Answer:
y = 4x-3
Step-by-step explanation:
First we need to determine the slope
Using two points on the line (0,-3) (1,1)
Using the slope formula
m = (y2-y1) /(x2-x1)
= (1- -3)/(1-0)
(1+3)/ (1-0)
4
We know the y intercept, -3
y = mx+b where m is the slope and b is the y intercept
y = 4x-3
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
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 $)
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
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)
What is the measure of
60° because it's an equilateral triangle
Which graph represents an exponential function?
Answer: where's the pic?
Step-by-step explanation:
Find the slope of the line for each pair of points (-17, -5) (15, -13)
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]
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].
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.
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
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
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:
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
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
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:
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:
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.
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:
At the bulk food store, Jerry bought 200 g of mixed nuts that cost $2.50.
What is the price of 450 g of nuts show ur work pls lol
Given:
Cost of 200 g of mixed nuts = $2.50.
To find:
The price of 450 g of nuts.
Solution:
We have,
Cost of 200 g of mixed nuts = 2.50 dollars
Cost of 1 g of mixed nuts = [tex]\dfrac{2.50}{200}[/tex] dollars
Cost of 450 g of mixed nuts = [tex]\dfrac{2.50}{200}\times 450[/tex] dollars
= [tex]\dfrac{2.50}{4}\times 9[/tex] dollars
= [tex]5.625[/tex] dollars
Therefore, the price of 450 g of nuts is $5.625.
In the xv-plane, the line determined by the
points (2,k) and (k, 32) passes through the origin.
Which of the following could be the value of k ?
Answer:
8
Step-by-step explanation:
If the diagonal line passes through the origin, that means it is proportional. That means that for every point on the line y/x is constantly the same value. So we have k/2=32/k.
Cross multiply: k^2=64
Square root both sides: k=8
Find the value of x. Write your answer in simplest form. WILL MAKE BRAINLIEST
============================================
Explanation:
Since we have an isosceles right triangle, the the length of the hypotenuse (let's call it y) is equal to sqrt(2) times the leg length x.
In other words, [tex]y = x*\sqrt{2}[/tex]
If we replaced y with 3*sqrt(2), then we could say,
[tex]y = x*\sqrt{2}\\\\3\sqrt{2} = x*\sqrt{2}[/tex]
in which we can see that x = 3 must be the case. Or you could divide both sides of that last equation by sqrt(2) to find x = 3.
-------------------------
Another method:
We'll use the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\x^2+x^2 = \left(3\sqrt{2}\right)^2\\\\2x^2 = 3^2*\left(\sqrt{2}\right)^2\\\\2x^2 = 9*2\\\\2x^2 = 18\\\\x^2 = 18/2\\\\x^2 = 9\\\\x = \sqrt{9}\\\\x = 3\\\\[/tex]
We get the same answer as before.
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]
Graph the function f(x) = - squared x + 2
One of the ways to graph this is to use plug in a few x-values and get an idea of the shape. Since the x values keep getting squared, there is an exponential increase on either side of the y-axis. You can see this by plugging in a few values:
When
x=0,f(x)=0
x=1,f(x)=1^2=1
x=2,f(x)=2^2=4
x=3,f(x)=3^2=9
x=4,f(x)=4^2=16
The same holds true for negative x-values to the left of the y-axis since a negative value squared is positive. For example,
x=−1,f(x)=(−1)2=1*−1=1
x=2,f(x)=(−2)2=−2*−2=4
The graph of f(x)=x^2 is called a "Parabola." It looks like this:
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.
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)
Will give brainiest
∆ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR. The side lengths of ∆ABC are , 5 units; , 4.2 units; and , 4 units. Match each side of ∆PQR to its length.
see file attached
Answer:
QR=5.25 units
PR=5 units
PQ=6.25 units
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.
find the value of 2/5 - 3
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
[tex]\sf{\dfrac{2}{5}-3 }[/tex] [tex]\sf{\dfrac{2-10}{5} }[/tex] [tex]\sf{\dfrac{-8}{5} }[/tex][tex]\sf{ }[/tex]
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.
