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Temka [501]
2 years ago
11

Sam studied guinea pigs for his science fair project. He found that the amount of weight the guinea pigs gained varied directly

with the number of calories they consumed.
The guinea pigs gained 1 ounce for every additional 218 calories in their diet. How many additional ounces would they gain if their diet was increased by 1,090 calories? Let W represent the weight in ounces, and let C represent the number of calories.
Mathematics
1 answer:
borishaifa [10]2 years ago
7 0

Answer: C= 1,090 and the W= 5.

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rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis reflection across the y-a
SpyIntel [72]

Answer:

The point O can be (x,y)  or (-x,y) or (-x,-y) or ( x,-y) reason being that you haven't given point O lies in which quadrant.

Rotation through 90° counter clockwise

(x,y) = (-y,x)

(-x,y)=(-y,-x)

(-x,-y)=(y,-x)

(x,-y) =(y,x)

Then Reflection across X axis has taken place.

(-y,x) = (-y,-x)

(-y,-x)=(-y,x)

(y,-x)=(y,x)

(y,x)=(y,-x)

Then a reflection across the y-axis has taken place.

(-y,-x)=(y,-x)

(-y,x) = (y,x)

(y,x) =(-y,x)

(y,-x)=(-y,-x)

Then a translation a units to the right and b units up has taken place.

(y,-x)=(y+a,-x+b)

(y,x) =(y+a, x+b)

(-y,x) =(-y+a,x+b)

(-y,-x)=(-y+a,-x+b)

Then a rotation of 180 degrees counterclockwise about the origin has taken place.

(y+a,-x+b)=[-(y+a),-(-x+b)]

(y+a, x+b)=[- (y+a), -(x+b)]

(-y+a,x+b)=[-(-y+a),-(x+b)]

(-y+a,-x+b) =[-(-y+a),-(-x+b)]

Now Again a reflection across the Y axis has taken place.

[-(y+a),-(-x+b)]=[(y+a),-(-x+b)]

[-(y+a),-(x+b)]=[(y+a),-(-x+b)]

[-(-y+a),-(x+b)]=[(-y+a),-(x+b)]

[-(-y+a),-(-x+b)]=[(-y+a),-(-x+b)]

Totally depends on value of a and b on which quadrant these point lies.



7 0
3 years ago
Find the distance from P to l.
ki77a [65]
Equation\ of\ a\ line\ from\ 2\ points (x_1;\ y_1);\ (x_2;\ y_2):\\\\y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\(-4;\ 2)\ and\ (3;-5)\\subtitute:\\\\y-2=\dfrac{-5-2}{3-(-4)}\cdot(x-(-4))\\\\y-2=\dfrac{-7}{7}\cdot(x+4)\\\\y-2=-(x+4)\\\\y-2=-x-4\ \ \ |add\ x\ and\ 4\ to\ both\ sides\\\\x+y+2=0\\-------------------\\

Point-line\ distance\\l:Ax+By+C=0;\ (x_0;\ y_0)\\\\d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}\\\\x+y+2=0\to A=1;\ B=1;\ C=2\\(1;\ 2)\to x_0=1;\ y_0=2\\subtitute\\\\d=\dfrac{|1\cdot1+1\cdot2+2|}{\sqrt{1^2+1^2}}=\dfrac{|1+2+2|}{\sqrt2}=\dfrac{|5|}{\sqrt2}=\dfrac{5}{\sqrt2}=\dfrac{5\cdot\sqrt2}{\sqrt2\cdot\sqrt2}\\\\=\boxed{\dfrac{5\sqrt2}{2}}
4 0
3 years ago
How do you do this problem?
faust18 [17]

The volume of the original cylinder is

... V = π·r²·h

For r=1 and h=1, this is

... V = π·1²·1 = π

For the new cylinder, the volume is 1.089 times that amount.

... V = 1.089π = π·1.1²·(1-k)

... 1.089/1.21 = 1-k

... k = 1 - 1.089/1.21 = 1 - 0.9 = 0.1 = 10%

The appropriate choice is (B) 10.

7 0
3 years ago
Read 2 more answers
Calculate the equation of a line passing through C(4;7) and D(9;17)
Ludmilka [50]

Answer:

it would be 10/5 or 2

Step-by-step explanation:

y2-y1/x2-x1

17-7/9-4

10/5 simplify

2

3 0
2 years ago
A line with a slope of 2 passes through the point (3,9).
Licemer1 [7]

Answer:

y-9=2(x-3)

Step-by-step explanation:

The point-slope formula is: y-y1=m(x-x1)

y1 and x1 is where you plug in the coordinate and m is the slope.

y1 is the second number of the coordinate (x, y)

So, y1 is 9 in this case

x1 is the first number of the coordinate (x, y)

So x1 is 3 in this case

Do you get it or do I need to explain further?

4 0
3 years ago
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