Let s be the plane's speed in still air and w the wind speed. Then
s - w = (6060 km)/(6 h) = 1010 km/h
s + w = (12,150 km)/(9 h) = 1350 km/h
Adding these equations together eliminates w and lets you solve for s :
(s - w) + (s + w) = 1010 km/h + 1350 km/h
2s = 2360 km/h
s = 1180 km/h
What is the measure of
60° because it's an equilateral triangle
Susan's graduation picnic will cost $78 if it has 26 attendees. At most how many attendees can there be if Susan budgets a total of $81 for her graduation picnic?
Answer:
27 attendees
Step-by-step explanation:
First, we can find the cost per attendee.
78÷26
3
So $3 per attendee.
Then divide 81 by 3 to find the number of possible attendees.
81÷3=27
I hope this helps!
Determine the value of K that will cause f(x)=Kx^2+4x-3 to intersect the line g(x)=2x-7 at one point. SHOW ALL YOUR STEPS, DON'T USE DECIMALS INSTEAD USE FRACTIONS PLEASE!!!!!
Given:
The function are:
[tex]f(x)=Kx^2+4x-3[/tex]
[tex]g(x)=2x-7[/tex]
The graph of f(x) intersect the line g(x) at one point.
To find:
The value of K.
Solution:
The graph of f(x) intersect the line g(x) at one point. It means the line g(x) is the tangent line.
We have,
[tex]f(x)=Kx^2+4x-3[/tex]
Differentiate this function with respect to x.
[tex]f'(x)=K(2x)+4(1)-(0)[/tex]
[tex]f'(x)=2Kx+4[/tex]
Let the point of tangency is [tex](x_0,y_0)[/tex]. So, the slope of the tangent line is:
[tex][f'(x)]_{(x_0,y_0)}=2Kx_0+4[/tex]
On comparing [tex]g(x)=2x-7[/tex] with slope-intercept form, we get
[tex]m=2[/tex]
So, the slope of the tangent line is 2.
[tex]2Kx_0+4=2[/tex]
[tex]2Kx_0=2-4[/tex]
[tex]x_0=\dfrac{-2}{2K}[/tex]
[tex]x_0=-\dfrac{1}{K}[/tex]
Putting [tex]x=x_0,g(x)=y_0[/tex] in g(x), we get
[tex]y_0=2x_0-7[/tex]
Putting [tex]x=-\dfrac{1}{K}[/tex] in the above equation, we get
[tex]y_0=2(-\dfrac{1}{K})-7[/tex]
[tex]y_0=-\dfrac{2}{K}-7[/tex]
Putting [tex]x=-\dfrac{1}{K}[/tex] and [tex]f(x)=-\dfrac{2}{K}-7[/tex] in f(x).
[tex]-\dfrac{2}{K}-7=K\left(-\dfrac{1}{K}\right)^2+4(-\dfrac{1}{K})-3[/tex]
[tex]-\dfrac{2}{K}-7=\dfrac{1}{K}-\dfrac{4}{K}-3[/tex]
[tex]-\dfrac{2}{K}-7=\dfrac{-3}{K}-3[/tex]
Multiply both sides by K.
[tex]-2-7K=-3-3K[/tex]
[tex]-2+3=7K-3k[/tex]
[tex]1=4k[/tex]
[tex]\dfrac{1}{4}=K[/tex]
Therefore, the value of K is [tex]\dfrac{1}{4}[/tex].
Choose the correct equation for the graph shown below
Answer:
the second option, y=1/2cos(x- pi/4)
Step-by-step explanation:
a student says the prime factors of 17 are 1 and 17. is the student correct?
Answer: yes
A prime factor is number that can only divided by itself and one
Since, 17 can only be divided by 17 and 1, the student is correct
Step-by-step explanation:
Which graph represents an exponential function?
Answer: where's the pic?
Step-by-step explanation:
Solve the equation x^2 - 4x + 6 = 9 by completing the square.
Hello!
x² - 4x + 6 = 9 <=>
<=> x² - 4x + 6 - 9 = 0 <=>
<=> x² - 4x - 3 = 0 <=>
<=> x = -(-4)±√(-4)²-4×1×(-3)/2×1 <=>
<=> x = 4±√16+12/2 <=>
<=> x = 4±√28/2 <=>
<=> x = 4±2√7/2 =>
=> x = 4+2√7/2 and x = 4-2√7/2 =>
=> x = 2+√7 and x = 2-√7
The equation has two solutions.
Good luck! :)
Answer: [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]
how i got it?
[tex]x^2 - 4x + 6 = 9[/tex]
*subtract 9 on both sides*
[tex]x^2 - 4x + 6 - 9 = 0[/tex] ( which turns to) [tex]x^2 - 4x - 3=0[/tex]
a=1 or x, b=-4, c=-3
Step 2: Use quadratic formula with a=1, b=-4, c=-3.
[tex]x= - (-4) + or - \sqrt{-4}x^{2} -4(1)(-3) / 2(1)[/tex]
which turns to: x= 4 + or - √28 divided by 2
the final answer should be [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]
which one of these numbers is a whole number?
Answer:
0 is the whole number
Step-by-step explanation:
negative numbers are negative so they can't be counted as whole numbers which means -5 isn't an option.
Whole numbers can't be stated in fraction form so 2/3 is not applicable here.
32.8 is also not the answer as decimals are part of a whole number, not actual whole numbers.
so, 0, is the only right answer here
help with geometry!!!!!
Answer:
NO
Step-by-step explanation:
To find the length of AB
AB = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt ( ( 2 - -1)^2+ ( -1 -3)^2)
= sqrt( 3^2 + (-4)^2)
= sqrt(9+16)
= sqrt(25)
= 5
To find the length of AC
AC = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt ( ( -4 - -1)^2+ ( -1 -3)^2)
= sqrt( ( -3)^2 + (-4)^2)
= sqrt(9+16)
= sqrt(25)
= 5
To find the length of BC
BC = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt ( ( -4-2)^2+ ( -1 --1)^2)
= sqrt( ( -6)^2 + (0)^2)
= sqrt(36)
= 6
This is not an equilateral triangle since BC is not equal to AB = AC
Answer:
AB = AC = 5 units BC = 6 units No it is not a equilateral triangleStep-by-step explanation:
Some coordinates of a triangle is given to us. And we need to find the length of AB , BC and AC . The given coordinates are ,
[tex]\rm\implies Coordinates = A(-1,3) , B(2,-1) \ and \ C(-4,-1) [/tex]
We can use the Distance Formula to find the length of sides of the triangle .
Finding length of AB :-
[tex]\rm\implies Distance =\sqrt{ ( x_2-x_1)^2+(y_2-y_1)^2} \\\\\rm\implies \overline{AB}= \sqrt{ (-1-2)^2+(-1-3)^2} \\\\\rm\implies \overline{AB}= \sqrt{ (-3)^2+(-4)^2} \\\\\rm\implies \overline{AB}= \sqrt{ 9 + 16} \\\\\rm\implies \overline{AB}= \sqrt{25} \\\\\rm\implies\boxed{\red{\rm \overline{AB}= 5 \ units}}[/tex]
Finding length of AC :-
[tex]\rm\implies Distance =\sqrt{ ( x_2-x_1)^2+(y_2-y_1)^2} \\\\\rm\implies \overline{AC}= \sqrt{ (-1+4)^2+(-1-3)^2 }\\\\\rm\implies \overline{AC}= \sqrt{ (-3)^2+(-4)^2} \\\\\rm\implies \overline{AC}= \sqrt{ 9 + 16} \\\\\rm\implies \overline{AC}= \sqrt{25} \\\\\rm\implies\boxed{\red{\rm \overline{AC}= 5 \ units}}[/tex]
Finding length of BC :-
[tex]\rm\implies Distance =\sqrt{ ( x_2-x_1)^2+(y_2-y_1)^2} \\\\\rm\implies \overline{BC}= \sqrt{ (-4-2)^2+(-1-1)^2} \\\\\rm\implies \overline{BC}= \sqrt{ 6^2+0^2} \\\\\rm\implies \overline{BC}= \sqrt{ 36+0} \\\\\rm\implies \overline{BC}= \sqrt{36} \\\\\rm\implies\boxed{\red{\rm \overline{BC}= 6 \ units}}[/tex]
Is it a Equilateral triangle ?
No the given triangle is not a equilateral triangle since the measure of all sides is not same.
Evaluate the expression for x = 10 . 3x + 4(x - 8) - 14
Answer:
[tex]{ \tt{3x + 4(x - 8) - 14}} \\ = { \tt{3x + 4x - 32 - 14}} \\ = { \tt{7x + 46}}[/tex]
The circumference of a circle is 2π m. Find its diameter, in meters.
Answer:
The diameter is 2 meters
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
2 pi = pi *d
Divide each side by pi
2 = d
The diameter is 2 meters
Please answer only questions 18 and 20 please help me
Answer:
18 is 64 days
20 is 1 37/128
Step-by-step explanation:
I looked it up if I am being completely honest with you but it should be correct
How many 3-digit numbers are possible to form with all the digits being different?
Answer:
We can make 120 three digit distinct numbers
Step-by-step explanation:
Answer:
648Step-by-step explanation:
If the number is xyz, we have:
x = 1 to 9, total 9 waysy = 0 to 9, total 10 ways minus 1 to prevent repetition, so 9 waysz = 0 to 9, total 10 ways minus 2 ways to prevent repetition, so 8 waysTotal number of possible 3-digit numbers:
9*9*8 = 648You have to evaluate the question for a and b
Answer:
11
Step-by-step explanation:
a+b^2
Let a=2 and b=3
2+3^2
2 + 9
11
Answer: 11
2 + (3 x 3 )
2 + 9
The required answer would be 11 :)
Step-by-step explanation:
what is the volume of the cylinder?
write you answer in terms of pi
The volume of a cylinder is V=πr^2*h.
The volume of this cylinder is V=π(7)^2*12, which it V=588π.
In 60 words or fewer, write what you think the term economy means. Think about how money fits into your definition.
Step-by-step explanation:
An economy is made up of every single activity that has to do with production, consumption, and the buying and selling of goods or rendering services.
In an economy there are combinations of market transactions and decisions made collectively or in hierarchy. Individuals, families, businesses, governments make up the decision-making process.
Money is the legal tender of an economy. It is the medium of exchange that an economy uses for transactions.
Find the value of x.
Find the greatest common factor of 15 x²y³ and -18 x³yz.
_x--y--
Answer:
3x^2y
Step-by-step explanation:
Its common factor it this ^ this symbol represent power
Which shows the numbers One-tenth, 0.9, Three-tenths in order from least to greatest?
Which equation can be used to find one multiple of 16?
Answer:
Simultaneously equation
Find the following sums. Please help.
Answer:
5m-n-4p
4a^2+6x-3
Step-by-step explanation:
3m-4n +7p
-5m +9n -6p
+7m -6n -5p
----------------------
Combine like terms
3m-4n +7p
-5m +9n -6p
+7m -6n -5p
----------------------
(3-5+7)m +(-4+9-6)n +(7-6-5)p
5m-n-4p
a^2 -3x +1
a^2 +9x -6
2a^2 +0x +2
----------------------
Combine like terms
a^2 -3x +1
a^2 +9x -6
2a^2 +0x +2
----------------------
(1+1+2)a^2 +(-3+9+0)x +(1-6+2)
4a^2+6x-3
#1
[tex]\\ \sf\longmapsto 3m-4n+7p+(-5m+9n-6p)+7m-6n-5p[/tex]
[tex]\\ \sf\longmapsto 3m-4n+7p-5m+9n-6p+7m-6n-5p[/tex]
[tex]\\ \sf\longmapsto 3m-5m+7m-4n+9n-6n+7p-6p-5p[/tex]
[tex]\\ \sf\longmapsto 5m-n-4p[/tex]
#2
[tex]\\ \sf\longmapsto a^2-3x+1+a^2+9x-6+2a^2+2[/tex]
[tex]\\ \sf\longmapsto a^2+a^2+2a^2-3x+9x+1-6+2[/tex]
[tex]\\ \sf\longmapsto 4a^2+6x-3[/tex]
Find the slope of the line for each pair of points (-17, -5) (15, -13)
What is the quotient ? 7-6 72 1 o 1 o 1 72 O 73 0 78
Answer:
A. 1/7^8
Step-by-step explanation:
Given
(7^-6) / 7²
Both numerator and denominator has the same base, so just one of the bases will be picked
Division sign changes to minus in indices
(7^-6) / 7²
= 7 ^(-6-2)
= 7^-8
= 1/7^8
Note: a^-b
= 1/a^b
The same rule is used at the last step of the calculation
Answer is
A. 1/7^8
A hall has 22 rows of chairs there are 18 chairs in each row how many extra rows of chairs are needed to seat 468
Answer:
Total chairs = 18×22= 396
so no. of extra chairs need = 468-396 = 72
Now( 72/18) rows = 4 rows
Therefore 4 more rows are needed here
Hope it helps you
Answer: 4
Step-by-step explanation:
The amount of chairs in the hall can be found by multiplying 22 by 18 and getting 396. The amount of chairs needed is 468, so 468-396 gets you the amount of chairs still needed and the number 72. There are 18 chairs in each row, and 72/18 is 4. So 4 more rows are needed.
Ms. Jones wants to paint her kitchen's wall. She knows that 2 gallons of paint cover 80 square feet, and each gallon costs $20.80. If the area of the kitchen is 320 square feet, how much will she pay to buy the gallons of paint needed? Round your answer to the nearest cent (HUNDRED TH), and write ONLY a number (NO $)
Which of the equations below could be the equation of this parabola?
O A. y = -1/2 x2
O B. y = 1/2 x2
O C. y= 1/2 y2
O D. x= -1/2 y2
After answering the question provided, we can predict that the result will be as The position and direction of the relevant parabola will determine the appropriate response.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
It is hard to tell which equation may be the equation of the parabola without further details on the parabola's orientation and location.
The equations in options A and B are parabolas with upward or downward openings and a vertex at the origin. The equation of a parabola with its vertex at the origin and an opening to the right or left is in Option C. The equation of a parabola with an upwards or downwards opening and its vertex at the point is in Option D. (0,0).
The position and direction of the relevant parabola will determine the appropriate response.
To know more about equation visit:
https://brainly.com/question/649785
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In Exercises 51−56, the letters a, b, and c represent nonzero constants. Solve the equation for x
bx = -7
Answer:
x = -7/b
Step-by-step explanation:
bx = -7
Divide each side by b
bx/b = -7/b
x =-7/b
Solve the equation for x : bx = -7
Solution :Here we are provided to find for x so from the equation by cross multiplying we will remove b to the right hand side of the equation and then we can get x
bx = -7
Now, to cross multiply
x = -7/b
Therefore, the required answer is -7/b
flor ha colocado ¹1/4 kg de papa sobre una balanza . si un cliente le quiere comprar 2 kg de papa , ¿cuantos kilogramos (kg) de papa debe agregar flor sobre l balanza para cumplir con el pedido?
a)3/4 kg de papa
b)¹ 3/4 kg de papa
c1/4 kg de papa
d)¹ 1/4
RAPIDO POR FAVOR E UN EXAMEN SALVEMME LA VIDA
Answer:
a). 3/4 kg de papa
Step-by-step explanation:
Given that,
Patata colocada en balanza = 1 1/4 Kg
Flor de papa total quiere = 2 kg
Encontrar,
Se agregará más peso en la báscula para que sea de 2 kg =?
Procedimiento:
Peso requerido para ser colocado = Peso total - peso colocado
= 2 - [tex]1\frac{1}{4}[/tex]
= 2 - 5/4
= (8 - 5)/4
= 3/4 kg
What is the greatest common factor of the polynomial below?
12x2-9x
A. 3x2
B. 3x
C. 4x2
D. 4x
Answer:
3x
Step-by-step explanation:
factoring it we get
3x(4x-3)
15. Mary was given data comparing students’ mark in math class and the number of classes missed. She plotted the data on the graph below and drew a line of best fit. Do you agree with Mary’s drawing of the line of best fit? Justify your answer. PLEASE HELP ITS RLLY IMPORTANT
Kevin jogged 2 1/2 miles in 1/3 of an hour. What was his average rate in speed in miles per hour? Show your work.
Answer:
7.5 miles per hour
Step-by-step explanation:
Average Speed = Total Distance/Total Time
[tex]\frac{2 \frac{1}{2} }{\frac{1}{3} }[/tex]= 7.5 miles/hour
Answer from Gauthmath
