Answer: 1: k 2: 12r-20 3: 10n-13 4: -14x
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(-9, -5) and (-1, -9)
Answer:
The answer is
[tex]( - 5 \: , \: - 7)[/tex]Step-by-step explanation:
The midpoint M of two endpoints of a given line segment can be found by using the formula
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-9, -5) and (-1, -9)
The midpoint M is
[tex]M = ( \frac{ - 9 - 1}{2} , \: \frac{ - 5 - 9}{2} ) \\ = ( - \frac{10}{2} , \: - \frac{14}{2} )[/tex]We have the final answer as
[tex]( - 5 \: , \: - 7)[/tex]Hope this helps you
x(z + 3) + 1 + 3 − y; use x = 6, y = −5, and z = 2
Answer: 39
Step-by-step explanation:
x(z+3)+1+3-y
plug in the values given for each variable
6(2+3)+1+3-(-5)
use pemdas to solve
6(5)+1+3+5
30+1+3+5
31+8
39
Answer: 39
Step-by-step explanation:
Given: x=6, y=-5, z=2
To solve this problem, plug all the variables in.
--------------------------------------------------------------------
x(z+3)+1+3-y
Plug in
=(6)[(2)+3]+1+3-(-5)
Take off parentheses
=6(2+3)+1+3+5
Add 2 and 3, and also add 1 and 3
=6(5)+4+5
Multiply 6 and 5, and add 4 and 5
=30+9
Add 30 and 9
=39
Hope this helps!! :)
Please let me know if you have any question
The water in a pool is evaporating at a rate of
5% per day. If the pool has
18,800 gallons in it today, how many gallons will it have in
9 days? Round your answer to the nearest whole number, if necessary.
Step-by-step explanation:
y = 18800 (1 − 0.05)ˣ
y = 18800 (0.95)ˣ
y = 18800 (0.95)⁹
y = 11849
Find the equation of the line through the points (−6,4) and (−5,−10). Enter your answer in slope-intercept form y=mx+b.
Answer:
y = -14x - 80
Step-by-step explanation:
jst did it and i got it right
The equation of the line passing through the points (−6,4) and (−5,−10) is y = -14x - 80.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The line through the points (−6,4) and (−5,−10).
(y + 10) = (-10-4)/(-5+6)[x + 5]
y + 10 = -14(x + 5)
y + 10 = -14x - 70
y = -14x - 80
Thus, the equation of the line passing through the points (−6,4) and (−5,−10) is y = -14x - 80.
Learn more about the straight line here:
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A woman measures the angle of elevation of a mountaintop as 12.00. After walking 1.00 km closer to the mountain on level ground, she finds the angle to be 14.00. Find the mountain’s height, neglecting the height of the women’s eyes above ground. Hint: Distances from the mountain (x and x-1 km) and the height y are unknown.
Answer:
Step-by-step explanation:
The equation v/2 -21=-15 is solved in several steps below.
For each step, choose the reason that best justifies it.
Step. Reason
* v/2-21=-15
v/2-21+21=-15+21
v/2=6
2·v/2=6·2
v=12
Options!
*Given equation
a. addition property of equality
b. subtraction propertyof equality
c. multiplication property of equality
d. division property of equality
e. simplifying
f. distributive property
Answer:
V/2 - 21 = -15
V/2 - 21 + 21 = -15 + 21
V/2 + 0 = 6
V/2 * 2 = 6 * 2
V = 12
Example 2
Find the equation of the tangent to the circle
x + y2 + 4x - 10y = 12 at the point (3, 1).
Answer:
-5x + 4y = -11.
Step-by-step explanation:
If it's a circle then it must be x^2 not x.
x^2 + y^2 + 4x - 10y = 12
Using implicit differentiation:
2x + 2y y' + 4 - 10 y' = 0
y'( 2y - 10) = -2x - 4
y' = (-2x - 4)/(2y - 10)
y' = (-x - 2) / (y - 5) = the slope of the tangent.
At (3, 1), y' = (-3-2) / (1 - 5)
= 5/4.
So the required equation is
y - y1 = 5/4(x - x1) where x1 = 3 and y1 = 1.
y - 1 = 5/4(x - 3)
y = 5/4(x - 3) + 1
Multiply through by 4:
4y = 5(x - 3) + 4
4y = 5x - 15 + 4
In standard form the equation is:
-5x + 4y = -11.
mike has $1.55 in dimes and nickels. if he has 7 more nickels than dimes, how many of each does he have?
Answer:
15 nickels and 8 dimes
Step-by-step explanation:
Create a system of equations where d is the number of dimes and n is the number of nickels:
0.1d + 0.05n = 1.55
n = d + 7
Solve with substitution by plugging in d + 7 as n:
0.1d + 0.05(d + 7) = 1.55
0.1d + 0.05d + 0.35= 1.55
0.15d + 0.35 = 1.55
0.15d= 1.2
d = 8
Plug in 8 as d to find n:
n = d + 7
n = 8 + 7
n = 15
So, there are 15 nickels and 8 dimes
If 9% of a number equals 30, find 27% of that number.
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Rewriting what is given: (0.09)(n)=30
Where n is the unknown number and 0.09 is the numerical form of 9%. Solving for n gives:
n=(30/0.09)=333.333....
27% as a number is 0.27. So 27% of n is:
(0.27)(n)=(0.27)(333.333...)=90
27% of that number is 90.
a bread recipe requires 3 cups of flour to make 24 servings
Nico earns $32.50 for each hour he works. last week Nico warned $1,300, and this week he earned $1,040. how many more hours did nick work last week than this week?
Answer:
8 hours
Step-by-step explanation:
$1,300/$32.50 = 40
$1,040/$32.50 = 32
40-32=8
Answer:
8 hours
Step-by-step explanation:
First, find the difference in the money
1300-1040=260
Then divide by 32.5
260/32.5=2600/325
8
So he worked for 8 more hours
Which value from the list below, when substituted for x, would represent an acute triangle with side lengths x, x+ 4, and 20? Assume that the longest side of the triangle is of length 20 units.
just finished this question the answers: D / 14
The value of x could be 8<x<12.
What is Triangle Inequality?According to the Triangle Inequality Theorem, any two triangle sides must add up to more than the third side's length.
Using Triangle Inequality
x+ x+4 > 20
2x+ 4 >20
2x > 16
x> 8
The angle across from the side with length 20 is the largest angle because it is the longest side length.
Therefore, x must be less than the value(s) that make that angle exactly 90 degrees. Simply determine the values of x for angles that are 90 degrees from the side with a length of 20.
Using Pythagorean theorem
x²+ (x+4)² = 20²
x² + x² +16 +8x = 400
2x² + 8x - 384= 0
x²+ 4x -192= 0
x= -16, 12
So, x has to be less than 12 i.e., x < 12
Hence, the value of x could be 8<x<12.
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a missle was fired from a submarine from 370 feet below sea level. if the missile reached a height of 8400 feet before exploding, what was the change in the altitiude of the missile?
Answer:
8770 feet
Step-by-step explanation:
Add 370 to 8400:
8400 - 370
= 8770 feet
Compare and Contrast the following diagrams by creating a list of at least 5
complete sentences.
Answer:
Both diagrams describe the representation of an object in space.
Step-by-step explanation:
1. The first diagram is a 2-dimensional plane in space.
2. it has two axes, the x-axis and y-axis, which is the length and width of the plane.
3. Both axes are perpendicular to each other.
4. The second diagram is a 3-dimensional plane with axis x, y and z representing the width, length and height of the plane respectively.
5. All three axes are perpendicular to each other like in the 2-dimensional plane.
The midpoint of (-4,15) and (22,3)
Answer:
(9, 9)
Step-by-step explanation:
midpoint of (-4,15) and (22,3)
[tex] = \bigg( \frac{ - 4 + 22}{2}, \: \: \frac{15 + 3}{2} \bigg) \\ \\ = \bigg( \frac{18}{2}, \: \: \frac{18}{2} \bigg) \\ \\ = ( 9, \: \: 9) \\ \\ [/tex]
Any help would be appreciated!
Answer:
this might help you....
Answer:
See below.
Step-by-step explanation:
In the figure above, ∠WXY and ∠YXZ are a linear pair.
What is a Linear Pair?
A Linear Pair is 2 angles that are adjacent, and form a straight line when combined. A Linear Pair contains 2 Supplementary Angles, angles that add up to 180°.
Their measures add up to 180°.
In order to find y, because they're a linear pair, we can set up an equation with the 2 angles equal to 180°.
[tex]4y+6y+30=180[/tex]
Combine Like Terms:
[tex]10y+30=180[/tex]
Subtract 30 from Both Sides:
[tex]10y=150[/tex]
Divide by 10:
[tex]\frac{10y}{10} = \frac{150}{10} \\y = 15.[/tex]
The value of y is 15.
Now since we know the value of y, we can substitute 15 into each angle to find their measure.
Substitute:
[tex]4(15)=60\\6(15)+30=120[/tex]
The measure of ∠WXY is 60° and the measure of ∠YXZ is 120°.
Will mark brainliest, 42 points
24. 1st one
Step-by-step explanation:
the X cancals out the x leaving the z so it is the 1st one
Answer:
24. [tex]-\frac{3}{2} z[/tex]
25. 6
Step-by-step explanation:
For number 24:
To simplify this down, we can break it up into this:
[tex]\frac{3}{-2} \cdot \frac{x}{x} \cdot \frac{z}{1}[/tex]
3 divided by -2 is [tex]-\frac{3}{2}[/tex], x over x is just 1, and z over 1 is z.
So [tex]-\frac{3}{2} z[/tex].
For number 25:
If we know the value of y and z we can just substitute inside the equation.
[tex]\frac{-18}{-3}[/tex]
A negative divided by a negative is the same as a positive over a positive.
[tex]18\div3=6[/tex]
Hope this helped!
Find the slope of the line containing the pair of points (7, 0) and (10, 6). The slope is nothing. (Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined.)
Answer:
Slope= 2
Step-by-step explanation:
To calculate the slope of a line containing the two points on a coordinate plain, the below formula is used.
Slope = (y2-y1)/(x2-x1)
Y2= 6
Y1= 0
X2=10
X1= 7
Slope = (y2-y1)/(x2-x1)
Slope=(6-0)/(10-7)
Slope= 6/3
Slope= 2
The midpoint of AB is M(6, -1). If the coordinates of A are (4,-4), what are the
coordinates of B?
Answer:
(8, 2)
Step-by-step explanation:
(x, y)=(6, -1)
(x1+x2)/2=6
(y1+y2)/2=-1
------------------
(4+x2)/2=6
4+x2=6*2
4+x2=12
x2=12-4
x2=8
---------------
(-4+y2)/2=-1
-4+y2=-1*2
-4+y2=-2
y2=-2-(-4)
y2=-2+4
y2=2
(x2, y2)=(8, 2)
Simplify by factoring. √1350x^4
Answer:
15[tex]x^{2}[/tex][tex]\sqrt{6}[/tex]
Step-by-step explanation:
√1350x^4= √2*5*5*3*3*3x^4 = 5*3x^2√2*3 =5[tex]x^{2}[/tex][tex]\sqrt{6}[/tex]
Could anyone help me with this?
Customers of a phone company can choose between two plans for long distance calls. The first plan has a $17 monthly fee and charges an additional $0.08 for each minute of calls. The second plan has an $8 monthly fee and charges an additional $0.13 for each minute of calls. How many minutes of calls Will the costs of the two plans be equal?
Answer:
180 minutes of calls
Step-by-step explanation:
Let x represent the minutes of calls
The first plan's cost can be represented by 0.08x + 17
The second plan can be represented by 0.13x + 8
Set them equal to each other and solve for x:
0.08x + 17 = 0.13x + 8
17 = 0.05x + 8
9 = 0.05x
180 = x
So, it will take 180 minutes of calls for the plans to be equal.
2+2 idk what is the answer and im just confused of what it is
2+2 = 4
Very Simple!▶Add 2 to 2 , you may count it with your fingers.
Additionally Information:(-) This sign means subtraction i.e. you must take out!(×) This sign means multiplication i.e.you must multiply ! (÷) This sign means division i.e. you must divide!This are for beginners ✔
Hope you understandAnswer:
The answer, my man, is 4.
Explanation:
2+2-2*2/2=2
Or... 2 plus 2 minus 2 times 2 divided by 2 equals 2.
A more complex way of doing this is: 2+2=4
Hopefully, this helps! :D
Here is the scale model of a fountain at a museum the scale is 1:30 how many boulders are in the real fountain
Answer:
When we do a scale model of something (like a building, a house, or whatever) al the properties of the original thing must also be in the model.
So for example, you want to do a model of a house, and in the backyard of the house there are 4 trees, then in the model of the house you also need to put 4 trees in the backyard (indifferent of the scale of the model).
Then the number of boulders in the really fountain should be the same as the number of boulders in the scale model of the fountain.
Answer:
c. 10
Step-by-step explanation:
i just took the test
6x - 3y + 2z - y - 4z + 2x
Step-by-step explanation:
8x-4y-2z
I think the question is incomplete
Suppose that we have a pair of random variables X and Y with joint distribution
X
2 4 6
2 0.04 0.02 0.04
Y 4 0.12 0.06 0.12
6 0.24 0.12 0.24
(a) If we have M = max(X Y) the larger of the two observations, then calculate P{M = 6}.
(b) Show that X ami Y are independent.
Answer:
P (m=6)= 0.60
Marginal probability of y= 0.4 , 0.2 and 0.4
Marginal probability of x= 0.1 0.3 and 0.6
Step-by-step explanation:
The data given is
X 2 4 6
2 0.04 0.02 0.04
y 4 0.12 0.06 0.12
6 0.24 0.12 0.24
So the maximum value M= max (X Y) is (2,6) (6,4)(6,6)
We pick the larger value for each of the two observations
P (m=6) = 0.24+ 0.12+ 0.24= 0.60
X 2 4 6 Marginal
2 0.04 0.02 0.04 0.1
y 4 0.12 0.06 0.12 0.3
6 0.24 0.12 0.24 0.6
M. 0.4 0.2 0.4 1
The total is always equal to 1 .
X and Y are independent as the product of the marginal probability gives the joint probability.
We find the marginal probability by adding the rows and columns and then check if their product equal the given joint distribution which is true.
A color printer prints 11 pages in 4 minutes.
How many pages does it print per minute?
Answer:
2.75
Step-by-step explanation:
11/4 = 2.75
Hoped I helped
Manny created a scatter plot and drew a line of best fit, as shown.
720
-18
-16
-14
+12
+10
-6
-2
2.
6
8
10
12
14
16
+++
18 20
What is the equation of the line of best fit that Manny drew?
Answer:
y = 2x + 7
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
We are only focusing on the line of best fit.
Step 1: Find 2 coordinates
(0, 7) y-intercept
(2, 11) random
Step 2: Find slope m
m = (11 - 7)/(2 - 0)
m = 4/2
m = 2
y = 2x + b
Step 3: Rewrite linear equation
y = 2x + 7
Answer:
y = 2x + 7
Step-by-step explanation:
if f(x)=ln x then limx→2 f(x)= 1 2 Infinite Does Not Exist None of the above
Answer:
[tex]\lim_{x \to 2^{+}} f(x) = 2[/tex]
None of the above.
Step-by-step explanation:
f(x) = [x], in the graphing calculator, is f(x) = int(x).
This means we take the floor of x, or round down all the time.
The question is asking us to find the limit as x approaches 2 from the right. Since the graph from [2, 3) is going to be y = 2, we know that if we are approaching from the right of x → 2, we will approach y = 2 (shown in graph).
If we were to approach x → 2 from the left, then we would approach y = 1 (shown in graph).
If we were to approach from both the left and the right, then we would get DNE.
Match the following differential equations with their solutions. The symbols A, B, C in the solutions stand for arbitrary constants. You must get all of the answers correct to receive credit.
1. d^2y/dx^2 + 25y = 0
2. dy/dx = 2xy/x^2 - 5y^2
3. d62y/dx^2 + 16 dy/dx + 64y = 0
4. dy/dx = 10xy
5. dy/dx + 24x^2y = 24 x^2
A. y = Ce^-8x^3 + 1
B. 3yx^2 - 5y^3 = C
C. y = Ae^-8x + Bxe^-8x
D. y = Ae^5x^2
E. y = A cos(5x) + B sin(5x)
Answer:
[tex]1 \rightarrow E, 2\rightarrow B, 3\rightarrow C, 4\rightarrow D, 5\rightarrow A[/tex]
Step-by-step explanation:
1. [tex]\frac{d^2y}{dx^2}+25y=0[/tex]
The characteristic equation for the given differential equation is:
[tex]r^{2} +25=0[/tex]
[tex]\Rightarrow r^2=-25[/tex]
[tex]\Rightarrow r=\pm 5i[/tex]
Since the roots are complex
Now, the general solution is:
[tex]y=A\cos 5x+B\sin 5x[/tex]
2. [tex]\frac{dy}{dx}=\frac {2xy}{x^2}-5y^2[/tex]
[tex]\Rightarrow \frac{dy}{dx}-\frac 2xy=-5y^2[/tex]
Divide both sides by [tex]y^{-1}[/tex]
Let, [tex]v=y^{-1} \Rightarrow \frac{dv}{dx}=-y^{-2}\frac{dy}{dx}[/tex]
[tex]\Rightarrow -\frac{dv}{dx}-\frac 2xv=-5[/tex]
[tex]\Rightarrow \frac{dv}{dx}+\frac 2xv=5[/tex]
Here, [tex]p(x)=\frac 2x\; \text{and}\;\; q(x)=5[/tex]
I.F. [tex]=e^{\int \frac 2xdx}=x^2[/tex]
Now, the general solution is:
[tex]vx^2=\int x^2 5dx=\frac {5x^3}3+c[/tex]
[tex]\Rightarrow \frac {x^2}y-\frac {5x^3}3=c[/tex]
[tex]\Rightarrow 3x^2-5x^3y=Cy[/tex]
3. [tex]\frac{d^2y}{dx^2}+16\frac{dy}{dx}+64y=0[/tex]
The characteristic equation is:
[tex]r^2+16r+64=0[/tex]
[tex]\Rightarrow r^2+8r+8r+64=0[/tex]
[tex]\Rightarrow r(r+8)+8(r+8)=0[/tex]
[tex]\Rightarrow (r+8)(r+8)=0[/tex]
[tex]\Rightarrow r=-8,-8[/tex]
Since the roots are real and repeated.
Now, the general solution is:
[tex]y=Ae^{-8x}+Bxe^{-8x}[/tex]
4. [tex]\frac {dy}{dx}=10xy[/tex]
[tex]\Rightarrow \frac {dy}{y}=10xdx[/tex]
Integrating both sides
[tex]\int\frac {dy}y=\int 10xdx+\log c[/tex]
[tex]\Rightarrow \log y=5x^2+\log c[/tex]
[tex]\Rightarrow y=e^{5x^2}+c[/tex]
5. [tex]\frac {dy}{dx}+24x^2y=24x^2[/tex]
Here, [tex]p(x)=24x^2 \; \text{and}\;\; q(x)=24x^2[/tex]
I.F.[tex]= e^{\int 24x^2dx}=e^{8x^3}[/tex]
Now, the general solution is:
[tex]y.e^{8x^3}=\int 24x^2 e^{8x^3}dx=24\int x^2e^{8x^3}dx[/tex]
Let, [tex]8x^3=t \Rightarrow 24x^2dx=dt\Rightarrow x^2dx=\frac {dt}{24}[/tex]
[tex]\Rightarrow ye^{8x^3}=\int e^tdt[/tex]
[tex]\Rightarrow ye^{8x^3}=e^{8x^3}+c[/tex]
[tex]\Rightarrow y=1+ce^{-8x^3}[/tex]