16. solve the equation
3x + (2x + 6) = 6x + 1.152

x=4.848

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3x+2x+6=6x+1.152

(3x+2x)+(6)=6x+1.152(Combine Like Terms)

5x+6=6x+1.152

5x+6=6x+1.152

Step 2: Subtract 6x from both sides.

5x+6−6x=6x+1.152−6x

−x+6=1.152

Step 3: Subtract 6 from both sides.

−x+6−6=1.152−6

−x=−4.848

Step 4: Divide both sides by -1.

−x

−1

=

−4.848

−1

x=4.848

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.