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Juliette [100K]
3 years ago
6

Will spent $3.75 for 3 pounds of granola. What is his unit rate in dollars per pound?

Mathematics
1 answer:
Drupady [299]3 years ago
6 0
The unit rate is $1.25 per pound
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The green triangle is a dilation of the red triangle with a scale factor of s=1/3 and the center of dilation is at the point (4,
klasskru [66]

Given:

The scale factor is s=\dfrac{1}{3} and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

(x,y)\to (k(x-a)+a,k(y-b)+b)

According to the given information, the scale factor is \dfrac{1}{3} and the center of dilation is at (4,2).

(x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)            ...(i)

Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)

C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)

C(-2,11)\to C'(-2+4,3+2)

C(-2,11)\to C'(2,5)

Therefore, the coordinates of Point C' are C'(2,5).

We assumed that point A is A(m,n).

Using (i), we get

A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)

From the given figure it is clear that the image of point A is (8,4).

A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)

On comparing both sides, we get

\dfrac{1}{3}(m-4)+4=8

\dfrac{1}{3}(m-4)=8-4

(m-4)=3(4)

m=12+4

m=16

And,

\dfrac{1}{3}(n-2)+2=4

\dfrac{1}{3}(n-2)=4-2

(n-2)=3(2)

n=6+2

n=8

Therefore, the coordinates of point A are (16,8).

5 0
3 years ago
2y = 2x = 8 y = x + 4​
padilas [110]

Answer:

I love algebra anyways

the ans is in the picture with the steps how i got it

(hope that helps can i plz have brainlist it will make my day :D hehe)

Step-by-step explanation:

4 0
3 years ago
Circle O and triangle OQR are shown below. What is the length of OQ?
zysi [14]

Answer:

Step-by-step explanation:

A circle is inscribed in an equilateral triangle PQR with centre O. If angle OQR = 30°, what is the perimeter of the triangle?

This is a circle inscribed in an equilateral triangle with side s.

If you are asking for the perimeter of PQR, it is 3s.

If you are asking for the perimeter of OQR, it is (3+23–√3)s

Since OR and SR are the hypotenuses of right triangles with adjacent side equal to ½ s, their length is ½s / cos 30° = (√3) /3.

(3/3)s + ((√3) /3)s + ((√3) /3)s = ((3 + 2√3)/3)s ≈ 2.1547s

Hope it helps

help me by marking as brainliest....

3 0
2 years ago
Help asap..............
MatroZZZ [7]

The common denominator for 25 and 20 would be 100

25 x 4 = 100

20 x 5 = 100

Rewrite 14/25 as 14 x 4 / 25 x 4 = 56/100

Rewrite 11/20 as 11 x 5 / 20 x 5 = 55/100

14/25 is greater than 11/20

14/25 > 11/20

3 0
3 years ago
Two numbers add to be 5 multiply to be -6
FrozenT [24]

Answer:

-1, 6

Step-by-step explanation:

x + y = 5

xy = -6

Take first equation and rewrite it. y = -x + 5

Then substitute the new equation in the second one.

x(-x + 5) = -6

-x^2 + 5x + 6 = 0

Divide by -1

x^2 - 5x - 6

(x + 1)(x - 6) = 0

x = -1, 6

3 0
3 years ago
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