Given:
First five consecutive positive integers.
To find:
The sum of the first 5 consecutive positive integers.
Sum of the first n consecutive whole numbers.
Solution:
First five consecutive positive integers are 1, 2, 3, 4 and 5.
Sum of these numbers is
[tex]1+2+3+4+5=15[/tex]
Therefore, the sum of the first 5 consecutive positive integers is 15.
First n consecutive whole numbers are 0, 1, 2, 3,..., (n-1). These numbers are in AP.
Here, first term is 0 and common difference is 1.
Sum of n terms of an AP is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where, a is first term and d is common difference.
Substitute a=0 and d=1 in the above formula.
[tex]S_n=\dfrac{n}{2}[2(0)+(n-1)(1)][/tex]
[tex]S_n=\dfrac{n}{2}[n-1][/tex]
Sum of first 5 consecutive positive integers is equal to the sum of first 6 consecutive whole number because in whole numbers 0 is extra number.
For n=6,
[tex]S_6=\dfrac{6}{2}[6-1][/tex]
[tex]S_6=3(5)[/tex]
[tex]S_6=15[/tex]
The sum of the first 5 consecutive positive integers is 15.
So, the sum of (n-1) consecutive positive integers is
[tex]S_n=\dfrac{n}{2}[n-1][/tex]
20 POINTS! HELP ME PLZZ I NEED HELP WITH THIS!!
Answer:
B
Step-by-step explanation:
Both 0.684 and 0.1222 are rational
Answer:
B.
Step-by-step explanation:
Because 0.12222222.... and 0.684 are rational numbers.
Pls consider marking my answer as Brainliest! It would mean a lot!
What is 8.51736 rounded to the nearest ten-thousandth?
What is the equation of a line that is parallel to the line y = 2x + 7 and passes through the point (–2, 4)? A. y = −12x + 3 B. y = 2x + 4 C. y = −12x − 2 D. y = 2x + 8
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept)
y = 2x + 7 ← is in slope- intercept form
with slope m = 2
Parallel lines have equal slopes, thus
y = 2x + c ← is the partial equation
To find c substitute (- 2, 4) into the partial equation
4 = - 4 + c ⇒ c = 4 + 4 = 8
y = 2x + 8 → D
please please help me!!
Answer:
g(x) = f(x+1) + 1
Step-by-step explanation:
Since the graph is only moved you don't have to worry about the slope.
To move the graph to the left you add to the x and in this case, it only moved 1 over.
to move the graph up you add to the whole function and in this case, it only moved up 1.
PLEASE HELP WILL GIVE BRAINLIEST
Answer:
1. x= 17
2. x= 31
3. x= 4
4. x= 40
Step-by-step explanation:
first one:
you pass the 10 dividing
x-7 = 100/10 ----> x-7 =10
Pass the 7 adding
x = 10+7 ---> x= 17
second one:
Pass the 7 multiplying
x+11= 6*7 ---> x+11= 42
Pass the 11 in substraction
x = 42-11 ----> x =31
third one:
Add the 3+8 = 11
Pass the 11 dividing
x*11 = 44 -----> x= 44/11 ---> x= 4
fourth one:
Rest the 8-4 = 4
Pass the 4 multiplying
x/ 4 = 10 -----> x = 4*10 ---> x= 40
A line with a slope of 1 passes through the point (18, 15). What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = x - 13
Step-by-step explanation:
Given parameters:
Slope of the line = 1
Coordinate = (18, 15)
Unknown:
Equation of the line in slope-intercept format = ?
Solution:
The equation of a line is expressed as;
y = mx + c
where y and x are the coordinates
m is the slope
c is the y-intercept
Now, sine x = 18 and y = 5, let us find c;
5 = 1(18) + c
5 = 18 + c
c = -13;
The equation of the line is;
y = 1(x) + (-13)
y = x - 13
FACTOR THE EXPRESSION 100 - 80 USING THE GCF
Answer: 45
Step-by-step explanation:
4567
Answer100-80= 2x2x2x4:
Step-by-step explanation:
3x-4y=-7 and 4x+3y=24 solve for x
Robin has read 3/4 of a book. Mark said he had read 1/2 as much as Robin. What fraction of the book has mark read.
Multiply the amount of book Robin read by 1/2.
3/4 x 1/2 = 3/8
Mark read 3/8 of the book.
what is a mathmatical expression? give an example
Answer:
In algebra, we begin to see variables or letters that are used to represent numbers. An example of a mathematical expression with a variable is 2x + 3. In the expression 2x + 3, the coefficient of x is number 2, and it means 2 times x plus 3.
What is the least common denominator of 1/14, 3/16, 2/15
the least common multiple of 14, 15, amd 16 is 1680
Simplify the expression. (6x+1/2)+(3x-3 1/2)
Answer:
Have a Spoopy Halloween lol its 9x-3
Step-by-step explanation:
(6x+1/2)+(3x-3 1/2)
= 6x+3x-3 1/2+1/2
= 9x-3
Answer:
[tex]9x - \frac{6}{2} [/tex]
Step-by-step explanation:
[tex](6x+1/2)+(3x-3 \: 1/2) \to \\ ( 6x + \frac{1}{2} ) +( 3x - 3 \frac{1}{2} ) \to \\ 9x + \frac{1}{2} - \frac{7}{2} \to \\ 9x - \frac{6}{2} [/tex]
♨Rage♨
given m<12 =121 and m<6 =75 find the measure of the missing angles
Answer:
a. m∠1 = 75°
b. m∠2 = 46°
c. m∠3 = 59°
d. m∠4 = 59°
e. m∠5 = 46°
f. m∠7 = 121°
g. m∠8 = 59°
h. m∠9 = 62°
i. m∠10 = 118°
j. m∠11 = 59°
k. m∠13 = 118°
i. m∠14 = 62°5
Example 5
m∠1 =78°
m∠2 = 102°
m∠3 = 59°
m∠4 = 102°
m∠5 = 38
m∠6 = 142°
m∠7 = 38°
m∠8 = 142°
m∠9 = 78°
m∠11 = 78°
m∠12 = 102°
m∠13 = 38°
m∠14 = 142°
Step-by-step explanation:
a. m∠1 ≅ m∠6 (Alternate angle theorem)
m∠1 = m∠6 = 75° (Definition of congruency)
m∠1 = 75°
b. m∠12 = m∠5 + m∠6 (Angle addition postulate/Corresponding angles)
m∠5 = 121° - 75° = 46°
m∠5 = 46°
m∠2 ≅ m∠5 (Alternate angle theorem)
m∠2 = m∠5 = 46° (Definition of congruency)
m∠2 = 46°
c. m∠3 = 180 - (m∠1 + m∠2) (Angle subtraction and sum of angles on a straight line)
m∠3 = 180 - (75 + 46) = 59°
m∠3 = 59°
d. m∠4 = 180 - (m∠1 + m∠5)
m∠4 = 180 - (75 + 46) = 59°
m∠4 = 59°
e. m∠12 = m∠5 + m∠6 (Angle addition postulate/Corresponding angles)
m∠5 = 121° - 75° = 46°
m∠5 = 46°
f. m∠7 = m∠12 = 121° (Alternate angle theorem)
m∠7 = 121°
g. m∠8 = 180 - m∠7 = 180 - 121 = 59°
m∠8 = 59°
h. m∠9 + m∠5 + m∠8 = 180 (The sum of the interior angles of a triangle)
m∠9 = 180 - (59 + 59) = 62°
m∠9 = 62°
i. m∠10 = 180 - m∠9 = 180 - 62 = 118°
m∠10 = 118°
j. m∠11 = m∠8 = 59°
m∠11 = 59°
k. m∠13 = m∠10 = 118°
m∠13 = 118°
i. m∠14 = m∠9 = 62°
m∠14 = 62°
Example 5
m∠5 = m∠7 = 38
m∠5 = 38°
m∠6 = 180 - 38 = 142°
m∠6 = 142°
m∠8 = m∠6 = 142°
m∠8 = 142°
m∠12 = m∠10 = 102°
m∠12 = 102°
m∠11 = 180 - m∠12 = 180 - 102 = 78°
m∠11 = 78°
m∠9 = m∠11 = 78°
m∠9 = 78°
m∠1 = m∠9 = 78°
m∠1 =78°
m∠3 = 78°
m∠2 = m∠4 = m∠10 = 102°
m∠13 = 360 - (m∠3 + m∠6 + m∠12) = 360 - (78 + 142 + 102) = 38°
m∠13 = 38°
m∠15 = 38°
m∠14 = m∠16 = 180 - m∠15 = 180 - 38° = 142°
m∠14 = 142°
m∠16 = 142°
Factor the following polynomial completely.
A.
B.
C.
D.
Step-by-step explanation:
Please write complete question
Answer:
lol u gotta put the thing first bro
Step-by-step explanation:
A number line is drawn left to right with integers spaced 1 centimeter apart. An ant crawls onto the number line at +2. It then crawls 3.5 centimeters left, 4.8 centimeters right, and 7.9 centimeters left.
Question 1
Part A
Where is the ant on the number line now?
Enter the correct answer in the box.
Answer:
Position = -5
Step-by-step explanation:
The number line is not shown, however the question can still be answered.
Given
Start Point: +2
Left Movement: 3.5cm and 7.9cm
Right Movement: 4.8cm
Required
Determine the Ant's position
To do this, we treat all left movements as negative and all right movements as positive.
So, we have:
Position = 2 - 3.5 - 7.9 + 4.8
Position = -4.6
Since the number line is spaced by 1cm, we have to approximate to the nearest integer.
Position = -5
If you multiply four negative numbers, what is the sign of the product? If you multiply five negative numbers, what is the sign of the product? Based on the answers to these questions and the product rules, write a general rule for the sign of the product based on the number of negative numbers in the expression.
Answer:
If you multiply four negative numbers, what is the sign of the product? positive
If you multiply five negative numbers, what is the sign of the product? negative
Based on the answers to these questions and the product rules, write a general rule for the sign of the product based on the number of negative numbers in the expression.
even numbers of negative= positive
odd number equals= negative
Step-by-step explanation:
hope this helps
Answer:
if you multiply 4 negative numbers, sign of product is positive
if you multiple 5 negative numbers, sign of product is negative
Step-by-step explanation:
a negative times a negative is positive. to figure out the sign of a product, we can use -1 as an easy example.
[tex]-1*-1*-1*-1=1\\-1*-1*-1*-1*-1=-1[/tex]
of two planes intersect is their intersection a point
20.
60
(x + 20)
Зх
Sum of angle
measures: 180°
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Sum of the interior angles of any triangle equal 180° .
Thus ;
[tex](x + 20) + 3x + 60 = 180[/tex]
[tex]4x + 80 = 180[/tex]
Subtract sides 80
[tex]4x + 80 - 80 = 180 - 80[/tex]
[tex]4x = 100[/tex]
Divide sides by 4
[tex] \frac{4}{4} x = \frac{100}{4} \\ [/tex]
[tex]x = 25[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer: definitely x=25
Step-by-step explanation:
Please look at the screenshot
Answer:
i believe its D
Step-by-step explanation:
Suppose on a particular day, the probability (among the entire population) of getting into a car accident is 0.04, the probability of being a texter-and-driver is 0.14, and p(car accident or being a texter-and-driver)=0.15. Find the probability a person was in a car accident given that they are a texter-and-driver. Is this higher or lower than the probability among the general population and why?
Answer:
0.2143
Step-by-step explanation:
Let A be the event denote that getting into a car accident and B be the event denote being a texter-and-driver.
Thus, P(A)=0.04, P(B)=0.14.
P(A or B)=0.15.
We have to find P(A/B).
P(A/B)=P(A and B)/P(B)
P(A and B)= P(A)+P(B)-P(A or B)
P(A and B)=0.04+0.14-0.15
P(A and B)=0.03.
Thus, P(A/B)=0.03/0.14
P(A/B)=0.2143 (rounded to four decimal places)
Thus, the probability a person was in a car accident given that they are a texter-and-driver is 0.2143. This probability is higher than the probability among the general population because texting while driving is fatal.
Select the correct answer.
Find the value of g(7) for the function below.
g(x)= 7/8x-1/2
A. 49/8
B. 53/8
C. 60/7
D. 45/8
Answer:
D. 45/8
Step-by-step explanation:
The value of function g (7) is,
⇒ g(7) = 45/8
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Function is,
⇒ g(x) = 7/8x - 1/2
Now, Plug x = 7 in above equation,
⇒ g(x) = 7/8x - 1/2
⇒ g(7) = 7/8 (7) - 1/2
⇒ g(7) = 49/8 - 1/2
⇒ g(7) = 49/8 - 4/8
⇒ g(7) = 45/8
Thus, The value of function g (7) is,
⇒ g(7) = 45/8
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
Given the median, how do you find x on a triangle?
Convert to Standard Form
13-6x-=y
Answer:
6x+y=13
Step-by-step explanation:
write the equation of the graph
help me plaseeeeeeeeee
Answer:
it would be b
Step-by-step explanation:
Please help me this is due tomorrow and I just need this. ALSO WHEN YOU ANSWER SHOW ME YOUR STEPS FOR BRAINLEST THANKS!
Answer:
x=3
Step-by-step explanation:
1/4(12x + 4) - 14= -1/2(8x - 16)
1. Simplify each side my multiplying
3x - 13 = -4x + 8
2. Add 13 on each side
3x = -4x + 21
3. Add 4x on each side
7x = 21
x=3
Plz answer them they are timed
PLEASEE HELP MEEE what is the standard form of the following equation y= 5x + 0.5
A- 5x + y= 0.5
B- -5x-y= 0.5
C- -5x+y= 0.5
D- -5x+y= -0.5
Answer:
the standard form of y=5x+0.5 is B=-5x+y=0.5
Answer:
the answer is 5x - y= -0.5
Please answer will mark brainliest
5(2к)
What expressions is equivalent to this?
Answer:
10k
Step-by-step explanation:
Answer:
10k
Step-by-step explanation:
distribute the 5 to the 2 and leave the k