25=5\cdot5 \end{gathered}[/tex]We broke down the two denominators into their factors, now we need to multiply the factors that are unique. This is done below:
[tex]\text{LCM}=3\cdot5\cdot5=75[/tex]Now we have to replace the denominators by 75 and calculate new numerators. The new numerators must be calculated as follows:
1 - Divide the LCM by the old denominator
2 - Multiply the result of 1 by the old numerator.
This is done below:
[tex]\begin{gathered} \frac{5\cdot8}{75}+\frac{3\cdot7}{75} \\ \frac{40}{75}+\frac{21}{75} \end{gathered}[/tex]Since both fractions have their denominators with the same value, we can just directly add them.
[tex]\frac{40+21}{75}=\frac{61}{75}[/tex]The fraction is already in its most reductable form, therefore the answer is 61/75.
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).
Decide whether the relation defines y as a function of x. Give the domain. x+2y=——— 5A) Does the equation describe y as a function of x?1. Yes2. NoB) Give the domainThe domain is _____
Answer:
A) 1.yes
B) The domain is All real numbers.
Explanation:
The problem gives us a relationship:
[tex]y=\frac{x+2}{5}[/tex]For this relationship to be a function, for each value of x, we should get a single value of y. We can see that this is true, given a value of x, we get a unique value of y. Thus, A is true.
Now, we need to find the domain. The domain is the set of all values of x for which the function is defined. In this case, the function is a line:
[tex]\begin{gathered} y=\frac{x+2}{5} \\ . \\ y=\frac{x}{5}+\frac{2}{5} \\ . \\ y=\frac{1}{5}x+\frac{2}{5} \end{gathered}[/tex]The equation is a line with slope 1/5 and y-intercept 2/5. We know that any line is defined for all real numbers.
Thus, the domain is all real numbers.
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.
Question 2 (5 points) (04.01 LC) Simplify +5x+6 X+2
A x²+1
B x²-1
C X +3
D X-3
[tex]\bf{\dfrac{x^{2} +5x+6 }{x+2} }[/tex]
Rewrite the term.
x² + 2x + 3x + 6
Group the terms into two fractional parts.
(x² + 2x + (3x + 6)
Factor the expression
x(x + 2) + 3 (x + 2)
[tex]\boldsymbol{\sf{\dfrac{(\not{x+2)(x+3)}}{\not{x+2}}=x+3 \to Option \ C }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{\cfrac{x {}^{2} + 5 x + 6 }{x + 2} }[/tex]
Answer :
Note: To solve a problem like this, we must first determine which of the two numbers add 5 and multiply 6, we know that they are 2 and 3 and then we must Rewrite the expression using the above.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{(x+2)(x+3)}[/tex]
Now, we must put a fraction since we can more easily solve the problem posed.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \cfrac{(x + 2)(x + 3)}{x + 2} }[/tex]
Now the last thing we have to do is Cancel [tex]\bold{x+2}[/tex] to have a final result that is the following:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x+3}[/tex]
For each row of the table, choose the equivalent expression
Ok, so:
Let's make all operations and then choose the equivalent expression for each one.
Let's start in order:
a. 4/12 + 4/12 = 8/12
b. 1/12 + (3/12 + 3/12) = 7/12
c. 4/12 + 5/12 = 9/12
d. 2/12 + 2/12 + 2/12 = 6/12.
Notice that the last operations are the columns of the table.
So, let's do it the same with the upper rows:
e. 5/12 + 4/12 = 9/12
f. (1/12 + 3/12) + 3/12 = 7/12
g. 1/12 + 2/12 + 3/12 = 6/12
h. 15/12 - 7/12 = 8/12.
Now, let me draw the table to make this problem more understandable.
This is the order you have to put the answer:
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
find the length of each chord. horizontal chord and vertical
Consider the circle
we have the intersecting chords theorem, which states that
[tex]a\cdot b=c\cdot d[/tex]In our case we have a=x, b=12, c=6 and d=x+4. So we have
[tex]12\cdot x=6\cdot(x+4)[/tex]distributing on the right side we get
[tex]12\cdot x=6x+6\cdot4=6x+24[/tex]Subtracting 6x on both sides, we get
[tex]24=12x\text{ -6x=6x}[/tex]Dividing boht sides by 6, we get
[tex]x=\frac{24}{6}=4[/tex]So, the value of x is 4. Now we replace this value to find the length of each chord, so we have
x---->4
12---->12
x+4----->4+4=8
6----->6
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.
Bea crió algunas vacas y algunos pavos. Crió un total de 28 vacas y pavo. habia 96 patas en total cuantas vacas y cuantos pavos crió bea?
1) Coletando los datos:
Vacas: v
Pavos: p
p+v =28
2p+4v=96 Como las vacas tienen 4 patas e los pavos tienen 2 patas
2) Multiplicando por - 2, la primera ecuación
-2p -2v =-56
2p +4v =96
-------------------
2v = 40
v= 20
3) Substituindo en la primera ecuación
p +20 =28
p =28 -20
p=8
Entonces, había 20 vacas y 8 perus
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]Cindy has a jacket with the first letter of her school's name on it. determine the area of the letter on Cindy's jacket.
To find the area of the letter, use the area of a rectangle formula below:
Area = Length x Width
Find the
Total area = ( 10 x 2) + (6 x 2) + (6 x 2)
= 20 + 12 + 12
= 44 in²
Therefore, the area of the letter on Cindy's jacket is 44 in²
ANSWER:
44 in²
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
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The baghrams make regular monthly deposits in a savings account. The graph shows the relationship between the numbers x of months and the amount y in dollars in the account.what is the equation for the deposit?A- y/x = $40/monthB- y/x = $25/monthC- y/x = $50/monthD- y/x = $75/month
The two point throught which line passes are (2,100) and (4,200).
Determine the equation of line passes through the points.
[tex]\begin{gathered} y-100=\frac{200-100}{4-2}(x-2) \\ y-100=50(x-2) \\ y=50x-100+100 \\ y=50x \\ \frac{y}{x}=50 \end{gathered}[/tex]T
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
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
11. Reflect quadrilateral CONE with C(5,1), 0(1,6),N(-7,0) and E(-2,-4) in the line y = -2.
Step 1
y = -2 is the mirror line.
Step 2
The graph below shows the result after reflection about y = -2.
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.
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
Joni took out a loan for $21,912. To pay it back, she will make 42 monthly paymentsof $931. How much will he pay in interest? Round answer to a whole number.
Given:
Loan of $21,912
42 monthly payments of $931.
Find amount of interest.
First, find the total amount that Joni will pay.
[tex]42\times\$931=\$39,102[/tex]Next, subtract the result by the amount of loan
[tex]\$39,102-$\$21,912=$\$17,190[/tex]Therefore, Joni will pay $17,190 in interest.
Jeff receive six dollars for each hour he babysits how much money will just make after six hours eight hours 10 hours in 12 hours right the function and then find each answer to the correct function table that matches this situation
Jeff receive six dollars for each hour he babysits
Function:
f(x) = 6x
Where x is the number of hours
for 6 hours:
F(6) = 6(6) = 36
For 8 hours:
F(8)= 6(8) = 48
For 10 hours:
F(10)= 6(10)= 60
For 12 hours:
F(12)=6(12)=72