Rewrite the series as a sum (show all work)
Answer:
1144
Step-by-step explanation:
100 + 98 + 96 +.... + 78+76 =
(12-0)/2 (176)
(6.5) (176) = 1144
The sum of the series will be 1068.
We have the following expression -
[tex]\sum_{i=0}^{12} 100 - 2i[/tex]
We have to rewrite the series as the sum.
What do you mean by Series ?A series in mathematics is the sum of a list of numbers that are generated according to some pattern.
We have the following expression -
[tex]\sum_{i=0}^{12} 100 - 2i[/tex]
The terms of this series can be calculated by calculating the value of the function at different values of i.
The series is as follows -
100 + 98 + 96 +.... + 78+76
This is an arithmetic progression with a = 100 and d = - 2 and n = 12. The sum of this series is -
[tex]S = \frac{n}{2} \times {2a + (n-1)d}[/tex]
S = [tex]\frac{12}{2} [{2 \times 100 + (12 -1)(-2)] = 6[200+ 11 \times -2] = 6[200 -22][/tex]
S = 6 x 178 = 1068
The sum of the series will be 1068.
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If a block weighs 8kg PLUS half a block.
What is the weight of a block and a half?
Answer:12kg
Step-by-step explanation:
8kg+4kg=12kg
the 4kg came from the half block
se um bloco pesa 8 kg meio bloco pesa 4 kg então é só juntar 8+4=12
What is the area of the obtuse triangle below?
11
13
A. 12 sq. units
7
B. 71.5 sq. units
C. 24.5 sq. units
D. 143 sq. units
find the length of x
Answer:
7/2 =x
Step-by-step explanation:
The triangles are similar so we can write a ratio to solve
2 4
---- = -------
x 7
Using cross products
2*7 = 4x
14 = 4x
14/4 = 4x/4
7/2 =x
Answer:
[tex]x=3\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{4}{2} :\frac{7}{x}[/tex]
x · 4 = 7 · 2
4x = 14
4x ÷ 4 = 14 ÷ 4
x = 3.5
A pitcher of juice holds 6 cups. How many 2/3 -cup servings of juice are in the pitcher?
serving-
please help ill give brainliest
Answer:
Step-by-step explanation:
6 ÷ (⅔) = 6 × (3/2) = 9
There are nine ⅔-cup servings per pitcher.
Type the correct answer in each box. Use numerals instead of words.
The domain of this function is {-12, -6, 3, 15}.
y = -2/3x + 7
Complete the table based on the given domain.
Answer:
hope it helps plz mark me brainliest!
Step-by-step explanation:
4x² - 3, x less than/equal to 0
Step-by-step explanation:
y = (-1/2)[(x+3)^½]
(x+3)^½ = -2y
Square both sides,
(x+3) = (-2y)²
x+3 = 4y²
x = 4y²-3
Interswitch x and y
Inverse is 4x²-3
Domain of inverse is the range of f.
The range of f is less than/equal to 0
Because at x = -3, f(x) = 0
For x > -3, f(x) is negative
Domain of inverse is x less than/equal to 0
I need help I don't understand at all.
please mark this answer as brainlist
Which expression gives the surface area of a sphere with radius 3x?
Answer:
=> 12πr²
Step-by-step explanation:
The Surface area of sphere is 4πr²
so the surface area of sphere with radius 3x will be
=> 4×3πr²
=> 12πr²
Point T is the centroid. Find TE if XE =21
Answer:
7
Step-by-step explanation:
Thing about centroids is they create segments that are spilt with one piece [tex]\frac{1}{3}[/tex] and the larger piece [tex]\frac{2}{3}[/tex] .
So, if the whole segment is 21, then the large piece is [tex]\frac{2}{3}[/tex] of 21. The small piece is [tex]\frac{1}{3}[/tex] of 21.
TE = 21 · [tex]\frac{1}{3}[/tex] = [tex]\frac{21}{3}[/tex] = 7
can anyone answer this please
Answer:
4
Step-by-step explanation:
x=3
x2 means 3 square (+3)
3×3+3
=9+3
12÷3
4
A photographer needs a frame for an 5 x 7 inch picture, such that the total area is 80 in? Calculate the width of
the frame. Which of the following quadratic equations would be used when solving this?
4x^2 + 24x = 45
4x^2 + 12x = 45
2x^2 + 24 = 45
2x^2 + 12x = 45
Answer:
4·x² + 24·x = 45
Step-by-step explanation:
The total area of the frame and picture needed by the photographer = 80 in²
The size of the picture that will be in the frame = 5 × 7 inch
The length of the picture = 7 inches
The width of the picture = 5 inches
Let x represent the width of the frame, we get;
The width of the total area = The width of the picture + 2 × The width of the frame
Therefore, the width of the total area = 5 + 2·x
The length of the total area = The length of the picture + 2 × The width of the frame
Therefore, the length of the total area = 7 + 2·x
We get;
The total area = Total length × Total width
∴ The total area = (5 + 2·x) × (7 + 2·x)
We are given that the total area = 80, therefore, by transitive property of equality, we have;
(5 + 2·x) × (7 + 2·x) = 80
35 + 10·x + 14·x + 4·x² = 80
4·x² + 24·x = 80 - 35 = 45
∴ 4·x² + 24·x = 45
Therefore, the quadratic equation that can be used in solving for the width is 4·x² + 24·x = 45.
Answer:
The answer is 4x^2+24x=45
Step-by-step explanation:
I got it right on my test.
I cant seem to get the answer right, please help me!!!
Answer:
6pi=2pi(r)(120/360)
r=9
C=(pi)d
C=(pi)18
c=18pi
Step-by-step explanation:
Answer:
Step-by-step explanation:
The measurement of AC = 6pi
120/360 * pi * 2 * R = 6*pi The pi values cancel out.
1/3 * 2 * R = 6 Multiply by 3
2R = 18 Divide by 2
R = 9
the circumference = 2 * pi * R
C = 2 * pi *9
C = 18 * pi
Now you want the measurement of arc AB
120 = 6 * pi
30 = x
120/30 = 6pi/x Cross multiply
120 * x = 180 * pi Divide by 120
x = 180 pi / 120
x = 3/2 * pi
So the measurement of arc AB = 1.5 * pi
Use the ordered pairs to give a function rule. Give the rule in slope intercept form {(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)}
Answer:
[tex]y = -0.25x -1.5[/tex]
Step-by-step explanation:
Given
[tex](x,y) = \{(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)\}[/tex]
Required
The function rule (in slope intercept)
First, we calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{-1.25 -1.5}{-1 - -12}[/tex]
[tex]m = \frac{-2.75}{11}[/tex]
[tex]m = -\frac{2.75}{11}[/tex]
[tex]m = -0.25[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = -0.25(x - -12) + 1.5[/tex]
[tex]y = -0.25(x +12) + 1.5[/tex]
Open bracket
[tex]y = -0.25x -3 + 1.5[/tex]
[tex]y = -0.25x -1.5[/tex]
Givenl || m | n, find the value of x.
m
44°
n
Submit Answer
PLS HELP
Answer:
x=136
Step-by-step explanation:
Solve 7n + 2 = 4n + 17.
Answer:
n=5
Step-by-step explanation:
7n+2=4n+17
Subtract 2 from both sides
7n=4n+15
Subtract 4n
3n=15
Divide by 3
n=5
I hope it helps!
Answer:
7n+2=4n+17
7n+2−2=4n+17−2
7n=4n+15
7n−4n=4n+15−4n
3n=15
3n/3=15/3
n=5
OAmalOHopeO
Make y the subject of this formulae X=a-2by^2
Answer:
[tex]y = \sqrt{\frac{x- a}{2b}}[/tex]
Step-by-step explanation:
Step 1: Make y the subject of this formula
[tex]x- a = a - a - 2by^{2}[/tex]
[tex]\frac{x- a}{2b} = \frac{2by^{2}}{2b}[/tex]
[tex]\sqrt{\frac{x- a}{2b}} = \sqrt{y^{2}}[/tex]
[tex]\sqrt{\frac{x- a}{2b}} = y[/tex]
Answer: [tex]y = \sqrt{\frac{x- a}{2b}}[/tex]
What number is 33% of 264?
Answer:
87.12
Step-by-step explanation:
Answer:
12.5
Step-by-step explanation:
find the value if x that will make A||B
Answer:
x=11
Step-by-step explanation:
The angles given are alternate exterior angles and alternate exterior angles are equal if the lines are parallel
5x+9 = 6x-2
Subtract 5x from each side
5x+9-5x = 6x-2-5x
9 = x-2
Add 2 to each side
9+2 =x-2+2
11=x
Now,
5x + 9 ( vertically opposite angle )
Then,
5x + 9 = 6x - 2 ( corresponding angle )
x = 11
I hope you understand...
Mark me as brainliest...♡♡
Show all work when answering the question for full credit. Do it as best as you can.
Solve the equation: 7(2x + 3) = 12x - 13
Answer:
x = -17
Step-by-step explanation:
7(2x + 3) = 12x - 13
Distribute
7*2x +7*3 = 12x-13
14x +21 = 12x-13
Subtract 12x from each side
14x-12x+21 = 12x-12x-13
2x+21 = -13
Subtract 21 from each side
2x+21-21 = -13-21
2x = -34
Divide by 2
2x/2 = -34/2
x = -17
Question 3
Find FS If BS =16 .
Answer:
FS = 48
Step-by-step explanation:
The distance from the vertex to the centroid is twice the distance from the centroid to the midpoint, so
FB = 2 BS = 2 × 16 = 32
Then
FS = FB + BS = 32 + 16 = 48
What is the domain of the function y=sqrt x+6-7
Answer:
[tex]x \geqslant 1[/tex]
Step-by-step explanation:
[tex] \sqrt{x + 6 - 7} = \sqrt{x - 1} \\ \\ x - 1 \geqslant 0 \\ x \geqslant 1[/tex]
IF B=
3 4 8
4 2 1
find b12, b21, b22 and b23
Answer:
since b is 348421 and we are looking for b21 it is 348421(12)
find the cost of four score of plate at 50k each and three dozens of spoon at 20k each
Joel and Kevin are each putting money in a savings account to buy a new bicycle. The amount, in dollars, in Joel’s savings account, x weeks after the start of the year, is modeled by function j. The amount of money in Kevin’s account, at the same time, is modeled by function k.
j(x) = 25 + 3x
k(x) = 15 + 2x
Which function correctly represents how much more money, in dollars, is in Joel’s account than in Kevin’s account x weeks after the start of the year?
A.
(j − k)(x) = 40 + 5x
B.
(j − k)(x) = 40 + x
C.
(j − k)(x) = 10 + 5x
D.
(j − k)(x) = 10 + x
Given:
The amount of money in Joel’s account is:
[tex]j(x)=25+3x[/tex]
The amount of money in Kevin’s account is:
[tex]k(x)=15+2x[/tex]
To find:
The function that correctly represents how much more money, in dollars, is in Joel’s account than in Kevin’s account x weeks after the start of the year.
Solution:
We need to find the difference between the function j(x) and function k(x).
[tex]j(x)-k(x)=(25+3x)-(15+2x)[/tex]
[tex](j-k)(x)=25+3x-15-2x[/tex]
[tex](j-k)(x)=(25-15)+(3x-2x)[/tex]
[tex](j-k)(x)=10+x[/tex]
Therefore, the correct option is D.
Charlie wants to order lunch for his friends. He'll order 5 sandwiches and a $3
kid's meal for his little brother. Charlie has $28. How much can he spend on
each sandwich if they are all the same price?
Choosqtwo answers: one for the inequality that models this situation and
one for the correct answer,
A. Inequality: 5x+3 = 28
B. Answer: $7.66 or less
C. Inequality: 3x+ 5 <28
D. Answer: $5 or less
E, Inequality: 3x + 5 5 28
F, Inequality 5x + 3 5 28
Step-by-step explanation:
some of your answer options were not copied well in here.
so, I tell you the right information and how would sure it, and you need to pick the right option on your end :
the inequality is
5x + 3 <= 28
and based on that
5x <= 25
x <= 5
he can spend $5 or less on each sandwich.
Gloria forgot to account for two walkways. Using the work from Plan A,
subtract the two walkways to find the new perimeter. The width of each
walkways is x + ½ .
Show work here (put in simplest form)
Step-by-step explanation:
w
A farmer needs to cross the river with his fox, his chicken and a bag of corn. However, the boat can only fit the farmer and one other thing at a time. The problem is, the fox and the chicken are both hungry, so if he leaves the fox and chicken together, the fox might eat the chicken. If he leaves the chicken and corn together, the chicken might eat the corn. So how can the farmer get everyone across the river safely
first send the fox alone to the other side then send the corn, the fox wont eat the corn so that should be fine then lastly go with the farmer and the chicken, hope this helps!
Let V(x)=−x2+2x−4 and W(x)=−x3+2x2+x+5. Find V(x)−W(x).
Answer:
Step-by-step explanation:
v(x) - W(x) = x² + 2x - 4 - [x³ + 2x² + x + 5]
= x² + 2x - 4 - x³ - 2x² -x - 5
= x² - 2x² - x³ + 2x - x -4 - 5
= -x² - x³ + x - 9
Answer:
x³ - 3x² + x - 9
Step-by-step explanation:
V(x) - W(x) =
- x² + 2x - 4 - (- x³ + 2x² + x + 5) ← distribute parenthesis by - 1
= - x² + 2x - 4 + x³ - 2x² - x - 5 ← collect like terms
= x³ - 3x² + x - 9
Algebra 1 proportional relationships
Answer:
It always pass through the origin.(0,0)
Please help me out . Find ? please
Answer:
Cos Θ= 21/34
Θ=cos^-1(21/36)
= 54°
OAmalOHopeO
