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3 years ago

Can someone please give me the answer.

Mathematics

2 answers:

statuscvo [17]3 years ago

8 0

Answer:

x = 9

Step-by-step explanation:

Vertical angles are congruent, so their measures are equal.

4x + 6 = 7x - 21

Subtract 7x from both sides.

-3x + 6 = -21

Subtract 6 from both sides.

-3x = -27

Divide both sides by -3.

x = 9

noname [10]3 years ago

5 0

Because of the postulate "Vertical angles are equal" we can write the equation:

4x + 6 = 7x - 21

Then solve:

(4x + 6) + 21 = (7x - 21) + 21

(4x + 27) - 4x = (7x) - 4x

27/3 = 3x/3

x = 9

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3 years ago

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$x = 2-t$ and $y = -5\cdot t +21$

Step-by-step explanation:

Given that $y = 5\cdot x + 11$ and $t = 2-x$ , the parametric equations are obtained by algebraic means:

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2) $y = 5\cdot x +11$ Given

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4) $y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11$ Existence of multiplicative inverse/Commutative property

5) $y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11$ Associative property

6) $y = -5\cdot (-x)+11$ $\frac{a}{-b} = -\frac{a}{b}$ / $(-1)\cdot a = -a$

7) $y = -5\cdot (-x+0)+11$ Modulative property

8) $y = -5\cdot [-x + 2 + (-2)]+11$ Existence of additive inverse

9) $y = -5 \cdot [(2-x)+(-2)]+11$ Associative and commutative properties

10) $y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11$ Distributive property

11) $y = (-5)\cdot (2-x) +21$ $(-a)\cdot (-b) = a\cdot b$

12) $y = (-5)\cdot t +21$ By 1)

13) $y = -5\cdot t +21$ $(-a)\cdot b = -a \cdot b$ /Result

14) $t+x = (2-x)+x$ Compatibility with addition

15) $t +(-t) +x = (2-x)+x +(-t)$ Compatibility with addition

16) $[t+(-t)]+x= 2 + [x+(-x)]+(-t)$ Associative property

17) $0+x = (2 + 0) +(-t)$ Associative property

18) $x = 2-t$ Associative and commutative properties/Definition of subtraction/Result

In consequence, the right answer is $x = 2-t$ and $y = -5\cdot t +21$ .

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3 years ago

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Step-by-step explanation:

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simplify and cross-multiply to get:

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8) 22/8 = x/6

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8 0

2 years ago