Mary = (1/3)x
Erin = x - 8
John = x
Here is your equation:
(1/3)x + (x - 8) + x = 267
Take it from here.
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<span><span> 5x2-23x=-26</span> </span>Two solutions were found :<span><span> x = 2
</span><span> x = 13/5 = 2.600
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Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5*x^2-23*x-(-26)=0
Step by step solution :Skip Ad
<span> Step 1 :</span><span>Equation at the end of step 1 :</span><span> (5x2 - 23x) - -26 = 0
</span><span> Step 2 :</span>Trying to factor by splitting the middle term
<span> 2.1 </span> Factoring <span> 5x2-23x+26</span>
The first term is, <span> <span>5x2</span> </span> its coefficient is <span> 5 </span>.
The middle term is, <span> -23x </span> its coefficient is <span> -23 </span>.
The last term, "the constant", is <span> +26 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> 5 • 26 = 130</span>
Step-2 : Find two factors of 130 whose sum equals the coefficient of the middle term, which is <span> -23 </span>.
<span><span>
-130
+
-1
=
-131
<span>
</span>
</span>
<span>
-65
+
-2
=
-67
<span>
</span>
</span>
<span>
-26
+
-5
=
-31
<span>
</span>
</span>
<span>
-13
+
-10
=
-23
That's it</span></span>
Answer: The two roots are x = 3/2 and x = -2
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Explanation:
You have the right idea so far. But the two numbers should be 3 and -4 since
The -1 being the coefficient of the x term.
This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.
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Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.
If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2
Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x
So we have the factor -x-2 along the top
The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.
We have the factor 2x-3 along the left side.
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The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)
The last thing to do is set each factor equal to 0 and solve for x
- 2x-3 = 0 solves to x = 3/2 = 1.5
- -x-2 = 0 solves to x = -2
The two roots are x = 3/2 and x = -2
Answer: 44 gallons
Step-by-step explanation:
Using proportion,
33 gallons = 3hours
X = 4hours
Cross multiply
3 × X = 33 × 4
3X = 132
Divide bothside by 3
3x/3 =132/3
X = 44
Therefore the helicopter uses 44gallons for 4 hours.
Answer:
1. (c)
2. (c)
Step-by-step explanation:
