Answer:
101 + 102 + 103 + ... + 998 + 999 + 1000
Step-by-step explanation:
=====================================================
Explanation:
This series is arithmetic since the common difference is 1. In other words, we're adding 1 to each term to get the next one.
The quickest way to find the sum is to use the formula below
S = (n/2)*(a+b)
where n is the number of terms, 'a' is the first term, and b is the last (or nth) term. This formula only works for arithmetic series.
We can see that n = 100, a = 1 and b = 100, so....
S = (n/2)*(a+b)
S = (100/2)*(1+100)
S = 50*101
S = 5050
-----------
This can be confirmed by noticing that we have 100/2 = 50 pairs of terms. Pair up the terms such that 1 goes with 100, 2 goes with 99, 3 goes with 98, and so on.
We have these fifty sums
1+100 = 101
2+99 = 101
3+98 = 101
....
48+53 = 101
49+52 = 101
50+51 = 101
We have 50 copies of 101 being added, which leads to 50*101 = 5050
--------------
The slowest and most tedious way to confirm this is to type 1+2+3+...+98+99+100 into your calculator. The result should say 5050. Using a spreadsheet would be a better option instead of using a handheld calculator. I don't recommend this unless you need more proof that we end up with 5050 as the final answer.
Solve 3n – 5p + 2n = 10p for n.
Answer:
n = 3p
Step-by-step explanation:
3n−5p+2n=10p
5n−5p+5p=10p+5p
5n=15p
5n/5 = 15p/5
n = 3p
Answer:
3n+2n=10p+5p
5n=15p
Divide both sides by 5
n=3p
How do you solve this?
=================================================
Explanation:
If we plugged (x,y) = (0,8) into the first inequality, then we get
y < x^2+6
8 < 0^2+6
8 < 0+6
8 < 6
which is false. So we can rule out choice A.
----------------
Trying choice B leads us to
y < x^2+6
2 < 4^2+6
2 < 16+6
2 < 22
That last statement is true, so the first inequality is true for (x,y) = (4,2)
Let's try the other inequality
y > x^2-4
2 > 4^2-4
2 > 16-4
2 > 12
That's false. Since one of the inequalities is false (it doesn't matter which one), this means the entire system is false. We cross choice B off the list.
----------------
Now onto choice C
You should find that y < x^2+6 becomes -4 < 10 after plugging in (x,y) = (-2,-4). Since -4 < 10 is true, we move onto the next inequality.
The inequality y > x^2-4 becomes -4 > 0 after plugging in those mentioned x,y values. The inequality -4 > 0 is false.
We cross choice C off the list.
----------------
The only thing left is choice D. It has to be the answer.
Let's find out if we get true inequalities when plugging in (x,y) = (2,6)
y < x^2+6
6 < 2^2+6
6 < 10 ... true
and
y > x^2-4
6 > 2^2-4
6 > 4-4
6 > 0 .... also true
Both inequalities are true, so the entire system is true. Therefore, (x,y) = (2,6) is one of the infinitely many solutions to this system.
Choice D is confirmed as the answer
----------------
Refer to the diagram below. I've graphed the two dashed boundary curves and the shaded region between. This region is above the y = x^2-4 curve, and below the y = x^2+6 curve. So we're ignoring the stuff above the y = x^2+6 curve.
Points A through D represent the four answer choices in the order given. We see that point D is the only point in the shaded region, so that visually confirms we have the correct answer.
Note: points on the dashed boundaries do not count as solutions.
Find the equation of a vertical line passing through the point B(2,-1)
Answer:
x = 2
Step-by-step explanation:
In a vertical line, all x-coordinates are the same.
x = 2
Answer:
x =2
Step-by-step explanation:
A vertical line means the x value remains constant
The x value is 2
x =2
FIND THE TOTAL NUMBER OF COMBINATIONS
How many ways could a 3 topping pizza be selected if you have 10 toppings
to choose from?
A 720
B 120
60
D 30
Answer:
B.120 i took the test and got it right.
Answer:
Its letter B.
Step-by-step explanation:
hopefully i got it right loll
Mr. Theorem writes the expression 6^2 Divided bye 23 on the board. What is the value
Answer:
[tex]1\frac{13}{23}[/tex]
Step-by-step explanation:
6² ÷ 23
36 ÷ 23
[tex]1\frac{13}{23}[/tex]
Jeremy uses 2 feet 3 inches of board for each birdhouse he builds. How many inches of board does he need to make 6 birdhouses? Use a number line to solve?
Answer:
The length of board required is 13 feet 6 inches .
Step-by-step explanation:
Board required to make one bird house = 2 feet 3 inches
= 2 x 12 + 3 = 27 inches
Number of bird houses = 6
So, the board required
= 6 x 27 = 162 inches
13.5 feet = 13 feet 6 inches
A TV has a listed price of $695.95 before tax. If the sales tax rate is 7.75%, find the total cost of the TV with sales tax included. Round your answer to the nearest cent, if necessary.
Answer:
$749.89
Step-by-step explanation:
TV price = 100% = 695.95
Sales TAX = 7.75% = x
Total price = 107.75% = x dollars
1.0775 * 685.95 = 749.886125 ≈ 749.89
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Two tangents are drawn to a circle from an external point. If the measure of the major arc is 260º, what is the measure, in degrees, of the angle formed by the two tangents?
Answer:
80degrees
Step-by-step explanation:
Using the expression to get the minor arc;
minor arc + major arc = 360degrees
minor arc + 260 = 360
minor arc = 360 - 260
minor arc = 100degrees (central angle)
Note that the central angle and that formed from the intersection of the tangents (X) are supplementary. Hence;
100 + X = 180
X = 180 - 100
X = 80degrees
REAL ANSWER FOR BOTH OF THEM PLEASE THERES MORE POINTS ON THIS ONE
Answer:
the answer to your first question is 235 degrees or B
the answer to your second question is 83 degrees
Step-by-step explanation:
for the first question simply add all of the angles
for the second question a straight line/angle is 180 degrees so simply subtract 97 from 180 to get 83 degrees
Which expression is the result of factoring the expression below by taking out its greatest common factor?
4x^2+16x-4=?
Choose 1 answer:
A. 2x(2x^2+8x−2)
B. 2(2x^2+8x−2)
C. 4x(x^2+4x−1)
D. 4(x^2+4x−1)
Answer:
4(x^2 +4x-1)
Step-by-step explanation:
4x^2+16x-4
Factor out a 4
4(x^2 +4x-1)
Answer:
D. 4 ( x² + 4 x - 1 )
Step-by-step explanation:
4 x ² + 16 x - 4
Taking out common factor = 4
4 ( x² + 4 x - 1 )
This figure is known as a triangular prism. Find the surface area in square feet.
10 ft
3 ft
7 ft
8 ft
For the function f(x)= |x+2| -3 , explain the difference between f(2x) and 2f(x). Comparing the y-intercept , x-intercepts
Answer:
For a function f(x), the y-intercept is the value of f(0), while the x-intercepts are the values of x such that:
f(x) = 0.
Here we can also start with some information about dilations.
For a function f(x), a vertical dilation of scale factor k is written as:
g(x) = k*f(x)
While, again, for a function f(x), an horizontal dilation of scale factor k is written as:
g(x) = f(x/k)
So when here they ask us the difference between f(2x) and 2f(x)
We can say that the first one is a horizontal dilation of scale factor 1/2, while the second is a vertical dilation of scale factor 2.
Now let's analyze the intercepts for each case.
if f(x) = |x + 2| - 3
2*f(x) = 2*(|x + 2| - 3)
= 2*|x + 2| - 6
The y-intercept is:
2*f(0) = 2*|0 + 2| - 6 = 4 - 6 = -2
and the x-intercepts are given by:
2*f(x) = 0 = 2*|x + 2| - 6
6 = 2*|x + 2|
6/2 = |x + 2|
3 = |x + 2|
Here we have two solutions for x,
x = 1: 3 = |1 + 2| = |3| = 3
x = -5: 3 = |-5 + 2| = |-3| = 3
Now for the other transformation, we have:
f(2*x) = |2*x + 2| - 3
the y-intercept is:
f(2*0) = |2*0 + 2| - 3
= |2| - 3 = -1
(So the y-intercept is different)
And the x-intercepts are given by:
f(2*x) = 0 = |2*x + 2| - 3
3 = |2*x + 2|
3 = 2*|x + 1|
3/2 = |x + 1|
Here the two solutions are:
x = 1/2
x = -5/2
So the x-intercepts are also differents.
This happens because in one case, we affect the function horizontally and in the other case vertically, so one could expect that the resulting functions are different (thus, have different intercepts)
According to exponent rules, when we divide the expressions we
exponents.
HELPPPPPPPPPPPPPPPPPPP ASAP!!!!!!
Answer:
there is 8 quadrilateral shapes
the sum of two integers is 310. if one of them is - 52. find the other
Answer:
Integer = 362
Step-by-step explanation:
Let the two integers be x and y
Sum of two integers, x + y = 310 ------(1)
Given one of the integer, Let x = -52
Substitute x = -52 in (1) ,
-52 + y = 310
y = 310 + 52
y = 362
(-6)(4) preform indicated operation
Answer:
-24
Step-by-step explanation:
(-6)(4)
The indicated operation is multiplication
-24
Answer:
-24
Step-by-step explanation:
Multiply -6 and 4
In the decimal expansion of the fraction 1/13, what digit is in the 2021st decimal place?
please answer correctly (full answers)
Answer:
2
Step-by-step explanation:
1/13 = 0.07692307692307
1/13 has a 6 place repeating decimal
076923 076923
2021/6 = 336 5/6
There will be 336 complete sets and then
2021 will be the 5th place of 076923
For which set of numbers is the number 4 a common multiple?
A
B.
C.
D.
4.8 and 16
2.4 and 8
1, 2 and 4
0 and 4
ОА
Answer:
A is the answer
Step-by-step explain
Answer:
Hello There!!
Step-by-step explanation:
I believe the answer is O A.4.8 and 16.
hope this helps,have a great day!!
~Pinky~
If P = (-3,5), find the image
of P under the following rotation.
90° counterclockwise about the origin
([?], [
[]
Enter the number that belongs in
the green box
Answer:
(-5 , -3)
Step-by-step explanation:
use formula of 90 degree counterclockwise rotation about the origin
formula:
(x , y) = (-y , x)
(-3 , 5) = (-5 , -3)
The required coordinate of the point after 90° clockwise rotation is (-5, -3).
What does it mean by rotation?A shape or item is rotated when it is spun around a certain point (center) without being moved in any other way. Size and shape are unaffected by rotation.
The given coordinate of the point is (-5, -3).
Counterclockwise rotation about the origin is given as,
(x , y) = (-y , x)
(-3, 5) = (-5 , -3)
Thus, the required coordinate of the point after 90° clockwise rotation is (-5, -3).
Learn more about rotation here:
https://brainly.com/question/1571997
#SPJ2
Suppose y varies directly with x, and y = 65 when x = 13. What direct variation equation relates x and y?
Answer:
y = 5x
Step-by-step explanation:
y = kx
65 = k (13)
65/13 = k
k = 5
~~~~~~~~~~~~
y = 5x
will mark brainliest
show workings
Answer:
a) 20 km away fro the starting point.
b) The bearing from P to R is 80°.
c) Q is 60 km North P.
d) Q is - 60 km west of P
Step-by-step explanation:
Stating Facts in the Question:
P to Q is 80 km and bearing 330°
It turned around, Q to R is 60 km and bearing 250°.
a) Picture a number line (Look at the first image)
You go 80 to the right. You turn around and go 60 to the left.
80 - 60 = 20
20 km away fro the starting point
b) Picture a number line (Look at the second image)
P to Q is bearing 330°
Q to R is 60 km is bearing 250°
P to Q is red
Q to R is blue
330° - 250° = 80°
The bearing from P to R is 80°
c) P to Q is 60 km
The plane went forward or North so the answer is 60 km.
Q is 60 km North P.
d) Q to P is 60 km
Q is not to the west of P
Q is - 60 km west of P
Place the following linear equation in slope intercept form: 6x - 4y = 9
Answer:
y = 3/2 x - 9/4
Step-by-step explanation:
bring all the y's to one side.
4y = 6x-9
divide by 4 to isolate the y
y = 6/4x - 9/4
simplify
y = 3/2 x - 9/4
Answer:
y = (3/2)x - 9/4
Step-by-step explanation:
Slope intercept form is
y = mx + b
------------------
6x - 4y = 9
subtract 6x from both sides
-4y = -6x + 9
Divide both sides by -4
y = (3/2)x - 9/4
HELP, I don’t understand as this is due today!!!!
Answer:
in orange you cost 5.52
in apple you cost 3.9
Step-by-step explanation:
1 1/2=2×1+1=3
so multiplied the 3 in the price per pound
so in orange you got this solution
3×1.84=5.52
and in apple you got this solution
3×1.30=3.9
#CARRY ON LEARNING
#MARK ME AS BRAINLIEST
#100% SURE
Find the perimeter of the figure. SOMEONE PLS HELP ME IVE ASKED THIS QUESTION 3 TIMES NOW
Answer:
Step-by-step explanation:
The lengths of the tangents drawn from an external point tot he circle are equal.
RA = RB = 12.2
QA = QC = 5.9
PC = PQ - QC = 27.4 - 5.9 = 21.5
PC = PB = 21.5
QR = QA + RA = 5.9 + 12.2 = 18.1
PR = PB + RB = 21.5 + 12.2 = 33.7
Perimeter = PQ + QR + PR
= 27.4 + 18.1 + 33.7
= 79.2
how many zeroes are there
Answer:
infinity zeros are there
Step-by-step explanation:
please make me brainlsit answer
PLEASE SOMEONE HELP ME I WILL GIVE BRAINLIEST
Find the area of a quadrilateral wxyz with wx =24m, xy= 50m, yz = 40m, zw = 30m and diagonal being 50m
Answer:
The area of the quadrilateral is 1,182.46 m2.
Step-by-step explanation:
In order to find the area of a quadrilateral WXYZ, with WX=24m, XY=50m, YZ=40m, ZW=30m and the diagonal being 50m, the following calculation has to be done:
X = 0,5 24 × 30 × sen 24 + 0,5 × 50 × 40 × sen 40
X = 1,182.46 m2
CAN I GET THE REAL ANSWER I NEED THIS 100% MY MOM IS GOING WHOOP ME TILL I GOT 10 STAINS ON MY BUTT AND LEGS PLEASE HELP
Answer:
Haha sure mate! Its 116 :) Your thing is wrong but I would select 106 because it seems like a more reasonable mistake
Step-by-step explanation:
Give me braiest answer if I saved you a whooping
Answer:
The answer to your question is 244 degrees
Step-by-step explanation:
Simply add 60, 90, 82, and 12 to get 244 degrees.
Given the inequality -8<2, explain what happens when you multiply or divide both sides by 2 and what happens when you multiply or divide both sides by -2.
Answer:
When you multiply or divide both sides by 2, the result is going to be a negative number.
When you multiply or divide both sides by -2, the results are going to be positive.
Step-by-step explanation:
When you multiply or divide a negative and a negative, it's going to be a positive.
When you multiply or divide a negative and a positive, it's going to be a negative.
The cost of a High Definition television now averages $700, but the cost is decreasing about 15% per year. In how many years will the cost be under $200?
Answer: 7.7 years
Step-by-step explanation:
Given
The cost of HD TV is $700 and it is decreasing at the rate of 15% per year
After one year it becomes
[tex]\Rightarrow 700-700\times 15\%\\\Rightarrow 700(1-0.15)[/tex]
after 2 year it becomes
[tex]\Rightarrow 700(1-0.15)-700(1-0.15)\times 15\%\\\Rightarrow 700(1-0.15)(1-0.15)\\\Rightarrow 700(1-0.15)^2[/tex]
Suppose, after x years it becomes $200
[tex]\Rightarrow 200=700(1-0.15)^x\\\\\Rightarrow \dfrac{2}{7}=0.85^x\\\\\text{Taking log both sides}\\\\\Rightarrow x=\dfrac{\ln (\frac{2}{7})}{\ln (0.85)}\\\\\Rightarrow x=7.7\ \text{years}[/tex]
Thus, it takes 7.7 years for the cost to come under $200.