Answer:
- 2 x y^2+3 x^2 y -xy
-120
Step-by-step explanation:
xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2
Combine like terms
xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2
- x y+3 x^2 y - 2 x y^2
Let x = 4 y = -2
-(4)(-2) +3(4)^2 (-2) -2(4)(-2)^2
Exponents first
-(4)(-2) +3(16) (-2) -2(4)(4)
Multiply
+8 -96-32
Add and subtract
-120
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!
Which of the following is the equation of a line that passes through the point
(1.4) and is parallel to the x-axis?
A.x=1 B.y=4 C.x=4 D.y=1
Given:
A line passes through the point (1,4) and is parallel to the x-axis.
To find:
The equation of the line.
Solution:
If a line is parallel to x-axis, then the line is a horizontal line. We know that the slope of a horizontal line is always 0. So, the slope of the required line is 0.
The point-slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is the slope and [tex](x_1,y_1)[/tex] is the point.
The slope of the required line is 0 and it passes through the point (1,4). So, the equation of the line is:
[tex]y-4=0(x-1)[/tex]
[tex]y-4=0[/tex]
[tex]y-4+4=0+4[/tex]
[tex]y=4[/tex]
The required equation is [tex]y=4[/tex].
Therefore, the correct option is B.
Can someone help me with this math homework please!
Answer:
The answers are options A and C.
They are (-2,0) and (0,0).
Step-by-step explanation:
x-intercept
(-2,0) and (0,0)
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 = 648Find the value of x.
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
Dilate the figure by the scale factor. Then enter
the new coordinates.
A(1,3)
B(4,2)
K=3
A'([?],[ ]
B'([ ],[])
c'[[)
C(1,-3)
Answer:
i think (4,2)
Step-by-step explanation:
Show that 4^(x+2)+4^(x+1)+4^x is divisible by 7 for all positive integers of x.
Answer:
Below.
Step-by-step explanation:
4^(x+2)+4^(x+1)+4^x
= 4^x*4^2 + 4^x*4 + 4^4
= 4^x(16 + 4 + 1)
= 21*4^x.
As 21 is divisible by 7, 21*4^x is also divisible by 7 for all positive integers of x.
Thus the original expression must be also divisible by 7 for all positive integers of x.
The scale of a map is 1:40000. What distance on the map represents a real distance of 5km?
Answer:
0.125
Step-by-step explanation:
1=40000
x-5000
x=5000÷40000=1/8=0.125
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.
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)
The system of equations shown below is graphed on a coordinate grid:
3y + x = 4
2y − x = 6
Which statement is true about the coordinates of the point that is the solution to the system of equations?
A. It is (−2, 2) and lies on both lines.
B. It is (−5, 3) and lies on both lines.
C. It is (−5, 3) and does not lie on either line.
D. It is (−2, 2) and does not lie on either line.
Please help asap!! WILL GIVE BRAINlIEST!! tysssm if u help!!!
Answer:
add 2 equations given
3y+x+2y- x = 10
5y =10
y = 2
find x using the value of y
x = - 2
these values of x and y are can satisfy both equations .so (-2,2) lies on both lines
Which graph represents an exponential function?
Answer: where's the pic?
Step-by-step explanation:
Identify the transformations of the graph of f(x) = x3 that produce the graph of the given function
g(x). Then graph g(x) on the same coordinate plane as the graph of f(x) by applying the
transformations to the reference points (-1,-1),(0,0), and (1,1).
Answer:
Step-by-step explanation:
Find the missing segment in the image below
Answer:
If there are two line which is parallel in a triangle the triangle has a ratio
Step-by-step explanation:
So we can see one side has 6cm and 4cm length. and other side has 20cm in totally. But we know that the small line divided the side with 6/4 ratio and we can say ?=12 and other is 8
Answer:
Step-by-step explanation:
I need help with this I don't understand
Answer:
Sin ? = 4/7
? = arcSin (4/7)
? = 35° (rounded to the nearest degree)
So the answer is 35°
Answered by GAUTHMATH
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.
Choose the correct equation for the graph shown below
Answer:
the second option, y=1/2cos(x- pi/4)
Step-by-step explanation:
American airlines requires that total outside dimensions (length+width+height) of a checked bag not exceed 62 inches.Suppose you want to check a bag whose height is same as its width.What is the biggest volumn bag of this shape that you can check on an american flight
Answer:
The maximum volume is 35316.4 in^3.
Step-by-step explanation:
Length + width + height is less than equal to 62 inches
Height = width = W
Let the length is L .
[tex]L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)\times W \times W\\\\V = 62 W^2 - 2 W^3\\\\\frac{dV}{dW}=124 W - 6 W^2\\\\So, \frac{dV}{dW} =0\\\\124 = 6 W\\\\W = 20.67 inches[/tex]
So, the maximum volume is
[tex]V =124\times 20.67\times 20.67 - 2 \times 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3[/tex]
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].
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
Jeanette wants to raise $3,200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
Total amount she wants to raise = $3200
Amount she'll get for each kilometer = $35
So, number of kilometers she need to run
= Total amount she wants to raise/Amount she'll get for each kilometer
= $3200/$35
= 91.42....
Since her sponser is will donate only for whole kilometers she'll have to run 92 km.
Help Now!!!!
The Base Of A triangle prism
Answer:
Volume=Area × height
=35×7
volume = {245} m³
OAmalOHopeO
Answer:
Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.
7 x 35 = 245 m3 is your answer
You can picture it too:
(sorry my drawing is bad with the marker)
Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level
Answer:
It must be a positive number since it represents a number of hours.
Step-by-step explanation:
Given Pieter's equation :
7h – 5(3h – 8) = –72
Opening up the bracket
7h - 15h + 40 = - 72
7h - 15h = - 72 - 40
-8h = - 112
Divide both sides by -8
-8h / -8 = - 112 / - 8
h = 14
Since, h represents the number of hours, and the value of h equals 14 (h cannot be negative), hence, option 2 is correct.
Answer:
B.It must be a positive number since it represents a numbers of hours.
Step-by-step explanation:
Given the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the area?
A = LW
P = 2L+2W
P = 100
w should be 625 units
w should be 25 units
w should be 0 units
w should be 50 units
Answer:
the second option : w should be 25 units
Step-by-step explanation:
the area of the rectangle is length×width = L×W
the perimeter of a rectangle = 2L + 2W
now, we know that the perimeter is 100 units.
and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.
in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?
now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.
W = 0 would render the whole rectangle to a flat line with L = 50 because of
100 = 2L + 2W = 2L + 0 = 2L
L = 50
and A = L×W = 50×0 = 0
an area of 0 is for sure not the largest possible area.
w = 50 would cause L = 0
100 = 2L + 2W = 2L + 2×50 = 2L + 100
0 = 2L
L = 0
and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.
so, the only remaining useful answer is W = 25
100 = 2L + 2W = 2L + 2×25 = 2L + 50
50 = 2L
L = 25
A = L×W = 25×25 = 625 units²
and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.
Chris and Josh have a total of 1,800 stamps in their collections, Josh and Jessica have a total of 2,200 stamps, and Jessica and Chris have a total of 2,000. How many stamps in all the three children have?
Answer: 3000 stamps
Step-by-step explanation:
Given
Chris and Josh have 1800 stamps
Josh and Jessica have 2200 stamps
Jessica and Chris have 2000 stamps
Suppose Chris, Josh, and Jessica have [tex]x,y, \text{and}\ z[/tex] stamps
[tex]\therefore x+y=1800\quad \ldots(i)\\\Rightarrow y+z=2200\quad \ldots(ii)\\\Rightarrow z+x=2000\quad \ldots(iii)\\\text{Add (i), (ii), and (iii)}\\\Rightarrow 2(x+y+z)=1800+2200+2000\\\Rightarrow x+y+z=3000[/tex]
Thus, all three have 3000 stamps
please answer quick!
Answer:
-4/5
Step-by-step explanation:
sin theta = opp/ hyp
sin theta = -3 /5
Using the Pythagorean theorem
opp ^2 + adj ^2 = hyp ^2
(-3) ^2 + adj ^2 = 5^2
9+ adj ^2 = 25
adj ^2 = 25 - 9
adj ^2 = 16
Taking the square root of each side
adj = ±4
Since we are in the 3rd quadrant sin and cos are both negative so adj must be negative
adj = -4
cos theta = adj / hyp
cos theta = -4/5
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
Find the slope of the line for each pair of points (-17, -5) (15, -13)
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.
