Using the relation between velocity, distance and time, it is found that:
The rate of the plane is of 840 km/h.The rate of the wind is of 210 km/h.What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}[t}[/tex]
Flying against the wind, an airplane travels 2520 kilometers in 4 hours, that is:
[tex]v - v_w = \frac{2520}{4}[/tex]
[tex]v - v_w = 630[/tex]
[tex]v = 630 + v_w[/tex]
Flying with the wind, the same plane travels 9450 kilometers in 9 hours, hence:
[tex]v + v_w = \frac{9450}{9}[/tex]
[tex]v + v_w = 1050[/tex]
[tex]v = 1050 - v_w[/tex]
Hence, solving for the wind's speed:
[tex]630 + v_w = 1050 - v_w[/tex]
[tex]2v_w = 420[/tex]
[tex]v_w = \frac{420}{2}[/tex]
[tex]v_w = 210[/tex]
For the plane, we have that:
v = 1050 - 210 = 840.
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Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. what is the value of this function
The range of y will be all real numbers such that 0≤y≤40
The complete question is:
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? all real numbers such that y ≤ 40 all real numbers such that y ≥ 0 all real numbers such that 0 ≤ y ≤ 40 all real numbers such that 37.75 ≤ y ≤ 40
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute.
The amount of water remaining in the bathtub = y
The function of time in minutes, that it has been draining = x
At 0 minutes the amount of water is 40 gallons.
The highest volume of water is 40 which is decreasing at the rate of 1.5 gallons per minute.
The given function is a linear function
y = 0
However, the volume of water can be 0 but cannot ever be negative.
Therefore the range of y will be all real numbers such that 0≤y≤40
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Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros
of -3, -3, 4, and 2.
y(x) =
The factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)
How to determine the factored form?The given parameters are:
Leading coefficient, a = 1Zeros = -3, -3, 4, and 2.Rewrite the zeros as:
x = -3, x = -3, x = 4 and x = 2
Set the zeros to 0
x + 3 = 0, x + 3 = 0, x - 4 = 0 and x - 2 = 0
Multiply the zeros
(x + 3) * (x + 3) * (x - 4) *(x - 2) = 0
Express as a function
y(x) = a(x + 3) * (x + 3) * (x - 4) *(x - 2)
Substitute 1 for a
y(x) = (x + 3)²(x - 4)(x - 2)
Hence, the factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)
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The y-intercept of the line whose equation is 2x - 3y = 6 is
-2
3
6
Answer:
y = -2
(first option listed)
Step-by-step explanation:
a y-intercept is a point where the line crosses over the y-axis, which happens when x = 0.
So, the y-intercept is actually pretty each to find.
this is the easier way to find it: {plug directly into equation given}
2x - 3y = 6
(set x equal to 0)
[0] - 3y = 6
(divide both sides by -3)
y = -2
but you might have seen/ learned to solve the equation like this {to actually find the equation of the line and solve from that}
[this method is helpful to know/practice for when equations for functions get more complex]
2x - 3y = 6
+ 3y + 3y {add 3y to both sides}
2x = 3y + 6
-6 -6 {subtract 6 from both sides}
2x - 6 = 3y
÷3 ÷3 {divide both sides by 3 to isolate y}
[tex]\frac{2}{3}x[/tex] [tex]- 2 = y[/tex] [flip sides of the equation]
[tex]y=\frac{2}{3}x-2[/tex]
set x equal to 0 (x = 0)
y = [tex]\frac{2}{3} (0)[/tex] - 2
y = 0 - 2
y = -2
So, the y-intercept is -2.
Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the x-values in order from least to greatest (read the graph from left to right). Then, state the domain and range of the function.
The points are follows as (0, -3), (-1, -2), (-2, -1) and (-3, 0).
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
The Graph shows the line function;
When the value of x is 0, y will be -3.
When the value of x is -1, y will be -2.
When the value of x is -2, y will be -1.
When the value of x is -3, y will be 0.
The points are (0, -3), (-1, -2), (-2, -1) and (-3, 0).
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Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height. [Assume π = 22/7]
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Curved surface area of right circular cylinder is 4.4 m².
★ Radius of base of the cylinder is 0.7 m.
★ [tex]\tt \pi = \dfrac{22}{7}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The height of cylinder.
[tex] {\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}[/tex]
[tex] \star \: \tt C.S.A \: of \: cylinder = \boxed{ \tt \pink{{ 2πrh}}}[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let,
❍ The height of circular cylinder be [tex]h[/tex]
❍ Radius [r] of base of cylinder be 0.7 m
We know,
[tex] \star \: \tt C.S.A \: of \: cylinder = 2πrh[/tex]
Putting,
☆ [tex]\tt \pi = \dfrac{22}{7}[/tex]
☆ r as 0.7
[tex] \longrightarrow \tt 4.4 {m}^{2} = 2πrh[/tex]
[tex] \longrightarrow \tt 4.4 {m}^{2} = \bigg( 2 \times \dfrac{22}{7} \times 0.07 \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( {2 }\times \dfrac{22}{ \cancel{7}} \times \dfrac{ \cancel{7}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( 44 \times \dfrac{ {1}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{ \cancel{10}} \times \cancel{10} \: m = \bigg( 44 \times 1 \times h \bigg)[/tex]
[tex] \longrightarrow \tt 44 m = 44h[/tex]
[tex]\longrightarrow \tt \dfrac{44}{44} m = h[/tex]
[tex]\longrightarrow \tt \red{ 1 m } = h[/tex]
Therefore, the height of cylinder = 1 m.
[tex]\begin{gathered} {\underline{\rule{290pt}{2pt}}} \end{gathered}[/tex]
Please help quick!!
Answer:
the answer will be similar, because if you divide 2, 3, 2.25 by 3 you will get the answer.
if a tap leaks at the rate of 1 L per half minute, how many litres are Lost after 10 minutes?
Answer:
The answer is 20 L
Step-by-step explanation:
if 1/2 minutes = 1 L
10 minutes = 20 L
Answer:
20 liters
Step-by-step explanation:
when working with math problems about the rate that something is happening, it is typically helpful to find the unit rate.
In this case, the unit rate will be how many liters are lost in 1 minute (per unit essentially means per "1" )
we know that 1 liter is lost in 1/2 minute
1/2 minute = 1 liter
×2 ×2 {multiply both sides by 2 to find "1 minute"}
1 minute = 2 liters
So, for every 1 minute, we lose 2 liters
if we have 10 minutes, we can multiply both sides by 10:
1 minute = 2 liters
×10 ×10
10 minutes = 20 liters
So, after 10 minutes, 20 liters are lost
hope this helps!!
The ages of Sonu and Monu are in the ratio 5:7.If Sonu were 9 years older and Monu 9 years younger, the age of Sonu would have been twice the age of Monu .Find their p present age 2 ) The ages of Sonu and Monu are in the ratio 5 : 7.If Sonu were 9 years older and Monu 9 years younger , the age of Sonu would have been twice the age of Monu .Find their present age.
Answer:
Sonu is 15years and Monu is 21 years
The function f is defined on the real numbers by f(y) = y + 2y − 2: What is the value of f(5)?
Answer:
f(5)=5+2(5)-2
f(5)=5+10-2
f(5)=15-2
f(5)=13
Solve each inequality and graph the solution set and a number lined, express the Solution set in interval notation. 6 < x + 3 < 8 Solve each inequality and graph the solution set and a number lined , express the Solution set in interval notation . 6 < x + 3 < 8
The solution set for the given inequality is 3<x<5.
The given inequality is 6<x+3<8.
What is the solution set?In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
Now, solve the given inequality:
6<x+3<8⇒6<x+3 and x+3<8
6-3<x ⇒3<x
x+3<8⇒x<5
Thus, 3<x<5.
Therefore, the solution set is 3<x<5.
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Inequality and graph the solution set and a number line, express the Solution set in interval notation is 3 < x < 5
6<x+3<8
[tex]6 < x+3\quad \mathrm{and}\quad \:x+3 < 8[/tex]
What is the rule of inequality?[tex]\mathrm{If}\:a < u < b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u < b[/tex]
[tex]\mathrm{Combine\:the\:intervals}[/tex]
[tex]x > 3\quad \mathrm{and}\quad \:x < 5[/tex]
[tex]3 < x < 5[/tex]
Therefore the Inequality and graph of the solution set and a number line, express the Solution set in interval notation as 3 < x < 5.
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Find a solution to the linear equation 11x−y=−11.Find a solution to the linear equation 11x−y=−11.
Answer:
(0,11)
Step-by-step explanation:
If we let x=0, then -y = -11, and so y=11.
Thus, (0,11) is a solution to the linear equation.
log(2t+4)=log(14-3t)
Answer:
t = 2
Step-by-step explanation:
[tex]2t + 4 = 14 - 3t[/tex]
[tex]5t = 10[/tex]
[tex]t = 2[/tex]
Checking:
[tex] log(2(2) + 4) = log(8) [/tex]
[tex] log(14 - 3(2)) = log(8) [/tex]
17, 18, 22, 31, 47 what is the next number
Answer:
the next number is 47+ 16 =63
what steps do you need to do to evaluate the following expression? Select two options. –5(–2) Drag 5 sets of –2 tiles to the window. Drag zero pairs to the window. Remove the 5 groups of –2 tiles. Remove 5 negative tiles from the window.
To solve the expression given , Drag zero pairs to the window and then Remove the 5 groups of –2 tiles , Option b and c is the right answer
What is an Integer Tile method ?It is a teaching method in which materialistic representation is done for concepts like addition and subtraction .
It is used for kids who find it difficult to understand adding a negative integer etc.
For the expression given
-5 (-2)
Drag zero pairs to the window and then Remove the 5 groups of –2 tiles.
Therefore Option B and C is the right answer.
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Can someone please help me with this!!
Answer: -7
Step-by-step explanation:
[tex]f(-8)=-5\\\\g(4)=3\\\\\therefore -1 \cdot f(-8) -4\cdot g(4)=-1(-5)-4(3)=5-12=\boxed{-7}[/tex]
Suppose there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates. Everything else equal, what is likely to happen to value of the MXN?
The value of MXN will increase.
The official currency of Mexico is The Mexican peso (MXN).
MXN is simply an abbreviation of the currency the Mexican peso, which is the official currency of the country of Mexico.
Similarly, the drop value in currency is defined as the expression that the currency is worth less as compared to all other countries.
When a currency's country interest rate drop, then the value of the currency increase. Here given in the question as there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates, the value of MXN will increase as the drop is more in Mexico which affects its currency MXN.
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Which of the following is a requirement for multiple regression?
3.
Categorical variables only
O b. A small sample size
O c. Obiective measures only
O d. Absence of multicollineerity between variables
0 e.
Subjective measures onlv
Answer:
insectistics a category variable also called various validity variable is a variable that can take on a limited as usually fixed number two possible values assigning each into visual or other unit of the vision 2 a particular group aur nominacle category of the basis some qualitative
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
2(x2 + 6x + 9) = 3 + 18
2(x2 + 6x) = –3
2(x2 + 6x) = 3
x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot
2(x2 + 6x + 9) = –3 + 9
The correct answers are option 1, Option 3 and option 4 which are:-
2(x² + 6x + 9) = 3 + 18
2(x² + 6x) = 3
x+3 = ±√21/√2
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
We will check all three options one by one:-
2(x² + 6x + 9) = 3 + 18
2x² + 12x + 18 = 3 + 18
2x² + 12x -3 = 0
We are getting the original equation so it is correct.
2(x² + 6x) = 3
2x² + 12x = 3
2x² + 12x - 3 = 0
This is also right.
x+3 = ±√21/√2
Squaring on both the sides:-
( x + 3 )² = 21 / 2
x² + 6x + 9 = 21 / 2
2x² + 12x + 18 = 21
2x² + 12x = 21 - 18
2x² + 12x -3 = 0
This is also right
Therefore the correct answers are option 1, Option 3 and option 4 which are:-
2(x² + 6x + 9) = 3 + 18
2(x² + 6x) = 3
x+3 = ±√21/√2
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Answer:
A, C, D
A: 2(x2 + 6x + 9) = 3 + 18
C: 2(x2 + 6x) = 3
D: x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot
Step-by-step explanation:
Got 100% on quiz
Which graph shows the solution to the system of linear inequalities?
y≥ 2x + 1
y≤2x-2
Answer:
g
Step-by-step explanation:
jjnnkvigific and it's a boy f a horse y
Express the radical using the imaginary unit, i sqrt{-27}
Answer:
27i
Step-by-step explanation:
Since we define i as [tex]\sqrt{-1}[/tex], [tex]\sqrt{-27} = 27i[/tex]
Answer:
Step-by-step explanation:
i [tex]i \sqrt{-27} =i\sqrt{-1 \times 27} =i\sqrt{27i^2} =i \times i\sqrt{27} =i^2\sqrt{9 \times 3} \\=-1\times 3\sqrt{3} \\=-3\sqrt{3}[/tex]
The following table shows the probability distribution for a discrete random
variable.
13
16
17
21
23
25
26
31
P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08
What is the mean of this discrete random variable? (That is, what is E(X), the
expected value of X?)
A. 21.5
B. 22
) C. 21
D. 20.42
HELPPPPPPP
What are the solutions to the system of equations graphed below?
A. (2,0) and (0,-4)
B. (-2,0) and (2,0)
C. (0,-2) and (0,2)
D. (0,2) and (-4,0)
Answer:
It's A. (2, 0) and (0, -4)
PLS answer quick
Which formula can be used to find the volume, V, of the composite solid figure represented below?
OA V = r2h + ³
r²h +
3
r²2h + 3r3
r²h + ³
OB. V
OC.
V =
V =
V =
OD. V =
The formula to find the volume of the composite solid is: C. V = πr²h + ⅔πr³.
How to Find the Volume of a Composite Solid?The volume of the composite solid in the image given = Volume of cylinder + volume of hemisphere.
Volume of cylinder = πr²h
Volume of hemisphere = ⅔πr³
Therefore, formula to find the volume is: C. V = πr²h + ⅔πr³.
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Answer:
C
Step-by-step explanation:
I Just Took the Test.
0.0000000019 written in scientific notation is
Answer:
1.9x10^8
hope I helped
Answer:
0.0000000019= 1.9*10^ -9
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
A and B
Step-by-step explanation:
Vertical angles are angles that are opposite of each other on two crossing lines.
They have equal angle measure.
When we look at the image, we can tell that, from the given options:
A. <LRA and <FRA and
B. <TRF and <NRL are vertical angles.
Prove that the function
Answer:
See proof below
Step-by-step explanation:
Important points
understanding what it means to be "onto"the nature of a quadratic functionfinding a value that isn't in the rangeOnto
For a function with a given co-domain to be "onto," every element of the co-domain must be an element of the range.
However, the co-domain here is suggested to be [tex]\mathbb R[/tex], whereas the range of f is not [tex]\mathbb R[/tex] (proof below).
Proof (contradiction)
Suppose that f is onto [tex]\mathbb R[/tex].
Consider the output 7 (a specific element of [tex]\mathbb R[/tex]).
Since f is onto [tex]\mathbb R[/tex], there must exist some input from the domain [tex]\mathbb R[/tex], "p", such that f(p) = 7.
Substitute and solve to find values for "p".
[tex]f(x)=-3x^2+4\\f(p)=-3(p)^2+4\\7=-3p^2+4\\3=-3p^2\\-1=p^2[/tex]
Next, apply the square root property:
[tex]\pm \sqrt{-1} =\sqrt{p^2}[/tex]
By definition, [tex]\sqrt{-1} =i[/tex], so
[tex]i=p \text{ or } -i =p[/tex]
By the Fundamental Theorem of Algebra, any polynomial of degree n with complex coefficients, has exactly n complex roots. Since the degree of f is 2, there are exactly 2 roots, and we've found them both, so we've found all of them.
However, neither [tex]i[/tex] nor [tex]-i[/tex] are in [tex]\mathbb R[/tex], so there are zero values of p in [tex]\mathbb R[/tex] for which f(p)= 7, which is a contradiction.
Therefore, the contradiction supposition must be false, proving that f is not onto [tex]\mathbb R[/tex]
At a sale this week, a desk is being sold for $561. This is 68% of the original price. What is the original price?
Answer:
825
Step-by-step explanation:
hope it helps.good day
Flying against the jetstream, a jet travels 1710 miles in 3 hours. Flying with the jetstream, the same jet travels 5820 miles in 6 hours. What is the rate of the jet in still air and what is the rate of the jetstream
The rate of the jet against jetstream will be 570 miles per hour and the rate of the jet in still air will be 970 miles per hour.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
Flying against the jetstream, a jet travels 1710 miles in 3 hours. Flying with the jetstream, the same jet travels 5820 miles in 6 hours.The rate of the jet against the jetstream will be calculated as:-
V = [tex]\dfrac{1710}{3}[/tex] = 570 miles per hour
The rate of the jet in still air will be calculated as:-
V = [tex]\dfrac{5820}{6}[/tex] = 970 miles per hour.
Therefore the rate of the jet against jetstream will be 570 miles per hour and the rate of the jet in still air will be 970 miles per hour.
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solve for a
(log(a-1))^2 =log10
A function assigns the values. The value a is 11.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The given logarithmic function can be solved as shown below.
[tex](\log(a-1))^2 =\log10\\\\(\log(a-1))^2 =1\\\\(\log(a-1)) =\sqrt1\\\\\log(a-1) = 1\\\\10^1 = a-1\\\\a = 11[/tex]
Hence, the value a is 11.
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Caitlyn and Steve are planning their wedding reception and must decide between two catering halls. The first site, A Wedding Space, rents for $900 for one day and charges $50 per person for dinner. The second venue, A Wedding Place, costs $450 to rent for one day and charges $75 per person for the same dinner. Solve the equation 900+50x=450+75x to determine how many guests they can invite so that the cost they pay will be the same at both wedding catering halls.
The guest they can invite so that the cost they pay will be the same at both wedding catering halls is 18.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given equation is
900+50x=450+75x
To solve;
900 - 450 = -50x +75x
450 = 25x
x = 450 /25
x = 18
The guest they can invite so that the cost they pay will be the same at both wedding catering halls is 18.
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