Answers
Answer:
The tangent line is: y = 8x - 58
The tangent point is at (7, -2)
===================================================
Explanation:
One of the definitions of derivatives is
[tex]\displaystyle f'(a) = \lim_{x\to a} \frac{f(x)-f(a)}{x-a}[/tex]
where f ' (a) represents the derivative evaluated at x = a.
The value of f ' (a) will get us the slope of the tangent at x = a.
The idea is that x is getting closer and closer to 'a'. In doing so, the secant lines slowly approach the tangent line.
Keep in mind that x will never reach 'a' itself (if it did, then we'd have a division by zero error).
---------------
The given limit we have is
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)+2}{x-7} = 8[/tex]
and that is equivalent to
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)-(-2)}{x-7} = 8[/tex]
and also equivalent to
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)-f(7)}{x-7} = 8[/tex]
Compare that to the template I mentioned at the top to see that
a = 7f(a) = f(7) = -2f ' (a) = f ' (7) = 8Therefore, we can say the tangent slope is 8 and the tangent touches the f(x) curve at (x,y) = (a, f(a)) = (7,f(7)) = (7,-2)
---------------
[tex]m = 8 = \text{slope}\\\\(x_1,y_1) = (7,-2) = \text{tangent point}\\\\[/tex]
Let's use that info to determine the equation of the tangent line.
I'll use point-slope form to isolate y.
[tex]y-y_1 = m(x-x_1)\\\\y-(-2) = 8(x-7)\\\\y+2 = 8x-56\\\\y = 8x-56-2\\\\y = 8x-58\\\\[/tex]
That's the equation of the tangent line to the point (7,-2).
Related Questions
Find the interest rate for the given deposit and compound amount.
$4000 accumulating to $5994.75, compounded monthly for 7 years.
Answers
Answer:
The interest rate is 5.79% (to the nearest hundredth).
Step-by-step explanation:
To find the interest rate for the given deposit of $4000 accumulating to $5994.75, compounded monthly for 7 years, use the compound interest formula.
Compound Interest Formula[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $4,000A = $5,994.75n = 12 (monthly)t = 7 yearsSubstitute the given values into the formula and solve for r.
[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{12 \times 7}[/tex]
[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{84}[/tex]
[tex]\implies \sf \dfrac{5994.75}{4000}=\left(1+\dfrac{r}{12}\right)^{84}[/tex]
[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}=1+\dfrac{r}{12}[/tex]
[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1=\dfrac{r}{12}[/tex]
[tex]\implies \sf r=12\left(\sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1\right)[/tex]
[tex]\implies \sf r=0.057937950...[/tex]
[tex]\implies \sf r=5.7937950...\%[/tex]
Therefore, the interest rate is 5.79% (to the nearest hundredth).
A tank in the shape of a hemisphere has a diameter of 12 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
In linear equation, 1161.8 lb is the total weight of the liquid in the tank, to the nearest full pound.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
d = 12 ft
r = 12 ft/2 = 6 ft
volume of sphere = (4/3)πr³
volume of hemisphere = (1/2)(4/3)πr³
volume = (2/3)π(6 ft³) = 12.56 ft³
weight = volume × density
weight = 12.56 ft³ × 92.5 lb/ft³
weight = 1161.8 lb
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Please Hurry!!
Which polar coordinates represent the point plotted on the graph? Select all that apply and explain your answer.
Answers
Answer:
D
[tex]3. \frac{11\pi}{6} [/tex]
Step-by-step explanation:
When we determine the point's coordinates, first we have to write the polar ones (they are on the horizontal line) and then the south ones (they are around the circle)
I think this is the right answer
A business organization needs to make up a 8 member fund-raising committee. The organization has 6 accounting majors and 7 finance majors. What is the probability that at least 4 accounting majors are on the committee?
a) 0.4079
b) 0.0171
c) 0.1795
d) 0.0163
e) 0.5874
Answers
The probability that at least 4 accounting majors are on the committee is E. 0.5874.
How to find the probabilityProbability operates on the principle of dividing the number of expected outcomes by the number of total outcomes. To find the probability that at least 4 accounting majors are on the committee, we can begin by determining the probability of having exactly 4, 5, 6, and 7 accounting majors on the committee. After finding these probabilities, we can then sum up the figures.
First, the total number of ways to choose 8 members from a group of 6+7=13 is:
13! / (8! * 5!) = 1287
Next, we will find the number of ways to choose exactly 4 accounting majors and 4 finance majors is:
6 choose 4 * 7 choose 4 = 15 * 35 = 525
Also, the number of ways to choose exactly 6 accounting majors and 2 finance majors is:
6 choose 6 * 7 choose 2 = 1 * 21 = 21
Finally, the number of ways to choose exactly 7 accounting majors and 1 finance major is:
6 choose 7 * 7 choose 1 = 0 * 7 = 0
Now, we will sum the total number of ways to choose a committee with at least 4 accounting majors as follows:
525 + 210 + 21 + 0 = 756
756 / 1287 = 0.587
Therefore, the probability of selecting a minimum of 4 accounting majors is thus 0.5874.
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How do you convert 72 kilograms to pounds? show the mathmatical steps
Answers
1 kilogram = 2.20462 pounds
To convert 72 kilograms to pounds, you can multiply 72 by 2.20462 as follows:
72 kilograms = 72 x 2.20462 pounds
72 kilograms = 158.73264 pounds (rounded to five decimal places)
Therefore, 72 kilograms is equal to approximately 158.73264 pounds.
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Compare the square root of 32 and twenty one fourths using >, <, or =. twenty one fourths is less than the square root of 32 the square root of 32 is less than twenty one fourths twenty one fourths is equal to the square root of 32 the square root of 32 is less than twenty one fourths
Answers
Answer: >
Step-by-step explanation:
Part 1
Use the Pythagorean theorem to find the unknown side of the right triangle.
Answers
Answer:
Hypotenuse length = 37Step-by-step explanation:
According to the question we are given with a right traingle Where base is 35 and the perpendicular is 12.
We need to find the unknown side that is the longest side (Hypotenuse) .
By using pythagoras theorem :
[tex]\longrightarrow \rm \: \: (H)^2 = (B)^2 + (P)^2 \\ [/tex]
here,
H represents hypotenuseB represents base P represents Perpendicular.Putting the required values in the Pythagoras theorem we will get,,
[tex]\longrightarrow \rm \: \: (H)^2 = (35)^2 + (12)^2 \\ \\ \longrightarrow \rm \: \:(H)^2 =1225 + 144 \\ \\ \longrightarrow \rm \: \:(H)^2 = 1369 \\ \\ \longrightarrow \rm \: \:H = \sqrt{1369} \\ \\ \longrightarrow \rm \: \:H = 37 \\ [/tex]
Therefore, Unknown side of the right triangle i.e hypotenuse is 37 .
A circular path 2feet wide has an inner diameter of 550 feet . How much farther is it around the outer edge of the path than around the inner edge?
Answers
Answer:
[tex]L_c=12.56 \ \text{feet}[/tex]
Step-by-step explanation:
From the question we are told that
Width of circular path [tex]w_c=2 \ \text{feet}[/tex]
Inner Diameter [tex]d_{in}=550 \ \text{feet}[/tex]
Outer diameter [tex]d_{out}=550+2\times2[/tex] (inner diameter + 2 circular path width)
[tex]d_{out}=550+4[/tex]
[tex]d_{out}=554 \ \text{feet}[/tex]
Generally the equation for inner circumference of the circle is mathematically given by
[tex]C_1=\pi d_{in}[/tex]
[tex]C_1=3.14\times550[/tex]
[tex]C_1=1727 \ \text{feet}[/tex]
Generally the equation for outer circumference of the circle is mathematically given by
[tex]C_2=\pi d_{out}[/tex]
[tex]C_2=3.14\times554[/tex]
[tex]C_2=1739.56 \ \text{feet}[/tex]
Generally the difference in length of the two circumference is mathematically given by
[tex]L_c=C_2-C_1[/tex]
[tex]L_c=1739.56-1727[/tex]
[tex]L_c=12.56 \ \text{feet}[/tex]
Solve the equation 101 = k +33 for k
K=
Answers
Answer:
101 = k + 33
101 - 33 = k + 33 - 33
68 = k
this is your required answer
Kayne runs a specialty running store. Last year, he earned $50,000 in revenue and had explicit costs of $20,000. Kayne could have made $42,000 selling video games on the Internet and received an additional $5,000 if he rented out the store and equipment. Calculate Kayne’s implicit costs.
Answers
economic profit = total revenue - explicit costs - implicit costs
We are given that Kayne earned $50,000 in revenue and had explicit costs of $20,000. We also know that if he had sold video games on the Internet, he could have made $42,000, and if he had rented out the store and equipment, he could have received an additional $5,000. These represent the opportunity costs of running his specialty running store.
So, we can calculate Kayne's implicit costs as follows:
implicit costs = opportunity cost of selling video games + opportunity cost of renting out the store and equipment
implicit costs = $42,000 + $5,000
implicit costs = $47,000
Now, we can substitute this value into the economic profit formula:
economic profit = $50,000 - $20,000 - $47,000
economic profit = -$17,000
The negative value indicates that Kayne did not earn a positive economic profit, meaning that his explicit and implicit costs were greater than his revenue.
what is μ (∠FNL)? this is crazy stuff
Answers
The angle ∠FNL in the given trapezium shows that ∠FNL is 122°
What are the opposite angles of a trapezium?The opposite angles of a trapezium are not necessarily equal, unlike in a parallelogram.
However, the opposite angles of a trapezium are supplementary, which means that the sum of one pair of opposite angles equals 180 degrees.
In other words, if we label the angles of a trapezium as F, D, N, and L (with F and L being opposite angles, and D and N being opposite angles), then we have:
∠F + ∠L = 180 degrees
∠D + ∠L = 180 degrees
Thus, ∠FDL + ∠FNL = 180
4x - 14 + 9x - 40 = 180
13x - 54 = 180
13x = 234
x = 18
∠FNL = 9x - 40
∠FNL = 9(18) - 40
∠FNL = 122°
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(1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10
Answers
The value of simplification is 95.
What is simplification?
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easily with calculations and solving.
Here, we have
Given: (1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10
we have to simplify the given expression.
= (1000y) -1/2 * (3/x+1)
When x = 1/3 and y = 1/10
Now we put the value of x and y in the given equation and we get
= (1000/10) -1/2 × (3×3+1)
= 100 - 10/2
= 100 - 5
= 95
Hence, the value of simplification is 95.
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6. Find the first three terms of the expansion of the following in acceding powers of
x
2
1
2
x
x
Answers
The first three terms in decreasing powers of X are as follows.
x5−10x4X−1+40x3X−2+…
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from
A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
Hence, The first three terms in decreasing powers of X are as follows.
x5−10x4X−1+40x3X−2+…
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The following equation involves multiple angles. Solve the equation on the interval [0, 2π). cos 4x= 1/2
Answers
[tex]\cos(4x)=\cfrac{1}{2}\implies 4x=\cos^{-1}\left( \cfrac{1}{2} \right)\implies 4x= \begin{cases} \frac{\pi }{3}\\\\ \frac{5\pi }{3} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=\cfrac{\pi }{3}\implies \boxed{x=\cfrac{\pi }{12}}~\hfill 4x=\cfrac{5\pi }{3}\implies \boxed{x=\cfrac{5\pi }{12}}[/tex]
HELP PLEASE I DO NOT UNDERSTAND THIS
Answers
The simplified expression for x+2x-8+3x+1-2x is 4x - 4.
What is expression?Expression is a term used to describe a wide variety of communication methods such as verbal, nonverbal, written, and artistic. It is the way we communicate our thoughts, feelings, and ideas to others. It is an important part of our lives, from the simplest forms of communication like body language to more complex forms like written literature. Expression is a powerful tool for self-expression, communication, and connection.
The expression x+2x-8+3x+1-2x can be simplified by combining like terms.
First, the x-terms can be combined, resulting in 4x:
x + 2x + 3x - 2x = 4x
Next, the remaining constants can be combined, resulting in -4:
4x - 8 + 1 = -4
Finally, the resulting expression can be written as 4x - 4.
Therefore, the simplified expression for x+2x-8+3x+1-2x is 4x - 4.
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Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his
school, 1 mile from his house. The function d gives the distance d(t), in miles, of Tyler from his
house t minutes after 7:00 a.m.
On snowy days, Tyles's school has a 2 hour delayed start time (120 minutes). The function s
b. gives Tyler's distance s(t), in miles, from home t minutes after 7:00 a.m. with a 120 minute
delayed start time. If d(5) = 0.25, then what is the corresponding point on the function s?
c. Write an expression for s in terms of d.
5(1) -
Answers
The function m(t) shifts the time frame by 1hr later the original function d(t).
The function s can be written in terms of d as follows:
s (r) = d × [tex](r+7)^{-1}[/tex]
Define function?The core concept of calculus in mathematics is a function. The relations are certain kinds of the functions. In mathematics, a function is a rule that produces a different result for every input x. In mathematics, a function is represented by a mapping or transformation. Letters like f, g, and h are widely used to indicate these operations.
In this situation, d (5) = 0.25 means that Tyler is 0.25 minutes away from his home at 7:05am. This is because Tyler's distance from his house at time t after 7am is provided by the function d (t).
Tyler's school starts at 9 a.m. with a 120-minute delay. As a result, if d (5) = 0.25, Tyler has walked for 5 minutes, and his distance function s (r) calculates his distance starting at 7 minutes after 7 a.m. with a 120-minute start delay. The matching point, then, indicates Tyler's separation from his home at 7 minutes after 9 a.m. If he started walking at 7 am and took 5 minutes.
The function s can be written in terms of d as follows:
s (r) = d × [tex](r+7)^{-1}[/tex]
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100 points!!
f (x) = −√x + 2 + 3
Fully explain the three transformations required to produce this function from the
parent function.
Answers
Answer: the first thing is your answer :)
thx for the points
Step-by-step explanation:
g
(
x
)
=
x
2
−
3
The parent function is the simplest form of the type of function given.
f
(
x
)
=
x
2
The transformation being described is from
f
(
x
)
=
x
2
to
g
(
x
)
=
x
2
−
3
.
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
−
3
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
g
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
g
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
g
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
Vertical Shift: Down
3
Units
The graph is reflected about the x-axis when
g
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: None
The graph is reflected about the y-axis when
g
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: None
Compare and list the transformations.
Parent Function:
f
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: Down
3
Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
image of graph
Name two pairs of adjacent angles.
Answers
Answer:
the definition of adjacent mathematically means two angles if they have a common side and a common vertex.
Step-by-step explanation:
a would b adjacent to d. c would be adjacent to d.
Change the following equation of a line into slope-intercept form. X =(y-2)÷2
Answers
Equation in the standard slope-intercept form: y = 2X + 2
What is slope-intercept form?The slope intercept form of an equation is represented as follows:
y = mx + c
where, m = slope, c = y-intercept
We want to rewrite the equation X = (y - 2) ÷ 2 in slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y on one side of the equation by multiplying both sides by 2:
2X = y - 2
Next, let's add 2 to both sides:
2X + 2 = y
Finally, let's switch the sides to get the equation in the standard slope-intercept form:
y = 2X + 2
So the slope of the line is 2 and the y-intercept is 2.
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Find the 18th term.
-21, -14, -7, 0, 7, ...
18th term = [?]
Answers
The 18th term of the sequence is -140
How to determine the term
It is important to note that the formula for the nth term of an arithmetic sequence is expressed with the equation;
an = a + (n - 1) d
Such that the parameters are enumerated as;
an is the nth term of the arithmetic sequencea is the first term of the sequencen is the number of terms in the sequenced is the common differenceFrom the information given, we have;
The sequence is;
-21, -14, -7, 0, 7, ...
Then, the common difference = -14 - (-21) = -14 + 21 = -7
Substitute the value
a18 = -21 + (18 - 1) -7
expand the bracket
a18 =-21 + (17)-7
a18 = - 21 - 119
a18 = - 140
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please answer it asap.
Answers
Answer:
8^2
Step-by-step explanation:
PLEASE ANSWER THIS ASAP What is the exact surface area of a cylindrical propane tank with a radius of 1 m and a height of 10 m?
2π m²
20π m²
22π m²
24π m²
Answers
22π m² is the exact surface area of a cylindrical propane tank.
What are volume and surface area?
The entire area of all the faces makes up the surface area of a three-dimensional form. We measure the areas of each face and put them together to determine the surface area of a shape.
The surface-area-to-volume ratio, also known as the surface-to-volume ratio or abbreviated as SA:V, refers to how much surface area there is in each unit volume of an object or collection of objects.
A=2πrh+2πr²
=2π * 1* 10 +2π* 1²
= 2π( 10 + 1)
= 2π * 11
= 22π m²
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In a large population of nurses, suppose 20% of the nurses would prefer the night shift. If a random sample of 10 nurses is taken, what is the probability less than 3 are nurses that prefer the night shift?
Answers
We can use the binomial probability formula:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of nurses in the sample who prefer the night shift.
Using the binomial probability formula, we can calculate:
P(X = 0) = (10 choose 0) * 0.2^0 * 0.8^10 = 0.1074
P(X = 1) = (10 choose 1) * 0.2^1 * 0.8^9 = 0.2684
P(X = 2) = (10 choose 2) * 0.2^2 * 0.8^8 = 0.3019
Therefore,
P(X < 3) = 0.1074 + 0.2684 + 0.3019 = 0.6777
The probability that less than 3 nurses in the sample prefer the night shift is approximately 0.6777 or 67.77%.
Of 10 test scores, seven are less than or equal to 85. What is the percentile rank of a test score of 85?
Answers
Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test scores.
Explain about the Percentile?A percentile in statistics refers to a score's position in relation to other scores in a given set. Although percentile has no one fixed meaning, it is frequently described as the proportion of numbers within a collection of data scores that are lower than a particular value.
Percentile shows the proportion of persons who fall below a given value. When we declare that a score of 365 out of 400 represents the 90% percentile on an exam, it means that 90% of test-takers received scores that were lower than or equal to 365.
Give: Seven of the ten test results are inside the 85th percentile.
The percentage of those who received less than or equal to 85 is just as follows: 7/10 = 0.7.
percentile rank:
0.7*100 = 70
Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test scores.
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Arrange the following from least your greatest 1/3,5/6,3/8
Answers
Answer:
Step-by-step explanation:
make them all the same denominator so
the least common denominator for all of them is 24:
1/3 x 8/8=8/24
5/6x4/4=20/24
3/8x3/3=9/24
so from least to greatest it is:
1/3, 3/8, 5/6
If f(x) = 2x-3/5 , which of the following is the inverse of f(x)?
5
O A. f¹(x) =
OB. f¹(x) =
O C. f-¹(x) =
OD. f1(x) =
5x+3/
2
2x+3/
5
3x+5/
2
3x+2/
5
Answers
The inverse of the linear function, f(x), f(x) = (2x - 3)/5 is f⁻¹(x) = (5·x + 3)/2. The correct option is option A
A. f⁻¹(x) = (5·x + 3)/2
What is the inverse of a function?The inverse of a function is a function that reverses the effect the original function.
The original function is; f(x) = (2·x - 3)/5
The inverse of f(x) can therefore be found by making x the subject of the equation as follows;
f(x) = (2·x - 3)/5
5 × f(x) = (2·x - 3)
5 × f(x) + 3 = 2·x
2·x = 5 × f(x) + 3
x = (5 × f(x) + 3)/2
Plugging in x = f⁻¹(x) and f(x) = x, in the above equation, we get;
f⁻¹(x) = (5 × x + 3)/2
f⁻¹(x) = (5·x + 3)/2The correct option that is an inverse of f(x) is therefore, option A
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Incorrect Which statement is NOT one of the axioms of Euclidean geometry? XO A. C. D ****? All these pictures i got answers off of Bainly and here are the wrong ones!!
Answers
The statement that is NOT one of the axioms of Euclidean geometry is D. If two planes intersect, their intersection is a point.
What are the axioms of Euclidean geometry?Euclidean geometry is a branch of mathematics that deals with the study of two-dimensional and three-dimensional figures using a set of axioms or postulates.
The axioms of Euclidean geometry are a set of five statements that are used as the foundation for all of the theorems and proofs in Euclidean geometry.
The first two axioms are relatively straightforward and intuitive, while the third axiom involves the use of circles to construct geometric figures. The fourth axiom establishes the concept of a right angle, which is a 90-degree angle, while the fifth axiom deals with the concept of parallel lines and their relationship to intersecting lines.
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A pool can be filled by one pipe in 4 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill the pool?
Answers
Step-by-step explanation:
Rate A = 1 pool / 4 hrs = 1/4 pool/hr
Rate B = 1 pool / 5 hrs = 1/5 pool / hr
Now combine the rates to fill 1 pool
1 pool / ( 1/4 pool/hr + 1/5 pool / hr) = 1 / ( 1/4 + 1/5) hr = 2.22 hrs
( or 2 hrs 13.3 min)
Please help with this
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTSp
Answers
Answer:
f(x) = 3x-5
Step-by-step explanation:
Plug in the domain 0, in the other answer options
f(x) = -3x + 4 turns into f(x) = -3(0) + 4 and thats equal to 4, there is no value set to 4 in the range so that option is cancelled out
f(x) = x+2 turns into f(x) = 0+2 =2, there is no value set to 2 in the range so that option is cancelled out
f(x) = -5x + 3 turns into f(x) = -5(0) + 3, and thats equal to 3, there is no value set to 3 in the range so that option is cancelled out
f(x) = 3x-5 turns into f(x) = 3(0) - 5, and thats equal to -5, there is a value in the range that equals -5, you could also try any domain value into this equation and it would result into either -11, -5, 1, 7, or 13.
keep in mind f(x) is the range