A plane travels 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. when a tailwind is present, the plane’s speed increases by x kilometers per hour. the time it takes the plane to travel the same distance with the tailwind, t(x), is defined by the function . what is the meaning of the y-intercept for this function? the time it takes the plane to travel without the tailwind the speed of the plane when there is no tailwind present the minimum amount of time it takes the plane to travel 2,000 km the time it takes the plane to travel when the speed is decreased by 900 kph
The meaning of the y-intercept exists in the time required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. [tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
What is the meaning of the y-intercept for the function[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]?The time it takes the plane to travel 2,000 kilometers with the tailwind, t(x), exists determined by the function
[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]
where x exists the increase in speed when the plane travels with the wind (tailwind).
The y-intercept exists at x=0, then
[tex]$&t(0)=\frac{2,000}{900}+x \\[/tex]
[tex]$&t(0)=\frac{20}{9}=2 \frac{2}{9}[/tex] hours
[tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
To learn more about y-intercept for the function refer to:
https://brainly.com/question/19552756
#SPJ4
Enter the correct answer in the box. jackson needs to determine the value of x in this equation. rewrite the expression as a logarithmic quotient that he could enter in his calculator.
A logarithmic equation exists as an equation that uses the logarithm of an expression containing a variable. The value of the logarithmic equation x = log 2.97/log 1.13.
What is a logarithmic equation?A logarithmic equation exists as an equation that applies the logarithm of an expression having a variable. To estimate exponential equations, first, see whether you can note both sides of the equation as powers of the same number.
Given: [tex]$1.13^x = 2.97[/tex]
Taking log on both sides, we get
log [tex]$1.13^x[/tex] = log 2.97
x log 1.13 = log 2.97
x = log 2.97/log 1.13
Therefore, the value of logarithmic equation x = log 2.97/log 1.13.
To learn more about logarithmic equations refer to:
https://brainly.com/question/28041634
#SPJ4
What type of polynomial is: 3x^4 - 2x^3 - 2
This polynomial has only 3 terms, so it is a trinomial. Hope it helps!
A pencil at a stationery store costs $1, and a pen costs $1.50. stella spent $21 at the store. she bought a total of 18 items. which system of equations can be used to find the number of pencils (x) and pens (y) she bought? x 18y = 21 x = 1.5y 18x y = 21 x = 1.5y x 1.5y = 21 x y = 18 1.5x y = 21 x = 18y
Equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18
The correct option is C.
What is liner equation?One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.
According to the given information:Let x stand for the number of pencils Stella purchased, and y for the number of pens Stella purchased.
Since Stella purchased a total of 18 things, the quantity of pencils and pens purchased must equal 18 or one of the following:
x + y = 18
We also know she spent $21, that a pencil costs $1, and that a pen costs $1.50. Therefore,
1x + 1.5y = 21
Thus, the set of equations that may be utilized to determine the quantity of pencils (x) and pens (y) that she purchased is as follows:
X+1.5Y = 21, and X+Y = 18
equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18
To know more about liner equation visit:
https://brainly.com/question/1347950
#SPJ4
Which angle is the angle of depression for the man looking at his dog?
A
B
C
D
Answer:
D
Step-by-step explanation:
An angle of depression is measured from the horizontal downwards.
this is angle D in the diagram
What is the slope of the line that passes through the points (-5,7) and (-2,4)?
Answer:
m = -x
Step-by-step explanation:
Use the given Maclaurin series to evaluate the limit
The "given series" should be for [tex]\cos(x)[/tex], not [tex]x[/tex], so that
[tex]\cos(x) = 1 - \dfrac{x^2}2 + \dfrac{x^4}{24} - \dfrac{x^6}{720} + \cdots[/tex]
In the limit (which should say [tex]x\to\infty[/tex], not [tex]n[/tex]), we have
[tex]\displaystyle \lim_{x\to\infty} \frac{\frac{x^2}{1+\cos(x)}}{x^4} = \lim_{x\to\infty} \frac{1}{x^2\left(2 - \frac{x^2}2 + \frac{x^4}{24} - \cdots\right)} = \boxed{0}[/tex]
Enduro solved -4x > 120 by adding 4 to each side of the inequality. What mistake did he make?
The mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
What are inequalities?Inequalities are expressions that have unequal values, when compared
How to determine Enduro's mistake?The inequality is given as
-4x > 120
When 4 is added to both sides, the inequality becomes
4 - 4x > 120 + 4
The above is not the solution to the inequality.
The solution is as follows:
We have:
-4x > 120
Divide both sides inequality by -4
x < -30
Hence, the mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
Read more about inequality at:
https://brainly.com/question/24372553
#SPJ1
Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→[infinity] (5x − ln(x))
The limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.
According to the given question.
We have to find the limit of [tex]\lim_{x \to \infty} 5x - lnx[/tex]
As we know that L'hospital rule is a theorem which provides a technique to evaluate limits of indeterminate forms.
And the formual for L'hospital rule is
[tex]\lim_{x \to \ c} \frac{f_{x} }{g_{x} } = \lim_{x \to \ c} \frac{f^{'}( x)}{g^{'} (x)}[/tex]
[tex]\lim_{x \to \infty} 5x - lnx[/tex] can be written as
[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]
If we put the value of limit in lnx/x we get an indeterminate form ∞/∞.
Therefore, [tex]\lim_{x \to \infty} \frac{lnx}{x} = \frac{\frac{1}{x} }{1}[/tex]
[tex]\implies \lim_{x \to \infty} \frac{1}{x} = 0[/tex] (as x tends to infinity 1/x tends to 0)
So,
[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]
[tex]= \lim_{x \to \infty}x(5 -0)[/tex]
[tex]= \lim_{n \to \infty} 5x \\= \infty[/tex](as x tends to ∞ 5x also tends to infinity)
Therefore, the limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.
Find out more information about limit and L'hospital rule here:
https://brainly.com/question/14105620
#SPJ4
Three interior angles of a quadrilateral measure 55°, 117°, and 120°. What is the measure of the fourth interior angle?
68°
78°
88°
98°
Answer:
68
Step-by-step explanation:
We know the sum of interior angles for a quadrilateral must equal 360, so we can create the following equation
[tex]55+117+120+x=360[/tex]
Simplify
[tex]292+x=360[/tex]
Subtract 292 from both sides
[tex]x=68[/tex]
Answer:
68
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360. The sum of the interior angles or a triangle is 180. If you think about a rectangle, you can cut that up into two triangles, so 180 + 180 = 360.
Now subtract out the 3 angles that you know
360-55-117-120 = 68
help
4/10 as a decimal
Answer:
0.4
Step-by-step explanation:
4/10 is 4÷10 = 0.4
Select the correct answer. which exponential equation is equivalent to this logarithmic equation?
logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x
What is logarithmic equation?
A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.The given logarithmic equation is;
[tex]log x = 4[/tex]
Since, log with base 10 is written as [tex]log x[/tex] simply, therefore, we have:
[tex]log_{10} x[/tex] = 4
Using the definition of logarithm, we get;
[tex]x = 10^{4}[/tex]
Equivalently, [tex]10^{4} = x[/tex]
Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x
Learn more about logarithmic equation
brainly.com/question/3181916
#SPJ4
The complete question is -
Which exponential equation is equivalent to this logarithmic equation?
log x = 4
What is the value of x that makes AB |I CD?
Answer:
30°
30 is the value of x that’s makes AB//CD.
Step-by-step explanation:
the angles of measures 2x + 40 and 3x + 10 are two Alternate interior angles
If these two angle were congruent then the lines AB and CD
would be parallel .
2x + 40 = 3x + 10
⇔ 40 - 10 = 3x - 2x
⇔ 30 = x
⇔ x = 30
Can anyone tell me how you could describe this answer to the equation?
[tex]f(x)=\frac{5x}{x-25}[/tex]
The end behavior of the given polynomial is that as x → -∞ or x → ∞, then, f(x) → 5
What is the end behavior of the Polynomial?
We are given the polynomial;
f(x) = 5x/(x - 25)
Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get;
f(x) = 5/(1 - (25/x))
Thus, applying limits we have;'
lim x → ±∞ [5/(1 - (25/x))]
From algebraic limit laws we know that;
If f(x) = k, then;
lim x → +∞ [f(x)] = k
Also, lim x → -∞ [f(x)] = k
Thus, applying limits at infinity to our polynomial gives;
lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5
This is because lim x → ∞ for 1/x is 0.
Thus, f(x) has horizontal asymptotes at y = 5
Thus, we conclude that the end behavior is that as x → -∞ or x → ∞, then, f(x) → 5
Read more about Polynomial End behavior at; https://brainly.com/question/20347699
#SPJ1
14) Adelina is comparing prices for two brands of health and energy bars at the local grocery store.
She wants to get the best price for each bar. Feel Great energy bars are $18 for 12 bars. Super
Power bars cost $21.75 for 15 bars.
Answer:
Power Bars are cheaper!
Step-by-step explanation:
FG: $18/12 Bars = $1.50 per bar
PB: $21.75/15 Bars = $1.45 per bar
Answer:
Super Power bars
Step-by-step explanation:
In order to find the best price, we want to calculate the unit rate, or the price for each bar. Let's start with the Fee Great energy bars. Since they are $18 for 12 bars, we divide 18 by 12 to figure out how much each bar costs. We get 1.5, or $1.50 per bar. Next lets claculate the unit rate for the Super Power bars. Since its $21.75 for 15 bars, we divide 21.75 by 15. We get 1.45, or $1.45 per bar. Since the price for one bar is cheaper for the Super Power bars as $1.45 is less than $1.50, the Super Power bars are the best price for each bar.
We can fill a certain barrel with water if we use water from 6 small pitchers, 3 medium pitchers, and one large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, how many of them do we need to fill the barrel?
Answer:
Solution Given:
let pitcher which is small be S medium be M and large be L and barrel be B.
By question
6S+3M+1L= 1B...... eq. 1
2S+1M+3L=1B.......eq. 2
The difference in 2L from the first to the second is 4S and 2M
Therefore, each L=2S+M
In equation 2
2S+1M+3L=1B
replacing 2S +1M by L,we get
L+3L=1B
4L=1B
Therefore, 4 large pitcher is required
Answer:
4 large pitchers
Step-by-step explanation:
Define the variables:
Let x = volume of a small pitcherLet y = volume of a medium pitcherLet z = volume of a large pitcherLet b = volume of a barrelCreate two equations with the given information and the defined variables.
Equation 1
If the barrel can be filled with 6 small pitchers, 3 medium pitchers and 1 large pitchers:
⇒ 6x + 3y + z = b
Equation 2
If the barrel can be filled with 2 small pitchers, 1 medium pitcher and 3 large pitchers:
⇒ 2x + y + 3z = b
Substitute Equation 2 into Equation 1
⇒ 6x + 3y + z = 2x + y + 3z
Subtract 6x from both sides:
⇒ 3y + z = -4x + y + 3z
Subtract y from both sides:
⇒ 2y + z = -4x + 3z
Subtract z from both sides:
⇒ 2y = -4x + 2z
Divide both sides by 2:
⇒ y = -2x + z
Substitute the found expression for y into Equation 1:
⇒ 6x + 3(-2x + z) + z = b
⇒ 6x - 6x + 3z + z = b
⇒ 4z = b
Therefore, 4 large pitchers are needed to fill the barrel.
Learn more about systems of equations here:
https://brainly.com/question/28093918
https://brainly.com/question/27034625
would really appreciate help thank you!
Answer:
(2, 2) ⇒ (-2, 2)
(-5, 6) ⇒ (-6, -5)
(2, 6) ⇒ (-6, 2)
(-5, 2) ⇒ (-2, -5)
Step-by-step explanation:
The new coordinates can be found using the transformation function for figures rotated 90° about the origin.
TransformationRotation 90° (counterclockwise) about the origin can be described by ...
(x, y) ⇒ (-y, x)
ApplicationThe end points of the diagonal that comes closest to the origin will be transformed to ...
(2, 2) ⇒ (-2, 2)
(-5, 6) ⇒ (-6, -5)
The other diagonal end points will be on the same horizontal and vertical lines as these.
(2, 6) ⇒ (-6, 2)
(-5, 2) ⇒ (-2, -5)
Find the measure of two complementary angles of the measure of one angle is 3 more than the measure of its complement
ANSWER: 22.5 and 67.5
let, one angle be x then the another one is 3×(90-x)
x = 270 - 3x
x + 3x = 270
4x = 270
x = 270/4
x = 67.5 (first angle)
then, another angle = 90- 67.5 = 22.5
Suppose that a, b, c, d are positive real numbers such that a/b < c/d . What can you say about the fraction (a+c)/(b+d) ? Is it always, sometimes, or never between the fractions a/b and c/d ? Provide evidence of your claim. (If always or never, give an algebraic proof, otherwise, give two quadruples values of a, b, c, d in which one quadruple has (a+c)/(b+d) between a/b and c/d and the other does not.)
Answer: (a−c)(b−c)>0
Step-by-step explanation:
ab>1 and ac<01. a>0 if c<0 and also b>02. a<0 if c>0 and also b<0
how i did it:
At the vert first, write the inequality as an equation.
Solve the provided equation for one or more values.
Now, display all the values obtained in the number line.
Use open circles to show the excluded values on the number line.
Find the interim.
At the moment, take any random value from the interval and substitute it in the inequality equation to check whether the values reassure the inequality equation.
Intervals that reassure the inequality equation are the solutions of the given inequality equation.
hey im pretty bad at this homework stuff can someone please help me answer all this
Answer:
Step-by-step explanation:
1. $135
2. a. no
b. $340
3. a. 33
b. $135*33= $4455+340= $4795
4. a. $7630 = 135v + 340
b. 135v + 340 = 7630
135v = 7290
v = 54 vacuums
Use the quadratic formula to find the solutions to the equation.
3x^2- 10x+ 5 = 0
Answer:
[tex]x =\frac{5}{3} \pm \frac{\sqrt{10}}{3} \\\\x=2.72076\\x=0.612574\\[/tex]
Step-by-step explanation:
The quadratic equation is:
[tex]3x^2 - 10x + 5 = 0[/tex]
The roots (solutions) of a quadratic equation of the form
[tex]a^2 + bx + c = 0\\[/tex]
are
[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
in this case we have a = 3, b = -10, and c = 5
So, substituting for a, b and c we get
[tex]x = \frac{ -(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{ 2(3) }[/tex]
[tex]x = \frac{ 10 \pm \sqrt{100 - 60}}{ 6 }\\[/tex]
[tex]x = \frac{ 10 \pm \sqrt{40}}{ 6 }[/tex]
Simplifying we get
[tex]x = \frac{ 10 \pm 2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 10 }{ 6 } \pm \frac{2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 5}{ 3 } \pm \frac{ \sqrt{10}\, }{ 3 }\\\\\frac{ 5}{ 3 } + \frac{ \sqrt{10}\, }{ 3 } = 2.72076\\\\\\[/tex] (First root/solution)
[tex]\frac{ 5}{ 3 } - \frac{ \sqrt{10}\, }{ 3 } = 0.612574[/tex] (Second root/solution)
How many different orders of top-three finishers are possible? drag the tiles to the correct locations on the equation. not all tiles will be used.
Orders of top-three finishers that are possible is given as follows:
[tex]n P_{r}=\frac{14 !}{11 !}=2184[/tex]
What is the permutation?In a broad sense, a permutation of a set is the rearrangement of its elements inside an already ordered set, or the arrangement of its members into a sequence or linear order. The act or process of altering an ordered set's linear order is referred to as "permutation."
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]n P_{r}=\frac{n !}{(n-r) !}[/tex]
The order in which the cars finish is important, hence the permutation formula is used instead of the combination formula.
In this problem, 3 cars are taken from a set of 14, hence the number of different orders is given as follows:
Using the permutation formula, it is found that the number of different orders of top-three finishers that are possible is given as follows:
[tex]n P_{r}=\frac{14 !}{11 !}=2184[/tex]
To know more about the permutation visit:
brainly.com/question/25925367
#SPJ4
I understand that the question you are looking for is:
How many different orders of top-three finishers are possible? drag the tiles to the correct locations on the equation. not all tiles will be used.
Geometry: complete this proof (ASAP!!!! It’s urgent)
Answer:
1. Given.
2. Reflexive Property of Congruence.
3. Alternate Interior Angles Theorem.
4. SAS
5. <4 ~= <2
6. Converse of Alternate Interior Angles Theorem.
The Williard family was saving up for their summer vacation. Mrs. Williard had $475.88 in their savings account for the trip. Mr. Williard received a bonus at work for $609.00 that he is saving for the trip. If the trip will cost the Warren's a total of $1675.98, how much more money do they need for their vacation
Answer:
$591.10
Step-by-step explanation:
First, add up $475.88 and $609.00 together. Then, subtract it from $1675.88. They need $591.10 more for their vacation.
Consider the interval [2, 3) = {x € r : 2 <= x < 3}. Find the complement of this interval where the universal set is taken to be r, the set of real numbers.
The complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
According to the given question.
We have an interval [2, 3).
Let A = [2, 3)
Which is defined as
[2, 3) = {x ∈ r : 2 ≤ x < 3}
This means that the interval [2, 3) contains all the real numbers which are greater and equal to 2 and less than 3.
And, here it is also given that the universal set is r ( set of real numbers).
As we know that " the complement of an interval is a set A of real numbers that conatins all the elements of universal set U except the number that lying between the given two numbers in the inerval" i.e.
[tex]A^{c} = U - A[/tex]
Where,
[tex]A^{c}[/tex] is the complement of interval A
Thereofre, the complement of the given interval [2, 3) will be all the elements of universal set i.e real numbers except 2 and the real numbers which lies in between 2 and 3.
So, we can say that
[tex]A^{c} = (-\infty, 2) \cup(3, \infty)[/tex]
Where, [tex]A^{c}[/tex] is the complement of the interval A.
Hence, the complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
Find out more information about complement of an interval here:
https://brainly.com/question/13202631
#SPJ4
What is the proportion and time?
The constant of proportionality is 25 and the distance at 10 seconds is 250 m.
To find the constant of proportionality, find the slope of the graph.
m = Δy/Δxm = 50 - 25 / 2 - 1m = 25Now, input in slope intercept form of equation to find distance at 10 seconds.
y = mxy = 25(10)y = 250 mIn the power function f(x) = -2x, what is the end behavior of f(x) =-2x^3 as x goes to [infinity]?
The end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.
In this question,
The power function is f(x) =-2x^3
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The graph below shows the behavior of the function f(x).
The above equation has the degree of 3, which is odd and the leading coefficient has the negative coefficient.
Then the end behavior is
As x -> ∞,
[tex]\lim_{x \to \infty} f(x)[/tex]
⇒ [tex]\lim_{x \to \infty} -2x^{3}[/tex]
⇒ [tex]-2(\infty)^3[/tex]
⇒ - ∞
Hence we can conclude that the end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.
Learn more about end behavior of a polynomial function here
https://brainly.com/question/22443880
#SPJ4
I need help to complete this question
The complete fractional question given in the above picture is 55/3 = 1 + 52/3 = 2 + 49/3 = 5 + 40/3 = 8 + 31/3 = 10 + 25/3
FractionLet
Each empty box = x55/3 = 1 + x/3
55/3 = (3+x) / 3
55/3 × 3 = 3 + x
55 = 3 + x
55 - 3 = x
52 = x
55/3 = 2 + x/3
55/3 =(6+x) / 3
55/3 × 3 = 6+x
55 = 6 + x
55 - 6 = x
49 = x
55/3 = x + 40/3
55/3 = (3x+40) / 3
55/3 × 3 = 3x + 40
55 = 3x + 40
55 - 40 = 3x
15 = 3x
x = 15/3
x = 5
55/3 = x + 31/3
55/3 = (3x+31) / 3
55/3 × 3 = 3x + 31
55 = 3x + 31
55 - 31 = 3x
24 = 3x
x = 24/3
x = 8
55/3 = 10 + x/3
55/3 = (30+x) / 3
55/3 × 3 = 30 + x
55 = 30 + x
55 - 30 = x
25 = x
Learn more about fraction:
https://brainly.com/question/11562149
#SPJ1
find the domain and range
Answer:
domain should be x=1
range is all real numbers
Step-by-step explanation:
Answer:domain should be x=1
range is all real numbers
Step-by-step explanation:
If the circumference
of a circle is
62.8 feet, what is the radius of the
circle?
Use 3.14 for I.
Hint: C = 2Tr
radius-12] foot
Please explain how you got the answer for future problems
Answer:
Hope you like my answer
Answer:
radius = 10 feet
Step-by-step explanation:
C represents the circumference.
C = 2πr ,where r is the radius.
We are given C = 62.8 ft
Equating the two expressions of C :
2πr = 62.8
Then
2 × 3.14 × r = 62.8
Then
6.28 × r = 62.8
Then
[tex]r = \frac{62.8}{6.28} = 10[/tex]
