Please help, hurry... This lesson is called "Distance and Midpoint Formula" in Basic Geometry
Answer:
g(x) = x - 3
Step-by-step explanation:
An inverse function undoes a function meaning (x - 3) is the only function that undoes (x + 3).
Before the drawbridge starts to open, it is perfectly level with the ground. The dancer is standing still on one leg. What is the horizontal component of the friction force f⃗ ?.
Before the drawbridge starts to open, the horizontal component of the friction force f⃗ is zero (0)
The horizontal component of the friction force is the counter force that must overcome the friction force for a body to slide or move.
When the dancer is standing still on the drawbridge, the only force on the dances is the normal force exerted by the bridge. Thus, the horizontal frictional force acting on the dancer
This is given by:
[tex]f_{horizontal} =0[/tex]
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Write 2.01 × 105 in standard form.
The correct answer in the standard form or notation of the given number is 2.1105 x 10^6.
How to write the standard notation?
In mathematics, the standard form or the standard notation of a number can be written as the power of ten by putting the decimal in the calculated number. And these numbers can be written in certain rules.
According to the question, to convert the decimal number to standard form by removing the decimal from the given number.
The required expression can be written as"
2.01 x 105 = 201 x 100 x 105 = 21105 x 10²
Hence, the correct answer in the standard form or notation of the given number is 21105 x 10².
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There are 2.54 cm in an inch, 100 cm in a meter, 12 inches in 1 foot, and 5,280 feet in 1 mile. Jada ran 1.5 miles. How many centimeters and meters is that?
Answer:
1.5 miles = 241,401.6 centimeters
= 95,040 inches
1.5 miles = 2,414.016 meters
Step-by-step explanation: 5,280 feet x 12 inches = 63,360 inches
2,640 feet x 12 inches = 31, 680 inches
63,360 + 31,680 = 95,040 inches in 1.5 miles
95,040 x 2.54 centimeters per inch = 241,401.6
241,401.6 centimeters / 100 = 2,414.016 meters
The diagonal of a square is 6√3. Find the perimeter
Using the formulas
P=4a
d=2a
Solving forP
P=22d=2·2·6≈16.97056
Please helppp :)
Create a table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer
The following data table for two distinct linear functions utilizing identical x values for both functions is displayed:
[tex]\begin{tabular}{|c|c|c|}$\mathrm{x}$ & $\mathrm{y}=2 \mathrm{x}+7$ & $\mathrm{y}=-\mathrm{x}+4$ \\$-3$ & $2(-3)+7=-6+7=1$ & $-(-3)+4=3+4=7$ \\$-2$ & $2(-2)+7=-4+7=3$ & $-(-2)+4=2+4=6$ \\$-1$ & $2(-1)+7=-2+7=5$ & $-(-1)+4=1+4=5$ \\0 & $2(0)+7=0+7=7$ & $-(0)+4=0+4=4$ \\1 & $2(1)+7=2+7=9$ & $-(1)+4=-1+4=3$ \\2 & $2(2)+7=4+7=11$ & $-(2)+4=-2+4=2$ \\3 & $2(3)+7=6+7=13$ & $-(3)+4=-3+4=1$\end{tabular}[/tex]
The table demonstrates that the function y = 2x + 7 and the function y = -x + 4 both have values of 5 for x = -1.
As a result, the two functions' graphs will intersect at (1, 5)
First of all, we create 2 LINEAR function, i created the function f(x)=2x+5 and the function h(x)=3x+2, both are linear(without a quadratic term). Then
Choose a group of x values before creating the table. Add each x value from the left side column to the equation. To find the y value, evaluate the equation (middle column). Since the table of values really only contains x and y pairs, you can choose to omit the middle column from your table as an optional step.
you replace the x for a number:
Table 1 (F(X)=2X+5) Table 2 (H(X)=3X+2)
X=1----->Y=2+5=7 X=1------>Y=3·1+2=5
X=2---->Y=2·2+5=9 X=2----->Y=3·2+2=8
X=3---->Y=3·3+5=11 X=3----->Y=3·3+2=11
With both tables of data we can see that in the X=3/Y=11 point this two linear functions will intersect so the answer is that the two functions will intersect at (3,11)----->(X,Y)
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f(x)=
1
4
x–5 if x<
–
4
x+3 if x≥
–
4
The graph of each function in the piecewise function is added as an attachment
How to determine the plot of the piecewise function?The equation of the piecewise function is given as
f(x) = 1/4x - 5 if x < 4
x + 3 if x ≥ 4
In the above definition of the piecewise function, we have the following functions and the domains
f(x) = 1/4x - 5 at a domain of x < 4
f(x) = x + 3 at a domain of x ≥ 4
Note that:
The domain of the function is the set of input values of the graph
This in other words mean the domain of a function is the set of x values of the graph.
Next, we plot the graph of each function in the piecewise function in their respective domain
See attachment for the graph of each function in the piecewise function,
On the graph, the blue line represents f(x) = 1/4x - 5 while the other line represents f(x) = x + 3
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Possible question
Plot of the piecewise function
f(x) = 1/4x - 5 if x < 4
x + 3 if x ≥ 4
pls helppp!!!
1. Give an example of discrete data that might consist of some decimal numbers.
2. Give an example of continuous data that might not have any numbers with fractional parts
The discrete data might consist of number of legs, number of teeth. The continuous data might consist the length of tail, and the height of dog.
What is discrete data?The discrete data is a data whose value is obtained by counting and they can be described by an integer value. Those random variables, who take only distinct values, are called discrete random variables.
Consider the provided information; Something that will never change
So, the discrete data might consist of number of legs, number of teeth.
A continuous data is defined as a variable whose value is obtained by measuring.
The continuous data might consist the length of tail, and the height of dog.
The continuous variables are random variables, who take any value from a given continuous interval of real numbers.
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Ann, Ben, and Cindy were eating strawberries. The ratio of the numbers of berries they ate is 5:5:7. If Cindy ate 30 strawberry fewer than Ann and Ben together, what is the total number of strawberries the three of them ate
Answer:
170 strawberries
Step-by-step explanation:
Let strawberries be x, then:
Ann ate 5x, Ben ate 5x, and Cindy ate 7x
7x+30 = 5x+5x
7x+30 = 10x
30 = 3x
10 = x
5x = 50
7x = 70
total: 50+50+70 = 170
9 customers entered a store over the course of 18 minutes. At what rate were the customers entering the store in minutes per customer?
The rate at which the customers enter the store in minutes per customer is 2 minutes.
Based on the given question the number of customers is 9 so they take 18 minutes to enter. If each customer takes
(18÷9) minutes = 2 minutes.
Then all the customers will be inside the shop.
Fractions: The number of parts of a full portion is known as a fraction.
It is usually best to show an explanation using the easiest fraction. That is called Simplifying, or Decreasing the Fraction.
We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the total is separated into.
Represented as : [tex]\frac{Numerator}{Denominator}[/tex]
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Part 1 of 3
(Type an ordered pair.)
Suppose line h is the line with equation y = -2. Given A(7.-5), B(5,3), and C(-2,-5), what are the coordinates of the vertices of A'B'C' for the reflection?
Rh
The coordinates of the vertices of A'B'C' for the reflection are (7,1),(5,-7), and (-2,1) respectively.
What is reflection?A reflection is a transformation that uses a line to reflect a figure, much like a mirror. The mirror line is also known as the line of reflection.
The given coordinates are A(7,-5), B(5,3), and C(-2,-5).
The line of reflection is y = -2.
We have to determine the coordinates of the vertices of A'B'C' for the reflection.
In this case, the x-coordinate will remain the same and the y-coordinate will vary as the points are reflected across the line y = -2.
From the line of reflection i.e.y = -2, point A(7,-5) is located down at a distance of 3 units so its reflection A' is 3 units up of line y = -2 at (7,1).
From the line of reflection i.e.y = -2, point B(5, 3) is located up at a distance of 5 units so its reflection B' is 5 units down of line y = -2 at (5,-7).
From the line of reflection i.e.y = -2, point C(-2,-5) is located down at a distance of 3 units so its reflection C' is 3 units up of line y = -2 at (-2,1).
Hence, the coordinates of the vertices of A'B'C' for the reflection are (7,1),(5,-7), and (-2,1) respectively.
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please help, i am not sure what to do
cross multiplying
4/3(y-9/10)=5y(2/10)
expanding the bracket and collecting like terms
4y/3 - 6/5=y
4y/3 - y=6/5
((4y-3y)/3)=6/5
y/3=6/5
y=6/5x3
y=18/5
y=3.6
I hope this will help✨
the volume of the ice cream cone is increasing at the rate of 10 units3/sec and its radius is increasing at the rate of 1 14 units/sec when the radius r and height h are (r, h)
The rate of change for the height of the ice cream is [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.
What is the rate of change of the height of a cone?
The volume of an ice cream cone (V), in cubic units, is described by the following formula:
V = (1 / 3) · (π · r²) · h (1)
Where:
r - Radius of the cone, in units.h - Height of the cone, in units.The rate of change for the height of the cone is derived from differentiating (1) with respect to time:
V' = (1 / 3) · (2π · r) · h · r' + (1 / 3) · (π · r²) · h'
V' = (2π / 3) · h · r' + (π / 3) · r² · h'
h' = [V' - (2π / 3) · h · r'] / [(π / 3) · r²]
Where:
h' - Rate of change of the height, in units per second.V' - Rate of change of the volume, in cubic units per second.If we know that V' = 10 and r' = 1 / 14, then the rate of change for the height of the cone is:
h' = [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²]
The height of the ice cream cone changes at a rate of [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.
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Confused about the dimensions. If anyone can help me it's much appreciated.
Answer:
Its C
Step-by-step explanation:
I got it right on USA TEST PREP
Answer:
78m^3
Step-by-step explanation:
basically you have to split it into two rectangles and add the volumes
so think of it like this (first picture)
- looking at the bigger rectangle (blue rectangle) the 6 and the 4 are there as hints to the smaller rectangle so just kind of disregard them
- basically the bottom length is 6 but the top length is 5 and this is because the bottom length includes the other rectangle (smaller/pink rectangle), meaning the extra length from the other rectangle (smaller/pink rectangle) is 1.
- then height is given as 4 and 5. the height of 4 is caused by the line stopping when it meets the pink/smaller rectangle, meaning that the height from the other rectangle (smaller/pink rectangle) is 1.
- so using the correct measurements, the height is 5, the length is 5, and the width is 3 so:
5 • 5 • 3 = 75
~ so as stated above from evaluating the different measurements and how the rectangles “intersect” or meet:
the height is 1, the width is 1, and the length is then given as 3 so:
1 • 1 • 3 = 3
so then 75 + 3 = 78
so the full volume is 78 m^3
hope this helps :)
4 term in the sequence 3,9,15,21
The nth term in the sequence 3,9,15,21 will be 3 + 6(n - 1).
What is a sequence?It should be noted that a sequence simply means the order in which a particular thing happens or takes place.
From the information, four term in the sequence are given as 3,9,15,21 and we want to find the nth term. It should be noted that this is an arithmetic sequence.
The formula is illustrated as:
= a + (n - 1)d
where a = first term = 3
common difference = 9 - 3 = 6
The nth term will be:
= 3 + (n - 1)6
= 3 + 6(n - 1).
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Four term in the sequence 3,9,15,21. Find the nth term
which show a way to factor 14+35
Answer: The common factors of 14 and 35 are 7, 1, intersecting the two sets above. In the intersection factors of 14 ∩ factors of 35 the greatest element is 7. Therefore, the greatest common factor of 14 and 35 is 7.
Step-by-step explanation:
A number, x, rounded to 1 decimal place is 3.7
Write down the error interval for x.
The range of the error will be [3.65,3.75.
What is an error interval ?The accuracy range or limit where a number is rounded off or truncated is known as the error interval. This range merely depicts the possible range before rounding.
Given that :A number, x, rounded to 1 decimal place is 3.7
The mistake will be half of 0.1, which is[tex]\frac{0.1}{2} = 0.05[/tex], since the number is rounded to the nearest 0.1 unit.
3.7-0.05=3.65 will then be the lower limit of the error interval.
The error interval's upper limit will be 3.7 + 0.05 = 3.75.
The error will be 3.65≤x<3.75 milliseconds.
If the second decimal unit is more than 5, the first decimal unit will be 6, since we are rounding the first decimal unit. Similar to this, the first decimal unit will be 7 if the second decimal unit is less than 5.
The figures below, when rounded, result in 3.7.
3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74
As a result, the error range will be [3.65,3.75).
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I need help I’m stuck on this
question
x-c/2=d , for x
Answer:
I will answer this asap give me a few mins
Step-by-step explanation:
nun yet
Answer:
x = c/2 + d
Step-by-step explanation:
A bowl contained 58.3 grams of salt. Then, Brian poured in another 33.47 grams. How much salt does the bowl contain now
if x= 6 and y= -4, evaluate: 3x + x/y - y^2
Answer:
71/2 just
Step-by-step explanation:
just like that
ANSWER
Step-by-step explanation:
if x= 6 and y= -4, evaluate: 3x + x/y - y^2
we will just substitute for the values
3(6) + 6/-4 - (-4)²
=18 + 6/-4 - (16)
=18 + 6/-4 - 16
L.C.M=-4
= -72+6-(64)/-4
= -72-64+6/-4
=-136+6/-4
= -130/-4
=32.5 or 32 2/5
I hope I helped
25percent of what number is 18
Answer:
72%
Step-by-step explanation:
25percent of what number is 18
find unity18 : 25 = 0.72
find percent0.72 * 100 =
72%
OR25% = 1/4 so18 * 4 =
72%
Sarah created a graph to show the number of gallons in the tank as it is being filled with water over a 10 minute period.
Answer:
Can I see the graph, please?
Step-by-step explanation:
Answer:he graph shows the relationship between the number of miles she drives, y, and the number of gallons of gasoline in her car's tank, x.
Step-by-step explanation:
What is the opposite of each number?
Drag the answer into the box to match each number.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
0.005
12
0
−2
Answer:
0.1 == -0.1
1/7 == -1/7
10 == -10
-7 == 7
Step-by-step explanation:
I took the test
The opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
The numbers are:
0.005, 12, 0, -2
As we know, from the definition of the number, a number is a mathematical entity that can be used to count, measure, or name things.
The opposite of any number can be obtained by changing the sign of the number.
The opposite of the number 0.005 is -0.005
The opposite of the number 12 is -12
The opposite of the number 0 is 0
The opposite of the number -2 is 2
Thus, the opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.
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PLS HELP, IT'S ALMOST DUE! I'LL GIVE BRANLIEST TO THE CORRECT/BEST ANSWER. 40 Points! I'd appreciate if you help :)
A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp's incline?
A. 1/3 inch up per foot across
B. 1/2 inch up per foot across
C. 2 inches up per foot across
D. 3 inches up per foot across
Answer:
3 inches up per foot across
Step-by-step explanation:
rate of change = difference of y / difference of x
R = (18 - 12) / ( 6-4) = 6 / 2 = 3 inch / foot
Question «
Simplify this expression. √24
A 2√6
3√8
8√3
6√2
Answer:
A 2√6
Step-by-step explanation:
- Split the value under root into divisions of factors of 24
[tex]{ \sf{ \sqrt{24} = \sqrt{6 \times 4} }} \\ \\ { \sf{ \sqrt{24} = \sqrt{6} \times \sqrt{4} }} \\ \\ { \sf{ \sqrt{24} = \sqrt{6} \times 2 }} \\ \\ { \boxed{ \sf{ \: \sqrt{24} = 2 \sqrt{6} }}}[/tex]
1. Directed line segment QR has endpoints Q(8, 4) and R(-2, -1).
Find the coordinates of point Palong directed line segment QR so
that the ratio of QP to PR is 1 to 4.
The endpoints of the directed line segment QR are Q(8, 4) and R. (-2, -1).The x-coordinates of P is 6.2 and y-coordinates of P is 1.4.
Given that,
The endpoints of the directed line segment QR are Q(8, 4) and R. (-2, -1).
We have to find the coordinates of the QR line segment aimed at point P along that QP to PR is a 1 to 4 ratio.
QR has the endpoints Q(8, 4) and R. (-2, -1).
Line segment QR divides at point P in ratio 1:4.
Using section formula:
The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.
P(x,y)=[tex](\frac{mx_{2} +nx_{1} }{m+n},\frac{my_{2} +ny_{1} }{m+n},)[/tex]
Where m is 1 and n is 4. x₁=8,y₁=4 and x₂=-2,y₂=-1.
Substitute in the formulae we get,
P(x,y)=((1×-1+4×8)/1+4,(1×-1+4×4/1+4))
P(x,y)=((-1+32)/5,(-1+8)/5)
P(x,y)=(31/5,7/5)
P(x,y)=(6.2, 1.4)
Therefore, the x-coordinates of P is 6.2 and y-coordinates of P is 1.4
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PLEASE HELP MEEE !!!!!!!!!!!!!!!!!!
Answer:
x=20 degrees
I did what your teacher did down there; I added all the exterior angles and set them equal to 360°
Just combined the like terms and got the answer!
*3x + 4x + 3x = 10x
12 - 10 - 2 = 0
90 + 70 = 160
Put them "as an equation": 10x + 160 = 360
Get rid of what's surrounding the x, so subtract 160 from both sides.
10x = 200
To get rid of whats beside the x *again*, divided 10x by 10 on both sides.
x = 20
Describe how to transform the quantity of the sixth root of x to the fifth power, to the seventh power, into an expression with a rational exponent. Make sure you respond with complete sentences.
Please only CORRECT ANSWER. Don't answer if you don't know.
The quantity [tex](6\sqrt{x^5})^7[/tex] is transformed, into an expression with a rational exponent.
[tex]x^5 * 7 = 35[/tex]
This is further explained below.
What is the rational exponent. ?Exponents are said to be rational if they are able to be represented in the form of p/q, where the value of q is less than 0.
The notation for rational exponents is often written as xm/n, where x represents the base (a positive integer) and m/n is the rational exponent. Exponents may also be represented as xmn=nxm x m n = x m n.
This is another way to express rational exponents.
Generally, the equation is mathematically given as
[tex](6\sqrt{x^5})^7[/tex]
By bearing this in mind, we can make this process easier.
[tex](a^m)^n = a^m * n[/tex]
Therefore
[tex]x^5 * 7 = 35[/tex]
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What is the slope of a line perpendicular to the line whose equation is
2x + 3y = 21. Fully simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]2x+3y=21\implies 3y=-2x+21\implies y=\cfrac{-2x+21}{3} \\\\\\ y=\cfrac{-2x}{3}+\cfrac{21}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
well then, that simply means that
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}[/tex]
find the constant of the variation y=-12/11 x
By understanding the definition of a direct variation model, the constant of variation of the expression y = - (12 / 11) · x is - 12 / 11.
What is the constant of variation of a direct variation model?
In the statement we find a linear model of the form y = r · x, which represents a linear variation model, that is, a model where the variable x is directly proportional to the variable y and r is the constant of variation.
Graphically speaking, linear variation model represents a line whose intercept is at the origin. A representation of the expression y = - (12 / 11) · x is shown in the image attached below.
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