Question

example 3 translate each sentence into an equation or formula. 9 twice a increased by the cube of a equals b. 10. seven less than the sum of p and t is as much as 6. 11. the sum of x and its square is equal to y times z. 12. four times the sum of f and g is identical to six times g. 13. the area a of a square is the length of a side ℓ squared. 14. the perimeter p of a triangle is equal to the sum of the lengths of sides a, b, and c.

Explanation:

Step1: Translate "Twice a"

$2a$

Step2: Translate "the cube of a"

$a^{3}$

Step3: Form the equation for 9

$2a + a^{3}=b$

Step4: Translate "the sum of p and t"

$p + t$

Step5: Translate "Seven less than the sum"

$(p + t)-7$

Step6: Form the equation for 10

$(p + t)-7 = 6$

Step7: Translate "the square of x"

$x^{2}$

Step8: Translate "the sum of x and its square"

$x+x^{2}$

Step9: Form the equation for 11

$x + x^{2}=yz$

Step10: Translate "the sum of f and g"

$f + g$

Step11: Translate "Four times the sum"

$4(f + g)$

Step12: Translate "six times g"

$6g$

Step13: Form the equation for 12

$4(f + g)=6g$

Step14: Translate "the length of a side $\ell$ squared"

$\ell^{2}$

Step15: Form the equation for 13

$A=\ell^{2}$

Step16: Form the equation for 14

$P=a + b + c$

Answer:

1. $2a + a^{3}=b$
2. $(p + t)-7 = 6$
3. $x + x^{2}=yz$
4. $4(f + g)=6g$
5. $A=\ell^{2}$
6. $P=a + b + c$