The sum of the given finite series is 125
The given finite series is:
[tex]\sum\limits^{10}_{n=1} {(3n-4)}[/tex]
Use the properties of sum operator:
[tex]\sum\limits^{10}_{n=1} {(3n-4)}=\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}[/tex]
Calculate each term on the right side:
[tex]\sum\limits^{10}_{n=1} {4}=4+4+...+4=10\times4=40[/tex]
[tex]\sum\limits^{10}_{n=1} {3n}=3\sum\limits^{10}_{n=1} {n}[/tex]
= 3.(1 + 2 + 3 + ... + 10)
The series in the brackets is an arithmetic series with :
the first term: a(1) = 1
the last term: a(10) = 10
the common difference: d = 2 - 1 = 1
Use the sum formula for arithmetic series:
S(n) = n/2 [a(1) + a(n)]
S(10) = 10/2 [1 + 10]
=5 . 11 = 55
Therefore,
[tex]\sum\limits^{10}_{n=1} {3n}=3\times{55}=165[/tex]
Combine the sum:
[tex]\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}=165-40[/tex]
= 125
Learn more about sum of a series here:
https://brainly.com/question/28062936
#SPJ4
Determine whether y varies directly with x . If so, find the constant of variation.
y=-5 x
The required value of the constant of proportion is 5.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant of variation, rate of change, and constant ratio.
Solving for the value of constant of variation
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Given the relation is y = 5x —-- 2
On comparing both the equation 1 and 2, we have,
k = 5
Hence, the required value of constant of variation is 5.
To learn more about the constant of proportion, visit the link:
https://brainly.com/question/24868934
#SPJ4
How do I find angle x?
By using the fact that the internal angles of a triangle always add up to 180°, we will see that x = 100°.
How to find the angle x?Remember that the sum of all the internal angles of a triangle is always equal to 180°.
On the image we can see two triangles, let's define the angle at the right as A. and the angle at the left as B
We can write:
A + B + x = 180°
And for the inner triangle the angles give:
A/2 + B/2 + 140° = 180°
So we have a little system of equations:
A + B + x = 180°
A/2 + B/2 + 140° = 180°
If we multiply the second equation by 2 we get:
A + B + 280° = 360°
With the first equation we can write:
A + B = 180° - x
And replace that in the above equation
(A + B) + 280° = 360°
180° - x + 280° = 360°
Now we can solve this to get the value of x:
180° + 280° - 360° = x = 100°
We conclude that the measure of angle x is 100°
If you want to learn more about triangles:
https://brainly.com/question/2217700
#SPJ1
each brick is 3 1/4 inches tall if martina makes a stack of 4 bricks how much inches tall will it be
Answer:
13 inches
Step-by-step explanation:
Convert to improper fraction and multiply
13/4 x 4/1 (4's cancel out)
13
Can you please help? Write an equation of a line in slope-intercept form with the given slope and y-intercept. slope: 7, y-intercept: 1
Answer:
Y=7x+1
Step-by-step explain
formula is y=mx+b
your slope is your M and the y-intercept is your B
I need this answered please
When 32 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
The negative solution of the given statement is - 4.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the unknown number be 'n'.
∴ When 32 is subtracted from the square of a number, is n² - 32 and the result is 4 times the number which is equal to 4n,
So, n² - 32 = 4n.
n² - 4n - 32 = 0.
n² - 8n + 4n - 32 = 0.
n(n - 8) + 4(n - 9) = 0.
(n - 8)(n + 4) = 0.
n - 8 = 0 Or n + 4 = 0.
n = 8 Or n = - 4.
So, the negative solution is - 4,
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ2
The low temperature in degrees celsius for some cities on the same days in march are recorded in the dot plots. Decide if each statement is true or false
Answer:
the statement is true.
Step-by-step explanation:
Given f(x)=-2x-3, find f(-1).
Determine the probability of following event, spinning a spinner numbered 1-8 and not landing on 5
According to the question, to calculate the probability of the event which states that the spinning a spinner whose number is from one-eight and it is not landing on the number 5.
Therefore, the numbers which are greater than five are (6,7,8).
And the spinner numbers are (1,2,3,4,5,6,7,8).
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
Probability of spinning a number greater than 5 is:
P(E) = 3/8
And the probability of tossing a tail on a coin is: 1/2
Now, the total probability is: 3/8 [tex]\times[/tex] 1/2 = 3/16
To learn more about the Probability from the given link:
https://brainly.com/question/24756209
#SPJ4
Evaluate each expression 7^2
Answer:
PLEASE READ! Is that 7 to the second power? if so, here is your answer: 49
Step-by-step explanation:
Solve for x. It's telling me right but all have to ask is to just please answer quick
Answer: (7y+237) / 8 = x
Step-by-step explanation:
So your equation is:
(2y+50) + (7x-248) + (5y-17) + (x+44)
First thing to do is combine all the like terms. Lets start with y. So that would be 2y + 5y= 7y and 50 + -17 is 33. The new equation is:
(7y + 33) + (7x-248) + (x+44)
Now we will combine the x. We will do -248+44= -204
and 7x+x= 8x.
Now our new equation is:
(7y + 33) + (8x+-204)
Now we can subtract 33 from -204. That is 237.
Now we have 7y+237 = 8x
To isolate x we need to divide by 8. That will give us this:
(7y+237) / 8 = x
f(x) = 2x² + 5x - 3
g(x) = 4x - 5
Answer: 1.) 4x+5
2.) 4
Statement about translated figures
If two sides are parallel in the original figure, then those sides may not be parallel in the final figure.
True False
Determine the probability of following event, drawing a card from a standard deck and not getting a diamond.
According to the question, to calculate the probability of the event which states that to draw a card from the standard deck but the condition is not getting the diamond.
The total number of the playing cards are [tex]52[/tex]
And total number of diamond cards are [tex]13[/tex]
Therefore, the total number of favorable outcomes in which diamond is not there is [tex]52-13 = 39[/tex]
As per question, the probability can be written as:
P(no diamond card) = [tex]\frac{39}{52} = \frac{3}{4}[/tex]
Hence, the probability of not getting a diamond card is [tex]\frac{3}{4}[/tex].
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
To learn more about the Probability from the given link:
https://brainly.com/question/13604758
#SPJ4
the set of all real numbers less than -8 or greater than or equal to -4 in set builder notation
Answer:
[tex]\{x \in \mathbb{R}|-4 \le x \le -8\}[/tex]
Step-by-step explanation:
Describe the transformation of the parent function f(x) . h(x)=0.25 f(x)
The transformation applied to the parent function is vertical compression by a factor of 0.25.
In mathematics, functions can be manipulated algebraically to obtain graphs of functions through certain transformations. Such transformations are reflections of the x-axis or the y-axis. To flip a function f(x) on the x-axis, multiply the whole function by a negative value to get -f(x), and to flip a function f(x) on the y axis, f(-x ), specify the x variable with a negative value.
Vertical compression helps shrink features vertically. Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values are affected.
It is vertically compressed by a factor of 0.25.
More problems related to the graph transformation are given in the link below.
https://brainly.com/question/10059147?referrer=searchResults
#SPJ4
Simplify each sum or difference. State any restrictions on the variables.
d-3 / 2d+1 + d-1 / 2d + 1
Simplification of the each sum or difference of the given equation [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex] is equal to 2(d-2)/(2d+1). Restriction on the variables is given by d≠ (-1/2).
As given in the question,
Given equation is [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex]
Simplify it by taking least common multiple of the denominator,
[tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}\\\\\\=\frac{d-3+d-1}{2d+1}\\ \\=\frac{2d-4}{2d+1}\\ \\=\frac{2(d-2)}{2d+1}[/tex]
Restriction on the variables is given by d≠ (-1/2).
Therefore, simplification of the each sum or difference of the given equation [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex] is equal to 2(d-2)/(2d+1).Restriction on the variables is given by d≠ (-1/2).
Learn more about variables here
brainly.com/question/17344045
#SPJ4
Q18.
In a company, the ratio of the number of men to the number of women is 3:2
40% of the men are under the age of 25
10% of the women are under the age of 25
What percentage of all the people in the company are under the age of 25?
If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (s circle t) (negative 7)? HALP
-439 is the value which is equivalent to (s circle t) (negative 7).
Given,
s(x) = 2 - x²
t(x) = 3x
We have to find the value which is equivalent to (s circle t) (negative 7)
That is,
(s circle t) (negative 7) : This is a notation for compound function.
A function that takes another function as an argument is referred to as a compound function.
s(t(-7)) is the alternative notation for this compound function, which means that the value obtained from the function t(-7) will be used in the function s. (x).
Now, let's calculate the value of t(-7):
That is,
t(x) = 3x
t(-7) = 3 × (-7) = -21
Next, apply the value of t(-7) for s(x)
That is,
s(x) = 2 - x²
s(t(-7)) = s(-21) = 2 - (-21)^2 = 2 - 441 = -439
That is, -439 is the value which is equivalent to (s circle t) (negative 7).
Learn more about compound function here:
https://brainly.com/question/15320080
#SPJ1
Suppose you need to subtract a from b but mistakenly subtract b from a instead. How is the answer you get related to the correct answer? Explain.
answer:
it would be negative.
explanation:
when you subtract a value from a value, the result will be left to the larger number. if you subtract a larger number from a smaller number, the value will move left but since the value subtracted is more than the number minus itself, you would be subtracting from 0, therefore resulting in a negative number.
(-8) x (-2/3) =
1/3a = -5
URGENTTT
Answer: -8
Step-by-step explanation:
= 12 * (-2/3)
= -24/3
= -8
(−8) ⋅ (−2/3) = 1/3a = −5
The formula weights=mass of 1 mole of (−8) ⋅ (−2/3) = 1/3a = −5 = 0g
The three books in a series have 234 pages .301 pages, and 293 pages .about how many pages are in the series?
Identify a pattern and find the next three terms in the pattern.
8,9,10,11, . . .
Patterns of the given terms 8,9,10,11,.... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.
As given in the question,
Given pattern is 8,9,10,11,...
First term a₁ = 8
Second term a₂ = 9
Third term a₃ = 10
Fourth term a₄ =11
d =aₙ - aₙ₋₁
=a₂ -a₁
=9 -8
=1
8,9,10,11,... represents arithmetic progression
aₙ=8 + (n-1)d
a₅ =8+ 4(1)
=2
a₆ =8 + 5(1)
=13
a₇ =8 + 6(1)
=14
Therefore, patterns of the given terms 8,9,10,11,... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.
Learn more about patterns here
brainly.com/question/14720576
#SPJ4
Triangle ABC has coordinates A(2, 0), B(−1, 5), and C(4, 3). Determine the coordinates of the vertices of the image after a reflection in the x-axis.
Answer:
Co ordinate of A' = (1, -4)
Co ordinate of B' = (3, 2)
Co ordinate of C' = (4, -2)
Explanation:
The figure of the triangle is shown below.
If we are finding image of the triangle about X-axis all the x -co-ordinates will remain same, but y co-ordinate will change it's sign.
So, co ordinate of A' = (1, -4)
Co ordinate of B' = (3, 2)
Co ordinate of C' = (4, -2)
A triangle has base 8 cm and perpendicular height 5.2 cm work out the area of the triangle
The area of the triangle is mathematically given as
A=20.8cm
This is further explained below.
What is the area of the triangle?The region that is surrounded by the perimeter of the triangle, also known as the three sides of the triangle, is referred to as the area of the triangle.
The space that is encompassed by all three of a triangle's sides is referred to as the triangle's area.
It is computed with the assistance of a variety of formulae that differ according to the kind of triangle, and the results are represented in square units such as centimeters squared, inches squared, and so on.
Generally, the equation for Area the is mathematically given as
A = 1/2 * base * height
Therefore
A= 1/2 * 8 * 5.2
A=20.8cm
Read more about an area of the triangle
https://brainly.com/question/19305981
#SPJ1
What is the difference between the sum of the measures of the interior angles in an octagon and the sum of the measures of the interior angles in a hexagon?.
The difference between the sum of the measures of the interior angles in an octagon and the sum of the measures of the interior angles in a hexagon is 360°.
Interior angle refers to the angle inside a polygon that is formed by two of its adjacent sides. The sum of the measures of the interior angles of a polygon is given by the equation:
180°(n - 2)
where n is the number of sides
An octagon is a polygon that has 8 vertices and 8 sides. The sum of the measures of the interior angles of an octagon is:
180°(8 - 2) = 180°(6) = 1080°
On the other hand, a hexagon is a polygon that has 6 vertices and 6 sides. The sum of the measures of the interior angles of an octagon is:
180°(6 - 2) = 180°(4) = 720°
Subtracting the sum of the interior angles of the two polygons,
1080° - 720° = 360°
Learn more about interior angles here: brainly.com/question/7888180
#SPJ4
Question 7 of 10
Given NELR, solve for x.
R
(7x+33)
N
OA. 8
B. 7
O C. 6
O D. 5
(11x+21)
E
For the parallelogram NELR, we get the value of x as 7°.
We are given a parallelogram NELR.
We know that , the adjacent angles of a parallelogram are supplementary.
So, we get that:
∠ N + ∠ E = 180°
Substituting the values, we get that:
7 x + 33 + 11 x + 21 = 180
18 x + 54 = 180
18 x = 180 - 54
18 x = 126
x = 126 / 18
x = 7°
Therefore, for the parallelogram NELR, we get the value of x as 7°.
Learn more about parallelogram here:
https://brainly.com/question/970600
#SPJ9
Solve x+8 = -6.
A. x = 14
OB. x=2
C. x = -2
OD. x= -14
Answer:
-14
Step-by-step explanation:
if you add negative fourteen by 8 you would get 6 and you keep the sign of the greater number
Write an equation in slope-intercept form for the line.
(-7,2) and (5,8)
The equation in slope-intercept form for the line that passes from the points (-7,2) and (5,8) is y = (1/2)x -3/2.
We know that, the slope intercept form is given by:-
y = mx + b
Where,
(x,y) is the ordered pair of every point on the line
m is the slope of the line
b is the y-intercept of the line
We know that, slope = (8-2)/(5-(-7)) = 6/12 = 1/2
Putting (-7,2) in (x,y) and m = 1/2 in the slope intercept form, we get,
2 = (1/2)(-7) + b
2 = -7/2 + b
b = -3/2
Hence, the slope intercept form of the line is y = (1/2)x -3/2.
To learn more about slope-intercept form, here:-
https://brainly.com/question/9682526
#SPJ4
use the figure below to answer the following. What is congruent. Given MN=6x-1 and MP=3x+8
The value of x if the sides are congruent is 3
How to determine the congruent sides?The given parameters are
MN=6x-1 and MP=3x+8
For the sides to be congruent, then the following equation must be true
MN = MP
This gives
6x - 1 = 3x + 8
Collect the like terms
6x - 3x = 1 + 8
Evaluate the like terms
3x = 9
Divide by 3
x = 3
Hence, the value of x if the sides are congruent is 3
Read more about congruent lines at:
https://brainly.com/question/1675117
#SPJ1
