Answers
thus
[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 4}}\quad ,&{{ 6}})\quad % (c,d) &({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)[/tex]
[tex]\bf \left(\cfrac{{{ x}} + {{ 4}}}{2}\quad ,\quad \cfrac{{{ y}} + {{ 6}}}{2} \right)=(\underline{7,2})\implies \begin{cases} \cfrac{x+4}{2}=\underline{7}\\\\ x+4=14\\ x=14-4\\ \boxed{x=10}\\ ----------\\ \cfrac{y+6}{2}=\underline{2}\\\\ y+6=4\\ y=4-6\\ \boxed{y=-2} \end{cases}[/tex]
Related Questions
Use the arc length formula to find the length of the curve y = 5x − 4, −1 ≤ x ≤ 3. check your answer by noting that the curve is a line segment and calculating its length by the distance formula
Answers
The length of the arc is computed from the formula
[tex]S= \int_{-1}^{3} \,\sqrt{1+ (\frac{dy}{dx} )^{2}} \, dx[/tex]
The derivative is
y' = 5
Therefore
[tex]S = \int_{-1}^{3} \sqrt{1+25} \, dx =\sqrt{26}*(3-(-1))=20.396[/tex]
Note that
x = -1 +> y = 5(-1) - 4 = -9
x = 3 => y = 5(3) - 4 = 11
The distance between the points (-1, -9) and (3, 11) from the distance formula is
D = √[(3-(-1))² + (11-(-9))²] = √(16+400) = 20.396
This answer agrees with that obtained by integration.
Answer: 20.396
Obtained by integration and verified by the distance formula.
The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.
To find the length of the curve y = 5x − 4 over the interval −1 ≤ x ≤ 3, we can use the arc length formula for a function y = f(x). The formula for the arc length L is given as:
L = ∫ab√(1 + (dy/dx)2) dx, where dy/dx is the derivative of y with respect to x.
1. Calculate the derivative dy/dx:
y = 5x − 4, so dy/dx = 5.
2. Substitute the derivative into the arc length formula:
L = ∫-13√(1 + 5²) dx = ∫-13√26 dx.
3. Integrate the function:
L = √26 ∫-13 dx = √26 [x]-13 = √26 (3 − (-1)) = 4√26 ≈ 20.396.
To verify this using the distance formula (since the curve is a straight line), we take the points (−1,−9) and (3,11) from the given curve:
4. Apply the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) = (-1, -9) and (x2, y2) = (3, 11).
Therefore,
Distance = √((3 - (-1))² + (11 - (-9))²) = √((4)² + (20)²) = √(16 + 400) = √416 = 4√26 ≈ 20.396.
Thus, the arc length calculated using the formula and the distance formula are consistent.
The arc length is 4√26, which is confirmed by the distance formula for a line segment yielding approximately 20.396 units.
how would you solve it. I know the answer already. my problem working it out.
4b/2 + 3 = 11 + b.
Answers
4b/2 = 8 +b
multiply both sides by two
(4b/2 = 8 + b) X2 = 4b = 16+2b
subtract 2b from both sides
2b = 16
divide both sides by 2
b=8
1. Simplify any parentheses using the distributive property if needed.
2. Combine like terms if needed.
3. Use the addition principle of equality if needed.
4. Use the multiplication or division principle of equality if needed.
[tex]\frac{4b}{2} + 3 = 11 + b[/tex]
2b + 3 = 11 + b
b + 3 = 11 <-- Subtract b from each side
b = 8 <-- Subtract 3 from each side
So, b is equal to 8.
Oh Plz help - I can't handle this one :)
Answers
b: 4*0.5*1.5 = 3, 6*4 = 24, 6*2.5 = 15.5, 15.5*2 + 3*2 + 24 = 61m^2
c: 5.2*3.5 = 18.2, 2.4*3.5 = 8.4, 2.4*5.2 = 12.48, 12.48*2 + 8.4*2 + 18.2*2 = 78.16ft^2
A bit late but hope it helps
A = 2 *pi * r^2 + 2 * pi * r * h
A = 2 * pi * 5^2 + 2 * pi * 5 * 10
A = 50 pi + 100 pi
A = 150 * pi cm^2 (Exact Answer)
A = 471 cm^2 (Decimal Approximation)
b. A(triangles)
A = (1/2) * b * h * 2
A = (1/2) * 4 * 1.5 * 2
A = 6 m^2
A(rectangles)
A = L * W
A = 4 * 6 + 2.5 * 6 * 2
A = 24 + 30
A = 54 m^2
Total area = 6 + 54 = 60 m^2
c. A(rectangular prism)
A = 2LW + 2LH + 2WH
A = 2 * 5.2*2.4 + 2 * 5.2 * 3.5 + 2 * 2.4 * 3.5
A = 78.16 ft^2
d. A(rectangular prism)
A = 2LW + 2LH + 2WH
A = 2 *12 * 6 + 2 * 12 * 4.5 + 2 * 6 * 4.5
A = 306 ft^2
e. You have a large box to wrap and need to know how much wrapping paper will be needed to wrap the box.
The dimensions of the box are L = 10 in., W = 4 in., H = 6 in.
5 radians is the same as _____.
Answers
5rad(360°/2π rad)=900/π degrees
That is approximately:
286.48° (to nearest hundredth of a degree) or
286°28'44" (to nearest second)
Answer:
286°28'44
Step-by-step explanation:
Which system is the only inconsistent system?
Select one:
a.
y
y
=
=
x+4
2x+4
y=x+4y=2x+4
b.
y
y
=
=
x
−x
y=xy=−x
c.
y
y
=4
=
x−3
4x+3
y=4x−3y=4x+3
d.
y
2y
=2
=
x−3
4x−6
y=2x−32y=4x−6
Answers
Option (c) represents an inconsistent system of equations, as the constant terms are not proportional, while the coefficients of x are. This system (y=4x-3, y=4x+3) has no solutions.
Explanation:In mathematics, specifically in algebra, an inconsistent system is a system of equations that has no solutions. To check which system is inconsistent from the options you've given, we need to compare the coefficients of each equation within a system. An inconsistent system will have proportional coefficients of x and y between the two equations, but the constant terms will not be proportional.
Looking at each option:
Option (a): y=x+4 and y=2x+4
Option (b): y=x and y=−x
Option (c): y=4x−3 and y=4x+3
Option (d): y=2x−3 and 2y=4x−6
From here, we can see that option (c): y=4x-3, y=4x+3 is inconsistent. In this system, the coefficients of x are proportional (4), but the constant terms (-3 and +3) are not proportional.
Learn more about Inconsistent Systems here:https://brainly.com/question/35587704
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How can you eliminate the fraction from each side of the equation to make finding the
solution easier?
The equation is 1/2(x - 4) = 1/3x + 2
Answers
1/2(x - 4) = 1/3x + 2
multiply by : 6
3(x-4) = 2x +4
solution easier:
3x -12 = 2x +4
3x - 2x = 12+4
x = 16
Wich of the operations ,+,-,x➗are inverse o each other
Answers
The coordinates of the midpoint of GH¯¯¯¯¯¯¯¯are M(−2, 5) and the coordinates of one endpoint are H(−3, 7) .
The coordinates of the other endpoint are ( __ , __ )
Answers
(-3 + x) / 2 = -2
-3 + x = -4
x = -4 + 3
x = -1
(7 + y) / 2 = 5
7 + y = 10
y = 10 - 7
y = 3
so the other endpoint is (-1,3)
The coordinate point of the other endpoint, G is (-1, 3)
The given parameters;
the midpoint = M(-2, 5)
one end point = H(-3,7)
To find:
the coordinate point of the other endpoint, GLet the coordinate point of the other endpoint = G(x, y)
The coordinate point of the other endpoint, G will be calculated using midpoint formula.
[tex]M(-2, 5) =( \frac{x + (-3)}{2} , \frac{y + 7}{2} )\\\\-2 = \frac{x - 3}{2} \ \ \ and \ \ 5 = \frac{y+ 7}{2} \\\\x-3 = 2(-2)\\\\x - 3 = -4\\\\x = -4 + 3\\\\x = -1\\\\y+ 7 = 2(5)\\\\y + 7 = 10\\\\y = 10 -7\\\\y = 3\\\\G= (-1, 3)[/tex]
Thus, the coordinate point of the other endpoint, G is (-1, 3)
Learn more here: https://brainly.com/question/10812174
SOMEONE PLEASE HELP ME WITH MATH! WILL GIVE BRAINLIEST TO FIRST PERSON WHO ANSWERS!!
Solve each system by substitution.
1. -5x-8y=9
y= -3.
2. y= -3x
-6x-2y=3
3. 6x+5y=10
y=-8x+2
4.6x+2y= -6
y= -3x -3
Thank you!
Answers
-5x+24=9
-5x=-15
x=3
(3,-3)
2. -6x-2(-3x)=3
-6x+6x=3
0=3
No solution
3. 6x+5(-8x+2)=10
6x-40x+10=10
-34x+10=10
-34x=0
x=0
y=-8(0)+2
y=2
(0,2)
4. 6x+2(-3x-3)=-6
6x-6x-6=-6
-6=-6
Infinitely many solutions
Evaluate P(6,2).
A.) 12
B.) 30
C.) 360
Answers
[tex]6P2=\frac{6!}{(6-2)!}=\frac{4!\cdot 5 \cdot 6}{4!}=5 \cdot 6=30[/tex]
The value of the [tex]\rm ^6p_2[/tex] is 30.
We have to determineThe value of P(6,2).
According to the question
The value of the [tex]\rm ^6p_2[/tex] is determined by using permutation.
The probability of selecting an ordered set of 'r' objects from a group of 'n' number of objects.
The order of objects matters in the case of permutation.
The formula to find [tex]\rm ^np_r[/tex] is given by:
[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}[/tex]
Substitute n = 6 and r = 2 in the formula;
[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}\\ \\ \rm ^6p_2 = \dfrac{6!}{(6-2)!}\\ \\ \rm ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4!}\\ \\ ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4\times 3 \times2 \times 1}\\ \\ ^6p_2= 6 \times 5}\\ \\ ^6p_2= 30[/tex]
Hence, The value of the [tex]\rm ^6p_2[/tex] is 30.
To know more about Permutation click the link given below.
https://brainly.com/question/10148445
Factor this expression. With work please!
Answers
[tex]\bf x^6-9x^4-81x^2+729\qquad \begin{cases} x^6=x^{2\cdot 3}\\ \qquad (x^2)^3\\ 729=9\cdot 9\cdot 9\\ \qquad 9^3\\ 81=9\cdot 9\\ \qquad 9^2 \end{cases}\\\\ -------------------------------\\\\[/tex]
[tex]\bf (x^6+729)-(9x^4+81x^2)\implies [(x^2)^3+9^3]-(9x^2x^2+9^2x^2) \\\\\\\ [\underline{(x^2+9)}(x^4-9x^2+9^2)]\ -\ [9x^2\underline{(x^2+9)}]\impliedby \begin{array}{llll} notice\ the\\ \textit{\underline{common factor}} \end{array} \\\\\\ (x^2+9)\ [(x^4\underline{-9x^2}+9^2)\underline{-9x^2}]\impliedby \textit{now we add \underline{these two}} \\\\\\[/tex]
[tex]\bf (x^2+9)\ [x^4-18x^2+9^2]\impliedby \begin{cases} \sqrt{x^4}=x^2\\ \sqrt{9^2}=9\\ 18x^2=2(x^2)(9)\\ thus\ a\\ \textit{perfect square trinomial} \end{cases} \\\\\\ (x^2+9)\ [(x^2)^2-18x^2+9^2] \\\\\\ (x^2+9)(x^2-9)^2\implies (x^2+9)(x^2-3^2)^2 \\\\\\ (x^2+9)\ [(x-3)(x+3)]^2\implies \boxed{(x^2+9)(x-3)^2(x+3)^2} \\\\\\ \textit{and I guess you could be redundant and use} \\\\\\ (x^2+9)(x-3)(x-3)(x+3)(x+3)[/tex]
How can the average rate of change be found using a discrete graph?
Answers
The average rate of change can be found using a discrete graph by calculating the slope between two points on the graph. This provides insight into how the dependent variable changes as the independent variable varies.
Explanation:The average rate of change can be found using a discrete graph by calculating the difference in the y-values of two points and dividing it by the difference in the x-values of those same points. This will give you the slope of the line connecting the two points, which represents the average rate of change between those two points. For example, if you have two points (x1, y1) and (x2, y2), the average rate of change can be calculated as:
(y2 - y1) / (x2 - x1)
By finding the average rate of change at different intervals on the graph, you can analyze how the dependent variable changes in relation to the independent variable.
I want to make sure of my answer is right?
Answers
20 2/7 = 142/7 -20/35
find common denominator ( in this case it is 35)
35/7 =5 , multiply 142*5=710, 7*5 =35
142/7 = 710/35
710/35 - 20/35 = 710-20 = 690
690/35 now simplify that fraction
690/35 = 19.714
19*35 = 665
690-665=25
19 25/35
25/35 can reduce to 5/7
answer = 19 5/7
What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 2?
an = 5 − 2(n − 1); all integers where n ≥ 1
an = 5 − 2(n − 1); all integers where n ≥ 0
an = 5 − 3(n − 1); all integers where n ≥ 1
an = 5 − 3(n − 1); all integers where n ≥ 0
Answers
The easiest way to answer this is to try all choices, plug in values for the 1st term and 2nd term then check if the answer matches with 5 and 2. (n = 1 and n = 2)
We know that n starts with 1 because that is our 1st term, we do not have 0th term, therefore that leaves us with 2 choices.
Choice 1: an = 5 − 2(n − 1); all integers where n ≥ 1
n = 1
a1 = 5 – 2 (1 – 1) = 5 – 2 (0)
a1 = 5
n = 2
a2 = 5 – 2 (2 – 1) = 5 – 2 (1)
a2 = 3 (FALSE!)
Choice 2: an = 5 − 3(n − 1); all integers where n ≥ 1
n = 1
a1 = 5 – 3 (1 – 1) = 5 – 3 (0)
a1 = 5
n = 2
a2 = 5 – 3 (2 – 1) = 5 – 3 (1)
a2 = 2 (TRUE)
Therefore the correct answer is:
an = 5 − 3(n − 1); all integers where n ≥ 1
Answer:
A is INCORRECT
Step-by-step explanation:
Just finished the FLVS test
Walter bought a square plot of land. the perimeter is 544 feet. how wide is the property?
Answers
perimeter of a square = is side times 4
so divide 544 by 4
544/4 = 136
the property is 136 feet wide
A right triangle has legs that are 10.1in and 12.2 in long. What is the approximate length of the hypotenuse?
Answers
10.1^2 + 12.2^2 = c^2
102.01 + 148.84 = c^2
250.85 = c^2
sqrt 250.85 = c
15.838 = c <== ur hypotenuse
Juanita’s boss told her that once she has worked with the company for 10 years, her salary will be increased to 3 times what she makes now plus $2,000. If s represents her original salary, which expression represents what her salary will be after 10 years at the company?
Answers
A=3s+2000
Answer:3s+2,000
Step-by-step explanation:
You have a cone with a radius of 4 ft and a height of 12 ft. What is the height of the triangle formed by a perpendicular cross-section through the cone’s center?
Answers
ABC is the triangle formed by a perpendicular cross-section through the cone's center.
The height OC of this triangle, is the height of the cone.
So the height is equal to 12 ft.
Answer: 12 ft.
Let $f$ be a function such that $f(x+y) = x + f(y)$ for any two real numbers $x$ and $y$. if $f(0) = 2$, then what is $f(2012)?$
Answers
Given:
f(0) = 2
So first of all, we let x = 2012, y = 0:
Then, F(2012) = 2012 + f(0)
Since f(0) = 2, then f(2012) = 2012 + 2 = 2014.
To add, the process that relates an input to an output is called a
function.
There are always three main parts of a
function, namely:
Input
The Relationship
The Output
The classic way of writing a function is "f(x) = ... ".
What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.
What a function does with the input can be usually seen as:
f(x) = x2 reveals to us that function "f" takes "x" and squares it.
if f (x) =-14x-2, then f^-1 (x) =
Answers
Switch up the variables:
y = -14x - 2.
x = -14y - 2.
Add 2 to both sides.
x + 2 = -14y - 2 + 2.
x + 2 = -14y.
Divide by -14 on both sides.
(x + 2) / -14 = -14y / -14.
(x + 2) / -14 = y.
Change the y to f^-1(x).
f^-1(x) = (x + 2) / -14.
Hopefully, this helps! =)
One number is 2 more than 3 times another. their sum is 22. find the numbers. 8, 14
Answers
x = 3y + 2
3y + 2 + y = 22
4y + 2 = 22
4y = 22 - 2
4y = 20
y = 20/4
y = 5
x = 3y + 2 = 3(5) + 2 = 15 + 2 = 17
ur numbers are 5 and 17
Hence the other number is 2 + 3*x.
Their sum is 22;
x + 2 + 3x = 22
4x + 2 = 22
4x = 20
Therefore, x = 5
[ 2 + 3x = 2 + 3*5 = 2+15 = 17 ]
Hence the two numbers are, 5 and 17.
(48.9, -53.3) (84.6, -19.9) (-62.6, 81.7) (-14.4 ,-42.6) (71.2, -84.1) (71.2, 76.8 ) state the domain
Answers
33.
In quadrilateral PQRS, the coordinates are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). How can you use coordinate geometry to show that the diagonals are perpendicular?
Apply the Distance Formula to show that opposite sides to show they are congruent.
Find the slopes of their product is 1.
Apply the Distance Formula to show that opposite sides to show sides are congruent.
Find the slopes and show that their product is -1.
Answers
A technique that can help you to know if two straight lines are perpendicular is is you find their slopes. Let's say the slope of line 1 is m1 and the slope of line 2 is m2. If m1*m2 yields a product of -1, then the lines are perpendicular. This is because if m1 is the negative reciprocal of m2, the lines are perpendicular. But if m1=m2, the lines are parallel, meaning they don't intersect at all.
Therefore, the answer is: Find the slopes and show that their product is -1.
Answer: The answer is (d) Find the slopes and show that their product is -1.
Step-by-step explanation: Given in the question and shown in the attached figure that the vertices of the quadrilateral PQRS are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). We are asked to use geometry to show that the diagonals PR and QS are perpendicular to each other.
We know that the two lines are perpendicular if the product of their slopes is --1.
So, first we will find the slopes of PR and QS, multiply them, and check the value.If the value is -1, then the diagonals are perpendicular to each other.
That is, if 'm' and 'p' are the slopes of the diagonals PR and QS, and if m × p = -1, then the two diagonals are perpendicular.
Thus, the correct answer is (d).
Angles θ and Φ are supplementary, and theta equals 3pi/7 find the measure of theta
Answers
Φ + 3π/7 = π
Φ = π - 3π/7
Φ =4π/7
From Plato: Φ =7π/7 or π.
Suppose there are 10,000 civilizations in the milky way galaxy. if the civilizations were randomly distributed throughout the disk of the galaxy, about how far (on average) would it be to the nearest civilization? (hint: start by finding the area of the milky way's disk, assuming that it is circular and 100,000 light-years in diameter. then find the average area per civilization, and use the distance across this area to estimate the distance between civilizations.)
Answers
so the radius is 50, 000 lights year, thus
Area of the galaxy is [tex]A(galaxy)= \pi r^{2}= \pi (50,000)^{2}=25*10^{8} \pi [/tex] (lights year square)
The area per civilisation is [tex] \frac{25*10^{8} \pi }{10,000}=25*10^{4} \pi[/tex]
from this result we can assume as a circle of Radius=[tex]25*10^{2}=2500[/tex] lights year.
and assume that each civilisation lives in a planet at the center of these smaller circles.
Check the figure attached.
Planet A, and B are closest in distance. They are each at the center of a circle with radius 2500, and they are tangent. So the distance of A to B is 2500+2500=5000 (light years).
Answer: 5000 light years
Use the functions h(x) = 2x + 5 and t(x) = 7x − 6 to complete the function operations listed below.
Part A: Find (h + t)(x). Show your work. (3 points)
Part B: Find (h ⋅ t)(x). Show your work. (3 points)
Part C: Find h[t(x)]. Show your work. (4 points)
Answers
h ( x ) = 2 x + 5 and t ( x ) = 7 x - 6
Part A:
( h + t ) ( x ) = ( 2 x + 5 ) + ( 7 x - 6 ) = 9 x - 1
Part B :
( h · t ) ( x ) = ( 2 x + 5 ) · ( 7 x - 6 ) = 14 x² - 12 x + 35 x - 30 =
= 14 x² + 23 x - 30
Part C :
h [ t ( x ) ] = h ( 7 x - 6 ) = 2 · ( 7 x - 6 ) + 5 = 14 x - 12 + 5 =
= 14 x - 7
The sum of the first and third of three consecutive even integers is 136. find the three even integers.
Answers
For example: 42 + 46 = 88. I have to increase the numbers more to reach 136. Suppose: 82 + 86 = 168. That exceeded 136. So, it must be between 46 and 82. Suppose again: 66 + 70 = 136. Therefore, the sequence of the consecutive even integers are 66, 68, and 70.
The sum of the first and third even integers is 136. By setting up an equation and solving for x, where x is the first integer, we determine that the consecutive even integers are 66, 68, and 70.
The problem asks us to find three consecutive even integers where the sum of the first and third integer is 136. Let's denote the first integer as x, the second integer as x + 2, and the third integer as x + 4 (since consecutive even numbers have a difference of 2). To solve for the values, we set up the equation x + (x + 4) = 136. Simplifying, we get 2x + 4 = 136. Subtracting 4 from both sides gives us 2x = 132. Dividing both sides by 2, we find out that x = 66. So, the first integer is 66, the second integer is 66 + 2 = 68, and the third integer is 66 + 4 = 70.
Therefore, the three consecutive even integers are 66, 68, and 70.
if 6a-8b=0 and c=12b, the ratio of a to c is equivalent to the ratio of one to what number?
Answers
3a=4b
c=3*(4b)=3*3a=9a
c=9a
800x200 I know the answer is 160000 but I want to see how quick you guys answer...
Answers
8×2 = 16
and : four zero : 0000
you have : 160000
Which of the following is a factor of 6x2 + 2x − 21?
4x − 3
2x + 7
6x − 3
None of the above
Answers
None of the above
EXPLANATION
The quadratic expression given to us is
[tex]6 {x}^{2} + 2x - 21[/tex]
If the discriminant of this quadratic expression is a perfect square, then it has rational factors,
If we compare the above expression to the general quadratic expression,
[tex]a {x}^{2} + bx + c[/tex]
We have,
[tex]a=6,b=2,c=-21[/tex]
The discriminant is given by,
[tex] D = {b}^{2} - 4ac[/tex]
Thus
[tex] D = {2}^{2} - 4(6)( - 21)[/tex]
[tex] D = 4 + 504 = 508[/tex]
Since 508 is not a perfect square, the expression
[tex]6 {x}^{2} + 2x - 21[/tex]
has no rational factors.
Therefore D is the correct answer.