[tex]\sum\limits_{i=3}^{10}\big i^2[/tex]
or:
[tex]\sum\limits_{i=1}^{8}\left(2+i\right)^2[/tex]
or:
x₁=3, x₂=4, x₃=5, .... x₈=10
[tex]\sum\limits_{i=1}^{8}\big x_i^2[/tex]
The sigma notation of 3^2+4^2+5^2+...+10^2 is: [tex]\sum\limits^{10}_{n = 3} n^2[/tex]
How to express the sum as a sigma notation?The sum is given as;
3^2+4^2+5^2+...+10^2
The above means that the sum of the squares of integers from 3 to 10
Using the above statement, the sigma notation is:
[tex]\sum\limits^{10}_{n = 3} n^2[/tex]
Where n represents the current integer
Read more about sigma notation at:
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A man divided some apples among his two children and himself. If the man took 3 apples for
himself and divided the remaining apples evenly between each of his children and each child had
fewer than 5 apples. How many apples were there originally?
Answer:
15
Step-by-step explanation:
Hank’s age is 15 years less than twice his sister’ s age. If Hank’s sister is 22 years old, how old is Hank?
Answer:
29
Step-by-step explanation:
2s-15=h
2(22)-15=h
44-15=h
29=h
Answer:
29
Step-by-step explanation:
22 multiplied by 2 is equal to 44. Subtract 15 from 44 and you get 29.
Which interval notation accurately represents the domain?
(–∞, 7) U (7, ∞)
(–∞, 5) U (5, ∞)
(–∞, 0) U (0, ∞)
(–∞, 10) U (10, ∞)
The domain represents interval notation is (–∞, 7) U (7, ∞) which is the correct answer would be an option (A)
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
For all other x-values, the graph appears to be defined. Thus, with the exception of x = 7, all real numbers should fall under the function's domain. This is what that would look like in interval notation:
It is possible to write the interval (–∞, ∞). as the set of all real numbers. Keep in mind that infinity∞ or -∞ is not a real number. Both ends are shown to be excluded from the interval by the rounded brackets.
All real numbers less than but not equal to 7 are contained in the set (-∞,7). (both ends are excluded.) The collection of every real number greater than but not equal to is.
All real numbers less than and higher than are combined to form the set of all real numbers that are not equal to 7. The union operator joins two intervals together.
Hence, the domain represents interval notation is (–∞, 7) U (7, ∞)
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x+y= 2
y=-12? + 3
\right.V)
1. In two or more complete sentences, explain how to solve the system of equations algebraically.
2. Solve the system of equations. In your final answer, include all of your work.
Answer:
11
Step-by-step explanation:
11
I think it is 15 but I want to see what you guys get and break it down please because sometimes people will say what they got and y'all be saying "yeah it's correct yeah" when it's really not.
Answer:
10 + 10 + 10 = 30
5 + 5 + 10 = 20
4 + 4 + 5 = 13
5 + 19 x 2 = 43
Step-by-step explanation:
Pair of shoes = 10
Boy = 5
2 snow cones = 4
One shoe = 5
boy + 2 snow cones + a pair of shoes (his feet) x one snow cone = 43
I really hope this helps!
Answer:
30/3=10
two shoes is 10
20-10=10
10/2=5
each person is 5
13-5=8
8/2=4
Two cones is 4
2 (only 1 cone) x 19(two cones is 4 + each person 5 =9. 9 + 10 because of the two shoes = 19) = 38
38+5(only 1 shoe) = 43
Hope this helps
Step-by-step explanation:
Does the equation represent a direct variation? If so, find the constant of variation.
4x -5y = 0
a. yes; k = -5 b. no c. yes; k = 4/5 d. yes; k = - 4
Answer:
4/5
Step-by-step explanation:
4x-5y=0
subtract 4x on both the sides
4x-4x-5y = 0-4x
-5y = -4x
divide by -5 on both the sides
-5y/-5 = -4x/-5
y =( 4/5 )x
How many one-half cubes with dimensions of 1\2x1x1 fit in a unit cube?
0 1
O 2
Answer:
2 half cubes
Step-by-step explanation:
this has only half the width, you just need 1 more to make a whole, therefore 2
What is the solution to the equation 1/4x +2= -5/8x - 5
Answer:
x = -8
Step-by-step explanation:
1/4x +2= -5/8x - 5
Add 5/8x to each side
1/4x +5/8x +2= -5/8x+5/8x - 5
1/4x+5/8x +2= - 5
Subtract 2 from each side
1/4x+5/8x +2-2= - 5-2
1/4x+5/8x = - 7
Get a common denominator
1/4 *2/2 x + 5/8x = -7
2/8x + 5/8x = -7
7/8x = -7
Multiply each side by 8/7
8/7x * 7/8x = -7 *8/7
x = -8
Answer:
x=-8
Step-by-step explanation:
1/4x+2=-5/8x-5
find l.c.m=8
multiply through by l.c.m which is 8
x/4×8+2×8=-5x/8×8-5×8
2x+16=-5x-40
2x+5x=-40-16
7x=-56
divide both sides by 7
7x/7=-56/7
x=-8
11) Omar is flying a kite on a 50-foot string at a diagonal distance. The kite gets stuck at the top
of a 40-foot tree. How far is Omar from the tree?
Answer:
30 ft
Step-by-step explanation:
We have a right triangle.
Hypotenuse = c = 50 ft
Leg #1 = a = 40 ft
Leg#2 = b = ?
We need to use Pythagorean Theorem
c² = a² + b²
50² = 40² + b²
b² = 2500 -1600 = 900
b = 30
Use the distributive property to write the following expression without parentheses.
-6(3-m+n)
________________________________
Hey!!
Solution,
-6(3-m+n)
= -18+6m-6n
= 6m-6n-18
hope it helps....
Good luck on your assignment
______________________________
Answer:
[tex]= 6m + 6n - 18 \\ [/tex]
Step-by-step explanation:
[tex] - 6(3 - m + n) \\ = - 18 + 6m + 6n \\ = 6m + 6n - 18[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
question in attachment
Answer:
[tex]cos(x)=-\frac{\sqrt{3} }{2}[/tex]
[tex]sin(x)=\frac{1}{2}[/tex]
[tex]tan(x)=-\frac{1}{\sqrt{3} }[/tex]
[tex]csc(x)=2[/tex]
[tex]sec(x)=-\frac{2}{\sqrt{3}}[/tex]
[tex]cot(x)=-\sqrt{3}[/tex]
Step-by-step explanation:
(I'll just use x for ease of writing)
We have the trig equation [tex]cos(x)=-\frac{\sqrt{3} }{2}[/tex], and we know that its terminal side is in the 2nd quadrant. By using a unit circle, we can determine that the angle is [tex]\frac{5\pi}{6}[/tex] which has an ordered pair of [tex](-\frac{\sqrt{3} }{2},\frac{1}{2} )[/tex]
[tex]sin(x)=y[/tex], so [tex]sin(x)=\frac{1}{2}[/tex]
[tex]tan(x)=\frac{y}{x}[/tex], so [tex]tan(x)=\frac{\frac{1}{2} }{-\frac{\sqrt{3} }{2} }=-\frac{1}{\sqrt{3} }[/tex]
Now that we have sin, cos, and tan, we can just take the reciprocal of each of these to get our answers for csc, sec, and cot.
[tex]csc(x)=\frac{1}{sin(x)}[/tex], so [tex]csc(x)=2[/tex]
[tex]sec(x)=\frac{1}{cos(x)}[/tex], so [tex]sec(x)=-\frac{2}{\sqrt{3}}[/tex]
[tex]cot(x)=\frac{1}{tan(x)}[/tex], so [tex]cot(x)=-\sqrt{3}[/tex]
Step-by-step explanation:
I have finished the table but stuck in the question after...
Answer:
7/48
Step-by-step explanation:
there are 48 in total
there are 7 white females
7/48
Jasmine draws a circle with a radius of 9x². What is the area of her circle?
Answer:
Look at the attachment
if I weighed 12 stones and lost 5lb , how much would I weigh?
Answer: 163 pounds
Step-by-step explanation: 12 stones is 168 pounds
Answer:163 lbs
Step-by-step explanation:
12 stone in lbs is 168 so 168-5= 163 lbs
Which is greater 15/27 or 16/24
Answer:
16/24
Step-by-step explanation:
let’s use the GCF of both which is 3 for 15/27
15/27 divided by 3 is 5/9
for 16/24 the gcf is 8
16/24 / 8 is 2/3
now we have to multiply 2/3 times 3
2/3 times 3 6/3 which is 2
so 16/24 is greater.
Use the elimination method to solve the system of equations
Answer:
D
Step-by-step explanation:
2x + 3y = 18
3x - 3y = 12
the 3y and -3y cancel and you add the other like terms
5x = 30
x = 6
plug x back into any of the equations
2(6) + 3y = 18
12 + 3y = 18
3y = 6
y = 2
answer is (6,2)
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The
number b varies directly with the number a. For example b = 2 when a = -2. Which equation represents this direct
variation between a and b?
b = -a
-b= -a
b - a = 0
b(-a)=0
Answer:
b=-a
Step-by-step explanation:
we know that b is located the same distance from 0 as another number, a, but in the opposite direction.
so the sum of the two numbers equal zero
a+b=0
a=-b or b=-a
What is the equation of the line that is perpendicular to the linear
graph of y= -2/3x+5 and passes through the point (0, -2)?
Answer:
y=3/2x-2
Step-by-step explanation:
gradient line 1= -2/3
perpendicular meaning gradients when multiplied should be -1
gradient line 2=3/2
y+2=3/2
x-0
y+2=3/2(x-0)
y+2=3/2x-0
y=3/2x-2
The equation of the line perpendicular to the linear graph of y= -2/3x+5 and passes through the point (0, -2) is y = 3x/2-2 (1st option is correct)
What is slope?The slope of a line is a number that describes both the direction and the steepness of the line.
Given that, a line is perpendicular to the linear graph of y= -2/3x+5 and passes through the point (0, -2)
The standard equation of a line is y = mx+c, where m is the slope of the line.
We know that, the slopes of the lines which are perpendicular to each other are negative reciprocal of each other,
Therefore, the slope of the asked line is 3/2.
Finding the c,
-2 = 3/2X0 + c
c = -2
Therefore, the equation will be,
y = 3x/2-2
Hence, The equation of the line perpendicular to the linear graph of y= -2/3x+5 and passes through the point (0, -2) is y = 3x/2-2
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Which values of x make the inequality below true?
5 - 3 + 3x < 13
PLEASE HELP THIS IS URGENT I AM BEING TIMED!!
Four children have the following weights: 45.5 pounds, 61 pounds, 37.2 pounds, and 16.34 pounds. What is the average weight of the children?
Answer:
40.01 lb
Step-by-step explanation:
mean:
(45.5+61+37.2+16.34)/4
160.04/4
40.01
Answer:
40.01
Step-by-step explanation:
First add all of the weights together and it should give you 160.04 divide that by 4 children and there is your answer
Convert 7/15 to a decimal.
SHOW WORK
Answer:
.4666...
Step-by-step explanation:
What you do:
Too convert 7/15 to a decimal you need too divide it.
7/15 = 0.466666667 So its a repeating decimal.
There are two things you can do, either add a bar to the decimal to show its repeating or round it up like this: 0.467 or 0.47
^ that is more accurate.
Have a good day! :)
What is Two-thirds divided by one-sixth? An area model with 4 shaded parts and 2 unshaded parts. The shaded parts are labeled two-thirds. 2 3 4 6
Two thirds divided by one sixth is 4
Answer:
It is number four
Step-by-step explanation:
Calculate the mean given the frequency table
Class
Frequency
0-9
24
10-19
20
20-29
32
Answer:
So the mean of the given data set is approximately 15.55.
Step-by-step explanation:
The mean is calculated by taking the sum of the product of each class midpoint and its corresponding frequency and dividing by the total frequency.
The midpoint of each class can be calculated as the average of the lower and upper class boundaries:
Class 0-9: Midpoint = (0 + 9) / 2 = 4.5
Class 10-19: Midpoint = (10 + 19) / 2 = 14.5
Class 20-29: Midpoint = (20 + 29) / 2 = 24.5
Now we can find the sum of the product of each midpoint and its frequency:
(4.5 * 24) + (14.5 * 20) + (24.5 * 32) = 108 + 290 + 784 = 1182
Finally, we divide this sum by the total frequency (76) to find the mean:
1182 / 76 = 15.552632
So the mean of the given data set is approximately 15.55.
The function ƒ(x) = 4x + 1 is transformed to g(x) = 2x + 1. What type of transformation has occurred? A) Reflection and Vertical Translation B) Rotation C) Reflection D) Rotation and Vertical Translation
Answer:
B) Rotation
Step-by-step explanation:
The only difference between functions f(x) and g(x) is the slope. To get from f(x)=4x+1 to g(x)=2x+1, you would need to rotate slightly clockwise about point (0,1) - the y-intercept. This would make the graph less steep (2x is less steep than 4x) while still retaining the (0,1) y intercept.
Answer:
Rotation
Step-by-step explanation:
If a ball is dropped, how long does it take to fall 60.0 m?
Answer:
the ball takes 3.1944 sec
Step-by-step explanation:
Answer:
It takes 3.498 seconds.
Step-by-step explanation:
To calculate free fall you must use the formula: h=1/2gt^2
What is the distance from
23, 5) to (33, -12)
Answer: 19.723083
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) =
O A. g(x) = (x+4)2 - 3
O B. g(x) = (x - 42 - 3
O C. g(x) = (x – 4)2 + 3
O D. g(x) = (x+4)2 + 3
Answer:
A
Step-by-step explanation:
Given f(x) then the graph of f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Given f(x) then the graph of f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here f(x) has been shifted 4 units left and 3 units down, thus
g(x) = (x + 4)² - 3 → A
pls i need the help.
Answer:
3. 16a+24b
Step-by-step explanation:
I know this because I grouped the eqatiobs together
Answer:
#3. 16a + 24b
Step-by-step explanation:
P= 2( length plus width).
plz help asap im timed just this and ill give u 5 stars brainliest and a thank u no cap
no its not a
Answer:
D
Step-by-step explanation:
2 x 4 = 8
8 x 2 = 16
4 x 9 = 36
36 x 2 = 72
9 x 2 = 18
18 x 2 = 36
16 + 72 + 36 = 124
124 = D
Newton currently has an account balance of $6,225.18. He opened the account 15 years ago
with a deposit of $4,543.11. If the interest compounds daily, what is the interest rate on the
account?
30.3%
7.7%
58.3%
2.1%
Answer: 2.1%
Step-by-step explanation:
r = n [(A/P)^1/nt - 1
