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s344n2d4d5 [400]
2 years ago
5

In the figure, a||b , and both lines are intersected by transversal t. Complete the statements to prove that ∠2 and ∠8 are suppl

ementary angles.
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m∠2 = m∠7 ( )
m∠7 + m∠8 = 180° ( )

Mathematics
1 answer:
agasfer [191]2 years ago
8 0

Answer:

Step-by-step explanation:

m∠2 ≅ m∠7 [Alternate exterior angles]

m∠7 + m∠8 = 180° [Linear pair theorem]

m∠2 + m∠8 = 180° [Substitution property]

∠2 and ∠8 are supplementary [Definition of supplementary angles]

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Large reusable bottles cost $4 more than small ones. Eight large bottles cost $24 less than 12 small ones. How much does one sma
ss7ja [257]
A small bottle costs $14.

To solve the problem, the equation would be this:

 8(4+s)=12s-24

Let <em>s </em>represent a small bottle. Since one large bottle is $4 more than a small one, you would write out <em>(4+s)</em>. Then, multiply it by 8 to find one side of the equation, and get <em>8(4+s)</em>. To write out the right side of the equation, you would write out <em>12s </em>to represent 12 small bottles, and <em />subtract <em />24 from that to represent that 8 large bottles is $24 less than 12 small ones. 

Then, proceed to solve the equation to get the answer of <em>s=14</em>. Because a small bottle is $14, you can check your work by substituting the 14 in replace of <em>s</em>. <em />
5 0
3 years ago
Consider the function f(x) = x^3 - 7x^2 - 2x + 14
mars1129 [50]

Answer:

There are 3 zeros, which are:

x=7,\:x=-\sqrt{2},\:x=\sqrt{2}

Step-by-step explanation:

Given the function

f\left(x\right)\:=\:x^3\:-\:7x^2\:-\:2x\:+\:14

To get the zeros of f(x), set y or f(x) =0

so

0=x^3-7x^2-2x+14

as

x^3\:-\:7x^2\:-\:2x\:+\:14=\left(x-7\right)\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)

so

\left(x-7\right)\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)=0

Using the zero factor principle:

\mathrm{ \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)

so

x-7=0\quad \mathrm{or}\quad \:x+\sqrt{2}=0\quad \mathrm{or}\quad \:x-\sqrt{2}=0

solving

x-7=0

  • x=7

x+\sqrt{2}=0

  • x=-\sqrt{2}

x-\sqrt{2}=0

  • x=\sqrt{2}

Therefore, there are 3 zeros, which are:

x=7,\:x=-\sqrt{2},\:x=\sqrt{2}

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