The sum of first 20 terms of the AP will be -206.25
As in AP, let us assume that the "a" be the first term and 'd' be the common difference.
So, the value of nth term can be determined by using formula: a_n=a+(n-1)d, where, n = number of terms, and d = common difference.
So, the value of 19th terms = a+(19-1)d = a+18d = -5 -----(i)
And the value of 15th term = a+(15-1)d = a+14d = -7(1/2) ----(ii)
Now subtracting (ii) from (i),
We will get,
4d = 2(1/2)
=>4d = 2.5
=>d = (2.5/4) = 0.625
Now putting value of "d" in (i)
We will get,
a+(18*0.625) = -5
a=-5-11.25 = -16.25
We have, the formula for finding the sum of terms:
Sum of terms can be determined by using formula:
Sum = (n/2) × [2a + (n-1)d]
Here, n = 20, a = -16.25, d = 0.625
We will get sum of first 20 terms as:
[tex](n/2)\times [2a + (n-1)d]\\(20/2) \times [2 \times -16.25+(20-1)0.625]\\[/tex]
10[-32.5+11.875]
=10(-20.625) =-206.25
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The equations y+x^2+6x+8 and y =(x+2) (x+4) both define the same quadratic function. Without graphing, identify the x- and y-intercepts of the graph. Explain how you know.
please help!
Answer:
we get the
x-intercepts setting y=0 and the in the equation
y-intercept setting x=0 in the equation.
Step-by-step explanation:
x-intercepts( y=0)
[tex]0=x^2+6x+8=(x+2)(x+4)[/tex]
Hence x=-2 and x=-4 ( We got two x-intercepts)
y-intercept( x=0)
[tex]y=0^2+6(0)+8=8[/tex].
the y intercept is y=8 ( only is possible to find no more thant one).
Answer:
x-intercept=
x=-2
x=-4
y-intercept=
y=8
Step-by-step explanation:
0(y)=(x+2) (x+4)
so we had to substract it to get 0. therefore x intercept is that
y+x^2+6x+8
ax^2+bx+c
c is always y intercept
3. A mysterious metal medallion has a mass of 3,088 grams. Water is poured into a graduated glass container with a 10-by-10 cm square base with a water level of 53.0 cm. The medallion is dropped into the container and the water level rises to 54.6 cm. Find the volume and the density of the
Answer:
Initial volume:
10*10*53 = 5300 cm³Increased volume:
10*10*54.6 = 5460 cm³Volume of the medallion:
5460 - 5300 = 160 cm³Density = mass / volume
Density is:
3.088/160 = 19.3 g / cm³this diagram shows 3cm x 5 cm x 4 cm cubiod
find ac give your answer in 2 decimal place
The length AC will be 5.83 and the angle ACD will be 34.45°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
The length AC will be calculated as,
AC² = 5² + 3²
AC = √ ( 25 + 9 )
AC = √34
AC = 5.83
The angle ACD will be,
tanθ = P / B
θ = tan⁻¹ = ( 4 / 5.83)
θ = 34.45°
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could someone please check my answer and explain? im not sure if im doing this right
Answer:
[tex]V=1071.78\ cm^3[/tex]
Step-by-step explanation:
Given that,
The radius of the cone, r = 8 cm
The height of the cone, h = 16 cm
We need to find the volume of the cone. The formula for the volume of the cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2 h\\\\=\dfrac{1}{3}\times 3.14\times 8^2\times 16\\\\V=1071.78\ cm^3[/tex]
So, the volume of the cone is equal to [tex]1071.78\ cm^3[/tex].
I AM GIVING 30 POINTS!!!!!!!! TO WHOEVER ANSWERS THIS!!!! PLEASEPedro loves to try new adventures. His most recent was jumping out of an airplane. His special watch tells him his altitude. He set a timer at the moment he opened his parachute. His altitude relative to sea level, A, in feet, which is a function of time, in minutes, is shown in the table below. A t 11,100 4 7200 8 3300 12 A function could be written to describe the decent: Blank 1 = (Blank 2 )t + Blank 3
Answer:Sorry cant find
Step-by-step explanation:
The graph below models the value of a $20,000 car fyears after it was purchased.
20000
18000
16000
14000
12000-
10000
8000
6000
4000
2000-
Dollars
Value of Car
52:25
2 4 6 8 10 12 14 16 18 t
Years
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
A. Each car value y, is associated with exactly one time, t.
B. Each time, t, is associated with exactly one car value, y.
C.The rate at which car decreases in value is not constant.
Your answer should be B. Each time, t, is associated with precisely one car value, y.
Use an inverse function to write θ as a function of x.
Answer:
C
Step-by-step explanation:
Using the tangent ratio in the right triangle
tanθ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{3}[/tex] , then
θ = arctan [tex]\frac{x}{3}[/tex] → C
The required inverse function would be θ = arctan x/3. The correct answer would be an option (C).
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
The right triangle is given in the question, as shown.
Using the tangent ratio, we have:
tan θ = perpendicular/base
Here, perpendicular = x and base = 3
As per the figure, substitute the values in the above ratio:
tan θ = x/3
Using an inverse function to write θ as a function of x:
θ = tan⁻¹ x/3
This can be also written as:
θ = arctan x/3
Therefore, the required inverse function would be θ = arctan x/3.
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Sebastian has a bag that contains orange chews, apple chews, and lime chews. He
performs an experiment. Sebastian randomly removes a chew from the bag, records
the result, and returns the chew to the bag. Sebastian performs the experiment 26
times. The results are shown below:
A orange chew was selected 19 times.
A apple chew was selected 5 times.
A lime chew was selected 2 times.
If the experiment is repeated 1300 more times, about how many times would you
expect Sebastian to remove a orange chew from the bag? Round your answer to the
nearest whole number.
Answer:
I think it would be 950
Step-by-step explanation:
For the first example when he did 26 experiments and 19 orange chew was selected, if you subtract 7 from 26 you get 19.
How many 26's are in 1,300? 50
50 × 7 = 350
1,300 - 350 = 950
Maybe that's the answer
A gym offers classes for students to attend. If both the range and median number of students attending each class was 13 students, which of the following box-and-whisker plots could represent the number of students attending the classes?
Answer: C (The Last One)
Step-by-step explanation:
The answers correct because, If the range and median is 13 that means that the highest and lowest point equal 13 and the middle/the line in the graphs should be on 13. A doesn't have the line/median on 13 so it is not that answer. But B and C have the line/median on the line so we just have to check the range. The range of B is: 9, The range of C is: 13. So based off that we know that the answer is C.
Hope This Helps!
The graph of a quadratic function passes through the points (0,-4) and (-2,0). What is the zero of the function?
Please no links and if you can, show your work.
Answer:
2 I believe 2? hopefully I'm right
∠A and \angle B∠B are upplementary angle. If \text{m}\angle A=(7x-11)^{\circ}m∠A=(7x−11)
∘
and \text{m}\angle B=(x-25)^{\circ}m∠B=(x−25)
∘
, then find the meaure of \angle B∠B
The measure of ∠B is (x - 25)° = (27 - 25)° = 2°.
What are supplementary angles?
Supplementary angles are two angles that add up to 180 degrees. They are angles that when placed together will form a straight line. They are called "supplementary" because they "supplement" each other to form a straight angle.
When two angles are supplementary, their measures add up to 180 degrees. So, if ∠A and ∠B are supplementary, then:
m∠A + m∠B = 180
Given that m∠A = (7x - 11)° and m∠B = (x - 25)°, we can substitute these values into the equation:
(7x - 11)° + (x - 25)° = 180
Simplifying this equation by combining like terms:
8x - 36 = 180
Adding 36 to both sides:
8x = 216
Dividing both sides by 8:
x = 27
Hence, the measure of ∠B is (x - 25)° = (27 - 25)° = 2°.
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The measure of ∠B is (x - 25)° = (27 - 25)° = 2°.
What are supplementary angles?
Supplementary angles are two angles that add up to 180 degrees. They are angles that when placed together will form a straight line. They are called "supplementary" because they "supplement" each other to form a straight angle.
When two angles are supplementary, their measures add up to 180 degrees. So, if ∠A and ∠B are supplementary, then:
m∠A + m∠B = 180
Given that m∠A = (7x - 11)° and m∠B = (x - 25)°, we can substitute these values into the equation:
(7x - 11)° + (x - 25)° = 180
Simplifying this equation by combining like terms:
8x - 36 = 180
Adding 36 to both sides:
8x = 216
Dividing both sides by 8:
x = 27
Hence, the measure of ∠B is (x - 25)° = (27 - 25)° = 2°.
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Two dice are rolled at the same time. The first die shows a 2. Given that is a random variable that represents the sum of the results shown by the two dice, what are the possible values of X?
Answer:
3 ≤ X ≤ 8
Step-by-step explanation:
A die has 6 faces numbered from 1 to 6.
If two dice are rolled at the same time and the first die already shows a 2. Then the second die will show any number between 1 and 6 inclusive.
X which is the sum of the results shown by the dice will always be greater than or equal to 3 but less than or equal to 8. This is because the first die already shows a 2 and the second die will always be a number between 1 and 6 inclusive. i.e
X = result from die 1 + result from die 2
X = 2 + [1, 6]
X = [3, 8]
In other words, the minimum value of X is 3 and the maximum value of X is 8.
6000 plus 3000 plus 100 plus 40 plus 8
Answer:
9148
Step-by-step explanation:
6000 + 3000 would equal 9000.
100 + 40 + 8 would be 148
9000 + 148 = 9148
Answer:
9148
Step-by-step explanation:
Please help me I do not have much time and pls no scam answers
Copy each segment.Then construct its perpendicular bisector
(help plz i gift a crown
Answer:no explanation ?
Step-by-step explanation:
Audrey's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=59+6xy=59+6x, where yy represents the expected quiz score and xx represents hours spent on homework that week. What could the number 59 represent in the equation?
A student's expected quiz score if they spent no time on their homework.
A student's expected quiz score if they spent 65 hours on their homework.
The change in expected quiz score for every additional one hour students spend on their homework.
How many hours a student spends studying all year
The number 59 in the equation represents the following:
"A student's expected quiz score if they spent no time on their homework"
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
y=59+6x
When x=0, y=59+6*0 = 59+0 = 59
This means, y=59 is the student's expected quiz score if they spent no time on their homework.
The number 59 in the equation represents the following:
"A student's expected quiz score if they spent no time on their homework"
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Ava has 2 dozen pencils. 3/8 of them are sharpened. how many of them are sharpened?
Answer:
3/8 of 24 is 9
9 of her pencils are sharpened.
A scientist wants to know how many catfish are in
Clear Lake. She and her team capture 48 catfish,
which they tag and release. The next week, they
capture 60 catfish, 3 of which have been tagged.
About how many catfish are in Clear Lake?
Answer:
105 catfish
Step-by-step explanation:
48 - 3 = 45
45 + 60 = 105
Rearrange x = 3g + 2 to make g the subject
Answer:
[tex]g=\frac{x}{3} -\frac{2}{3}[/tex]
Step-by-step explanation:
You divide 3 from both sides leaving you with g=(x/3)-(2/3)
Please mark my answer as brainlyest.
The value of g can be rearranged by the expression x = 3g + 2 is [tex]\dfrac{x-2}{3}[/tex].
A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression
Example = 4y, 3x+4.
Given expression:
x = 3g + 2
Subtract 2 from both the sides:
x-2 = 3g + 2-2
x-2 = 3g
Divide both side by 3 to get the value of g
[tex]\dfrac{x-2}{3} = g[/tex]
Thus, the rearrangement of the expression x = 3g + 2 in the form of g is [tex]\dfrac{x-2}{3}[/tex].
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PLEASE HELP!! I will give brainliest!!
Drag the key features to the correct location on the image.
Each key feature can be used more than once, but not all key features will be used.
Which key features are present in these three functions?
Answer:
See screenshot attached that shows it is correct
Step-by-step explanation:
f(x) has a domain of (-infinity, 6) U (6, infinity). Horizontal asymptote of y= -2
g(x) has a domain of (-infinity, -3) U (-3,2) U (2,infinity). Horizontal asymptote of y=1.
h(x) has a domain of (-infinity, 6) U (6, infinity). Function has a oblique asymptote.
The function [tex]f(x)=\dfrac{\left(-2x+4\right)}{x-6}[/tex] will have a domain of [tex](-\infty,6)\cup(6,+\infty)[/tex], the function [tex]g(x)=\dfrac{\left(x^{2}-2x\right)}{x^{2}+x-6}[/tex] will have a domain of [tex](-\infty,-3)\cup(-3,2)\cup(2,+\infty)[/tex], and the function [tex]h(x)=\dfrac{\left(x^{2}-2x\right)}{x-6}[/tex] will have a domain of [tex](-\infty,6)\cup(6,+\infty)[/tex].
Given information:
The given functions are:
[tex]f(x)=\dfrac{\left(-2x+4\right)}{x-6}[/tex]
[tex]g(x)=\dfrac{\left(x^{2}-2x\right)}{x^{2}+x-6}[/tex]
[tex]h(x)=\dfrac{\left(x^{2}-2x\right)}{x-6}[/tex]
For a rational function, the denominator should not be equal to zero.
So, the domain of the first function will be,
[tex]x-6\neq0\\x\neq6\\(-\infty,6)\cup(6,+\infty)[/tex]
The function [tex]f(x)=\dfrac{\left(-2x+4\right)}{x-6}[/tex] will form a vertical asymptote at [tex]x=6[/tex].
The domain of the second function will be,
[tex]x^2+x-6\neq0\\x^2+3x-2x-6\neq0\\(x+3)(x-2)\neq0\\x\neq2, -3\\(-\infty,-3)\cup(-3,2)\cup(2,+\infty)[/tex]
The function [tex]g(x)=\dfrac{\left(x^{2}-2x\right)}{x^{2}+x-6}[/tex] will form a vertical asymptote at [tex]x=-3[/tex] and a horizontal asymptote at [tex]y=1[/tex].
The domain of third function h(x) will be,
[tex]x-6\neq0\\x\neq6\\(-\infty,6)\cup(6,+\infty)[/tex]
Now, the third function [tex]h(x)=\dfrac{\left(x^{2}-2x\right)}{x-6}[/tex] will form an oblique asymptote, and a vertical asymptote at [tex]x=6[/tex].
The graph of each function is attached to the image.
Therefore, the function [tex]f(x)=\dfrac{\left(-2x+4\right)}{x-6}[/tex] will have a domain of [tex](-\infty,6)\cup(6,+\infty)[/tex], the function [tex]g(x)=\dfrac{\left(x^{2}-2x\right)}{x^{2}+x-6}[/tex] will have a domain of [tex](-\infty,-3)\cup(-3,2)\cup(2,+\infty)[/tex], and the function [tex]h(x)=\dfrac{\left(x^{2}-2x\right)}{x-6}[/tex] will have a domain of [tex](-\infty,6)\cup(6,+\infty)[/tex].
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Can someone help me please? Picture attached
a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given
by pythagoras theorem
c2 = a2 + b2
18*18 = a2 + 12*12
324 - 144 = a2
a2 = 180
a = [tex]6\sqrt{5}[/tex]
a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.
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Which expression is equivalent to -9 - \left(-4\dfrac13\right)
Answer:
B) -9 + 4 2/3
Explanation:
The answer is B because -9 - (-4 1/3) is -4 2/3 which is equal to -14/3, so that means B also has the same sum.
I hope this helps you! :)
The Fudd family is attending a family reunion. They plan to rent a
car from the ABC Car Rental Company. Let m represent the number
of miles the family will drive. Let c represent the cost for renting a
car. Complete problems
The complete problem equation will be c = k*m + b
The cost equation for renting a car from the ABC Car Rental Company in terms of the number of miles driven, m, and the cost, c, would likely take the form of:
c = k*m + b where k is the rate of cost per mile and b is the fixed cost for renting the car independent of the miles driven.
It is important to note that this is a general equation and the specific cost equation of the ABC Car Rental Company is not provided. Also, this equation assumes that the cost of renting a car is linear to the miles driven, which may not be the case in practice. Other factors such as the type of car and duration of the rental period could also be included in the cost equation.
Therefore, the problem equation will be c = k*m + b
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Susannah bought eggs for $0.79/dozen. She spent a total of $6.32. How many dozen eggs did Susannah buy?
a. Write an equation of the form ax =b that will answer the question
Answer:
8 dozens ...............
Here is a piece of cake each piece of cake has the same number of candles how old is rongopai
Rongopai's age is equal to the total number of candles on the cake, thus I need to determine what that is.
How to estimate Rongopai's age?What I need to figure out because I am aware that Rongopai's age is equal to the total number of candles on the cake.
The number of pieces the cake was sliced into must first be determined. A quarter has a specific appearance to me. This is how it would seem (the teacher traces a quarter shape on the circle). There must have been more than four pieces since this one seems a little smaller.
Each cut's location may be identified using my finger. Given that all the pieces must be the same size, I'm predicting the locations of each line using the first piece as a reference.
Here would be the approximate location of the first line, followed by here and here (the teacher draws a line with her finger) (tracing two more lines). the third line. In my mind, the lines and parts are somewhat "visible." Four "invisible" pieces plus the one drawn in are present when I count backward.
The complete question is:
A teacher wants a student to see how visualising the size of a share (in this case, a piece of cake) can be used to work out how many shares are needed to make a whole:
“Here is a piece of Rongopai’s birthday cake. Each piece of cake has the same number of candles. How old is Rongopai?”
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Age of Rongopai is 20 years.
What means one fifth of a circle?One fifth of a circle means if a circle can be divided into five equal parts, then one fifth is one of them.
How old is Rongopai?
As per the figure given, there is shown a 1 fifth of a circular birthday cake.
As all the piece of cake is equal in size so the total number of cake piece is five.
the number of candles in each piece is four.
the total number of candles present in the whole cake is = 5 × 4
the total number of candles = 20
Therefore, Rongopai is 20 years old.
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Given function g, which is defined by g(x)=x to the power of 3 -x , what is the value of g(3)?
Really sorry, misunderstood the equation. This is the answer though.
Answer:
24
Step-by-step explanation:
We have our function g(x) = [tex]x^{3}[/tex] - x
Now, we will substitute 3 in for x, giving us:
[tex]3^{3} - 3[/tex]
Now, we will simplify our exponent, giving us:
27 - 3 = 24
So your answer is 24.
Hope this helped!
Pla answer asap I really need help on this
Answer:
measure of 1 = 117 degrees
measure of 2 = 63 degrees
*x = 39
Step-by-step explanation:
m1 = 3 x 39 = 117
m2 = 39 + 24 = 63
117 + 63 = 180 degrees
m∠1 = 3x and m∠2 = x + 24
now,
m∠1 + m∠2 = 180° (angle made in straight line)
3x + x + 24 = 180°
4x = 180-24
4x = 156
x = 156/4
x = 39°
also, 3x = 3×39 = 117
x + 24 = 39 + 24 = 63
help if you want brianleist!! :) uhm don't mind update- NO LINkS- Thank you to those who help! :)
plz help will mark brainliest
Answer:
50.4
Step-by-step explanation:
What’s 4/7x13/9 ?
Please help
0.82539682539 is the answer
Answer:
if it is a fraction then it is [tex]\frac{52}{63\\}[/tex]
Step-by-step explanation: