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Vikentia [17]
3 years ago
12

Find two numbers whose difference is 10 and whose product is a minimum

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
3 0
20 to 30 and this is to make it 20 characters long :3
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Solving multi-step equations <br><br> 2(x + 7) – 34 = 4x – 11x + 4(x - 1)
Zarrin [17]

Answer:

x = 16/5

Step-by-step explanation:

2x + 14 -34 = 4x - 11x + 4x - 4

2x - 20 = -3x - 4

5x = 16

6 0
3 years ago
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I need help please on #7
vredina [299]
X=-4 is the answer for this question
7 0
3 years ago
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Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola
mote1985 [20]

ANSWER

This is an ellipse. The equation is:

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

(a+b)^2=a^2+2ab+b^2

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

16x^2-32x=16(x^2-2x)

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

(x-1)^2=x^2-2x+1

To maintain the equation, we have to subtract 1,

16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

16(x-1)^2-16+9y^2+72y+16=0

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

9y^2+72y=9(y^2+8y)

Following the same reasoning as before, we have that the perfect binomial squared is,

(y+4)^2=y^2+8y+16

Remember to subtract the independent term to maintain the equation,

9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

16(x-1)^2-16+9(y+4)^2-144+16=0

Add like terms,

\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}

Add 144 to both sides,

\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}

As we can see, this is the equation of an ellipse. Its standard form is,

\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\  \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1

Note that we can simplify a and b,

\frac{12}{4}=3\text{ and }\frac{12}{3}=4

Hence, the equation of the ellipse is,

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

3 0
1 year ago
What are the x-intercepts of y=x^2+2x-15
Sedbober [7]

Answer:

(-5,0) and (3,0)

Step-by-step explanation:

Think about it.

What two numbers multiply to -15 and add up to 2?

The answers are 5 and -3.

So plug that into the factored form of a parabola.

y=(x+5)(x-3)

To find the x-intercepts, plug in 0 for y.

(x+5)(x-3)=0

Since we are multiplying, at least one of the terms has to equal 0.

x+5=0 \\ x-3=0 \\ \\ x=-5,3

So the x-intercepts are (-5,0) and (3,0).

8 0
3 years ago
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lbs and each b
german

Answer:

16 boxes

Step-by-step explanation:

160+50x=1000

Solve for the x and you'll get 16.8. Now, because you can't have a fraction of a box, and you can't go over the limit, the answer is 16 boxes.

(How to solve for x:

Get x by itself by subtracting 160 to both sides.

50x=1000-160

50x=840

Divide both sides by 50.

x=16.8)

8 0
3 years ago
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