How many times does forty-two go into eight hundred twenty?

Express the polynomial 6x^3-x^3+2x-4 in standard form.

Dennis_Churaev [7]

It was just simplifying, was basically in standard form already.

7 0

3 years ago

LN bisects KLM into two congruent angles measuring (3x-4) and (4x-27). Find klm

Vanyuwa [196]

Answer:  The m ∡KLM is: 130° .
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Explanation:
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(3x − 4) = (4x − 27) ; (Since these are "bisected, congruent angles", they are equal).

⇒ 3x − 4 = 4x − 27 ;

⇒ Subtract "4x" from EACH SIDE of the equation; and add "4" to EACH SIDE of the equation;

⇒    3x − 4 − 4x + 4 = 4x − 27 − 4x + 4 ;

to get:

⇒ - 1x = -23 ;

⇒ Divide EACH SIDE of the equation by "-1" ; to isolate "x" on one side of the equation; and to solve for "x" ;

⇒ -1x / -1 = -23 / -1 ; to get:

⇒ x = 23;
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To find m ∡KLM :

m ∡ KLM = (3x − 4) + (4x − 27) ;

{Note: Remember: (3x − 4) = (4x − 27) } ;

So, plug in our solved value for "x" ; which is: "x = 23" into one of the expressions for one of the congruent angles.

Let us start with: "(3x − 4)" .

(3x − 4) = 3x − 4 = 3(23) − 4 = 69 − 4 = 65 .

By plugging in our solve value for "x" ; which is: "x = 23" ; into the expression for the other congruent angle, we should get: "65" ;

Let us try:

(4x − 27) = 4x − 27 = 4(23) − 27 = 92 − 27 = 65. Yes!
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So to find m ∡KLM:

(3x − 4) + (4x − 27) = 65 + 65 = 130° .
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Alternate method:
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At the point which we have:
_______________________________________________
To find m ∡KLM :

m ∡ KLM = (3x − 4) + (4x − 27) ; and at which we have our solved value for "x" ; which is: "x = 23" ;
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We can simply plug in our known value for "x" ; which is: "23" ; into the following:
m ∡ KLM = (3x − 4) + (4x − 27) = [(3*23) − 4] + [(4*23) − 27] ;
                                                  = (69 − 4) + (92 − 7) = 65 + 65 = 130° .
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{Note: Using this method, we determine that each angle is equal; that is, "65° ".}.
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4 0

3 years ago

If f(x)=x/2-3and g(x)=3x^2+x-6 find (f+g) (x)

olga_2 [115]

Answer:

3x^2+1.5x-9

Step-by-step explanation:

(f+g) (x)

=f(x)+g(x)

=x/2-3+3x^2+x-6

=3x^2+1.5x-9

3 0

4 years ago

If you borrow $225 for eight years at an interest rate of 6% how much interest will you pay ?

weeeeeb [17]

Answer:$58.55

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers

Marine fuel is a combination of gasoline and motor oil. The standard gasoline and oil mixture is about 98% gasoline and about 2%

Georgia [21]

Answer:

0.98g+ 0.02m= 7.1224 gallons standard mixture

0.96g+ 0.04m= 6.25 gallons break oil

3.92 gallons of gasoline is required for 4 gallons the standard mixture

Step-by-step explanation:

If we have to use 6 gallons of gasoline this means that 98%= 6 gallons and 2% would be 6/98*2

Gasoline: Motor oil

6 : x

98 : 2

Using the product rule

x= 6*2/98= 0.1224 gallons of motor oil is required.

Let the gasoline be represented by g and motor oil by m then for the standard oil the equation would be

0.98g+ 0.02m= 7.1224 gallons standard mixture

For break in oil

Gasoline: Motor oil

6 : x

96 : 4

Using the product rule

x= 6*4/96= 0.25 gallons of motor oil is required.

Let the gasoline be represented by g and motor oil by m then for the break oil the equation would be

0.96g+ 0.04m= 6.25 gallons break oil

Part b. For 4 gallons of the "break in" mixture

96% of the 4 gallons of the "break in" mixture is gasoline = 3.84 gallons of gasoline

4% of 4 = 0.16 gallons of motor oil

Now the standard mixture 4 gallons would contain 98 % of gasoline and 2 % of motor oil

98% of 4 gallons= 3.92 gallons of gasoline

2% of 4 gallons= 0.08 gallons of motor oil.

6 0

3 years ago