Remark
You can use a formula to get the right answer. Otherwise you will use a lot of paper adding 100 numbers together.
Givens
A = 1
L = 100
n = 100 numbers to be added together. There are 100 numbers between 1 and 100 numbers inclusive.
Formula
Sum = (A + L)*n/2
Solution
Sum = (1 + 100)*100/2 Substitute in the givens. Add what is inside the brackets
Sum = (101) * 100 / 2 Divide by 2
Sum = 101* 50 Multiply
Sum = 5050 Answer
The sum of the numbers from 1 to 100 is 5050
Explanation:The sum of the numbers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers where the difference between two consecutive terms is constant. In this case, the difference between successive numbers is 1.
The formula for an arithmetic series's sum (S) is S = n/2 (a + l), where n is the number of terms, a is the first term, and l is the last term.
Here, n = 100 (because we're adding the numbers from 1 to 100), a = 1 (the first number) and l = 100 (the last number). Substituting these values into the formula gives us S = 100/2 * (1 + 100) = 50 * 101 = 5050.
So the sum of the numbers from 1 to 100 is 5050.
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BRAINLIEST!!PLEASE HELP
Which of the points satisfy the linear inequality graphed here?
A) (0, 0)
B) (10, 0)
C) (-10, 0)
D) (10, 10)
C . Find a point that lies in the shaded region, or plug the points in and determine which point makes the inequality true.
complete the first 4 steps for graphing the quadratic function given. (Use ^ on the keyboard to indicate an exponent.)
y = -x2 - 4x - 3
There are multiple ways that you could graph this quadratic equation. I would start by finding the vertex. The x-value in the vertex is found with -b/2a. The take you value and input back into the equation to find the y-value of your vertex. Then, you could make a list of points on both sides of the vertex to create a table with which to create the parabola.
Answer:
Step-by-step explanation:
is equal 45
HELP. Will give brainliest. MORE THAN ONE ANSWER FOR EACH QUESTION.
Question 1.
Find the equation of the line with a slope of -3, passing through the point (2, 5).
a. y = -3x - 1
b. y = -3x + 11
c. y = -3x + 5
d. y = 2x + 5
MULTIPLE ANSWERS.
Question 2.
Find the equation of the line passing through the points (2, -1) and (-6, -5)
a. y = 2x - 5
b. y = -1/2 x
c. y = 1/2 x
d. y = 1/2 x - 2
MULTIPLE ANSWERS
One
Slope
The general slope intercept equation for a line is
y = mx + b
If you are told outright what the slope is then you can write m = slope in this case - 3
So you have so far is y = -3x + b. Now you use the point to get the y intercept.
(2,5) means that when x = 2, y = 5. that allows you to solve for b
Y intercept
When x = 2, y = 5. Substitute that into the general equation with the slope.
5 = -3x + b Put 2 in for x
5 = -3 * 2 + b Multiply -3 * 2
5 = - 6 + b Add 6 to both sides
5 + 6 = b
11 = b
Answer
y = -3x + 11
Two
This question is a little harder. You have to find the slope.
Slope Formula
[tex]\text{m = } \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Givens
Points (2, -1), (-6, - 5)
y2 = -1 ; y1 = -5; x2 = 2; x1 = -6
Solve
m = (-1 - - 5)/(2 - - 6) = (-1 + 5)(2 + 6) = 4/8 = 1/2
Now find the y intercept. Use either one of the given points
(2,-1) when x = 2, y = - 1
y = 1/2 x + b Show what you have so far. Put in x = 2 for x and y = - 1 for y
-1 = 1/2(2) + b Multiply 2*1/2
-1 = 1 + b Subtract 1 from both sides.
-1 -1 = b
- 2 = b
Answer
y = (1/2)x - 2 which is D
Jill just made a purchase online. The store that she bought from gave her the option to pay with a check, money order, or credit card. The item will not be shipped until her payment arrives. Why would Jill want to use a credit card instead of a money order or check?
If Jill pays with a credit card, her payment will be recorded immediately. This means that the item could be shipped almost as soon as she pays for it. On the other hand, if she uses a check or money order, then her payment will take a while to be received, as she would have to send the physical item over the mail. Therefore, she would receive her package earlier if she paid with a credit card.
Which is more? (2 points) 1 kiloliter 1 centiliter 1 decaliter 1 milliliter
Today the 6th graders had 5 students absent, the 7th graders had 8 students absent,and the 8th graders had 9 students absent. If the attendance follows the same trend for the month (assume 20 days) how many times will a 7th grade student be absent during the month?
A 7th grade student will be absent approximately 0.4 times during the month.
Explanation:To find out how many times a 7th grade student will be absent during the month, we first need to determine the average number of absent students per day for each grade. The total number of absent students across all grades is 5 + 8 + 9 = 22. Since there are 20 school days in a month, the average number of absent students per day is 22 / 20 = 1.1.
Next, we need to determine the proportion of absent students that are 7th graders. The 7th graders had 8 absent students, so their proportion of absent students is 8 / 22 = 0.3636 (rounded to four decimal places).
Finally, to find out how many times a 7th grade student will be absent during the month, we multiply the average number of absent students per day (1.1) by the proportion of absent students that are 7th graders (0.3636). This gives us the final answer of approximately 0.39996 (rounded to five decimal places) or about 0.4 times.
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Which formula represents the hyperbola on the graph shown below?
Note: Answer choices and graph attached below...
Answer:
Your answer choice is appropriate
Step-by-step explanation:
The orientation is vertical, so the parent function is
... y² - x² = 1
The vertical offset is -3 and the horizontal offset is positive, so the variables will be of the form (y+3)² and (x-something)². At this point, you're able to choose the correct answer.
The distance center to vertex is 13, so we know the y-term denominator is 13². We cannot tell from this graph what the x-term denominator should be, but all the answer choices are in agreement that it should be 81.
The appropriate choice is ...
... (y+3)²/169 - (x-2)²/81 = 1
Answer:
If you are looking for the answer to a graph that looks similar but slightly different, the answer is C.
This graph looks like the one above, but it is inverted, the top hyperbola reaches 15, and the bottom reaches 10. This is correct for A.P.E.X
Hope this helps I couldn't find it anywhere else on brainly.
What is the x coordinate of the solution to the system?
-2x+6y=-38
3x-4y=32
I tried both linear combination and substitution, but I can't eliminate any variables. I know I'm doing something wrong, but I don't know what.
-2x + 6y = -38 ⇒ 3(-2x + 6y = -38) ⇒ -6x + 18y = -114
3x - 4y = 32 ⇒ 2(3x - 4y = 32) ⇒ 6x - 18y = 64
0 = 50
FALSE
False statement means there are no solutions.
Answer: No Solution
We will solve this system with method of opposing coefficients - Gaussian algorithm
-2x+6y= -38
3x-4y= 32
We will divide first equation with number 2 and get
-x+3y = - 19
then we will multiply the same equation with number 3 and get
-3x+9y = - 57
We will overwrite the second equation below the last one and get next equivalent system
-3x+9y = - 57
3x-4y = 32
We add first equation to the second and get
5y = -25 => y= -25/5 => y= -5
Now we will replace variable y= -5 in the equation -x+3y = - 19 and get
-x+3(-5) = -19 => -x-15 = -19 => x- 19-15=4 => x=4
The correct answer is (x,y) = (4,-5)
We can check in the first equation and get
-2*4+6*(-5) = -38
-8-30 = -38
-38 = -38 We get equality, the solutions are correct.
This system have one real solution.
Good luck!!!
Celine has a bottle that contains 20% milk and the rest water. The bottle has 1 liter of water. Part a: write an equation using one variable that can be used to find the total number of liters of milk and water in the bottle. Define the variable used in the equation. Hint: 0.2x represents the number of liters of milk in the bottle. (5 points) part b: how many liters of milk are present in the bottle? Show your work. (5 points)
The given condition is- A bottle contains 20% milk and the rest water. The bottle has 1 liter of water.
Part A:
Let the amount of mixture in the bottle be = x ; mixture will be amount of water plus milk
Given is- the bottle has 1 liter of water and 20% is milk. 20% is 0.2
Hence equation will be:
[tex]0.2x+1 =x[/tex]
Part B:
Solving the equation
[tex]x-0.2x=1[/tex]
[tex]0.8x=1[/tex]
[tex]x=\frac{1}{0.8}[/tex] = 1.25
Hence, total mixture is 1.25 liters.
Water is 1 liter so milk will be = [tex]1.25-1=0.25[/tex]
Or it can also be solved using milk percentage of 0.2%
[tex]0.2*1.25=0.25[/tex]
Hence, milk is 0.25 liter
Describe the graph of the function at its roots. f(x) = (x − 2)3(x + 6)2(x + 12) At x = 2, the graph crossesdoes not intersecttouches the x–axis. At x = −6, the graph crossesdoes not intersecttouches the x–axis. At x = −12, the graph crossesdoes not intersecttouches the x–axis.
For the graph of given function ,
At x=2, the graph crosses x axis
At x=-6, the graph touches x axis
At x=-12, the graph crosses x axis
Given :
Equation of a function [tex]f\left(x\right)\:=\:\left(x\:-\:2\right)^3\left(x\:+\:6\right)^2\left(x\:+\:12\right)\:[/tex]
Lets find out the roots and analyze
lets set each factor =0 and solve for x
Exponent in each factor tell us the multiplicity . Using multiplicity we check whether crosses or touches x axis
When multiplicity is odd then graph crosses x axis .
when multiplicity is even then graph touches x axis.
[tex]f\left(x\right)\:=\:\left(x\:-\:2\right)^3\left(x\:+\:6\right)^2\left(x\:+\:12\right)\:\\(x-2)^3= 0\\x-2=0\\x=2[/tex]
Root is x=2 with multiplicity 3. 3 is odd
At x=2, the graph crosses x axis
[tex](x+6)^2=0\\x+6=0\\x=-6[/tex]
At x=-6, multiplicity is 2 that is even .
At x=-6, the graph touches x axis
[tex]x+12=0\\x=-12[/tex]
x=-12 with multiplicity 1. 1 is odd
At x=-12, the graph crosses x axis
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Points c, a and b are collinear. Which of the following are opposite rays
Answer:
Ac and ad
Step-by-step explanation:
The following are opposite rays; AC and AD. so option B is correct answer.
What do you mean by collinear?For points to be collinear means they lie on the same line. A rays to be opposite, they should be in the same line making a 180° or a straight line with each other.
A Coplanar means the points lie in the same plane. For these rays to be opposite and collinear the points should lie in the same plane.
Given; Points c, a and b are collinear.
A, B, C are coplanar and also A, B, C are collinear.
The following are opposite rays; AC and AD. so option B is correct answer.
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Mark earned some money doing odd jobs last summer and put it in a savings account that earns 2% interest compounded quarterly. After 5 years, there is $300.00 in the account. How much did Mark earn doing odd jobs?
Here we will use the formula of compound interest which is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where,
A=amount
P=principal
r=rate of interest
n=number of times interest is compounded in a year
t=time
We are given,
r=2% or 0.02
t= 5 years
n =4( compounded quarterly)
A= $300
Let us plug these in the formula to find Principal
[tex]300=P(1+\frac{0.02}{4})^{4*5}[/tex]
[tex]300=P(\frac{4.02}{4})^{4*5}[/tex]
[tex]300=P(1.005)^{20}[/tex]
[tex]300=P(1.105)[/tex]
Principal = $271.49
Answer: Mark earned $271.49 during odd jobs.
To calculate the original amount Mark earned, the compound interest formula is used with the given interest rate, compounding frequency, future amount, and time period. After solving for the principal amount, it's determined that Mark originally earned approximately $271.73.
In order to determine how much Mark originally earned, we need to use the formula for compound interest which is A = P(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for in years.Given that the final amount A is $300.00, the annual interest rate r is 2%, the interest is compounded quarterly (so n is 4), and the time t is 5 years, we can plug these values into the formula and solve for P:
300 = P(1 + 0.02/4)⁴*⁵
300 = P(1 + 0.005)²⁰
300 = P(1.005)²⁰
To find P, we divide both sides by (1.005)²⁰:
P = 300 / (1.005)²⁰
Using a calculator, we can find that:
P ≈ 300 / 1.10408
P ≈ 271.73
Therefore, Mark originally earned approximately $271.73 doing odd jobs last summer.
What is the area of a flour tortilla that has a 14-centimeter radius?
Final answer:
The area of the flour tortilla with a 14-centimeter radius is approximately 615.75 square centimeters.
Explanation:
The area of a circle is given by the formula A = πr², where r is the radius. Given a 14-centimeter radius, the area of the flour tortilla would be:
A = π(14 cm)² = 196π cm² ≈ 615.75 cm²
Thus, the area of the flour tortilla is approximately 615.75 square centimeters.
A triangle has a perimeter of 90 centimeters write and use a linear system
We are given sides of the triangle by expression
First side : n
Second side : m = 5n-5.
Third side : l = 5/4 m - n.
Perimeter is 90.
Therefore, first equation could be set :
n +m +l = 90 --------------equation(1)
Second equation would be
m = 5n-5 --------------equation(2)
Third equation would be
l = 5/4 m - n --------------equation(3)
Let us solve the system of equations by substitution.
Substituting m = 5n-5 and l = 5/4 m - n in first equation.
We get
n +5n-5 +5/4 m - n= 90
Now, substituting m = 5n-5 in above equation we get
n +5n-5 +5/4 (5n-5) - n= 90
5n + 25n/4 -5 - 25/4 =90
5n + 6.25n -5-6.25 = 90.
11.25n-11.25 = 90
Adding 11.25 on both sides, we get
11.25n-11.25+11.25 = 90+11.25
11.25n = 101.25.
Dividing both sides by 11.25, we get
n=9.
Plugging n=9 in 2nd equation.
m = 5(9)-5 = 45 -5 = 40.
Plugging n=9 and m=40 in first equation, we get
9 +40 +l = 90
49 +l = 90.
Subtracting 49 from both sides, we get
49-49 +l = 90-49
l = 41.
Therefore, sides are of lengths l = 41, m= 40 and n=9.
14|x| - 14 = 41
Algebra
14|x| - 14 = 41 |add 14 to both sides
14|x| = 55 |divide both sides by 14
|x| = 55/14 ↔ x = - 55/14 or x = 55/14
6. The ABC Book Club charges a $40 monthly fee, plus $2 per book read in that month. The Easy Book Club charges a $35 monthly fee, plus $3 per book read in that month. For each club, how many books must be read in 1 month for the total charges from each club to be equal?
The expression for the cost of the ABC Book Club is 2x + 40. The expression for the cost of the Easy Book Club is 3x + 35. To find when the total charge for both book clubs is equal, the two expressions must equal each other. (x = the number of books read)
2x + 40 = 3x + 35
Subtract 35 from both sides.
2x + 5 = 3x
Subtract 2x from both sides.
5 = x
So, the total charge for each club is equal when 5 books are read.
The number of books read from both ABC and Easy book clubs must be 5 in other to have a equal monthly charge.
Let the number of books read = b
ABC Book club :
Monthly charge = $40
Fee per book read = $2
Total monthly charge = 40 + 2b - - - - (1)
Easy Book Club :
Monthly charge = $35
Fee per book read = $3
Total monthly charge = 35 + 3b - - - (2)
To obtain an equal monthly charge ;
Equation(1) = Equation(2) and solve for b
40 + 2b = 35 + 3b
40 - 35 = 3b - 2b
5 = b
Hence, to have an equal monthly charge, the number of books read from each club must be 5.
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WIll give brainiest answer if you are correct.
Express x in terms of y for the linear equation 2/3X + 4Y = -7
ANSWER
[tex]x=-6y-\frac{21}{2} [/tex]
EXPLANATION
We have
[tex]\frac{2}{3}x +4y=-7[/tex].
Expressing [tex]x[/tex] in terms of [tex]y[/tex] means we should rewrite the relation such that [tex]x[/tex] will remain on one side of the equation while [tex]y[/tex] and any other constant will be at the other side.
To make [tex]x[/tex] the subject, we add [tex]-4y[/tex] to both sides of the equation.
[tex]\frac{2}{3}x =-4y-7[/tex].
we now multiply the whole equation by the reciprocal of the coefficient of [tex]x[/tex], which is [tex]\frac{3}{2}[/tex].
This implies that;
[tex]\frac{3}{2} \times \frac{2}{3} x=\frac{3}{2} \times (-4y)-\frac{3}{2} \times 7[/tex]
This simplifies to;
[tex]x=-6y-\frac{21}{2} [/tex]
56.7 x41 how to work out without calculator
How do you finish this graph?
The slope is [tex]m=\dfrac{\Delta y}{\Delta x}[/tex]
We have slope m = 3.
[tex]m=3=\dfrac{3}{1}[/tex]
3 > 0 - up 3 units
1 > 0 - right 1 unit
Answer in attachment.
You have two credit cards. One has a balance of $3,745.00 at a 6.25% apr and the other has a balance of $1,045.00 and is dependent upon your credit score. Your score is 500. How much total interest is accrued in the first month? Score <500 500-650 651-750 751-800 rate (apr) 12.75% 10.25% 7.5% 5.75% $28.44 $24.51 $30.41 $26.04
The total interest accrued on two credit cards in the first month is $28.44, with $19.51 coming from the first card with a balance of $3,745 at 6.25% APR and $8.93 from the second card with a balance of $1,045 at 10.25% APR based on a credit score of 500.
The question involves calculating the total interest accrued on two credit cards in the first month. The first credit card has a balance of $3,745.00 at an annual percentage rate (APR) of 6.25%, and the second credit card has a balance of $1,045.00 with an APR that depends on the credit score. Given a credit score of 500, the APR for the second card is 10.25% (per the provided table).
First, to find the monthly interest for each card, we can use the formula: Monthly Interest = (Balance) x (APR) / 12 months.
For the first card: Monthly Interest for $3,745.00 at 6.25% APR is ($3,745.00) x (0.0625) / 12 = $19.51.
For the second card: Monthly Interest for $1,045.00 at 10.25% APR is ($1,045.00) x (0.1025) / 12 = $8.93.
To find the total interest accrued from both credit cards in the first month, simply add the monthly interest amounts from each card: $19.51 + $8.93 = $28.44.
What is the answer to this question 34+0+18+26 please help and fast
Match the following conditional statement: if two lines intersect, then their intersection is one point.
1.if the lines intersections of two lines is a point, then they intersect
2. If two lines do not intersect, then their intersection is not one point
3. If the intersection of two lines in not one point, then the two lines do not intersect
1. If the intersection of two lines is a point, then they intersect. = Converse
2. If two lines do not intersect, then their intersection is not one point. = Inverse
3. If the intersection of two lines is not one point, then the two lines do not intersect. = Contrapositive
I did the assignment already, it's correct.
The conditional statement 'If two lines intersect, then their intersection is one point' is matched with three possible related statements.
The conditional statement 'If two lines intersect, then their intersection is one point' can be matched with the following:
If the intersection of two lines is a point, then they intersect
If two lines do not intersect, then their intersection is not one point
If the intersection of two lines is not one point, then the two lines do not intersect
Explanation:
This question is about conditional statements related to the geometric properties of lines. The given statement is that if two lines intersect, their intersection is exactly one point. Statement 1 is the converse, meaning if their intersection is a point, then the lines must intersect. Statement 2 is the contrapositive, asserting that if two lines do not intersect, they can't have a single intersection point. Statement 3 reason that if the intersection is not exactly one point, then they do not intersect at all.
Write the equation of the line that contains the given point and has the given slope. (–1, 1), slope = –2
The equation of the line that passes through the point (–1, 1) and has a slope of –2 is y = -2x - 1.
Explanation:The question is asking for the equation of the line that passes through the point (–1, 1) and has a slope of –2. The formula for a line is y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope (m) is -2, and we have the coordinates of a point on the line (-1,1), we can substitute these values into the formula to solve for 'b', the y-intercept.
So, 1 = -2*(-1) + b, which simplifies to 1 = 2 + b. Solving this for b gives us a y-intercept (b) of -1.
Therefore, the equation of the line that contains the given point and has the given slope is y = -2x - 1.
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Which equation has the following characteristics?
y varies directly with x
y=30 when x =3
A. y=27+x
B. y=10x
C. y=33-x
D. 30x
I think it's B
Lea buys 6 model cars that each cost 15$. She also buys 4 bottles of paint that each cost $11. How much does lea spend on model cars and paint?
Lea spends $134 on model cars and paint.
Explanation:To find out how much Lea spends on model cars and paint, we need to calculate the total cost of each item and then add them together. The cost of 6 model cars is 6 x $15 = $90. The cost of 4 bottles of paint is 4 x $11 = $44. Adding these two amounts together, Lea spends $90 + $44 = $134 on model cars and paint.
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To make 7 bowls of punch, you need 5 bottles of soda. How many bottles do you need to make 12 bowls of punch?
To determine how many bottles of soda are needed for 12 bowls of punch, we use the given ratio of 7 bowls to 5 bottles and set up a proportion. We find that 9 bottles of soda are needed for 12 bowls of punch.
The question asks us to figure out how many bottles of soda we need to make a larger amount of punch based on a known ratio. Since it is given that 7 bowls of punch require 5 bottles of soda, we can set up a proportion to find out how many bottles of soda we need for 12 bowls of punch. To do this, we use the initial ratio (7 bowls/5 bottles) and set it equal to the desired ratio (12 bowls/x bottles), where x represents the unknown number of bottles needed for 12 bowls.
We can solve for x by cross-multiplying and dividing:
Set up the proportion: (7 bowls / 5 bottles) = (12 bowls / x bottles)
Cross-multiply: 7 * x = 5 * 12
Simplify: 7x = 60
Divide both sides by 7: x = 60 / 7
Since 60 divided by 7 is not a whole number, we round up, because you can't have a fraction of a bottle in this context. Therefore, x
= 9 bottles (rounded up from 8.57)
So, we would need 9 bottles of soda to make 12 bowls of punch.
a student concluded that has infinitely many solutions. Which statement BEST describes the student’s conclusion?
A: The conclusion is incorrect because there is exactly one solution to the equation.
B: The conclusion is correct because there are exactly two solutions to the equation.
C: The conclusion is correct because when simplified, both sides of the equation are equivalent.
D: The conclusion is incorrect because the equation has no solution.
What's the equation?
Without knowing the specific equation, it's difficult to definitively judge the student's conclusion. Assuming the equation is correctly simplified, if both sides of the equation are identical, then it has infinitely many solutions.
Explanation:The student's claim about the equation having infinitely many solutions is valid only if, upon reducing the equation to its simplest form, both sides are completely identical. Unfortunately, without knowing the specific equation in question, it's impossible to precisely identify whether the conclusion is correct or not. However, if we assume the student has correctly simplified the equation and found that both sides match exactly, then we can say that statement C: 'The conclusion is correct because when simplified, both sides of the equation are equivalent' is valid.
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Which of the following are measures of supplementary angles? A. 60° and 30° B. 122° and 58° C. 180° and 90° D. 45° and 45°
Answer: B) 122 and 58
Supplementary angles add to 180 degrees. In other words, they form a straight angle or a straight line when you combine them together (make sure they don't overlap and that there isn't any gap between them).
Choice B is the only pair of angles where they add to 180 since 122+58 = 180. The values in choice A and choice D add to 90; the values in choice C adds to 270.
Note: complementary angles add to 90 degrees. One way to remember "supplementary" vs "complementary" is to think "S for straight, C for corner". By "corner", I mean a 90 degree corner.
In July, 3/5 of the 160 babies born in an area hospital were girls. Seventy of the babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more. Which of the following tables shows relative frequency by row?
Imma guess the middle one
Answer:
B
Step-by-step explanation: