Solve the system:
10r-4t=6
7r +5t=12

t=1

r=1

Step-by-step explanation:

10r-4t=6   equation 1

7r +5t=12   equation 2

using equation 1 we have:

10r-4t=6  

10r = 6+4t

r= (6+4t)/10  equation 3

using equation 3 in equation 2 we have:

7((6+4t)/10)) +5t=12

4.2 + 2.8t  +5t =12

7.8t = 12-4.2

7.8t= 7.8

t = 7.8/7.8

t=1

so we have:

r= (6+4(1))/10

r= 10/10

r=1

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.