Answers
Answer:
a) Its first term, a₁ -1,190
b) Its second term, a₂ = -1,186
c) Its third term, a₃ = -1,182
Step-by-step explanation:
The 100th term of the arithmetic progression, AP = 406
The common difference of the AP = 4
The formula to find the nth term of an AP, aₙ is given as follows;
aₙ = a + (n - 1)·d
Where;
aₙ = The nth term of the AP
a = The first term of the AP
a) Given the 400th term and the common difference, we have;
a₄₀₀ = 406 = a + (400 - 1) × 4
406 = a + 399 × 4
a = 406 - 399 × 4 = -1,190
The first term of the AP, a = -1,190
b) The second term of the AP, a₂ = -1,190 + (2 - 1) × 4 = -1,186
The second term of the AP, a₂ = -1,186
c) The third term of the AP, a₃ = -1,190 + (3 - 1) × 4 = -1,182
The third term of the AP, a₃ = -1,182.
Related Questions
Graph the line that passes through the points (8, -3) and (4, 1) and
determine the equation of the line.
Answers
Answer:
y = -x + 5
Step-by-step explanation:
The equation is y= mx + b
m = the slope or rise/run or (y2 - y1) / (x2 - x1)
b = y-intercept
The slope here is -1, and the y-intercept is 5, so our equation is
y = -x + 5
Misha says that if a line crosses the x-axis before it crosses the y-axis, the
values of m and b in its equation will both be positive. Is she correct?
Answers
No, Misha is not correct in her statement that the equation will be positive.
Define Slope.A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
What are coordinate pairs?An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
No, Misha is not correct. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. A line can cross the x-axis before it crosses the y-axis, and the values of m and b in its equation can still be either positive, negative or zero.
For example, a line with the equation y = -2x + 1 will cross the x-axis at x = 1/2 and y-axis at (0,1) , so it crosses x-axis first but both m and b have negative values (-2 and 1 respectively).
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Ash and Bea are engravers. Ash charges a flat fee of $\$1.50$ for the first $21$ letters engraved, and $8$ cents per letter thereafter. Bea charges a flat fee of $\$1.60$ for the first $15$ letters engraved, and $7$ cents per letter thereafter. For what nonzero number of letters will Ash and Bea's engraving prices be the same?
Answers
The number of nonzero letters that will see Ash and Bea's engraving prices being the same, is 25 letters
How to find the number of letters ?The formula for the cost to engrave with Ash, given that the number of letters engraved is x, would be :
= Flat fee + Cost per letter x Number of letters after 21 letters
= 1. 50 + 0. 08 x
The formula for the cost to engrave with Bea, given that the number of letters engraved is x, would be :
= Flat fee + Cost per letter x Number of letters after 15 letters
= 1. 60 + 0. 07 x
Equating these equations together will show the number of letters :
1. 50 + 0. 08 x = 1. 60 + 0. 07 x
0. 08 x - 0. 07 x = 1. 60 - 1. 50
0. 01 x = 1. 10
x = 0. 10 / 0. 01
x = 10 letters
Number of non zero number of letters would be 25 letters :
= 15 + 10
= 25 letters
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How do you find the f of G in a pair of functions?
Answers
To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.
What is function ?
A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Have given ,
f of G in a pair of functions ,
Let a example that f(x) = [tex]x^{2}[/tex] and g(x) = √x + 2
To find f(g(x)), we take f(x) and everywhere there's an x, we replace it with g(x).
f(x) = x2
f(g(x)) = g(x)2
= (√x + 2)2
= x + 2√x + 4
To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.
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What is the measure of ∠A if it is congruent to ∠B?
Answers
If measure of angle A is congruent to measure of angle B, then angle will be equal to angle B.
Define the term congruent angles?Angles that really are identical to each other are referred to as congruent angles (and to themselves).
Angles that are congruent can also be acute, obtuse, exterior, and interior. No matter what kind of angle you have, if indeed the measure for angle one and angle two are the same, the angles are congruent.Two or more angles must have equal measurements in degrees as well as radians to be considered congruent. Congruent angles don't have to be created with the same figures or face the same direction (rays, lines, or the line segments). Both angles are congruent if the two measurements of the angles are equivalent.Thus, if measure of angle A is congruent to measure of angle B, then angle will be equal to angle B.
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What is the value 8?
Answers
The value 8 is a numerical value that represents the quantity of eight. It is the natural number following seven and preceding 9. It is an even number and can be written as the sum of two squares: 8 = 3^2 + 2^2 = 4^2. In binary, it is 1000.
Eight is in the first position and has a place value of 8. Understanding the place value of digits in numbers aids in number comparison. It also aids in the composition of numbers in their enlarged form. For example, the extended version of the previous number, 13,548, is 10,000 + 3,000 + 500 + 40 + 8.
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What is the volume of the rectangular prism?
Answers
Answer:
200
Step-by-step explanation:
Find the slope of the line from two points (9, 6) (13,11) Use the equation of the line
O A. 3/5
OB. 5/4
OC. 6/13
O D. 4/7
Answers
Answer:
C
Step-by-step explanation:
Combine like terms
1.5x + 3y + 5 + 4x + 3y + y + 8
Answers
Answer:
9x+7y+13
Step-by-step explanation:
add all the x's, y's, and no exponents together
If we know the circumference of the tree trunk is 20 inches, what is the radius of that tree?
Answers
Answer:
[tex]\frac{10}{\pi}[/tex] or 3.183
Step-by-step explanation:
[tex]C=2\pi r[/tex]
If the circumference is 20 inches, plug 20 into C and solve for r.
[tex]20=2\pi r[/tex]
Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers,n,of hourse he could read on each of the 5 weekdays this week. The graph is shown. Which describes the solution set of the inequality.
Answers
Answer:
It appears that the solution set of the inequality 5n + 1.5 ≥ 4 is the set of all real numbers greater than or equal to -0.3. This can be determined by looking at the graph and noting that the region to the right of the vertical line x = -0.3 is shaded, which indicates that all values of x in that region are included in the solution set.
To verify this, we can substitute -0.3 into the inequality in place of n to see if the inequality is satisfied:
5(-0.3) + 1.5 ≥ 4
This simplifies to:
-1.5 + 1.5 ≥ 4
Which further simplifies to:
0 ≥ 4
Since this is not true, -0.3 is not a solution of the inequality. However, all values of x that are greater than or equal to -0.3 are solutions, as indicated by the shaded region on the graph.
Step-by-step explanation:
EASY POINTS PLEASE ANSWER!!
Answers
Hope this helps ;-)
Answer:
6.68 hours
Step-by-step explanation:
Tyler drove 52\tfrac{1}{2}52
2
1
mile in 1\tfrac{2}{3}1
3
2
hour. If he drove at a contant rate, how far did he travel in one hour? Enter your anwer a a whole number, proper fraction, or mixed number in implet form
Answers
Tyler drove 40 miles in one hour.
To find how far Tyler drove in one hour, we need to divide the total distance he traveled (52 21/32 miles) by the total time it took him (1 2/3 hours). To do this, we first need to convert the time to a common denominator, which in this case is 32. We can convert 1 2/3 hours to 32/3 hours by multiplying the numerator and denominator of 2/3 by 32/32.
So, we have:
(52 21/32) miles / (32/3) hour = (52 21/32) miles * (3/32) hour
= (52 21/32) * (3/32)
= (52 213/3232)
= (52 63/32) miles/hour
= 40 miles/hour
So, Tyler drove 40 miles in one hour.
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Why is 15.6 divided by 3.12 the same as 1560 divided by 312
Answers
Answer:
they are proportionate
Step-by-step explanation:
1560/100 = 15.6
312/100 = 3.12
Answer: Because they're based off the power of 10.
Step-by-step explanation:
I think the answer is correct because, to make 15.6 to 1560 you just need to multiply by 100, and to get 3.12 to 312 all you have to do is multiply by 100. So if you divided 1560 and 312 which is 5, all you have to do is divide by 100 and you get the same answer thats why its basically considered the same because of the power of tens.
Hope This Helps!
What is a 100 sided shape called?
Answers
Answer:
hectogon or hecatontagon or 100-gon
Step-by-step explanation:
It is a hundred - sided polygon ( shape ). The sum of all hectogon's interior angles are 17640 degrees.
Answer:
Regular exercise has been shown to aid in the prevention and management of noncommunicable illnesses such as diabetes, heart disease, stroke, and a number of malignancies. Additionally, it lowers blood pressure, supports healthy body weight, and enhances well-being through enhancing mental health.
Step-by-step explanation:
How do you tell if a log function is increasing or decreasing?
Answers
If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x) = log_b(x)[/tex] is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex]. where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x)=log_b(x)[/tex]. is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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- Find the perimeter and area of the rectangle shown.
3 m
12 m
Answers
Answer:
perimeter of the rectangle=2(12m+3m)
=30m
area of the rectangle=12m×3m
=36m
▬▬▬▬▬▬▬▬▬▬▬▬▬
→ Perimeter of Rectangle = 2(l + b)
= 2(12 + 3)
= 2 × 15
= 30m
→ Area of Rectangle = l × b
= 12 × 3
= 36m
∴ The Perimeter and area of Rectangle are 30m and 36m respectively.
▬▬▬▬▬▬▬▬▬▬▬▬▬
If the Standard Deviation was 3 and the average was 52, between what 2 values would contain
the middle 68%?
A) between 52 and 58
B) between 49 and 55
C) between 48 and 56
D) between two ferns
Answers
Answer:
between 49-55.
find the length of the hypotenuse of a right triangle and both legs have a length of 6
Answers
Answer:
6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
a^2+b^2=c^2
6^2+6^2=c^2
36+36=c^2
72=c^2
square root 72 is the hypotenuse
Or simplified 6[tex]\sqrt{2}[/tex]
Or decimal form 8.48528137424
Rounded 8.49
B= short leg
C= hypotenuse
A^2+B^2=C^2
So that means 6^2+6^2=C^2
36+36=C^2
72=C^2
C≈ 8.485
How to solve y-2=-2(x+3) when x equals -3
Answers
Y=-2(x+3)+2
Then plug in -3 for x and simplify.
Y=-2(-3+3)+2
Y=-2(0)+2
Y=2
Which set of angle measures could be the measures of the interior angles of a triangle?
60°, 45°, and 70°
30°, 85°, and 25°
55°, 90°, and 35°
110°, 15°, and 45°
Answers
A quadrilateral
is a polygon with four sides. Consider
the quadrilateral and the dashed segment. What is the sum
of the measures of the four interior angles of this quadrilateral?
Draw a different quadrilateral. Can you guess the sum
of the measures of its angles? Is it possible to generalize about
the angles of a quadrilateral?
Answers
Whatever the case a quadrilateral has always a sum of interior angles = 360°.
What is quadrilateral?A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which cannot be collinear. A quadrilateral has four sides, four angles, and four vertices. The word "quadrilateral" is derived from the Latin words "quadra" (four) and "latus" (sides). A quadrilateral may or may not have equal lengths on each of its four sides.
A quadrilateral is a polygon with four sides, four angles, and four vertices. The arrangement of the vertices must be considered whenever a quadrilateral is named. For instance, the following quadrilateral should be referred to as ABCD, BCDA, ADCB, or DCBA. Since they alter the order of vertices in which a quadrilateral is formed, it cannot be called ACBD or DBAC.
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find the value of 15/4 divided 5/8.show you reasong
Answers
[tex]\dfrac{15}{4} \div\dfrac{5}{8}[/tex]
In order to divide two fractions, you will need to use the KCF method.
Keep
Change
Flip
This means that we will keep the first fraction, change the division to multiplication, and flip the second fraction(reciprocal).
[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]
Multiply:
[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]
[tex]\dfrac{15\times8}{4\times5}[/tex]
[tex]=\dfrac{120}{20}[/tex]
Simplify:
[tex]120\div20[/tex]
[tex]=\fbox{6}[/tex]
Answer: 6
Step-by-step explanation:
1. 15/4 divided by 5/8 = 120/20
15/4 / 5/8 = 15/4 times 8/5 = 15 time 8 over 4 time 5 = 120/20
2. 120/6 = 6
A die is rolled once what is the probability of rolling not a 4
Answers
Answer:
I think 1/6
Step-by-step explanation:
A die has 6 sides so every side has 1/6 chance to land on
whats the length of A, B and C
Answers
Answer:
B should be 3 inches long because the area of the square above is 48 inches squared, so that long side is probably 8. B is 3 inches long. As for A, this should be simple. since we know the longer side of the room has the area of 27, we can tell the length(longest side) is 9. 14 minus 9 is equal to 4. A's width is 4 inches long.
Step-by-step explanation:
for the rest, since we know one of the widths is 6 inches, we know that the length of the room with an area of 32 inches is 8. therefore, since 8 times 4 equals the number 32, C is 4 inches long. back to B. since we know that c is 4 inches long and that there is a length of 11 inches, we can tell the longest side of room A is 7. 4 Times 7 equals 28, so B is 28 inches squared.
please help! it is so confusing
Answers
Answer:
4 maybe I don't understand what or how to do this but W is similar to M. I don't really know.
Step-by-step explanation:
EMERGENCY NEED HELP PLEASE HELP THE QUESTION IS ATTACHED TO THE QUESTION THING PLEASE HELP!!!
Answers
The required graph of the system of linear equations has been attached below.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The system of linear equations is given in the question, as follows:
2x + y = 8 .....(i)
-x + 2y = 6 .....(ii)
To graph the equations using the slope and y-intercept,
1) To determine the slope m and the y-intercept, write the equation in the form y = mx + b. (0, b).
Plot the y-intercept next.
3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.
Thus, the required graph of the system of linear equations.
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HELP. PLEASEPLEASE!!!
Answers
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers
Please solve with explanation
Answers
Answer:
a) -1535.5
b) 0
Step-by-step explanation:
A) We do this problem according to its parenthesis. First, let's evaluate the first half, -2[(-1/4)-12(-1)^2]. We have to do (-1)^2 first, because of PEMDAS. (-1)^2 is just 1. Now, our equation is -2[(-1/4)-12*1]. Thus, we get -2[(-1/4)-12] because 12*1 is just 12. Then, we do (-1/4)-12, giving us -12.25. Our equation becomes -2(-12.25). Then, we just get 24.5.
The next half, -5[24+2(-12)^2] is similar. We first evaulate (-12)^2 because of PEMDAS, giving us 144. Then, we have -5[24+2(144)]. 2 times 144 is 288, so we get -5[24+288]. 24 + 288 is 312, so we have -5(312). This finally gives us -1560.
Putting the two together, we get 24.5 - 1560, which is -1535.5.
--------------------------------------------------------------------------------------------------------------B) We substitute a = -1/3 and b = -1 into the equation, -a^2b^2 - 3a^3b^2.
We plug in -1/3 where a is and -1 where b is. So:
-(-1/3)^2(-1)^2 - 3(-1/3)^3(-1)^2.
The tricky part of this problem is making sure you follow PEMDAS. We evaluate the exponents first.
-1/9 * 1 - 3(-1/27) * 1
= -1/9 + 1/9
= 0
Step-by-step explanation:
good answer .qanda app Also use
Jack spends a total of $16.50 on one bag of popcorn and three drinks.
Jill spends a total of $29.75 for two bags of popcorn and five drinks.
Write a system of equations. Determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.
Answers
Answer:
Sure! Here's a system of equations we can set up to represent this situation:
Let x be the price of a bag of popcorn and y be the price of a drink.
Then we can set up the following system of equations:
x + 3y = 16.50 (equation for Jack's purchases)
2x + 5y = 29.75 (equation for Jill's purchases)
To solve this system of equations, we can use the substitution method.
First, we can solve for x in equation 1:
x = 16.50 - 3y
Then, we can substitute this expression for x into equation 2:
2(16.50 - 3y) + 5y = 29.75
Simplifying this equation, we get:
33 - 6y + 5y = 29.75
Combining like terms, we get:
33 - y = 29.75
Subtracting 29.75 from both sides, we get:
33 - 29.75 - y = -y
Simplifying, we get:
3.25 - y = 0
Subtracting 3.25 from both sides, we get:
-y = -3.25
Dividing both sides by -1, we get:
y = 3.25
So, the price of a drink is $3.25.
Now we can substitute this value for y back into equation 1 to solve for x:
x + 3(3.25) = 16.50
Simplifying, we get:
x + 9.75 = 16.50
Subtracting 9.75 from both sides, we get:
x = 6.75
So, the price of a bag of popcorn is $6.75.
To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.
Step-by-step explanation: