The expression is 8n – 3; The 100th term is 797
How to calculate the 100th term in sequence?The nth term of an arithmetic sequence is given by:
an=a1+(100-1)d ....[1]
where
a1 is the first term
d is the common difference of two consecutive terms.
n is the number of terms.
Given the sequence:
5, 13, 21, 29, 37, 45, …
This is an arithmetic sequence with first term = 5 and common difference(d) = 8
Since;
13-5 = 8,
21-13 = 8,
29-21 = 8 and so on....
We have to find the 100th term in the sequence
Substitute in [1] we have;
an=a1+(100-1)d
an=5+(n-1)8=5+8n-8 = 8n-3
Substitute the given values and n=100 we have;
a100= 800 - 3 = 797
Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;
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Why is y 4 a horizontal line?
The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.
Now, According to the question:
Let's know:
What is Horizontal lines?
If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.
The equation is y = 4.
The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.
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AYUDAAA ES PARA HOY.!!!
NOTA: Los angulos no están necesariamente dibujados a escala.
NOTE: Angles not necessarily drawn to scale.
AYUDENME PLEASE.!
Answer:
AGD=180-90
=90
FGD=CGE=23
AGF=90-23
=67degrees
5 mop and 7 broom cot a total of $855. 0. A mop cot $15. 00 more than a broom. Find the cot of:
a) 1 mop
b) 1 broom
pleae how working
the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
What is the system of equations?
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.
To find the cost of a mop and a broom, we can set up a system of equations using the information given:
Let x be the cost of a broom
Let y be the cost of a mop (which is $15 more than a broom)
From the problem, we know that:
y = x + 15 (since a mop costs $15 more than a broom)
5x + 7y = 855 (since 5 mops and 7 brooms cost a total of $855)
We can substitute the first equation into the second equation:
5x + 7(x + 15) = 855
5x + 7x + 105 = 855
12x = 750
x = 62.5
Hence, the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.
Therefore,
a) 1 mop cost $77.50
b) 1 broom cost $62.50
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A toaster has 4 slots for bread. Once the toaster is warmed up, it takes 35 seconds to make 4 slices of toast, 70 seconds to make 8 slices, and 105 seconds to make 10 slices. Explain how to predict the time it takes to toast any number of slices of toast.
It will take the toaster about 175 seconds to make 20 slices.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
Given that The toaster takes 35 seconds to make 4 slices of toast.
It takes 70 seconds to make 8 slices of toast, It also takes 105 seconds to make 12 slices.
We are required to calculate how long it may probably take the toaster to make 20 slices.
To calculate the time it takes the toaster to make 1 slice:
4 slices ---------- 35 seconds
1 slice ----------- ? seconds
1/4 × 35 = 35/4 seconds
Now, if 1 slice will be made in 35/4 seconds,
20 slices will be made in:
1 slice --------- 35/4 seconds
20 slices ------ ? seconds
(20/1) × 35/4 = 175 seconds
Hence It will take the toaster about 175 seconds to make 20 slices.
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If the figure is translated 2 units left and 4 units down what are the coordinates of L
Answer:
(2 , -2)
Step-by-step explanation:
L (4 , 2) -> (4-2 , 2-4) -> (2 , -2)
Parabola Skate Rental rents skate boards for $4.50 per hour with a rental fee of $35. Arc Hawk Skate Rental rents skate boards for $5.25 per hour with a rental fee of $25.
Give an example when renting from Parabola's would be a better deal than renting from Arc of Hawk's? Justify your answer.
An example of when renting from parabolas would be a better deal than renting from Arc of Hawk's is when the rental period is 8 hours.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
The total cost of renting parabolas would be 8 × $4.50 + $35 = $43.
The total cost of renting from Arc Hawk's would be 8 × $5.25 + $25 = $45.75
So Parabola is cheaper by $2.75
In general, any rental period of 8 hours or less would be a better deal with Parabola's, as per hourly rate is cheaper and the rental fee is higher than Arc Hawk but still, the total cost is lesser.
As the rental period increases beyond 8 hours, the per-hour rate difference becomes negligible and Arc Hawk becomes cheaper.
It is important to compare the cost for the same rental period, to accurately determine which rental company offers a better deal.
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Benjamin traveled at an average speed of 65 miles per hour for 4.5 hours and then traveled at an average speed of 70 miles per hour for 3.5 hours. What was the total distance in miles that Benjamin traveled during this time?
Answer:
542 miles
Step-by-step explanation:
65 miles/hour x 4.5 hours = 297 miles for the first part
70 miles/hour x 3.5 hours = 245 miles for the second part
297 + 245 = 542 miles
How do you find the domain for the composition of two functions FG?
All x-values that are within the scope of both f and g make up the domain of the (f g)(x). In this instance, f has a domain of {"x | x ≥ 0"} and g has a domain of "all real numbers"; as a result, (f - g)(x) has a domain of {"x | x ≥ 0"} as these values of x fall inside both f and g's domains.
What is domain?A function's domain is the collection of all potential inputs. All x-values, or inputs, and all y-values, or outputs, make up a function's domain and range, respectively. When viewing a graph, the domain consists of all of the graph's values from left to right. The graph's whole range, from the bottom to the top, is the range.
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pleaseee solve i need in at least 5 mins
For the function
g(x)=5x−−√
gx=5x
, find
g(3), g(7), and g(11).
g3, g7, and g11.
The find the average rate of change, to the nearest hundredth, over each of the following intervals. (MAFS.912.F-IF.2.6)
A.
3≤x≤7
3≤x≤7
__________
B.
7≤x≤11
7≤x≤11
_________
Given:
sin (C) 4/9
Find tan (C)
[tex]sin(C)=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{9}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{9^2 - 4^2}=a\implies \sqrt{65}=a \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(C)=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{\sqrt{65}}}\implies tan(C)=\cfrac{4}{\sqrt{65}}\cdot \cfrac{\sqrt{65}}{\sqrt{65}}\implies tan(C)=\cfrac{4\sqrt{65}}{65}[/tex]
Don’t know just need help with answer
The length AB is 15.
What is length ?
Distance is measured by length. The quantity of length has the dimension of distance in the International System of Quantities. Most measurement systems choose a base unit for length from which all other units are derived. The metre serves as the fundamental unit of length in the International System of Units.
The definition of length is the measurement or extent of something from end to end. In other terms, it is the largest of the two or the highest of the three dimensions of geometrical forms or objects.
In contrast to width, which is used to gauge an object's width from side to side, length is used to gauge an object's length from one end to the other.
As it is a isosceles the two sides are equal
5x = 4x + 3
x = 3
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What is the nature of roots of quadratic equation x^2 =- 2x 1?
The nature of roots of quadratic equation x² = -2x + 1 is real and distinct.
The standard form of a quadratic equation is:
ax² + bx + c = 0
The discriminant is defined as:
D = b² - 4ac
Using the value of discriminant, we can determine the nature of roots of a quadratic equation.
If:
D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.
D = 0, the quadratic equation has 1 real equal roots or the roots are unique
D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.
In this case, the quadratic equation is:
x² = -2x + 1
transform it into the standard form:
x² + 2x - 1 = 0
Calculate the discriminant:
D = 2² - 4 (-1) = 8
Since D > 0, the roots are two distinct real roots.
Your question is incomplete, but most probably your question was:
What is the nature of roots of quadratic equation x² = -2x + 1?
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Can anyone answer what 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000x1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 is? Calculators are definitely acceptable, expecting a big number.
Answer:
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Step-by-step explanation:
big number
1 and double the zeros you just type
Judy tosses a coin four times. Draw a tree diagram showing the possible outcomes. Select the probability of getting 2 heads
then 2 tails.
a. 1
5
4
16
C.
b.
1
8
d.
1
16
This is fractions
Answer:
d. 1/16
Step-by-step explanation:
Flipping the coin 4 times gives a total of 16 possible outcomes. Only one of those gives 2 heads followed by 2 tails. So the probability is 1/16.
Hope this helps!
In a right triangle, a = 14.2 cm and b = 13.9 cm. Find c. Round to the
nearest tenth.
Applying the Pythagorean theorem, the value of c in the right triangle, to the nearest tenth is: B. c = 19.9 cm
What is Pythagorean Theorem?The Pythagorean theorem is used to find any side of a right triangle. If c is the hypotenuse, and a and b are the legs, the Pythagorean theorem states that, c = √(a² + b²).
Given:
a = 14.2 cmb = 13.9 cmThus:
c = √(14.2² + 13.9²)
c = 19.9 cm.
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Melissa wants to check the accuracy of the finance charge on her loan. She has a $6,000, 4-year loan at an APR of 3.11%. What is her monthly payment? Round to the nearest cent.
Answer: $133.10.
Step-by-step explanation:
Answer:
To calculate the monthly payment for a loan, you can use the following formula:
Monthly payment = (APR/12) * loan amount / (1 - (1 + APR/12)^(-number of payments))
In this case, the loan amount is $6,000, the APR is 3.11%, and the loan is for 4 years, or 48 months. Plugging these values into the formula, we have:
Monthly payment = (0.0311/12) * $6,000 / (1 - (1 + 0.0311/12)^(-48))
Calculating, we find that the monthly payment is approximately $147.26. Rounded to the nearest cent, the monthly payment is $147.26.
Step-by-step explanation:
An office manager spent $4870 on a
total of 14 chairs and desks. Each chair
costs $125, and each desk costs $515.
How many chairs and how many desks
did he buy?
Answer:
6 chairs
8 desks
Step-by-step explanation:
First, we assume that all 14 items he bought were chairs, if that was to be true then the office manager would spend...
125 x 14 = 1750$
We see that he spent less then he should have so now we start to substitute desks instead of chairs, and we have to keep in mind that if we change 1 chair to a desk then the total will increase by...
515 - 125 = 390$
Now we just find the difference between the needed total and the total that we get if the office manager would by only chairs and then divide the result by 390 in order to find the number of desks, and so we get...
(4870 - 1750) / 390 = 3120 / 390 = 8 desks
And now that we know the number of desks we just subtract the number of desks from 14 and get the number of chairs, and so...
14 - 8 = 6 chairs
In March, Derrick had $25.50 in credit card debt.
He recorded the amount as -$25.50 in his
4.
account book. In April, he had the amount of
5
credit card debt that he had in March. How did he
record his amount of debt in April in his account
book?
Answer:
-20.50?
Step-by-step explanation:
I think you said he added 5 dollars in his account which would get some of his debt removed. But he would still have a remaining -20.50 dollars to get rid of.
Finding the Probability of Simple Events
Answer:
th chicken
Step-by-step explanation:
PLS ANSWER QUICK THANK YOU
Answer:
0.001
Step-by-step explanation:
i hope this helps :)
Answer: 0.001
Because the numerator and denominator both have 4 as a term, they can cancel each other out. This leaves the fraction as [tex]\frac{10^{-6} }{10^{-3} }[/tex]. When dividing terms with exponents, the exponents should be subtracted. -6-(-3)=-3. Because the term is [tex]10^{-3}[/tex], it needs to be changed into a fraction, so the exponent is positive. This would equal [tex]\frac{1}{10^{3} }[/tex]. This equals 1/1000, which is 0.001.
х
x
(1) Find the value of 7x + 3y
when
= 12 and
y = -6
Answer:
66
Step-by-step explanation:
Answer:
66 is the correct answer
Step-by-step explanation:
when 7(12)+3(-6)
= 84+(-18)
66
Can someone help me with this? It’s due today :c
The statement x+y= y + x is an example of
what number property? a. Commutative Property of Addition b. Associative Property of Addition C. Identity Property of Addition d. Inverse Property of Addition
Answer:
A
Step-by-step explanation:
Commutative Property of Addition states that a change in the order of terms does not change your sum.
The given statement is example of the commutative property of addition. So, option A is the correct answer.
What is commutative property of addition?According to the commutative property of addition, changing the order of addends has no impact on the sum.
The given statement is x+y=y+x.
Only addition and multiplication operations are under the scope of the commutative property. As a result, it means that while adding or multiplying any two integers, we can swap the positions of the numbers.
Example, 3+8=8+3
⇒ 11=11
So, x+y is same as y+x
Therefore, option A is the correct answer.
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(two-step equation)
7c-2c=45
what is c? explain.
Answer:
c = 9
Step-by-step explanation:
simplify terms first
7c -2c=45
5c = 45
divide both sides by 5
c = 9
Answer:
7c-2c=45
5c=45
c=45/5
c=9
PLEASE HELP FAST !!
Animal Is a bird Can fly Ostrich Emu ✓ Canary ✓ Pig Seagull ✓ ✓ ✓ ✓ Crow Mosquito ✓ Let event A = The animal is a bird. Let event B = The animal can fly. Which outcomes are in A and B? A. {ostrich, emu, canary, seagull, crow, mosquito} B. {canary, seagull, crow} C. {canary, seagull, crow, mosquito} D. {ostrich, emu, canary, seagull, crow}
Answer:
in explanation
Step-by-step explanation:
The canary, the seagul, and the crow, All have both checkmarkes that shows that they Can fly AND they are birds (so B)
Bro this is easy you dont need Brainly for this just read it carefully and look at the graph.
Answer:
canary, seagull, crow
Step-by-step explanation:
just took the test
Write an equation to match this graph.
Answer:
y - 5 = 5(x - 1)
Step-by-step explanation:
Two points on the graph are (1, 5) and (7, 35). Going from the first to the second, we see x (the 'run') increasing by 6 and y (the 'rise') increasing by 30. Hence the slope of this line is m = rise / run = 30/6, or 5.
Using the point-slope equation, we get
y - 5 = 5(x - 1)
anyone know the equation to this?
Answer:
y = -3/4x + 36
Step-by-step explanation:
In slope-intercept form, (y = mx + b), m is the slope and b is the y intercept. The slope is the rise/run. You can count from one point to another that you move down 3 and to the right 4. So your rise/run is -3/4.
The y-intercept is 36, because that is where the line crosses the y-axis.
So you can substitute the values into the equation:
y = mx + b
y = (-3/4x) + (36)
y = -3/4x + 36
I don’t understand the question and I can’t find anything in my notes to help
Step-by-step explanation:
The problem states that you have a linear function so expect your equation to have this form:
y = mx + b
where m is the slope and b is the y-intercept. You are also given two points: P1(5, 6) and P2(14, 60). Use these points to solve for the slope m.
m = (y2 - y1) / (x2 - x1) = (60 - 6)/(14 - 5)
= 54/9 = 6
So our equation now becomes
y = 6m + b
To solve for b, plug in the values of P1:
6 = 6(5) + b ---> b = -24
Therefore, our equation is
y = 6m - 24
The rest of the points are
(8, 24)
(11, 42)
300 grams of type a raisin bran is mixed with 500 grams of type b raisin brad to produce a mixture which is 11% raisins. Type A raisin bran has twice as many raisins per kilogram as type b. What percentage of raisins are each type of raisin bran?
The blend contains 16% of type A and 8% of type B.
What is meant by percentage?When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
Let p be the percentage of type b used for the mix
2p be the percentage of type a used for the mix
2p × 300 + p × 500 = 0.11 × 800
simplifying the above equation, we get
p = 0.08 or 8%
Substitute the values in the above equation
2p = 2 × 0.08 = 0.16 or 16%
16 % of type a and 8 % of type b exists utilized for the mix.
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The required percentage of raisins are each type of raisin bran are 16% and 8%.
What is meant by percentage?When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
Let p be the percentage of type b used for the mix
2p be the percentage of type a used for the mix
2p × 300 + p × 500 = 0.11 × 800
simplifying the above equation, we get
p = 0.08 or 8%
Substitute the values in the above equation
2p = 2 × 0.08 = 0.16 or 16%
16 % of type a and 8 % of type b exists utilized for the mix.
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A rectangle has a length of 5x - 2 and a width of 3x. If the perimeter is 76, what is the width?
Answer:
w = 15
Step-by-step explanation:
p = 2l + 2w
76 = 2(5x - 2) + 2(3x)
76 = (10x - 4) + (6x)
Combine like terms
76 = 16x - 4
add 4 to both sides
80 = 16x
Divide both sides by 16
5 = x
x = 5
-------------------------
width
w = 3x
w = 3(5)
w = 15