We will see that the first term is $50, and the common difference is $25, then the recursive formula is:
aₙ = aₙ₋₁ + $25.
How to get the recursive formula?Here we will have something like an arithmetic sequence, such that the recursive sequence is something like:
aₙ = aₙ₋₁ + d
Where d is the common difference.
We know that the first value (the first amount that she has in her savings account) is $50, so we can write the first term as:
a₁ = $50
Now, each new year (the subindex "n" represents the number of the year) $25 are added to that savings account, then we will have:
a₂ = $50 + $25 = $75
a₃ = $50 + $25 + $25 = $100
And so on..
So the common difference is d = $25, then the recursive relation is:
aₙ = aₙ₋₁ + $25.
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find f'(x) when f(x) = (x^2) - 2x. find the equation of the tangent line and the normal line at x=4
The derivate of a function f(x) is determinated as:
[tex]f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}[/tex]For the function
[tex]f(x)=x^2-2x[/tex]First we have to determine de f ( x + h ) as follow:
[tex]f(x+h)=(x+h)^2-2(x+h)[/tex][tex]f(x+h)=x^2+2xh+h^2-2x-h^{}[/tex]Then we calculate and simplify the coeficient in the first formula
[tex]\frac{f(x+h)-f(x)}{h}[/tex][tex]\frac{(x^2+2xh+h^2-2x-h^{})-(x^2-2x)}{h}[/tex][tex]\frac{x^2+2xh+h^2-2x-h^{}-x^2+2x}{h}=\frac{h^2+2xh-h}{h}[/tex][tex]\frac{h^2+2xh-h}{h}\text{ = }\frac{h(h+2x-1)}{h}=h+2x-1[/tex]So the derivate is:[tex]f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}=\lim _{h\to0}h+2x-1[/tex][tex]f^{\prime}(x)=0+2x-1[/tex][tex]f^{\prime}(x)=2x-1[/tex]------------------------------------------------------------------------------------The equation of the tangent:
First you need to know that the derivate of a function is equal to the slope (m) of the tangent of this function
And the equation to thist tangent in a specific point will be find using the next formula:
[tex]y-f(x_0)=m(x-x_0)_{}[/tex]We have to calculate the slope in the point x =4 using the derivate:
[tex]m=2x-1[/tex][tex]m=2(4)-1=7[/tex]In the point x=4
Calculate the value of f(x0) substituting in the function the given point x:
[tex]f(4)=4^2-2(4)\text{ = }8[/tex]Knowing that we put the value of m and f(x0) in the equation of the tangent:
[tex]y-8=7(x-4)_{}[/tex][tex]y-8=7x-28[/tex][tex]y=7x-28+8[/tex]So the equation of the tangent in x= 4 is:[tex]y=7x-20[/tex]---------------------------------------------------------------------------
The normal line
The slope of the normal line is the opposite of the slope of theu tangent in an espesific point:
[tex]m_n=-\frac{1}{m_t}[/tex]So in this situation is:
[tex]m_n=-\frac{1}{7}[/tex]The equation of the normal line is given by the next formula:
[tex]y-f(x_0)=m_n(x-x_0)_{}[/tex]Replacing the data we obtain:
[tex]y-8=-\frac{1}{7}(x-4)_{}[/tex][tex]y-8=-\frac{1}{7}x+\frac{4}{7}[/tex]So the equation of the normal line is:[tex]y=-\frac{1}{7}x+\frac{60}{7}[/tex]Hanna wants to buy fruit snacks to share with four of her friends. how many snacks will each person get if she shares a bag of 120 fruit snacks equally?
Answer:
are u 6 it's 30 fruit snacks
Step-by-step explanation:
120÷4(she has more friends then u lol)=30
Is 9 a factor of 76r+46s?
Answer:
No, 9 is not a factor of 76 and 46.
Step-by-step explanation:
No, 9 is not a factor of 76 and 46. 9 is a factor of 72 and 45.
I hope this helps!
work out (7.3 x 10^5) + (4x 10^5) in standard index form
The sum written in standard index form is 1.13*10^6
How to add numbers in scientific notation?
So here we want to add two numbers that are written in scientific notation, these are:
(7.3*10^5) + (4*10^5)
Now we can take the factor "10^5" as a common factor, so we can write:
(7.3*10^5) + (4*10^5) = (7.3 + 4)*10^5 = 11.3*10^5
Now we want to write this in standard index form (this is scientific notation), so we can have only one decimal on the left side of the decimal point, then we can write this as:
11.3*10^5 = 1.13*10^6
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the temperature in montreal was -15 degrees. in nyc the temperature was 11 degrees . how many degrees warmer was the temperature in nyc
at the grocery store you can get 2 bags of chips for $6 what would 10 bags cost
Answer:
10 bags would cost $30
Step-by-step explanation:
We have been given we can get 2 bags for $6
so we need to how many bags we would get for a dollar =
6/2 = 3
now we need the value for 10 bags =
10 times 3 =
$30
I have attached a image which makes the equation much more pleasing to look at, do check it out. :)
(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)
Stay positive and Take care,
A fellow mate,
Cheers !
4.66 let x represent the number that occurs when a green die is tossed and y the number that occurs when a red die is tossed. find the variance of the random variable (a) 2x − y ; (b) x 3y − 5.
The variance of each random variable is given as follows:
a) Var(2x - y) = 10.4165.
b) Var(x + 3y - 5) = 20.833.
What is the variance of random variable?The number that occurs when each dice is thrown is represented by an uniform variable, with bounds a = 1 and b = 6, hence the variance of each variable is calculated as follows:
Var(x) = Var(y) = (6 - 1)²/12 = 2.0833.
When two variables are added, the variance is calculated as follows:
Var(aX + bY) = a²Var(X) + b²Var(Y)
Hence, for item a, the variance is calculated as follows:
Var(2x - y) = 2²Var(x) + (-1)²Var(y) = 4Var(x) + Var(y)
The variances were calculated before, which are both of 2.0833, hence:
4Var(x) + Var(y) = 4 x 2.0833 + 2.0833 = 10.4165.
For item b, the variance is calculated as follows:
Var(x + 3y - 5) = Var(x) + 3²Var(y) + (-1)²Var(-5).
The variance of a constant is of zero, hence Var(-5) = 0, and then:
Var(x + 3y - 5) = Var(x) + 3²Var(y) + (-1)²Var(-5) = 2.0833 + 9(2.0833) = 20.833.
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A salesperson earns a commission of $336 for selling $2800 in merchandise find the commission rate
Answer:
12% commission rate
Step-by-step explanation:
A salesperson earns a commission of $336 for selling $2800 in merchandise find the commission rate:
336 ÷ 2,800 = 0.12
0.12 = 12% commission rate
POSSIBLE POINTS 162 + 122Which equation written below in vertex form is equivalent to the equation y = 22Oy= (x – 3)Oy= (2-6)² + 12Oy= (x+3)+ 3Oy= (2 – 3)2 +3
Given:
[tex]y=x^2-6x+12[/tex][tex]y=x^2-6x+3^2-3^2+12[/tex][tex]y=(x-3)^2-9+12[/tex][tex]y=(x-3)^2+3[/tex]prtion D is the correct answer.
Which of the following is the BEST possible first step to solve for n:
Answer:
Subtract 8 from both sides
Step-by-step explanation:
You want to isolate the term with the variable you want to solve for.
Answer:
Subtract 8 from both sides.
The probabilities of randomly picking a green counter from three different bags are given below.
Order these bags from the lowest probability to the highest probability.
Answer:
Lowest to highest
7/10 , 11/15, 4/5
Step-by-step explanation:
Probably the easiest way to do this is to convert each of the fractions to decimals which will clearly indicate which is the highest and which the lowest etc.
4/5 = 0.80
11/15 = 0.73
7/10 = 0.7
0.7 is less than 0.73 is less than 0.80
So 7/10, 11/15, 4/5
However, I am assuming they want you to work with fractions
To compare fractions you have to get all the denominators equal and then compare the numerator
To get a common denominator find the Least Common Multiple of the denominators. This is the lowest number that can be divided by all three denominators
Looking at 5, 15 and 10 we can see that 30 is divisible by each denominator. So that becomes our common denominator
Now multiply each fraction denominator by a factor to make the denominator equal to the common denominator. At the same time multiply the numerator by the same factor
4/5 = (4 x 6) / (5 x 6) = 24/30 Highest
11/15 = (11 x 2) / (15 x 2) = 22/30
7/10 = (7 x 3) / (10 x 3) = 21/30 Lowest
Looking at the numerator alone we can see that 7/10 is the lowest, 11/15 is next lowest and 4/5 the highest
Wyatt, a chemist at a chemical supply company, has carefully measured out 100 gallons of a solution containing 14% acetone. He also has access to unlimited quantities of a 9% acetone solution. How many gallons of the 9% acetone solution must Wyatt add to the 14% acetone solution to create a solution that contains 10% acetone?
A veterinarian divided 1/2 of a bottle of medicine equally among some sick cats. She gave each cat 1/8 of a bottle of medicine. How many sick cats were there?
Answer:
4
Step-by-step explanation:
1/2 the bottle is equal to 4/8. giving 1/8 to each sick cat is 4
Answer this please.
Solve the equation.
–2d = –11.18
A. 22.36
B. –9.18
C. –13.18
D. 5.59
Answer:
d =5.59
Step-by-step explanation:
Solve the equation.
–2d = –11.18
Divide each side by -2
–2d/-2 = –11.18/-2
d =5.59
........................................
Answer:
0
Step-by-step explanation:
You inputted nothing.
Evaluate the expression: 9² × 2 - 4²2 × (10-2) ÷ 2²30 - (3³ - 8)
We have to evaluate the expressions.
We have to solve each operation in the correct order: first the operations within the parenthesis, and within them, first the powers, then the multiplication/quotients and lastly the adds/subtractions. Then, we apply the same sequence for the terms outside the parenthesis.
a)
[tex]\begin{gathered} 9^2\cdot2-4^2 \\ 81\cdot2-16 \\ 162-16 \\ 146 \end{gathered}[/tex]b)
[tex]\begin{gathered} \frac{2\cdot(10-2)}{2^2} \\ \frac{2\cdot8}{2^2} \\ \frac{2\cdot8}{4} \\ \frac{16}{4} \\ \\ 4 \end{gathered}[/tex]c)
[tex]\begin{gathered} 30-(3^2-8) \\ 30-(9-8) \\ 30-1 \\ 29 \end{gathered}[/tex]Answer: a) 146, b) 4 c) 29
Find the volume of the triangular prism
The Volume of the given Triangular Prism is calculated with the given parameters to be; 63 in³
What is the Volume of the Triangular Prism?
The formula for Volume of a Triangular Prism is;
V = ¹/₂a*c*h
where;
V is volume
a is height of prism
c is length of shorter side of base
h is length of longer side of base
Now, from the triangular prism we are given, we can see that;
a = 3.5 inches
c = 4 inches
h = 9 inches
Thus;
V = ¹/₂ * 3.5 * 4 * 9
V = 63 in³
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how is the Associative Property of Multiplication similar or different from addition?
what is the best way to describe a porportion
what is the best way to describe the term monomials
According to the definition of proportion, two ratios are in proportion when they are equal.
A monomial is an expression consisting of a single term.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
A polynomial with only one term is called a monomial. An algebraic expression known as a monomial typically has one term, but it can also have several variables and a higher degree. When 9 is the coefficient, x, y, and z are the variables, and 3 is the degree of the monomial, for instance, 9x³yz is a single term.
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Can somebody help me with this please? I've been stuck for a hot minute.
Answer:
x = 30, and the measure of NMO is 64°
Step-by-step explanation:
Since MO bisects LMN, it follows that LMO is congruent to NMO, and the measure of LMN is twice the measure of LMO and of NMO. So we have:
[tex]5x - 22 = 2(x + 34)[/tex]
[tex]5x - 22 = 2x + 68[/tex]
[tex]3x = 90[/tex]
[tex]x = 30[/tex]
So the measure of NMO is equal to the measure of LMO:
[tex]30 + 34 = 64[/tex]
LMO and NMO are 64°.
Answer:
x=30
MO bisects LMN
so LMO = NMO
then LMO+NMO=LMN
help me i dont get this
Answer:
Irrational Rational
7.12 ✔
7.122 ✔
7.123123 ✔
7.123231... ✔
This should be right I apologize if it's not!
Mark me brainiest if it is tho :D
Please answer the two questions ( Look at photo + will mark brainliest if correct )
1. x = ____
2. t = ___
Answer:
x=90*
Step-by-step explanation:
t=40
SALE
50% OFF
original price!
Owen wants to buy a rocking chair. The original price is $34.58. How much will Owen pay if
he buys it during the sale?
Answer:
$17.58
make sure to mark me as the brainliest
PLEASE HALP WHAT IS THIS
Answer:
See below
Step-by-step explanation:
Given expression
[tex](\cfrac{4^{-2}}{3^4*4^{-3}})^3[/tex]Simplify it as below:
[tex](\cfrac{4^{-2-(-3)}}{3^4})^3=[/tex] Negative exponent rule[tex](\cfrac{4^1{}}{3^4})^3=[/tex] Simplify[tex]\cfrac{4^3{}}{3^{4*3}}=[/tex] Power of power rule[tex]\cfrac{4^3{}}{3^{12}}=[/tex] Simplify, can be left as is[tex]\cfrac{64}{531441}[/tex] or calculated1. The graph shows the height of a plant after a certain amount of time measured in days. Do you think that there may be a proportional relationship between the number of days and the height of the plant? Explain your reasoning. The graph shows how much snow fell after a certain amount of time measured in hours. 2. Do you think that there may be a proportional relationship between the number of hours and the amount of snow that fell? Explain your reasoning.
Neither graph in this problem represents a proportional relationship, as they have different rates of change. Examples are as follows:
1. Different rates between days 0-10 and 30-40.
2. Different rates between hours 0 - 1 and 2 - 3.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as the rule below shows.
y = kx
Hence, a function will only be proportional if the rate of change is constant for all intervals.
For item 1, we have that:
Between days 0 and 10, the rate of change is of approximately 0.4 cm a day, as the height grows from 0 cm to 4 cm in 10 days.Between days 30 and 40, the rate of change is of approximately 0.8 cm a day, as the height grows 8 cm in 10 days.Hence it is not a proportional relationship, due to the different rates.
For item 2, we have that:
During the interval from hour 0 to hour 1, the function is not constant, meaning that snow fell.During the interval from hour 2 to hour 3, the function is not constant, meaning that snow did not fell and the rate of change is of 0.For the same reason as item 1, of the different rates, it does not represent a proportional relationship.
What is the missing information?The graphs are missing and are given by the image at the end of the answer.
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jklm and nopq are quadrilaterals given jklm nopq describe a sequence of rigid motions followed by a dilation with center (0,0) that maps jklm to nopq
The transformations that maps polygon jklm to polygon nopq are described as follows:
C. Reflection across the y-axis, translation 2 units left and 6 units up, dilation with center (0,0) and scale factor 1/2.
What are the transformations that map jklm to nopq?The first transformation was a reflection, changing the orientation of the polygon.
Due to the orientation assumed with the equivalent vertices, NL, KO, PJ and MQ, the reflection was over the y-axis, with vertex O assuming coordinates (2,-2).
Since vertex O is at the y-axis, the polygon was translated 2 units left and 6 units up, with O assuming coordinates (0, 4).
The final coordinates of O are (0,2), hence the polygon was dilated with a scale factor of 1/2, as 4 x 1/2 = 2, which is the final y-coordinate of O.
What is the missing information?The problem is incomplete, and the complete problem is given by the image at the end of the answer.
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two cards are selected without replacement from a standard deck of 52 cards. what is the probability that both cards are the same color (either both black or both red)? round to three decimal places.
The probability of getting both the card with same color is 0.245
Total No. of cards in a deck = 52
The cards having the same color (either black or red ) = 26 out of 52
which is 26/52
The probability of finding a card having the same color without a replacement
P = 26/52 x 25/51
[∵ After taking one card, the total no . of cards will be 51 and the card having the same color is 25]
= 1/2 x 25/51
= 0.5 x 0.49
P = 0.245098
Therefore, the probability that both cards are the same color is 0.245098
We need to round off it to three decimals, Thus
The probability that both cards are the same color is 0.245
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question is in picture
The correct option is (D) △ABC and △FED are not similar because the corresponding sides of the triangles are not in proportion.
What is the congruency of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.So, the two given triangles are:
△ABC and △DEF with no sides identical to the other.
Then, we can conclude that no congruency condition with a side statement is true.So, options (A) is (C) are incorrect.
∠B and ∠E do not seem to be identical.So, option (B) is also incorrect.
Since no sides are identical to each other then we can say that the given two triangles are not congruent when concluding that the answer to this problem is an option (D).
Therefore, the correct option is (D) △ABC and △FED are not similar because the corresponding sides of the triangles are not in proportion.
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P+4<10
The solution of the inequality is
[tex]p < 10-4\\p < 6[/tex]
P<6 is the solution
Be reminded <> change direction when you divide or multiply by a negative number.
Dionne has six steel balls of equal mass. If she puts five of them in one pan of a beam balance and one ball and a 100 g mass in the other pan, the pans balance each other. What is the mass of each steel ball?
PLEASE HELP
Answer:
25g
Step-by-step explanation:
If one ball + 100g = 5 balls, then 100g = 4 balls
100/4 = 25