Find the midpoint of the segment with the following endpoints.
(4, 2) \text{ and } (7, 6)
(4,2) and (7,6)
Answers
Answer:
( 5.5 , 4 )
Step-by-step explanation:
Use mid point formula shown in image
first x= (X+X)/2
x=(4+7)/2
x=11/2
x=5.5
y=(Y+Y)/2
y=(2+6)/2
y=8/2
y=4
(5.5,4)
Related Questions
What is the average rate of change of the function over the interval x = 0 to x = 8?
f(x)=2x−1/3x+5
Enter your answer, as a fraction, in the box.
Answers
====================================================
Work Shown:
Plug in x = 0
[tex]f(x) = \frac{2x-1}{3x+5}\\\\f(0) = \frac{2*0-1}{3*0+5}\\\\f(0) = \frac{0-1}{0+5}\\\\f(0) = -\frac{1}{5}\\\\[/tex]
Repeat for x = 8
[tex]f(x) = \frac{2x-1}{3x+5}\\\\f(8) = \frac{2*8-1}{3*8+5}\\\\f(8) = \frac{16-1}{24+5}\\\\f(8) = \frac{15}{29}\\\\[/tex]
Now use the average rate of change formula
[tex]m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(8)-f(0)}{8-0}\\\\m = \frac{15/29 - (-1/5)}{8}\\\\m = \frac{15/29 + 1/5}{8}\\\\m = \frac{(15/29)*(5/5) + (1/5)*(29/29)}{8}\\\\m = \frac{75/145 + 29/145}{8}\\\\[/tex]
[tex]m=\frac{104/145}{8}\\\\m = \frac{104}{145} \div \frac{8}{1}\\\\m = \frac{104}{145} \times \frac{1}{8}\\\\m = \frac{104*1}{145*8}\\\\m = \frac{104}{1160}\\\\m = \frac{13}{145}\\\\[/tex]
I need help I don't understand this at all.
Answers
please mark this answer as brainlist
what is the radius of the semicircle
Answers
20
Step-by-step explanation:
Hint: Use the Pythagorean Theorem
———————————————————
We’ll just listen to what the hint says
Pythagorean theorem: a^2 + b^2 = c^2
where a = 16 b = 12 and c = radius
16^2 + 12^2 = c^2
256 + 144 = c^2
c^2 = 400
square root 400
sqrt rt 400 = 20
The radius of the semicircle is 20
The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)?
g(x) = (x + 9)2 + 4
g(x) = (x + 9)2 − 4
g(x) = (x − 4)2 + 9
g(x) = (x + 4)2 + 9
Answers
Answer:
The function that represents g(x) is the third choice: g(x) = (x − 4)^2 + 9
Step-by-step explanation:
The original function has been shifted 9 units up (a vertical transformation). To show a vertical transformation, all we have to do is either add or subtract at the end of the function.
To show a shift upwards, we add the value of change.
To show a shift downwards, we subtract the value of change.
In this case, the original function f(x) = [tex]x^{2}[/tex] was translated 9 units up. Since we shifted up, we simply add 9 to the end of the function: g(x) = [tex]x^{2}[/tex] + 9
The original function has also been shifted 4 units to the right. This is a horizontal transformation. To show a horizontal transformation, we need to either add or subtract within the function (within the parenthesis).
To show a shift to the left, we add the value of change.
To show a shift to the right, we subtract the value of change.
*Notice: Moving left does NOT mean to subtract while moving right does NOT mean to add. The rules above are counterintuitive so pay attention when doing horizontal transformations.
In this case, the original function f(x) = [tex]x^{2}[/tex] was translated 4 units to the right. Since we shifted right, we must subtract 4 units within the function/parenthesis: g(x) = [tex](x-4)^{2}[/tex]
When we combine both vertical and horizontal changes, the only equation that follows these rules is the third choice: g(x) = (x − 4)^2 + 9
Answer: C
Step-by-step explanation:
7.
Which kind of function best models the data in the table? Graph the data and write an equation to model the data.
A. exponential; y = 3x – 1
B. linear; y = x – 1
C. quadratic; y = x2 – 1
D. linear; y = –x – 1
Answers
Answer:
D. linear; y = –x – 1
Step-by-step explanation:
Linear; y=-x - 1
The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x
...............................................................................................................................................
Answer:
The correct answer is D) linear; y = –x – 1
Step-by-step explanation:
To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.
(4, 5)
y = -x - 1
-5 = -4 - 1
- 5 = -5 (TRUE)
(0, -1)
y = -x - 1
-1 = 0 - 1
-1 = -1 (TRUE)
use the formula v=u+at to find the velocity when the initial velocity is 3m/s2 the time is 7 seconds
Answers
Answer:
Step-by-step explanation:
hello
add me on s
ghazalp2186
love xx
and i dont know the answer
find the perimeter of the isosceles trapezoid
Answers
Answer:
A =136 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) *h where b1 and b2 are the lengths of the bases and h is the height
A = 1/2( 22+12) *8
A = 1/2 ( 34)*8
A =136 cm^2
Solve using the Pythagorean theorem
a^2+b^2=c^2 with This you should get 9.43 (rounded) as your values.
Then just add up the side lengths.
2(9.43)+22+12, which gives a perimeter of 52.87 (rounded)
5^2+8^2=c^2
Amy has four more 20c coins than 5c coins. The total value of all her 20c and 5c is $3.80. How many 5c coins does Amy have?
Answers
Answer: 12
Step-by-step explanation:
16 X 20c = 3.20
12 x 5c = 0.60
total is 3.80
Amy has 12 five c coins.
Select the correct answer.
Which statement best describes the solution to this system of equations?
3x + y= 17
x + 2y = 49
Ο Α.
It has no solution.
B.
It has infinite solutions.
O c.
It has a single solution: x = 15, y= 17.
OD.
It has a single solution: x = -3, y = 26.
Answers
esto es verdadero oh falso
como se resuelve
3/4 + 1/2 + 1/3 + 2/9 + ...... = 9/4
Answers
Answer
The missing value is 4/9
100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT
a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal
places.
Answers
Answer:
See Below (Boxed Solutions).
Step-by-step explanation:
We are given the two complex numbers:
[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]
First, convert z to polar form. Recall that polar form of a complex number is:
[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]
We will first find its modulus r, which is given by:
[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]
In this case, a = √3 and b = -1. Thus, the modulus is:
[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]
Next, find the argument θ in [0, 2π). Recall that:
[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]
Therefore:
[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]
Evaluate:
[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]
Since z must be in QIV, using reference angles, the argument will be:
[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]
Therefore, z in polar form is:
[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]
Part A)
Recall that when multiplying two complex numbers z and w:
[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]
To find the complex form, evaluate:
[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]
Part B)
Recall that when raising a complex number to an exponent n:
[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]
Therefore:
[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]
Substitute:
[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]
Simplify:
[tex]\displaystyle z^{10} = 1024\left(\cos\frac{55\pi}{3}+i\sin \frac{55\pi}{3}\right)[/tex]Simplify using coterminal angles. Thus, the polar form is:
[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]
And the complex form is:
[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]
Part C)
Recall that:
[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]
And the complex form is:
[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]
Part D)
Let a be a cube root of z. Then by definition:
[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
From the property in Part B, we know that:
[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]
Therefore:
[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:
[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]
The first equation can be easily solved:
[tex]r=\sqrt[3]{2}[/tex]
For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:
[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]
Solve for the argument:
[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]
There are three distinct solutions within [0, 2π):
[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]
Hence, the three roots are:
[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]
Or, approximately:
[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]
solve this question :
-10k2+7
Answers
Answer:
-10k×2+7
= -20k+7
Step-by-step explanation:
is the answer
Rebecca can paint a room in 12 hours Guadalupe can paint the same room in 16 hours how long does it take for both Rebecca and Guadalupe to paint the room if they are working together
Answers
Guadalupe can paint in 16hrs (and Guadalupe G)
How long ? = (RxG) x 24 divided by 2
(12x16)24/2
2304/60
38.4hrs.
How do you find the diameter of a quarter circle?
Answers
Answer:
um 1/4
Step-by-step explanation:
Prachi was 555 kilometers east of her home when she began driving farther east at 707070 kilometers per hour. Let f(n)f(n)f, left parenthesis, n, right parenthesis be Prachi's distance from her home at the beginning of the n^\text{th}n th n, start superscript, start text, t, h, end text, end superscript hour of her drive.
Answers
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Whenever she began to drive farther east, at 70 km per hour, Prachi was 5 km east of her home.
Let f(n) at the beginning of her nth hour drive be Prachi's distance to her home.
f is a sequence of arithmetic.
Write a series explicit form.
[tex]\to f(n) = 70n + 5[/tex]
Answer:
Arithmetic Sequence, f(n)=5+70(n-1)
Step-by-step explanation:
checked on khan
7)On subtracting 8 from x, the result is 2 . Form a linear
equation for the statement.
Answers
Answer:
8-x=2
-x=2-8
-x=-6
x=6
if 8 is subtract from 6answer is 2
Multiply: (2x+y) (n2-3xy+y2)
Answers
Answer:
[tex]{ \tt{(2x + y)( {n}^{2} - 3xy + {y}^{2} )}} \\ = { \tt{(2x {n}^{2} - 3 {x}^{2}y + 2x {y}^{2} + {n}^{2}y - 3x {y}^{2} + {y}^{3} )}} \\ = { \tt{ {y}^{3} - xy(y + 3x) + {n}^{2} y }}[/tex]
Hello!
(2x+y) (n2-3xy+y2)
2x* n²= 2xn²
2x* -3xy = -6x²y
2x* y² = 2xy²
y*n² = yn²
y*-3xy = -3xy²
y* y² = y³
=>
2xn²- 6x²y + 2xy² +yn²- 3xy² +y³
23. Insert the missing number.
4
6
9
14
23
40
?
138
266
Answers
Answer:
hey mate !!!
The pattern followed is
4x2-2= 8-2=6
6 x 2-3= 9
9 x 2- 4= 14
14 x 2-5 = 23
23 x 2-6= 40
40 x 2-7= 73
So, the next number will be 73.
What value of x is in the solution set of -2(3x + 2) >-8x + 6
Answers
Answer:
x >5
Step-by-step explanation:
-2(3x + 2) >-8x + 6
Distribute
-6x-4 > -8x+6
Add 8x to each side
-6x-4+8x > -8x+8x+6
2x-4 > 6
Add 4 to each side
2x-4+4 > 6+4
2x> 10
Divide by 2
2x/2 >10/2
x >5
Step-by-step:
-2(3x+2)>-8x+6. divided by 2,-3x-2>-4x+3. the solution set of -2(3x+3)>-8x+6 is {x/x>5}
Answer:
6
Which of the following numbers has exactly two significant digits? OA) 3.40 OB) 2.125 OC) 1.0475 OD) 0.00050
Answers
Answer:
Here, option (d) has significant digits. hence , option (d) ✓ is correct.Suppose we have 12 books.
How many ways are there to put four of them on a shelf?
PLS HELP ME
Answers
Answer:
1) first book can be at any of 4 places
2) Second book can be on any of leftover 3 places
3) Similarly third book on 2 and forth on 1 place
total : 4 * 3*2 * 1 = 24 ways .
other way we have formula 4!/1! =24 , here ordering is important
It is called arrangement or permutations, while if you need to group some objects it is called combination and there we need to consider unique groups only.
example if you need to choose 2 friends for a party out of 4 friends ,
answer will be 4!/2!*2! = 6 groups. (Ordering doesn’t matter hence division)
hope it hleps
PLEASE MARK BRAINLIEST
0.25(4f-3)=0.005(10f-9)
Simplify the following
Answers
Answer:
apoco la propiedad asociativa en los siguiente ejercicio 25x11x18=
Anyone any good at math?
Is the relationship shown by the data linear? If so, model the data with an equation
Answers
Answer:
yes the x increases by 6 and the y decreases by 3.
y = -1/2x - 7/2
Step-by-step explanation:
find the slope :
(1,-4), (7, -7)
y2- y1 / x2 - x1
substitute those numbers and you get -1/2.
point slope form :
y - y1 = m(x- x1)
y - (-4) = -1/2 ( x - (1))
y+4 = -1/2(x-1)
slope intercept form :
y = -1/2x - 7/2
does this help ?
Intuitively, does it make sense that all circles are similar? Why or why not?
Answers
Answer with explanation:
Yes, each point on a circle is a fixed distance from the center of the circle. This is called the radius of the circle. By definition, all radii of a circle are equal.
Similar polygons have corresponding sides in similar proportion. Regardless of how large a circle is, each point on the circle will still be a fixed distance away from center of the circle. Therefore, the radii are in a constant proportional and all circles are similar.
n the graph below determine how many real solutions the quadratic function has, and state them, if applicable. List solutions in order from left to right on the graph, or least to greatest. If the function has only one solution, type the solution in both of the boxes. If there are no real solutions type “none” in both boxes.
Answers
Answer:
There are no real solutions.
Step-by-step explanation:
There are 3 options.
2 real solutions: This happens if in the graph, each arm intersects the x-axis, this means that there are two different values of x such that the equation:
a*x^2 + b*x + c
is equal to zero.
Another way to see this, is if the determinant:
b^2 - 4*a*c
is larger than zero.
1 real solution: This happens when the vertex of the graph intersects the x-axis. This means that there is a single value of x such that:
a*x^2 + b*x + c
is equal to zero.
Another way to see this is if the determinant:
b^2 - 4*a*c
is larger equal zero.
No real solution: if in the graph we can not see any intersection of the x-axis, then we do not have real solutions (only complex ones).
Another way to see this is if the determinant:
b^2 - 4*a*c
is smaller than zero.
Now that we know this, let's look at the graph.
We can see that the vertex is below the x-axis, and the arms of the graph go downwards. So the arms will never intersect the x-axis (and neither the vertex).
So the graph does not intersect the x-axis at any point, which means that there are no real solutions for the quadratic equation.
The correct answer would be "none"
What is the answer to the question 3x+5x
Answers
Answer:
8x
Step-by-step explanation:
=3x+5x
=8x
Find the value of a. Round
the nearest tenth.
Answers
Answer:
side A should be about 44cm
Which series represents this situation? 1+1*7+1*7^ 2 +...1*7^ 6; 1+1*7+1*7^ 2 +...1*7^ 7; 7+1*7+1*7^ 2 +... 1*7^ 6; 7+1*7+1*7^ 2 +...1*7^ 7
Answers
Answer:
Step-by-step explanation:
The series is missing from the question. I will answer this question with a general explanation by using the following similar series:
[tex]\sum\limits^6_{n=0} 7^n[/tex]
Required
The series
To do this, we simply replace n with the values
[tex]\sum\limits^6_{n=0}[/tex] means n starts from 0 and ends at 6
[tex]\sum[/tex] means the series is a summation series
So, we have:
[tex]\sum\limits^6_{n=0} 7^n = 7^0 + 7^1 + 7^2 + ...... + 7^6[/tex]
[tex]\sum\limits^6_{n=0} 7^n = 1 + 7 + 7^2 + ...... + 7^6[/tex]
A seat’s position on a Ferris wheel can be modelled by the function y = 18 cos 2.8(x + 1.2) + 21, where y represents the height in feet and x represents the time in minutes. Determine the diameter of the Ferris wheel.
Answers
Step-by-step explanation:
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320
Could I get the answer don’t understand
Answers
Answer:
DE = 21.4
Step-by-step explanation:
The parallel lines divide the transversals proportionally, that is
[tex]\frac{DE}{EB}[/tex] = [tex]\frac{DF}{FC}[/tex] , substitute values
[tex]\frac{DE}{10.7}[/tex] = [tex]\frac{32}{16}[/tex] = 2 ( multiply both sides by 10.7 )
DE = 21.4
