You are climbing a mountain by the steepest route at a slope of 10∘ when you come upon a trail branching off at a 45∘ angle from

9 / 16 + 1/2 =?

Step 1. To add fractions, they must share the same denominator. Here the denominators are 16 and 2. Since 16 is 8 times 2, multiply 1/2 by 8 to match denominators.

(1 * 8) / (2 * 8) = 8 / 16

Step 2.  Add the numerators over the common denominator.

9/16 + 8/16 = (9+8) / 16 = 17 / 16

Step 3. Reduce the fraction if possible.

17/16 is already in simplest form. Therefore, 9/16 + 1/2 = 17/16

We observe that
the vertex of f(x) is located at the point (0,0)
and
the vertex of g(x) is situated at (0,5)

thus,
(x,y) in f(x)  becomes -------> (x,y+5) in g(x)
g(x)---------> f(x)+5

g(x)=x²+5

the answer is
g(x)=x²+5

Answer:

  2.5 hours

Step-by-step explanation:

Distance equals speed multiplied by time. For constant distance, time varies inversely with speed. When traveling at 60/50 = 6/5 times the original speed, the return journey takes 5/6 of the initial duration:

  (5/6)(3 hours) = 2.5 hours... return trip duration

We consider all workers as either full-time or part-time. 36 = 24 + 12 If there are 24 or fewer full-time workers, there must be at least 12 part-time workers. (This conclusion is based on the understanding of sums.) You can formulate the inequality in two steps. First, present and resolve an equation for full-time workers in relation to part-time workers. Then, apply the specified limit on full-time workers. This results in an inequality that can be solved for part-time workers. Let f and p represent full-time and part-time positions, respectively. f + p = 36... given f = 36 - p... subtract p to express f in terms of p. f ≤ 24......... given (36 - p) ≤ 24.... substitute for f. This gives your inequality in terms of p. 36 - 24 ≤ p.... rearranging gives p ≥ 12........ this is the solution to the inequality

Let C denote the quantity of compost

T represent the quantity of topsoil

Each cubic yard of compost is priced at $25

Thus, the cost of C cubic yards of compost is 25C

Each cubic yard of topsoil costs $15

Therefore, the cost for T cubic yards of topsoil is 15T

Together, the amount of compost plus topsoil equals 10

C + T = 10 -------> Equation 1

The total cost for compost and topsoil is $180

25C + 15T = 180 --------> Equation 2

Rearranging the first equation to find C

C + T = 10

results in

C = 10 - T

Now substitute into the second equation

25C + 15T = 180

25 ( 10 - T) +15T = 180

Using like terms: 250 - 25T + 15T = 180

From which we can simplify to 250 - 10T = 180 by removing 250 from both sides

-10T = 180 - 250

yielding -10T = -70 (dividing both sides by -10)

results in T = 7