Answer:
Explanation:
The formula for calculating the distance between two points is:
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Substituting the values from the points in the problem gives:
d
=
√
(
−
6
−
−
3
)
2
+
(
−
4
−
−
5
)
2
d
=
√
(
−
6
+
3
)
2
+
(
−
4
+
5
)
2
d = √ ( − 3 ) 2+ 1 2
d = √ 9+ 1
d = √ 10
Or
d = 3.162
rounded to the nearest thousandth
Write the equation in vertex form. Then identify the vertex, axis of symmetry, and direction of opening.
y = 2x^2 + 2
Step-by-step explanation:
y-2=2(x-0)^2
Vertex: (0,2)
Axis of Symmetry is x=0
Opens upward
Hope that helps :)
Pls help me with this
Answer:
D
Step-by-step explanation:
Its d because if she feeds her dog 1/8 every day for 3 days 3 times 8 is 24. I'm not very good at explaining things but its 24 days
A chi-square goodness-of-fit test will be performed using a simple random sample of 100 homes to investigate
whether the proportion of homes heated with each source is the same as what is reported by the newspaper.
Which of the following represents the alternative hypothesis of the test?
А
The proportions for the different heating systems match those reported by the newspaper.
B
At least one of the heating source proportions is the same as the corresponding proportion
reported by the newspaper.
c) The heating sources are not evenly distributed between homes.
D
At least one of the heating source proportions is different from the proportion reported by the
newspaper
E
Wood stove heating represents the highest proportion of heating source.
Answer:
D At least one of the heating source proportions is different from the proportion reported by the newspaper.
Step-by-step explanation:
H o: proportions are the same as the model
H a: at least one proportion is not the same
Find the general solution of DE 4y "+ y '= 0
Answer:
y=a+be^(-1/4t)
Step-by-step explanation:
We can solve the characteristic equation, 4r^2+r=0 to help.
Factor:
r(4r+1)=0
This implies r=0 or 4r+1=0.
The second equation can be solved by subtracting 1 on both sides and then dividing boths sides by 4 like so:
4r+1=0
4r+1-1=0-1
4r=-1
4r/4=-1/4
r=-1/4
So r=0 and r=-1/4 which means the general solution is y=ae^(0t)+be^(-1/4t)
Simplifying gives y=a+be^(-1/4t) since e^0=1.
Let's check our solution.
y=a+be^(-1/4t)
y'=0+-1/4be^(-1/4t)
y''=0+1/16be^(-1/4t)
Plug in:
4y''+y'=0
4*1/16be^(-1/4t)+-1/4be^(-1/4t)=0
1/4be^(-1/4t)+-1/4be^(-1/4t)=0
0=0 is a true equation so the solution has been verified.
15 points math :D yayayayayya
Answer:
The imagine isnt loading....
Step-by-step explanation:
What is the answer for B
Please help and use the proper theorem!
an exponential function f is defined by f(x)=c^x where c is a constant greater than 1 if f (7) = 4 x f (5) what is the value of c
From the above, it can be seen that the nature of polynomial functions is dependent on its degree. Higher the degree of any polynomial function, then higher is its growth. A function which grows faster than a polynomial function is y = f(x) = ax, where a>1. Thus, for any of the positive integers n the function f (x) is said to grow faster than that of fn(x).
Thus, the exponential function having base greater than 1, i.e., a > 1 is defined as y = f(x) = ax. The domain of exponential function will be the set of entire real numbers R and the range are said to be the set of all the positive real numbers.
It must be noted that exponential function is increasing and the point (0, 1) always lies on the graph of an exponential function. Also, it is very close to zero if the value of x is mostly negative.
Exponential function having base 10 is known as a common exponential function. Consider the following series:
Derivative of logarithmic and exponential function 5
The value of this series lies between 2 & 3. It is represented by e. Keeping e as base the function, we get y = ex, which is a very important function in mathematics known as a natural exponential function.
For a > 1, the logarithm of b to base a is x if ax = b. Thus, loga b = x if ax = b. This function is known as logarithmic function.
Derivative of logarithmic and exponential function 2
For base a = 10, this function is known as common logarithm and for the base a = e, it is known as natural logarithm denoted by ln x. Following are some of the important observations regarding logarithmic functions which have a base a>1.
The domain of log function consists of positive real numbers only, as we cannot interpret the meaning of log functions for negative values.
For the log function, though the domain is only the set of positive real numbers, the range is set of all real values, i.e. R
When we plot the graph of log functions and move from left to right, the functions show increasing behaviour.
The graph of log function never cuts x-axis or y-axis, though it seems to tend towards them.
Derivative of logarithmic and exponential function 3
Logap = α, logbp = β and logba = µ, then aα = p, bβ = p and bµ = a
Logbpq = Logbp + Logbq
Logbpy = ylogbp
Logb (p/q) = logbp – logbq
Exponential Function Derivative
Let us now focus on the derivative of exponential functions.
The derivative of ex with respect to x is ex, i.e. d(ex)/dx = ex
It is noted that the exponential function f(x) =ex has a special property. It means that the derivative of the function is the function itself.
(i.e) f ‘(x) = ex = f(x)
Exponential Series
Exponential Functions
Exponential Function Properties
The exponential graph of a function represents the exponential function properties.
Let us consider the exponential function, y=2x
The graph of function y=2x is shown below. First, the property of the exponential function graph when the base is greater than 1.
Exponential Functions
Exponential Function Graph for y=2x
The graph passes through the point (0,1).
The domain is all real numbers
The range is y>0
The graph is increasing
The graph is asymptotic to the x-axis as x approaches negative infinity
The graph increases without bound as x approaches positive infinity
The graph is continuous
The graph is smooth
Exponential Functions
Exponential Function Graph y=2-x
The graph of function y=2-x is shown above. The properties of the exponential function and its graph when the base is between 0 and 1 are given.
The line passes through the point (0,1)
The domain includes all real numbers
The range is of y>0
It forms a decreasing graph
The line in the graph above is asymptotic to the x-axis as x approaches positive infinity
The line increases without bound as x approaches negative infinity
It is a continuous graph
It forms a smooth graph
Exponential Function Rules
Some important exponential rules are given below:
If a>0, and b>0, the following hold true for all the real numbers x and y:
ax ay = ax+y
ax/ay = ax-y
(ax)y = axy
axbx=(ab)x
(a/b)x= ax/bx
a0=1
a-x= 1/ ax
Exponential Functions Examples
The examples of exponential functions are:
f(x) = 2x
f(x) = 1/ 2x = 2-x
f(x) = 2x+3
f(x) = 0.5x
Solved problem
Question:
Simplify the exponential equation 2x-2x+1
Solution:
Given exponential equation: 2x-2x+1
By using the property: ax ay = ax+y
Hence, 2x+1 can be written as 2x. 2
Thus the given equation is written as:
2x-2x+1 =2x-2x. 2
Now, factor out the term 2x
2x-2x+1 =2x-2x. 2 = 2x(1-2)
2x-2x+1 = 2x(-1)
2x-2x+1 = – 2x
A line has a slope of 1/2 and passes through the point (6,2).
a) Write the equation of this line in point-slope form
(b) What is the y-intercept of this line?
Answer:
a) y-2=1/2(x-6) b) The y-intercept of this line is -1.
Step-by-step explanation:
y-y1=m(x-x1)
y-2=1/2(x-6)
------------------
y=1/2x-6/2+2
y=1/2x-3+2
y=1/2x-1
y=mx+b where m=slope and b=y-intercept.
Please help! What is the area of this figure?
Answer and explanation please! <3
Answer:
19 units²
Step-by-step explanation:
Divide into three shapes:
Large rectangle BEFA
Large triangle - BCE
Small triangle - CDE -
BEFA = 4x3 = 12
BCE = 1/2x4x2 = 4
CDE = 1/2x3x2 = 3
12+4+3=19
Find the value of x
Answer:
x=80
Step-by-step explanation:
(x+30)=110 because they are vertically opposite angles.
x+30=110
x=110-30
x=80
Answer:
x = 80 degrees
Step-by-step explanation:
x + 30 = 110
- 30 = -30
x = 80 degrees
The Adams family drove 319 miles in 5.5 hours. At this same rate, how many miles would they drive in
3 hours?
A:164 B:174 C:180 D:144
please help me asap
Answer C
Step-by-step explanation:
If someone makes as many slices of toast as possible in 4 minutes and 40 seconds, how many slices do think they can make
Answer:
If they can do x slices per second, they could do 280x slices
Step-by-step explanation:
4 min 40 sec -> 280 secs
280 * 5 = 1400
How are land parcels valued?
You are given two functions f(x) and g(x). How has the graph of g(x) changed from that of f(x)?
f(x) = log (x + 1)
g(x) = log (x - 2) + 5
A)
g has been shifted up five units and to the left two units from f
B)
g has been shifted up five units and to the right three units from f
C)
g has been shifted down five units and to the left two units from f
D)
g has been shifted down five units and to the right three units from f
Answer:
C. g has been shifted down five units and to the left two units from f
Step-by-step explanation:
Sana makatulong
A community is considering raising funds to pay for improvements to the community swimming pool. To measure the
level of interest, community leaders went door-to-door in a few neighborhoods and interviewed residents. Of the 230
residents contacted, 157 support raising funds to pay for improvements. Which of the following represents the
sample in this setting?
O all residents of the community
O the 230 residents who were interviewed
O all residents who use the community pool
O the 157 residents who support raising funds
Mark this and return
Save and Exit
Next
Submit
Answer:
All residents of the community
Step-by-step explanation:
Not sure if this is fully correct but the 2nd and 3rd option is wrong (Edg 2021)
The correct option is b. the 230 residents who were interviewed.
Given,
A community is considering raising funds to pay for improvements to the community swimming pool. community leaders went door-to-door in a few neighborhoods and interviewed residents. Of the 230 residents contacted, 157 support raising funds to pay for improvements.
Now we have to find the sample in this setting.
A sample is the specific group that you will collect data from.
Here, 230 residents contacted, so the Sample is 230 residents.
Hence the correct option is b.the 230 residents who were interviewed.
For more details on Sample follow the link:
https://brainly.com/question/350477
(13x+2)+(7x-10) add and find the answer
Answer:
[tex](13x + 2) + (7x - 10) \\ = 13x + 2 + 7x - 10 \\ = 13x + 7x + 2 - 10 \\ = 20x - 8[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
Answer:
It should be 20x-8
Step-by-step explanation:
(13x+7x)(2-10)
add like terms and get..
20x-8
Which of the following numbers would be to
the left of the number -1 on a number line?
8
4
0
-0.5
-4
Answer:
-4
Step-by-step explanation:
Numbers decrease on a number line as you go left. So, to find a number to the left of -1, you need to find a number that is smaller. Since negative numbers decrease in value as they get further from 0, -4 must be smaller than -1. All other values listed will be to the right of -1.
PLEASE HELP!!
Solve for m
m+7=3+m+4
Answer:
M = -7
Step-by-step explanation:
It makes sense if you replace it in for M! Hope this helps and have a great day!
help asap i am struggling see image for problem
Answer:
p = 132 - 30d
Step-by-step explanation:
Here, we can plug in x = 6 into the equation provided at the end of the problem.
p = 6[25 - (3 +5d)]
p = 150 - 18 - 30d
p = 132 - 30d
Evaluate the expression: 1/3 (4x3)+2^3.
show proof and work for brainliest
Eighth grade Y 11 Write a linear equation from two points A line includes the points (4, 6) and (3, 3), What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form у y- Submit Work it out
Answer:
[tex]y = 3x - 6[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (4,6)[/tex]
[tex](x_2,y_2) = (3,3)[/tex]
Required
Equation in slope intercept
First, calculate the slope.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{3-6}{3-4}[/tex]
[tex]m = \frac{-3}{-1}[/tex]
[tex]m = 3[/tex]
The equation is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 3(x - 4) +6[/tex]
[tex]y = 3x - 12+6[/tex]
[tex]y = 3x - 6[/tex]
the 20% tip on a $8 sandwich
Answer:
Tip of $1.60
The total is $9.60
Step-by-step explanation:
(20% × $8) + $8
$1.60 + $8
$9.60
Find the missing side x=
What is the value of arccos(−1/2)in radians?
Answer:
2.0943951 radians
Step-by-step explanation:
Solve for x:
-2x + 11 = 23
6
-6
12
-12
Answer:
x = -6
Step-by-step explanation:
what is the value of tan0 in the unit circle below
Answer: ( 60 ) , or ( -4)
Step-by-step explanation:
Answer:
√3/3
Step-by-step explanation:
tan=sin/cos=1/2/sqrt(3)/2=1/sqrt(3)
hope it helps
have a great day
Simplify and find the undefined values of 4x^4+6x^3/6x^2+9x .
Answer:
x^5+4x^4+9x is what I would simplify it to.
Change the following expression to an equivalent expression in exponential form
Answer:
12^4/5
Step-by-step explanation:
When doing this you put the number the base is raised to on top of the fraction and the root number on the bottom