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Nezavi [6.7K]
3 years ago
9

What is this expression?

Mathematics
1 answer:
Liula [17]3 years ago
4 0

Answer:

2) 4/3

Step-by-step explanation:

(4^-3 * 3^4 * 4^2)/(3^5 * 4^-2)

4^-3 * 3^4 * 4^2 = 4^-1 * 3^4

(4^-1 * 3^4)/(4^-2 * 3^5)

(3^4)/(3^5) = 1/(3^5-4)

(4^(-1))/(4^-2 * 3^(5-4)

(4^-1)/(4^-2 * 3)

4^(-1 - (-2)) / (3)

-1 - (-2) = 1

4/3

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The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?
daser333 [38]

Answer:

d=\frac{3}{2}=1.5

Step-by-step explanation:

We have the function:

y=a(x-2)(x-1)

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are <em>(x-2) </em>and <em>(x-1)</em>.

Therefore, our roots/zeros are <em>x=1, 2</em>.

So, the average of them are:

d=\frac{1+2}{2}=3/2=1.5

Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

x=-\frac{b}{2a}

So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:

x=-\frac{-3a}{2a}=\frac{3}{2}=1.5

Confirming our answer.

4 0
3 years ago
How to solve this problem?
makkiz [27]
The answer is c because, if u change 15% to a decimal (0.15) then u get 5,250 and when u add that to 35,000 you get 40,250
3 0
3 years ago
If Gina leaves now and drives at 66km/h she will reach Alton just in time for her appointment on the other hand if she has lunch
Stolb23 [73]

Answer:

165km

Step-by-step explanation:

If Gina leaves now and drives at 66km/h she will reach Alton just in time for her appointment

Now:

Distance=Speed X Time

D=66 X t=66t.....(I)

If she leaves in 40 minutes,and she must get there at the same time, her new drive time will be:

t hours - 40 minutes

=(t-40/60)hours=( t-2/3) hours

Her Distance this time

D=90(t-2/3)=90t-60.....(ii)

Since the distance to Alton does not change, we equate (I) and (ii)

66t=90t-60

60=90t-66t

60=24t

t=2.5 hours

From equation (I)

Distance=66t=66X2.5=165km

Distance to Alton is 165km.

3 0
3 years ago
The product of the number of songs and $0.99 is $7.92 please help algebraic expression / equation
Step2247 [10]

Lets x = the number of songs

The product of the number of songs and $0.99 = 0.99 times x = 0.99x

The product of the number of songs and $0.99 is $7.92:

=

0.99x = 7.92

Hope that helps.

7 0
3 years ago
Read 2 more answers
I think of a number and multiply it by 4. I then add 8 and I'm left with an answer of 30. What number did I think of? Form and s
postnew [5]

Answer: number= 5.5; equation: 4x+8=30

Step-by-step explanation:

Take x for the unknown number. Then just follow the words and turn them into mathematical symbols. Easy.

5 0
3 years ago
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