Answer:
28 i think
Step-by-step explanation:
51+47=98
98-12 the ones that flew away that takes it to 86
86/3 the 3 balloons buntch than is 28
p.s. i mght of got some equations wrong but this is what i got
5 3/4 - (-3 7/8) = H
What is H ?
Answer:
Step-by-step explanation:
convert mixed fraction into improper fraction
[tex]5\frac{3}{4}=\frac{23}{4}\\\\\\3\frac{7}{8}=\frac{31}{8}\\\\5\frac{3}{4}-[-3\frac{7}{8}]=\frac{23}{4}+\frac{31}{8}\\\\=\frac{23*2}{4*2}+\frac{31}{8}\\\\=\frac{46}{8}+\frac{31}{8}\\\\=\frac{46+31}{8}\\\\\\=\frac{77}{8}\\\\=9\frac{5}{8}[/tex]
Answer:
9 5/8.
Step-by-step explanation:
5 3/4 - (-3 7/8)
= 5 3/4 + 3 7/8
= 5 + 3 + 3/4 + 7/8
= 8 + 3/4 + 7/8
The LCD of 4 and 8 is 8 so we get
8 + 6/8 + 7/8
= 8 + 13/8
= 8 + 1 5/8
= 9 5/8.
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 6 gallons.
Answer:
3.625 gpm
Step-by-step explanation:
find the value of X in X-X³=17
Answer:
Step-by-step explanation:
Step1: find the interval of roots. Consider -3 and -2
[tex]f(-3) = -7 <0[/tex]
[tex]f(-2) = 18 >0[/tex]
Hence, the root must be on [-3,-2]
Step2: consider the middle point -2.5
[tex]f(-2.5) = 3.875 >0[/tex]
Then, the root must be on [-3, -2.5]
Step 3: Repeat step 2 by finding the value of f at the middle point -2.75
[tex]f(-2.75) = -1.0468 <0[/tex]
Step 3: Repeat step 2 by finding the value of f at the middle point of the interval [-2.75,-2.5] which is -2.625
[tex]f(-2.625) = 1.537 >0[/tex]
Step4: Repeat step 2 on [-2.75, -2.625]
Repeat step 2 until you got the root which is -2.701
ACME Hardware is introducing a new product called Greener Cleaner. Complete the table by finding the cost per milliliter for each size based on the sales price. One liter is 1,000 milliliters. (Answer the questions too, please!)
Answer:
Step-by-step explanation:
a). 'Per ml' cost of the small size = [tex]\frac{\text{Sale price of small cane}}{\text{Amount of liquid}}[/tex]
= [tex]\frac{4.50}{250}[/tex]
= $0.018
'Per ml' cost of the medium size = [tex]\frac{\text{Sale price of medium cane}}{\text{Amount of liquid}}[/tex]
= [tex]\frac{9.95}{500}[/tex]
= $0.0199
'Per ml' cost of the large size = [tex]\frac{\text{Sale price of large cane}}{\text{Amount of liquid}}[/tex]
= [tex]\frac{16.95}{1000}[/tex]
= $0.01695
Therefore, expression to compare per ml cost of three containers will be,
$0.0199 > $0.018 > $0.01695
b). Least expensive way to buy the cleaner is to choose the container with least per ml cost.
Cost of 1500 ml cleaner = Cost of 1000 ml cleaner + Cost of 500 ml of cleaner
= Cost of 1000 ml cleaner container + Cost of 'n' containers of 250 ml container
Total cost of 1500 ml = $16.95 + $4.50n
= 16.95 + 2(4.5) [For n = 2]
= $25.95
c). Most expensive way to purchase 1500 ml cleaner is to choose the most expensive cleaners
Cost of 1500 ml cleaner = Cost of 'n' containers of medium size containers
= 9.95(n)
= 9.95(3)
= $29.85
32.
What is the value of x for ∆DEF?
HELP! Answer if you can!!
Step-by-step explanation:
[tex]c^{2} = {a}^{2} + { b}^{2} [/tex]
Pythagoras theorem
x²=12² + 5²
x²=144+25
x²=169
[tex]x = \sqrt{169} [/tex]
x=13
Answer:
x = 13
Step-by-step explanation:
Using the Pythagorean Theorem to find the missing hypotenuse side:
[tex]a^2+b^2=c^2[/tex]
12 and 5 are a and b. 'x' would be c.
[tex]12^2+5^2=c^2\\\\12^2=144\\5^2=25\\\\144+25=c^2\\\\169=c^2\\\\\sqrt{169}=\sqrt{c^2}\\\\\boxed{13=c}[/tex]
'x' should be equal to 13.
I need help asap!!!
6 times the sum of a number and four is forty- two
Answer:
3
Step-by-step explanation:
6(x+4)=42
x=3
check:
6*(3+4)=42
PLEASE HELP f(x)=x^2 and g(x)=(x-3)^2+2 Describe how the graph of g(x) relates to the graph of its parent function, f(x). (HINT: Think about how f(x) was shifted to get g(x))
Answer:
The graph f(x) was shifted 3 units to the right and shifted 2 units up to get the graph of g(x).
Step-by-step explanation:
From the original graph to the transformed one, we can see that the transformations (x - 3) and + 2 were added to the equation.
The (x - 3) means that the x-value of the vertex will increase by 3, meaning that the graph will shift 3 units to the right.
The +2 will increase the y-value of the vertex by 2, meaning that the graph will move up 2 units.
So, the graph of g(x) relates to f(x) as it is a transformation 3 units to the right and 2 units upwards.
Someone help me plzz
Step-by-step explanation:
distance around the running track means to find the perimeter of whole solid figure
radius(r) = 30/2 =15m
perimeter = 50+ pi× r + 50+ pi × r
= 100 + 2 × pi ×r
= 100 + 2× 22÷7 × 15
= 1360/ 7 m
= 194.285 m
X-5y=-15x−5y=−15x, minus, 5, y, equals, minus, 15 Complete the missing value in the solution to the equation. (-5,(−5,left parenthesis, minus, 5, comma ))
Answer:
The missing value is 2. The coordinate will be (-5, 2)Step-by-step explanation:
The question is not properly written. Find the correct question below.
If x – 5y = -15 . Complete the missing value in the solution to the equation (-5, ____)
Let the coordinate of the variables be (x, y). Comparing the coordinates (x, y) with the given coordinate (-5, __), we will discover that x = -5. To get the y coordinate, we will substitute x = -5 into the given expression as shown;
If x – 5y = -15
-5 - 5y = -15
Adding 5 both sides
-5-5y+5 = -15+5
-5y = -10
Dividing both sides by -5;
-5y/-5 = -10/-5
y = 2
Hence the missing value in the solution of the equation is 2. The coordinate will be (-5, 2)
Answer:
2
Step-by-step explanation:
I did the khan :)
Two angles are adjacent and form an angle of 160. Their difference is 34. Find the angles
Answer:
The angles are 63 , 97
Step-by-step explanation:
Let one angle be x
As sum of two angles is 160, the other angle = 160 - x
Their difference = 34
x - [160- x] = 34
Use distributive property to remove the brackets
x - 160 + x = 34
Add like terms
x + x - 160 = 34
2x - 160 = 34
Add 160 to both sides
2x = 34 + 160
2x = 194
Divide both sides by 2
2x/2 = 194/2
x = 97°
One angle = 97°
Other angle = 160 - 97 = 63°
Please help. Calculate the area of the shaded region in each figure use 3.14 for π and round to the nearest 10th if necessary
If the average of 5, 8, b, 9 and 4 is 7. Find the value of b.
A. 9 B. 8 C. 7 D. 5
So our set of numbers is 5,8,b,9,4 . And we know the average is 7. So first, you have to add all the numbers in the set : 5+8+9+4 which gives you 26. We also know that to get the average of a set of numbers you have to add all the numbers and divide that sum by the how many numbers you have, in thsi case we have 5 numbers including b . So our equation now is : 26+b÷5=7. And if you plug in 9 for b you get 26+9÷5=7 and 26+9÷5 does equal 7 so therefore A is your answer
Write an expression to represent the product of 6 and the square of a number plus 15.
Answer:
6x^2 + 15
Step-by-step explanation:
We don't know what the square of a number is, so we represent it as x^2
The first part tells us to find the product of 6 and the square of a number, so
6x^2
The second part tells us to add 15 so,
6x^2 + 15
The expression that should be represented is [tex]6x^2 + 15[/tex]
Given that
The product of 6.The square of number + 15.Based on the above information,
Let us assume the number should be x
So, from the above information, the expression should be [tex]6x^2 + 15[/tex]
Therefore we can conclude that The expression that should be represented is [tex]6x^2 + 15[/tex]
Learn more about the equation here:brainly.com/question/21105092?
Help!!!! Which number line shows the solution to 6 + (−6)?
Answer: Hi!
The solution to positive 6 and -6 is 0. A negative and a positive of the same absolute value cancel out.
Hope this helps!
Answer:
the answer is zero !
Step-by-step explanation:
when a negative and a positive of the same number go against each other they cancel out
The functions q and r are defined as follows
g(x) = -2x-2
r(x) = x² – 2
Find the value of r(q(4)).
r(9 (4)) =
Answer:
98
Step-by-step explanation:
So we have the two functions:
[tex]g(x)=-2x-2\text{ and } r(x)=x^2-2[/tex]
And we want to find the value of r(g(4)).
To do so, first find the value of g(4):
[tex]g(x)=-2x-2\\g(4)=-2(4)-2\\[/tex]
Multiply:
[tex]g(4)=(-8)-2[/tex]
Subtract:
[tex]g(4)=-10[/tex]
Now, substitute this into r(g(4)):
[tex]r(g(4))\\=r(-10)[/tex]
And substitute this value into r(x):
[tex]r(-10)=(-10)^2-2[/tex]
Square:
[tex]r(-10)=100-2[/tex]
Subtract:
[tex]r(-10)=98[/tex]
Therefore:
[tex]r(-10)=r(g(4))=98[/tex]
Answer:
Step-by-step explanation:
Jeremy drove 180 miles in 3 hours. Find his average rate of change.
Answer:
60 miles per hour
Step-by-step explanation:
Total distance= 180 miles
Total time =3 hours
Average rate of change= ?
Distance= Rate × time
Make Time the subject of the formula
Time= Distance / Rate
Make average rate of change the subject of the formula
Average rate of change = Distance / time
= 180 miles / 3 hours
= 60 miles per hour
Given that p=x^2-y^2/x^2+xy
I. Express p in the simplest form
ii. Find the value of p if x=-4 and y=-6
Answer:
p = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
p = [tex]\frac{x^2-y^2}{x^2+xy}[/tex] ( factorise numerator and denominator )
x² - y² ← is a difference of squares and factors as (x - y)(x + y)
x² + xy ← factor out x from each term
= x(x + y) , thus
p = [tex]\frac{(x-y)(x+y)}{x(x+y)}[/tex] ← cancel (x + y) on numerator/ denominator
= [tex]\frac{x-y}{x}[/tex] ← substitute x = - 4, y = - 6
= [tex]\frac{-4-(-6)}{-4}[/tex]
= [tex]\frac{-4+6}{-4}[/tex]
= [tex]\frac{2}{-4}[/tex] = - [tex]\frac{1}{2}[/tex]
A.) pinky bought 1 1/2 kg of apples and 5 1/4 kg of mangoes and 1 1/2 Kg of oranges. Find the total weight of fruits B.) If her family eats 3/4 Kg of apples and 2 1/2 kg of mangoes and 1/2 Kg of oranges. Find the weight of the fruits left (Can any one say the answer please with explanation if who say the answer first I will mark them as the brainliest)
Answer:
a) The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms, b) The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.
Step-by-step explanation:
a) The total weight of fruits ([tex]m_{T}[/tex]) is calculated by the following formula:
[tex]m_{T} = m_{a} + m_{m}+m_{o}[/tex]
Where:
[tex]m_{a}[/tex] - Total weight of apples, measured in kilograms.
[tex]m_{m}[/tex] - Total weight of mangoes, measured in kilograms.
[tex]m_{o}[/tex] - Total weight of oranges, measured in kilograms.
If [tex]m_{a} = 1\,\frac{1}{2} \,kg[/tex], [tex]m_{m} = 5\,\frac{1}{4}\,kg[/tex] and [tex]m_{o} = 1\,\frac{1}{2}\,kg[/tex], then:
[tex]m_{T} = 1\,\frac{1}{2}\,kg + 5\,\frac{1}{4}\,kg + 1\,\frac{1}{2}\,kg[/tex]
[tex]m_{T} = \frac{6}{4}\,kg + \frac{21}{4}\,kg + \frac{6}{4}\,kg[/tex]
[tex]m_{T} = \frac{33}{4}\,kg[/tex]
[tex]m_{T} = 8\,\frac{1}{4}\,kg[/tex]
The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms.
b) The weight eaten by her family is determined by the following expression:
[tex]m_{E} = m_{a,e} + m_{m,e} + m_{o,e}[/tex]
Where:
[tex]m_{a,e}[/tex] - Eaten weight of apples, measured in kilograms.
[tex]m_{m,e}[/tex] - Eaten weight of mangoes, measured in kilograms.
[tex]m_{o,e}[/tex] - Eaten weight of oranges, measured in kilograms.
Given that [tex]m_{a,e} = \frac{3}{4}\,kg[/tex], [tex]m_{m,e} = 2\,\frac{1}{2}\,kg[/tex] and [tex]m_{o,e} = \frac{1}{2}\,kg[/tex], the weight eaten by her family is:
[tex]m_{E} = \frac{3}{4}\,kg + 2\,\frac{1}{2}\,kg + \frac{1}{2}\,kg[/tex]
[tex]m_{E} = \frac{3}{4}\,kg + \frac{10}{4}\,kg + \frac{2}{4}\,kg[/tex]
[tex]m_{E} = \frac{15}{4}\,kg[/tex]
[tex]m_{E} = 3\,\frac{3}{4}\,kg[/tex]
The weight of the fruits left is found by subtraction:
[tex]m_{R} = m_{T}-m_{E}[/tex]
[tex]m_{R} = 8\,\frac{1}{4} \,kg -3\,\frac{3}{4}\,kg[/tex]
[tex]m_{R} = \frac{33}{4}\,kg-\frac{15}{4}\,kg[/tex]
[tex]m_{R} = \frac{18}{4}\,kg[/tex]
[tex]m_{R} = 4 \,\frac{1}{2}\,kg[/tex]
The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.
ILL GIVE BRAINLIEST!!!! HELP
Two planes have a cruising speed of 750 km/h without wind. The first plane flies for 13 hours against a constant headwind. The second plane flies for 11 hours in the opposite direction with the same wind (a tailwind). The second plane flies for 250 km less than the first plane. Determine two equations that could be used to solve for the wind speed,w, and the distance traveled by the first plane,d.
1. (750+w)(13)=d (750+w)(11)=d+250 2. (750−w)(13)=d (750+w)(11)=d−250 3. (750+w)(13)=d (750−w)(11)=d−250 4. (750−w)(13)=d (750−w)(11)=d+250
Answer:
The correct option is;
2. (750 - w)(13) = d (750 + w)(11) = d - 250
Step-by-step explanation:
The items with information given are;
The cruising speed of the planes = 750 km/h
The first plane flies against a constant headwind = w
The second plane flies against a constant tailwind in magnitude to the headwind
The time duration of flight of the first plane = 13 hours
The time duration of flight of the second plane = 11 hours
The distance flown by the second plane = The distance flown by the first plane - 250 km
When we take the headwind magnitude as, w and the distance flown by the first plane as d, we have;
Speed of flight of the first plane = 750 - w
Speed of flight of the second plane = 750 + w
Therefore, the distance flown by the first plane in 13 hours is given as follows;
(750 - w) × (13) = d
Then we have;
The distance flown by the second plane in 11 hours is (750 + w) × (11) = d.
The correct option is (750 - w)(13) = d, (750 + w)(11) = d - 250
Yazmin is investigating the growth of plants under different conditions for her science class. Once the little sprouts were 1 inch tall, she found that they were growing at a steady rate of about 1/2 inch per day. Write a function that helps Yazmin to see how many days it takes for the plants to reach a given height. Let h = height of the plant (inches), and let d = number of days (days)
Answer:
0.5+d=h
Step-by-step explanation:
If a plant is growing at a steady rate of 0.5 inches (h) in 1 day (d) then after one day your equation should look like: 0.5+1 which would give you the height of the plant in inches. If this is true, then you would keep the height per day the same (0.5) substitute the 1 for d (one day); then your equation would look like this: 0.5+d which would give you the height of the plant in inches (h).
0.5+d=h
The function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.
What is a function?Functions were originally the idealization of how a varying quantity depends on another quantity.
Now it is given that,
Height of sprout = 1 inch
Growth per day = 1/2 inch
Let h = height of the plant (inches), and let d = number of days (days)
∵ Growth per day = 1/2 inch
So, Growth of plant in d days = d * 1/2 = d/2 = 0.5d
Thus, height of the plant, h = 1 + Growth of plant in d days
⇒ h = 1 + 0.5d
Thus, the function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.
To learn more about the function :
https://brainly.in/question/610635
#SPJ2
30 POINTS!! Quadratic function F(x) =2x^2- 4x- 6 is shown below. Which describes the domain of this function.
A. All real numbers greater than or equal to -8
B. All real number less than or equal to -8
C. All real number greater than 10
D. All real numbers
Answer:
D. All real numbers
Step-by-step explanation:
The domain is the set of values that can be used for x. There is no restriction on x, so the domain is all real numbers.
Answer:
all real numbers
Step-by-step explanation:
The domain is the possible input values
Since x can be any value, the domain is all real numbers
Please help! Brainliest answer gets 10 points! what is x^2+x^4?
Answer:
Step-by-step explanation:
You cannot add these because they are not like. IF you have a value for x, then the expression could be evaluated at the x value, but you can't add them.
An octagonal pyramid ... how many faces are there, how many vertices and how many edges? A triangular prism ... how many faces are there, how many vertices and how many edges? a triangular pyramid ... how many faces are there, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
At what rate per annum will N250 amount to N330 in 4 years.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{8 \: \% \: }}}}}[/tex]Step-by-step explanation:
Given,
Principal ( P ) = N 250
Time ( T ) = 4 years
Amount ( A ) =N 330
Rate ( R ) = ?
First, finding the Interest :
According to definition of Amount ,
Amount = Principal + Interest
plug the values
⇒[tex] \sf{330 = 250 + I}[/tex]
Move i to left hand side and change it's sign
⇒[tex] \sf{ - I = 250 - 330}[/tex]
Calculate
⇒[tex] \sf{ - I = - 80}[/tex]
Change the signs of the both equation
⇒[tex] \sf{I = 80 }[/tex]
Interest = 80
Finding the rate :
Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]
plug the values
⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]
Multiply the numbers
⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]
Apply cross product property
⇒[tex] \sf{1000R = 100 \times 80}[/tex]
Multiply the numbers
⇒[tex] \sf{1000R = 8000}[/tex]
Divide both sides of the equation by 1000
⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]
Calculate
⇒[tex] \sf{R = 8 \: \% \: }[/tex]
Thus, Rate = 8 %
-------------------------------------------------------------------------
Let's learn about Principal , Interest , Time , Rate and Amount :
Principal = The money which is borrowed or deposited is called principal.Interest = The additional amount of money which is paid by borrower to the lender is called interest.Time = The duration of time for which principal us deposited or borrowed is termed as time period.Rate = The condition under which the insterest is charged is called rate.Amount = The sum of principal and Interest is called an amount.Hope I helped!
Best regards!!
complete the square to solve
f(x)=x^2-6x+5
-2(8 - 1)= complete the following statement
We simplify the expression by subtracting 1 from 8, resulting in 7. We then multiply 7 by -2 to obtain the final answer of -14.
To simplify the given expression, -2(8 - 1), we can start by evaluating the expression inside the parentheses,
8 - 1 = 7
Now, we substitute this value back into the original expression:
-2(7)
Multiplying -2 by 7, we get:
-2 * 7 = -14
Therefore, -2(8 - 1) simplifies to -14.
In this case, we simplified the expression inside the parentheses first and then applied the multiplication operation. It's important to remember that when there is a negative sign in front of parentheses, it distributes to each term inside the parentheses. So, -2 multiplied by 8 gives -16, and -2 multiplied by -1 gives +2. The sum of -16 and +2 is -14.
In summary, when we evaluate the expression -2(8 - 1), the result is -14. This means that if we follow the order of operations (parentheses first, then multiplication), we simplify the expression by subtracting 1 from 8, resulting in 7. We then multiply 7 by -2 to obtain the final answer of -14.
For more such questions on expression
https://brainly.com/question/29070527
#SPJ8
Find the product.
7,352 x 48 =
A. 7,400
B. 88,224
C. 352,886
D. 352,896
Answer:
D
Step-by-step explanation:
7 3 5 2
x 4 8
-----------
352,896
Hey There!!~
Because, First thing to do is mulpity 2 x 8 = 16 so, You bring the 6 and bring up the 1. Then, 5 x 8 = 40 + 1 = 41. So, we bring down the 1 and bring up the 4. Then, 3 x 8 = 24 + 4 = 28. Then, The same thing bring down the 8 and let the 2 stay up there. 7 x 8 = 56 + 2 = 58. So, Right now the answer is 58, 816. So, We just completed the first step, But we're are not done yet... 4 x 2 = 8. Then, 5 x 4 = 20. So, we bring down the 0 and bring up the 2. Then, 4 x 3 = 12 + 2 = 14. So, The 4 stay down and 1 goes up. Then, 7 x 4 = 28 + 1 = 29. So, we just completed the second step. The last step is to add 58, 816 + 29, 408 = 352, 896. Hope This helps!!
Marcus is shopping for pants. The available styles are boot cut (B), skinny (S), and relaxed fit (R). Make an organized list to show all possible outcomes if he buys two new pairs of pants.
Answer:
list in the explanation
Step-by-step explanation:
BOOT x2
SKINNY x2
RELAXED x2
BOOT, SKINNY
BOOT, RELAXED
SKINNY, BOOT
SKINNY, RELAXED
RELAXED, BOOT
RELAXED, SKINNY
The solution set is given by Set A = { BB , SS , RR , BS , BR , SR } , where B , S and R are boot cut (B), skinny (S), and relaxed fit (R) respectively
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set be represented as A
Now , the equation will be
Marcus is shopping for pants and the available pants are boot cut (B), skinny (S), and relaxed fit (R)
He wants to buy 2 pair of pants , and the possible ways of 2 pants are
Set A = { BB , SS , RR , BS , BR , SR }
So , the total number of elements in set A = 6 pairs
Therefore , the value of A is 6 pairs
Hence , the set A is { BB , SS , RR , BS , BR , SR }
To learn more about sets click :
https://brainly.com/question/28278437
#SPJ2
Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....
Answer:Answer:
[tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]
Step-by-step explanation:
Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;
The sum of an arithmetic series is expressed as [tex]S_n = \frac{n}{2}[2a+(n-1)d][/tex]
n is the number of terms
a is the first term of the sequence
d is the common difference
Given parameters
n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2
Required
Sum of the first seven terms of the sequence
[tex]S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70[/tex]
The sum of the nth term of the sequence will be;
[tex]S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)[/tex]
The sigma notation will be expressed as [tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]. The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.
