Choose the correct simplification of the expression (x2y)2. x4y3
x6y6
x4y2
xy4

Answers

Answer 1

Answer:

Answer: The correct option is (C) $x^4y^2.$

Step-by-step explanation: We are given to select the correct expression that is equivalent to the expression below:

$E=(x^2y)^2.$

We will be using the following properties of exponents:

$(i)~(a^b)^c=a^(b* c),\n\n(ii)~(ab)^c=a^cb^c.$

We have

$E=(x^2y)^2=(x^2)^2y^2=x^(2* 2)y^2=x^4y^2.$

Therefore, the required equivalent expression is $x^4y^2.$

Thus, (C) is the correct option.

Answer 2

Answer:

The correct simplification of the expression $(x^2y)^2$ is $x^4y^2$ .

Option C. is correct.

Here, we have,

To simplify the expression, we apply the power of a power rule,

which states that $(a^m)^n = a^{m*n$ .

In this case, $x^2y$ raised to the power of 2 can be simplified as follows:

$(x^2y)^2 = x^{2^(2) * y^(2)$

$=x^4y^2$

Therefore, the correct simplification of $(x^2y)^2$ is $x^4y^2$ .

Option C. is correct.

To learn more on Expression click:

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An oil reﬁnery produces gasoline from crude oil. For every 10,000 barrels of crude oil supplied, the reﬁnery can produce 6,500 barrels of gasoline. How many barrels of gasoline can be produced from 3,500 barrels of crude oil?

Answers

2,275 barrels of refined oil will be produced from 3,500 barrels of crude oil.

with the information that from 10,000 barrels of crude oil, 6,500 barrels of refined oil are produced, it immediately pops out that from x amount of crude oil, 65% will be refined.

now we need to find what is 65% of 3,500

$(65)/(100)$ = $(x)/(3,500)$
to find x, we multiply 65 × 3,500 and that amounts to 227,500
that then is divided by 100 so 227,500 ÷ 100 = 2,275

10000 barrels of crude oil produces 6500 barrels gasoline
1 barrel of crude oil will produce 6500÷10000 barrels of gasoline
3500 barrels of crude oil will produce 6500 × 3500 ÷10000 barrels
= 3500 barrels of crude oil produce 2275 barrels of gasoline

Jenny is a 60 percent free-throw shooter. She gets to shoot a second free throw if and only if she makes her first shot. She can score 0 points( if she misses her first shot), 1 point (she makes her first but misses her second), or 2 points ( she makes both shots.) Assuming that the probability for each shot is independent, what number of points is Jenny most likely to make?
How many points on average, can Jenny expect to make when she shoots a one-and-one (when she only gets a second shot if she makes the first)?

A.
0

B.
2

C.
1

D.
.96

E.
.36

Answers

Let the points be X.

x 0 1 2
P(X = x) 0.4 0.24 0.36

The expected points, E(X), are found as follows:
$E(X)=(0*0.4)+(1*0.24)+(2*0.36)=0.96$

The graph of which function has an axis of symmetry at x =-1/4 ?f(x) = 2x2 + x – 1

f(x) = 2x2 – x + 1

f(x) = x2 + 2x – 1

f(x) = x2 – 2x + 1

Answers

The graph of which function has an axis of symmetry at x = -1/4 is :

f(x) = 2x² + x – 1

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

An axis of symmetry of quadratic equation y = ax² + bx + c is :

$\large {\boxed {x = (-b)/(2a) } }$

Option 1 :

f(x) = 2x² + x – 1 → a = 2 , b = 1 , c = -1

Axis of symmetry → $x = (-b)/(2a) = (-1)/(2(2)) = -(1)/(4)$

Option 2 :

f(x) = 2x² – x + 1 → a = 2 , b = -1 , c = 1

Axis of symmetry → $x = (-b)/(2a) = (-(-1))/(2(2)) = (1)/(4)$

Option 3 :

f(x) = x² + 2x – 1 → a = 1 , b = 2 , c = -1

Axis of symmetry → $x = (-b)/(2a) = (-2)/(2(1)) = -1$

Option 4 :

f(x) = x² – 2x + 1 → a = 1 , b = -2 , c = 1

Axis of symmetry → $x = (-b)/(2a) = (-(-2))/(2(1)) = 1$

Learn more

Solving Quadratic Equations by Factoring : brainly.com/question/12182022
Determine the Discriminant : brainly.com/question/4600943
Formula of Quadratic Equations : brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number

The graph of function $\boxed{f(x)=2x^(2)+x-1}$ has an axis of symmetry as $\boxed{x=-(1)/(4)}$ .

Further explanation:

The standard form of a quadratic equation is as follows:

$\boxed{f(x)=ax^(2)+bx+c}$

The vertex form of a quadratic equation is as follows:

$\boxed{g(x)=a(x-h)^(2)+k}$

Axis of symmetry is the line which divides the graph of the parabola in two perfect halves.

The formula for axis of symmetry of a quadratic function is given as follows:

$\boxed{x=-(b)/(2a)}$

The first function is given as follows:

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

The above function is in standard form with $a=2$ , $b=1$ and $c=-1$ .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-(b)/(2a)\n&=-(1)/(2*2)\n&=-(1)/(4)\end{aligned}$

The axis of symmetry of first function is $x=-(1)/(4)$ .

Express the function $f(x)=2x^(2)+x-1$ in its vertex form,

$\begin{aligned}f(x)&=2x^(2)+x-1\n&=(√(2)x)^(2)+\left(2* √(2)x* (1)/(2√(2))\right)-1+\left((1)/(2√(2))\right)^(2)-\left((1)/(√(2))\right)^(2)\n&=\left(√(2)x+(1)/(2√(2))\right)^(2)-1-(1)/(8)\n&=\left[√(2)\left(x+(1)/(4)\right)\right]^(2)-(9)/(8)\n&=2\left(x-\left(-(1)/(4)\right)\right)^(2)-(9)/(8)\end{aligned}$

The above equation is in the vertex form with $a=2$ , $h=-(1)/(4)$ and $k=-(9)/(8)$ .

Therefore, its axis of symmetry is given as,

$\begin{aligned}x&=h\nx&=-(1)/(4)\end{aligned}$

The graph of function $f(x)=2x^(2)+x-1$ is shown in Figure 1.

The second function is given as follows:

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

The above function is in standard form with $a=2$ , $b=-1$ and $c=1$ .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-(b)/(2a)\n&=-((-1))/(2*2)\n&=(1)/(4)\end{aligned}$

The axis of symmetry of second function is $x=(1)/(4)$ .

The third function is given as follows:

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

The above function is in standard form with $a=1$ , $b=2$ and $c=-1$ .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-(b)/(2a)\n&=-(2)/(2*1)\n&=-1\end{aligned}$

The axis of symmetry of third function is $x=-1$ .

The fourth function is given as follows:

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

The above function is in standard form with $a=1$ , $b=-2$ and $c=1$ .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-(b)/(2a)\n&=-(-2)/(2*1)\n&=1\end{aligned}$

The axis of symmetry of fourth function is $x=1$ .

Therefore, the function $\boxed{f(x)=2x^(2)+x-1}$ has an axis of symmetry as $\boxed{x=-(1)/(4)}$ .

Learn more:

1. A problem on graph brainly.com/question/2491745

2. A problem on function brainly.com/question/9590016

3. A problem on axis of symmetry brainly.com/question/1286775

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Functions

Keywords:Graph, function, axis, f(x), 2x^2+x-1, axis of symmetry, symmetry, vertex, perfect halves, graph of a function, x =- 1/4.

Suppose you throw a dart at a circular target of radius 10 inches. Assuming that you hit the target and that the coordinates of the outcomes are chosen at random, find the probability that the dart falls (a) within 2 inches of the center. (b) within 2 inches of the rim. (c) within the first quadrant of the target. (d) within the first quadrant and within 2 inches of the rim.

Answers

Answer:

a) The probability is 0.04

b) The probability is 0.36

c) The pprobability is 0,25

d) The probability is 0.09

Step-by-step explanation:

Lets calculate areas:

the target has a radius of 10 inces, hence the target area has a area on 10²*π = 100π square inches.

a) A circle of 2 inches of radius has an area of 2²π = 4π square inches, hence the probability of hitting that area is 4π/100π = 1/25 = 0.04

b) If the dart s within 2 inches of the rim, then it is not at distance 8 inches from the center (that is the complementary event). The probability for the dart to be at 8 inches of the center is 8²π/100π = 64/100 = 16/25 = 0.64, thus, the probability that the dart is at distance 2 or less from the rim is 1-0.64 = 0.36.

c) The first quadrant has an area exactly 4 times smaller than the area of the target (each quadrant has equal area), thus the probability for the dart to fall there is 1/4 = 0.25

d) If the dart is within 2 inches from the rim (which has probability 0.36 as we previously computed), then it will be equally likely for the dart to be in either of the 4 quadrants (the area that is within 2 inches from the rim forms a ring and it has equal area restricted on each quadrant). Therefore, the probability for the dice to be in the first qudrant and within 2 inches from the rim is 0.36*1/4 = 0.09.

Simplify this expression: 19 – (–8) – (–14) = ?
A. 41
B. –7
C. –3
D. 25

Answers

When you are subtracting a negative, you treat it as if you are adding a positive. So 19-(-8) would be 19 + 8 which is 27. Then do the same thing with the 14, so instead of 27 -(-14) it's 27 + 14 which is 41. So your answer is 41. I hope this helps! XD

The local newspaper has letters to the editor from 60,000 people. If this number represents 25% of all of the newspaper's readers, how many readers does the newspaper have?

Answers

Answer:

15,000 Letters

Step-by-step explanation:

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Choose the correct simplification of the expression (x2y)2. x4y3 x6y6 x4y2 xy4

Answers

Related Questions

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Answers

Answers

f(x) = 2x² + x – 1

Further explanation

D = b² - 4 a c

Option 1 :

Option 2 :

Option 3 :

Option 4 :

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Answer details

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Choose the correct simplification of the expression (x2y)2. x4y3
x6y6
x4y2
xy4