We can solve both limits by using Riemann sums, which is represented by the following:
[tex]\lim _{n\to a}\sum ^n_{i=1}f(x_{i-1})\Delta x,\text{ where }\Delta x=\frac{b-a}{n}[/tex]Then, for our function:
[tex]undefined[/tex]Find a and b such that
The coefficients (a, b) = (4, 2) are the solutions to the system formed by three equations with two variables.
How to find the coefficients associated with a linear coefficient
In this problem we must determine the values of two coefficients associated with a linear combination, which is equivalent to the following system of linear equations:
a + 4 · b = 12
a - b = 2
- 3 · a + 5 · b = - 2
Since the number of equations is greater than the number of variables, there are two posibilities: (i) No solution, (ii) A solution. Now we find the solution to the system formed by the first and second equations:
a + 4 · b = 12
a - b = 2
(a, b) = (4, 2)
Now we check in the third equation:
- 3 · 4 + 5 · 2 = - 2
- 12 + 10 = - 2
- 2 = - 2 (TRUE)
The coefficients (a, b) = (4, 2) are the solutions to the system.
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What is the distance between point R(-1, 7) and point T(-7, 7)?
O 1 unit
O 6 units
O 7 units
O 8 units
Answer: 6 units
Step-by-step explanation: first set up the distance formula
d= the square root of [(-7+1)^2+(7-7)^2}
the y values =0 so we are left with the square root of -6^2=d
and this simplifies out to d=6
1. What is the greatest commonfactor (GCF) for the following function. 2x +4 = 0? #2 Factor out the GCF and what is leftgoesinside the parenthesis.
We have the expression:
2x+4
Analyzing each term separately we have
2x=2*x
4=2*2
We can see there is one factor that both expressions have: the number 2
1. The GCF is 2
2.
The GCF is 2, and if we want to factor it out, we must divide both terms by 2:
2x+4=2(x+2)
Note the term 2x was divided by 2 to get x, and 4 by 2 is 2
The factored function is
2x+4=2(x+2)
What is -|-16| +(-8)*5²
PLEASE HELP IT FOR FINALS 15. Complete the paragraph proof below by selecting the missing justification. Given: CB bisects ZABD and ZACD. Prove: AABC ADCB А B n C D Gred that CB bisects ZABD and ZACD then by definition of angle bisector LABCLDBC and LACBEZDCB. Next, BC & CB by the Therefore by ASA, AABC ADCB Answer choices -Reflexive Property of CongruenceDefinition of Congruent Segments CPCTCTransitive Property of Congruence
Solution
For this case we can see that the correct solution would be;
Given that CB bisects angle bisector theorem
Therefore by ASA. Triangle ABC = Triangle DCB
PLEASE HELP DUE IN 23 and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
X is 44 - X = 44
Step-by-step explanation:
Please help me with mine.
A line has a slope of -8 and passes through the point (0,5)
A line has a slope of -8 and passes through the point (0,5)
Find out the equation of the line in slope-intercept form
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
in this problem
m=-8
b=5
therefore
y=-8x+5 -----> equation of the line in slope-intercept formConsider the expression.5n -2 =9Which statement best describes this expression?O A number less than two times five is 9.O Five times a number subtracted from two equals 9.O Five minus two times a number equals 9.Two less than five times a number is 9.
1) Looking at that expression
5n -2= 9
Since the expression is written this way, we can assume the wording is
Five times a number subtracted from two equals 9.
Because the number, n is 1 unit, then. We can read like that.
Plot (−134,412) on the coordinate plane.
Consider the coordinate (-1 3/4, 4 1/2).
Therefore, the x coordinate and y coordinate are - 1 3/4 and 4 1/2 respectively.
First, we must move back and forth between -1 and -2 by one and three.
In order to acquire 4 1/2, we must first get 4 above the y-axis, followed by half between 4 and 5.
The location at which the horizontal line at 4 1/2 and the vertical line at -1 3/4 would connect would be marked with a coordinate.
Or,
x = - 1 ( 3/4 ) = - 7/4 = - 1.75 and;
y = 4 1/2 = 9/2 = 4.5
Hence, ( -1 3/4, 4 1/2 ) = ( - 1.75, 4.5 ).
The shown red point on the graph is the coordinate (-1 3/4, 4 1/2).
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Factor the polynomial completely.
x3 + 6x + x2 + 6
Group of answer choices
(x2 + 1)(x + 6)
(6x + 1)(x + 1)
(x2 + 6)(x + 1)
Answer:
(x² + 6)(x + 1)
Step-by-step explanation:
x³ + 6x + x² + 6
x³ + x² + 6x + 6
(x³ + x²) + (6x + 6)
x²(x + 1) + 6(x + 1)
(x² + 6)(x + 1)
I hope this helps!
Find the equation of the line through the point (1,-1) with
slope 4?
Answer:
4x - y - 5 = 0
Step-by-step explanation:
Given:
Slope = m = 4
(x1,y1) = (1,-1)
Solution:
y - y1 = m (x - x1)
y - (-1) = 4 (x - 1)
y + 1 = 4x - 4
y = 4x - 4 - 1
y = 4x - 5
4x - y - 5 = 0
Please help me. Thank you. I’m supposed to move the coordinates on the plane.
The rectangle has upper-left coordinates (3,-3), upper-right coordinates (7,-3) and area 16 square units.
By these coordinates, we know that it's base length is 7 - 3 = 4 units.
And, since the area of a rectangle is given by it's base length times its height h, which is: 4*h = 16, which implies h = 4 units.
Therefore, the botton coordinates will be (3,-3-4) = (3,-7) and (7,-3-4) = (7,-7)
1. Green Forest Day Camp has 43 fewer girl campers than boy campers. There are 278 boy campers. Use rounding to estimate the total number of campers. 2. Green Forest Day Camp has 43 fewer girl campers than boy campers. There are 278 boy Campers. How many actual total campers does Green Forest Day Camp have?
Answer: 513 campers
Explanation
The total number of boys in the camp is 278
There are 43 fewer girl campers than boy
Let the total number of campers be x
Let the total number of girl campers be y
Since, there are 43 fewer girl campers than boy
Hence, the total number of girl campers is
y = Boy campers - 43
Boy campers = 278
y = 278 - 43
y = 235
Since, y is the total number of girl campers, hence, the total number of girl campers is 235
The total number of campers = number of boy campers + number of girl campers
The total number of campers = 278 + 235
The total number of campers = 513 campers
The answer is 513 camperst
help me pleasee!!
thank you
Step-by-step explanation:
so, we need to get the slope-intercept form
f(x) = y = ax + b
"a" is as always the slope, "b" is the y-intercept (the y-value when x = 0).
as we have the slope and a point, we can start with the point-slope form and transform it :
y - y1 = a(x - x1)
with (x1, y1) being a point on the line.
y - 7 = -9(x - 2) = -9x + 18
y = -9x + 25
therefore, the functional equation is
f(x) = -9x + 25
which is he mode of this data set? 55, 78, 43, 39, 78, 61, 75, 75, 43, 78
The height (in inches) of a plant after 't' days is (1/2t + 6). After how many days is the plant 21 inches tall? *
Height = 1/2t + 6
To find after how many days the plant is 21 inches tall, replace height by 21:
21 = 1/2t + 6
Solve for t (days)
21-6 = 1/2t
15 = 1/2t
Multiply both sides of the equation by 2:
15(2) = 1/2t (2)
30 =t
After 30 days
Assume that the function
f
is a one-to-one function.
(a) If
f
(
6
)
=
2
, find
f
−
1
(
2
)
.
Your answer is
(b) If
f
−
1
(
−
8
)
=
−
6
, find
f
(
−
6
)
.
Your answer is
Write each expression as a sum or difference or multiple of logarithms, assume the variables represents positive numbers
SOLUTION
The given expression is:
[tex]\log_6\frac{4x}{3}[/tex]This is simplified to give
[tex]\operatorname{\log}_6\frac{4x}{3}=\operatorname{\log}_64x-\operatorname{\log}_63[/tex]This further gives
[tex]\operatorname{\log}_64x-\operatorname{\log}_63=\operatorname{\log}_64+\operatorname{\log}_6x-\operatorname{\log}_63[/tex]Therefore the required answer is:
[tex]\begin{equation*} \operatorname{\log}_64+\operatorname{\log}_6x-\operatorname{\log}_63 \end{equation*}[/tex]please help me with this this math question thank you!
5m-2 = 12m -16
SOLVE
Answer:
m=2
Step-by-step explanation:
m=2 is the answer hope this helped
Answer:
m=2
Step-by-step explanation:
Follow this step by step solution.
Hope this was helpful.
(36yx-16y2²-315x)+(-4y³x³)
Answer:
36yx-64y-315x-4y^3x^3
Step-by-step explanation:
Expand and simplify (36yx-16y2²-315x)+(-4y³x³)
to get 36yx-16y x 2^2-315x-4y^3x^3
Simplifying further to get
36yx-64y-315x-4y^3x^3
The length of a rectangle is three more than twice the width. Determine the dimensions that give a total area of 27ft squareda. create an equation in terms of w to model this situationb. what are the solutions to this equation c. What are the length and width of the rectangle
ok
Area = 27ft^2
length = l
width = w
Equation
l = 2w + 3
Section A
Area
A = l*w
A = (2w + 3)* w or A = 2w^2 + 3w
27 = 2w^2 + 3w
2w^2 + 3w - 27 = 0 This is the equation
Section B
2w^2 - 6w + 9w - 27 = 0
2w(w - 3) + 9(w - 3) = 0
(w - 3)(2w + 9) = 0
w1 - 3 = 0 2w + 9 = 0
Solve the equation.
-x+8+ 3x = x-6
Answer:
x= -14
Step-by-step explanation:
-x + 8 + 3x = x -6
combine -x and 3x to get
8 + 2x = x -6
subtract x from both sides to get
8 + x = -6
subtract 8 from both sides to get
x= -14
y = 4x - 4graph the linear equation and identify the x-intercept
what is the solution set?
Answer:
the set of all the solutions of an equation or condition.
Over the last three evenings, Carmen received a total of 74 phone calls at the call center. The first evening, she received 6 fewer calls than the third evening. The second evening, she received 3 times as many calls as the third evening. How many phone calls did she receive each evening?
Let x be the amount of calls that Carmen received at the third evening.
The first evening she received 6 calls fewer than the third, so that is x-6. The second evening, she received 3 times the number of calls of the third evening. So that is 3*x. The sum of this three quantities should be 74,sinche she received 74 calls in total. So, we have the equation
[tex]x\text{ - 6 +3x+x = 74}[/tex]If we add all x values we get
[tex]5x\text{ - 6 = 74}[/tex]If we add 6 on both sides, we get
[tex]5x\text{ = 74+6 = 80}[/tex]Now, if we divide by 5 on both sides, we get
[tex]x\text{ = }\frac{80}{5}=16[/tex]So in the third evening she received 16 calls. The first evening she received 16-6 = 10 calls and the second evening she received 16*3 = 48 calls.
HELP PLEASEEEEEEEEEEE!! ILL MARK BRAINLIEST
Find the slope, y-intercept and equation of the line for the points (0,3) (2,-1) show work please
we are asked to determine the slope of the line that passes through the points (0, 3) and (2, -1). To do that we need to use the formula for the slope of a line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)=(0,3) \\ (x_2,y_2)=(2,-1) \end{gathered}[/tex]Replacing in the formula:
[tex]m=\frac{-1-3}{2-0}[/tex]Solving the operations:
[tex]m=-\frac{4}{2}=-2[/tex]therefore, the slope is -2.
To determine the y-intercept we can use the point (0,3), since this means that when x = 0, y = 3. Since the y-intercept is the value of "y" when x = 0, this means that the y-intercept is 3.
To determine the equation of the line we need to use the general form of a line equation:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" the y-intercept. Replacing the value of the slope and "b"
[tex]y=-2x+3[/tex]A shopkeeper wants to sell a shirt originally priced at $120. Which deal will result in the greatest sale price of the shirt?A. 20% offB. $30 couponC. 15% off and then a $15 rebateD. 10% off and then a $20 rebate
Let's determine which sale is better.
20% means that the shirt will cost:
[tex]120(0.8)=96[/tex]$30 coupon means that the shirt will cost $90
15% off and $15 rebate means:
[tex]120(0.85)-15=87[/tex]10% off and $20 rebate means:
[tex]120(0.9)-20=88[/tex]Comparing the prices we conclude that the best deal is C
Parallel lines with a transversal
Answer:
Same Side Interior Angles
? = 64
Step-by-step explanation:
180-116=?
64=?
