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3 years ago

Evaluate x(y-z)2 for =-1,y=5,and z=

Mathematics

1 answer:

Nata [24]3 years ago

6 0

Answer:

The value of $x(y-z)^2$ is -16.

Step-by-step explanation:

We need to evaluate $x(y-z)^2$ for x = -1, y = 5 and let us assume that z = 1

It can be simply done by putting the values of x,y and z in the given expression.

$x(y-z)^2=(-1)(5-1)^2\\\\=-1(4)^2$

We know that the value of 4² = 16

So,

$x(y-z)^2=16\times -1\\\\=-16$

So, the value of $x(y-z)^2$ is -16.

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Match the parabolas represented by the equations with their foci.

Elenna [48]

Function 1 $f(x)=- x^{2} +4x+8$

First step: Finding when $f(x)$ is minimum/maximum
The function has a negative value $x^{2}$ hence the $f(x)$ has a maximum value which happens when $x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2$ . The foci of this parabola lies on $x=2$ .

Second step: Find the value of y-coordinate by substituting $x=2$ into $f(x)$ which give $y=- (2)^{2} +4(2)+8=12$

Third step: Find the distance of the foci from the y-coordinate
$y=- x^{2} +4x+8$ - Multiply all term by -1 to get a positive $x^{2}$
$-y= x^{2} -4x-8$ - then manipulate the constant of y to get a multiply of 4
$4(- \frac{1}{4})y= x^{2} -4x-8$
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is $12- \frac{1}{4}=11.75$

Hence the coordinate of the foci is (2, 11.75)

Function 2: $f(x)= 2x^{2}+16x+18$

The function has a positive $x^{2}$ so it has a minimum

First step - $x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4$
Second step - $y=2(-4)^{2}+16(-4)+18=-14$
Third step - Manipulating $f(x)$ to leave $x^{2}$ with constant of 1
$y=2 x^{2} +16x+18$ - Divide all terms by 2
$\frac{1}{2}y= x^{2} +8x+9$ - Manipulate the constant of y to get a multiply of 4
$4( \frac{1}{8}y= x^{2} +8x+9$

So the distance of focus from y-coordinate is $\frac{1}{8}$ to the north of $y=-14$
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: $f(x)=-2 x^{2} +5x+14$

First step: the function's maximum value happens when $x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25$
Second step: $y=-2(1.25)^{2}+5(1.25)+14=17.125$
Third step: Manipulating $f(x)$
$y=-2 x^{2} +5x+14$ - Divide all terms by -2
$-2y= x^{2} -2.5x-7$ - Manipulate coefficient of y to get a multiply of 4
$4(- \frac{1}{8})y= x^{2} -2.5x-7$
So the distance of the foci from the y-coordinate is - $\frac{1}{8}$ south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when $x=8.5$ and $y=79.25$ . The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when $x=-2.75$ and $y=-10.125$ . Manipulating coefficient of y, the distance of foci from y-coordinate is $\frac{1}{8}$ to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when $x=1.5$ and $y=9.5$ . The distance of the foci from the y-coordinate is $\frac{1}{8}$ to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

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2 years ago

What is the length of segment AB? Consider the diagram. 07 09 O 18 O 25

Julli [10]

AB = 9.

It is given that BC = 9 and AB = BC. Hence, AB = BC = 9.

8 0

3 years ago

Plss help im bad at math:v 100 points!

vlabodo [156]

$\mathbb{MY \: ANSWER}$

35.A

36.C

37.B

38.B

39.D

Step-by-step explanation:

Hope it helps

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2 years ago

Please explain how to do this i am lost

mixas84 [53]

Answer: y = 7x - 6

Step-by-step explanation:

7 = m (slope)

-6 = y-intercept

8 0

3 years ago

Read 2 more answers

What is the simplified form of 12z^2-7z-12/3z^2+2z-8? ...?

gavmur [86]

It should go like this:

(4z + 3) (3z - 4) / (3z - 4) (z + 2)

Then you just cancel out (3z -4) and (3z -4), and the final simplified form of this polynomial is:

(4z +3) / (z + 2)

4 0

3 years ago