Josie wants to make 10 pounds of trail mix using nuts and raisins, and she wants the total cost of the trail mix to be $54. nuts cost $6 per pound and raisins cost $3 per pound. solve the system {n+r=106n+3r=54 to find n , the number of pounds of nuts, and r , the number of pounds of raisins she should use. program

The trail mix Josie wants to make should have 8 pounds of nuts and 2 pounds of raisins.

Step-by-step explanation:

Let's help Josie to solve for n and r, this way:

Our equations system is:

n + r = 10

6n+ 3r = 54

n = 10 - r

Now, let's substitute n in the second equation and solve for r:

6 (10 - r) + 3r = 54

60 - 6r + 3r = 54

-3r = 54 - 60

-3r  = -6

r = 2

Now, let's solve for n:

n = 10 - r

n = 10 - 2

n = 8

The trail mix Josie wants to make should have 8 pounds of nuts and 2 pounds of raisins.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .