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Viefleur [7K]
3 years ago
9

Diego's age `d` is 5 more than 2 times his sister's age `s`. This situation is represented by the equation `d=2s+5`. If we know

Diego's age, which equation will help us find his sister's age?
Mathematics
1 answer:
lutik1710 [3]3 years ago
4 0

Answer:  s=\dfrac{(d-5)}{2}.

Step-by-step explanation:

Given: d denotes Diego's age while s denotes his sister's age.

The situation is represented by the equation d=2s+5.

To find his sister's age we can write the above equation as s=\dfrac{(d-5)}{2} [we first subtract 5 from both sides and then divide both sides by 2]

Hence, the required equation: s=\dfrac{(d-5)}{2}.

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Which values of a and b make the following equation true? (5x7y2)(-4x4y5)=-20xayb
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Answer:

The values of a and b are a = 11 , b = 7

Step-by-step explanation:

* Lets explain how to solve the problem

* In the exponential functions we have some rules

1-  In multiplication if they have same base we add  the power

# Ex: b^m  ×  b^n  =  b^(m + n) ⇒ b is the base , m and n are the powers

2- In division if they have same base we subtract  the power

# Ex: b^m  ÷  b^n =  b^(m – n) ⇒ b is the base , m and n are the powers

3- If we have power over power we multiply them

# Ex: (b^m)^n = b^(mn) ⇒ b is the base , m and n are the powers

* Lets solve the problem

∵ The equation is (5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{a}y^{2} ⇒ (1)

- At first multiply the coefficients

∵ -4 × 5 = -20

- Multiply the base x

∵ (x^{7})(x^{4})=x^{7+4}=x^{11}

- Multiply the base y

∵ (y^{2})(y^{5})=y^{2+5}=y^{7}

∴ (5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{11}y^{7} ⇒ (2)

- By comparing (1) and (2)

∴ a = 11 and b = 7

* The values of a and b are a = 11 , b = 7

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