A local grocery store, a 16 ounce bottle of apple juice cost $3.20. What is the cost of the apple juice per ounce?

The answer is (C)

[tex]xy (x + 1), x(x+2)[/tex]

By multiplying x in equation

[tex]y(x^2 + x), x^2 + 2x[/tex]

[tex]y(x^2 + x), x(x+2)[/tex]

All the 4 factors are (x^2 + x), y, x, (x + 2)

So, the LCM is

[tex]xy(x + 1)(x + 2)[/tex]

Final answer:

The LCM of xy(x + 1) and x(x + 2) is found by including the highest powers of all variables and unique factors from both expressions, yielding x²y(x + 1)(x + 2).

Explanation:

The Least Common Multiple (LCM) of two algebraic expressions is the smallest expression that both original expressions can divide into evenly without leaving a remainder. To find the LCM of xy(x + 1) and x(x + 2), we look for the highest power of all the variables and factors included in both expressions.

The factor x appears in both expressions, but with different powers. The highest power of x in the given expressions is x² as seen in the second expression.

The factor y appears only in the first expression, so it must also be included in the LCM.

Next, the factors (x + 1) and (x + 2) are both unique, so they are also included in the LCM.

Therefore, the LCM of xy(x + 1) and x(x + 2) is x²y(x + 1)(x + 2), which corresponds to choice C. Hence, the correct answer is C.xy(x + 1)(x + 2).



The new dimensions are 6.75 inches by 9 inches

The dimensions of the new photo if, Sandra has a photo that is 9 inches by 12 inches, and The scale factor is 3 / 4, is 6.75 inches by 9 inches.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an object.

Given:

Sandra has a photo that is 9 inches by 12 inches,

The scale factor is, s = 3 / 4

Calculate the dimensions of the new photo as shown below,

The length = 9 × 3 / 4

The length = 27 / 4

The length = 6.75 inches,

The width of photo = 12 × 3 / 4

The width of the photo = 36 / 4

The width of the photo = 9 inches

Thus, the dimensions of the new photo will be 6.75 inches by 9 inches.

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2 1/9 divided 2/3 = 19/6 OR 3 1/6

3/5 divided 1 1/4 = 12/25

7 9/16 divided 2 3/4 = 11/4 OR 2 3/4

Answer:

2 1/9 divided 2/3 = 19/6 OR 3 1/6

3/5 divided 1 1/4 = 12/25

7 9/16 divided 2 3/4 = 11/4 OR 2 3/4

Step-by-step explanation:

Multiplication time!

10^6 = 1,000,000

93 × 1,000,000 = 93,000,000

Hope this helps!!!

The volume of the cone can be calculated using fofmula

[tex]V=\dfrac{1}{3}\cdot b\cdot h,[/tex] wher b is the area of the base and h is the hieght.

Multiply the whole equation by 3:

[tex]3V=b\cdot h.[/tex]

Divide this equation by b:

[tex]h=\dfrac{3V}{b}.[/tex]

Answer: [tex]h=\dfrac{3V}{b}.[/tex]

We rearranged the equation v=1/3bh to solve for h, the height of the cone, by first multiplying by 3 to cancel the 1/3 and then dividing by b, resulting in h=3v/b.

The question is asking to Solving for Variable for h in the formula v=1/3bh, where v is the volume of a cone, b is the base area, and h is the height.

To find h, we need to rearrange the equation by first multiplying both sides by 3 to cancel out the 1/3 in front of bh.

So, it becomes 3v=bh.

Then, we divide both sides by b to isolate h, which gives us h=3v/b.

So the height of the cone is h=3v/b.

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Answer:

We can not solve for a unique cost for each soldier.

Step-by-step explanation:

Let x be the daily cost for legionaries and y be the daily cost for archers.  

Upon using our given information we will get a system of linear equations as:

[tex]3x+3y=10...(1)[/tex]

[tex]x+y=3...(2)[/tex]

Now we will solve for x from our 2nd equation,

[tex]x = 3-y[/tex]

Now we will substitute this value in our 1st equation.

[tex]3(3-y)+3y=10[/tex]

[tex]9-3y+3y=10[/tex]

We can see that -3y cancels out with 3y  and 9 is not equal to 10. So this is an unsolvable system. Therefore, we can not find a unique cost for each soldier.

Answer: No solutions

Step-by-step explanation:

Answer:

- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet

- The ball rises by 16 in the first half second, but only 8 feet over the next one

- After it reaches 25 feet in the air, the ball drops

- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

Step-by-step explanation:

Let's rewrite the table:

Time (seconds) Height (feet)

0 0

0.5 16

1 24

1.25 25

1.5 24

2 16

2.5 0

By simply looking at the table, we can see that the following statements are all correct:

- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet

- The ball rises by 16 in the first half second, but only 8 feet over the next one

- After it reaches 25 feet in the air, the ball drops

- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

Answer: width = 30 m, length = 150 is one possible answer

Step-by-step explanation:

P = 2L + 2w                            A = L x w

  = 2(65) + 2(115)                       = 65 x 115

  = 130 + 230                            = 7,475

  = 360

360 ÷ 2 = 180

Find 2 numbers whose sum equals 180 and product is less than 7475

Sum: L + w = 180   ⇒   w = 180 - L

Product: Lw < 7475

Graph these 2 equations to see which coordinates of the sum fall into the shaded region of the product.

The truth value for the following conditional i.e., conjunction statement P is false and Q is true is False.

Answer:

Step-by-step explanation:

This conditional statement:

Has a truth value of true if:

And has a truth value of false, if

Then, for this statements:

As both p and q are true, then, this statement is true.

As p is true and q is false, this statement is false.

As p is false, this statement is true, no matter the truth value of q.

∼p its the negation of p. if p is true, then ∼p is false. And this statement is true, no matter the truth value of q.

Set the polynomial equal to each other.

x2 - 2x - 5 = x3 - 2x2 - 5x - 9

Move all the terms to the right side of the equation to make the left side equal to zero.

0 = x3 - 3x2 - 3x - 4

Now we use synthetic division to factor.

4 |  1       -3        -3           -4

                4         4             4

___________________________

       1       1          1            0

0 = (x - 4)(x2 + x + 1)

Now you can set the factors equal to zero and solve for x.   Since the quadratic factor has no real solutions, we ignore and focus on the linear factor. x = 4

Evaluate any of the function when x=4 to get the y-coordinate of the intersection point.

Answer:

The answer is 0.8 so A

Step-by-step explanation:

positive correlation

plz rate me

Answer:

Hello! I believe that this will help you find the line best fit.  

Step-by-step explanation:

Remember, for it to be a line best fit, you must find the two points that you think will be on the "line best fit".

Perimeter (P) = 2L + 2w

68 = 2L + 2w

68 - 2L = 2w

2(34 - L) = 2(w)

34 - L = w

********************                                

Area (A) = L * w

     240 = L (34 - L)

     240 = 34L - L²

L² - 34L + 240 = 0

(L - 10)(L - 24) = 0

L = 10  or  L = 24

w = 34 - L   = 34 - 10   = 24      or      w = 34 - 24   = 10

Answer: width = 10, length = 24  assuming length is bigger than the width

Perimeter (P) = 2L + 2w

68 = 2L + 2w

68 - 2L = 2w

2(34 - L) = 2(w)

34 - L = w

********************                                

Area (A) = L * w

     240 = L (34 - L)

     240 = 34L - L²

L² - 34L + 240 = 0

(L - 10)(L - 24) = 0

L = 10  or  L = 24

w = 34 - L   = 34 - 10   = 24      or      w = 34 - 24   = 10

Answer: width = 10, length = 24   assuming length is bigger than the width

3 × 4 × 3 - 2 × 4²

36 - 2 × 4²

36 - 2 × 16

36 - 32

The answer is 4

Is that right? I hoped it helped...

Answer:

The solution in the attached figure

Step-by-step explanation:

we have

[tex]50q+43 > -11q+70[/tex]

Solve for q

Adds 11 q both sides

[tex]50q+43 +11q > 70[/tex]

[tex]61q+43 > 70[/tex]

Subtract 43 both sides

[tex]61q > 70-43[/tex]

[tex]61q > 27[/tex]

Divide by 61 both sides

[tex]q > \frac{27}{61}[/tex]

The solution is the interval ------> (27/61,∞)

All real numbers greater than 27/61

In a number line the solution is the shaded area at right of 27/61 (open circle)

The answer is C) 2h + 1

First i factored out the negative sign, then i split the second term into two terms, then i factored out the common terms and i got -(h + 7) (2h + 1).

Answer:

One of the factor is (2h+1)

Step-by-step explanation:

[tex]-2h^2-15h-7[/tex]

Take out negative sign in common

[tex]-(2h^2+15h+7)[/tex]

Now factor the parenthesis

To factor this , we find out two factors whose product is 14 and sum is 15

[tex]-(2h^2+h+14h+7)[/tex]

Break first two terms and last two terms

[tex]-(2h^2+h)+(14h+7)[/tex]

[tex]-h(2h+1)+7(2h+1)[/tex]

[tex](-h+7)(2h+1)[/tex]

[tex](7-h)(2h+1)[/tex]

One of the factor is (2h+1)

If 8 of the picks are orange, then 6 of the picks will be green

Vertical angles are opposite each other when two lines intersect and are equal. Linear pairs of angles are adjacent angles that form a straight line and their sum is always 180 degrees. The difference lies both in their position and their angle sum.

So, in sum, the difference lies in their positioning (vertical angles are opposite, linear pair angles are adjacent) and in their sum (vertical angles are equal, linear pair angles sum to 180 degrees).

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Answer:

As per the given condition:  Rodrigo has a ladder that is 13 ft long. The ladder is leaned against a vertical wall. The top of the ladder is 10.8 ft above the ground.

The Orientation of the ladder with the wall forms a right triangle.  

The ladder length is the hypotenuse of the triangle,

the distance between the ladder at ground level and the base of the wall is the horizontal leg of the triangle,

and the height of the ladder is the vertical leg of the triangle.

⇒ Height of the ladder = 10.8 ft and hypotenuse = 13 ft

Using sine ratio formula;

[tex]\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse side}}[/tex]

Opposite side = height of the ladder = 10.8 ft and

Hypotenuse side = 13 ft.

then;

[tex]\sin \theta = \frac{10.8}{13} =0.830769230769[/tex]

or

[tex]\theta = \sin^{-1}(0.830769230769)[/tex]

Simplify:

[tex]\theta = 56.2^{\circ}[/tex] (nearest to tenth place)

Since, it is given that the angle the ladder makes with the ground needs to be 60 degree or less for safety purposes.

(a)

Yes, this ladder in a safe position.

as [tex]\theta = 56.2^{\circ} < 60^{\circ}[/tex]

(b)

You can see the diagram as shown below in the attachment.

In order to better find the points on this graph, we need to convert it from standard form to slope-intercept.

We can do that by solving for y.

-7y + 8 = 21x - 6

Subtract 8 from both sides.

-7y = 21x - 14

Divide both sides by -7

y = -3x + 2

Now that the equation is in slope-intercept, we can find two points on the line.

We know that (0, 2) will be the first point, because 2 is the y-intercept.

We can plug 1 into the x value of the equation to find the corresponding y value.

y = -3(1) + 2

y = -3 + 2

y = -1

The second point is (1, -1)

It's the linear function.

The slope-intercept form: y = mx + b.

-7y + 8 = 21x - 6      subtract 8 from both sides

-7y = 21x - 14     divide both sides by (-7)

y = -3x + 2

We need only two points:

for x = 0 → y = -3(0) + 2 = 0 + 2 = 2 → (0, 2)

for x = 2 → y = -3(2) + 2 = -6 + 2 = -4 → (2, -4)

Answer:

12 total picks, 4 green and 8 orange

Step-by-step explanation:

green(g)=4

orange(O)=2g

since g=4,

O=2(4)

O=8

8+4=12

C. 26 degrees Celsius

Answer:

The temperature on the thermometer is 26°C

Step-by-step explanation:

The image is very clear.

To answer this question you need to know the scale of the thermometer.

As between 20 and 30 there are 5 "spaces" (four lines) , we should divide

10 (the difference between 30 and 20) by 5.

10/5= 2

So each line means 2 °C

As there are 3 lines painted in red after 20, the answer is:

20+3*2= 26°C

Answer: D

Step-by-step explanation:

   y = x² - 8x + 5

  -5                -5

y - 5 = x² - 8x           complete the square by adding [tex](\frac{-8}{2})^{2}[/tex] to both sides

y - 5 + 16 =  x² - 8x + 16      the right side is a perfect square:  (x - 4)²

y + 11 = (x - 4)²

    -11            -11

y        = (x - 4)² - 11

To solve this, you first have to find the number of yards in one mile.

If three feet = 1 yard, and 5280 ft = 1 mile, all you have to do to find the number of yards in a mile is divide 5280 feet by 3 feet.

You end up with 1760 yards in 1 mile.

To find the number of yards in 2 miles, all you would have to do is multiply 1760 by 2

To convert 2 miles into yards, first change miles to feet (2 miles * 5,280 feet/mile = 10,560 feet). Then, convert feet to yards (10,560 feet ÷ 3 feet/yard = 3,520 yards). So, 2 miles is equal to 3,520 yards. therefore, option b is correct

To calculate the number of yards in 2 miles, we must first know the relationship between miles, feet, and yards. As the question mentioned, 1 mile = 5,280 feet and 1 yard = 3 feet.

So the first step is to convert 2 miles into feet: 2 miles * 5,280 feet/mile = 10,560 feet.

The second step is to convert feet into yards: 10,560 feet ÷ 3 feet/yard = 3,520 yards.

Therefore, there are 3,520 yards in 2 miles.

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Tony and Mike, factored the trinomial [tex]8x^2 - 12x - 8[/tex]

Tony factored it as 4(x - 2)(2x + 1) and

Mike factored it as (x - 2)(8x + 4)

[tex]8x^2 - 12x - 8[/tex]

GCF is 4. We factor out 4

[tex]4(2x^2 - 3x - 2)[/tex]

2*-2=-4. We find out two factors whose product is -4  and sum is -3

two factors are -4  and 1. Split middle term -3x using two factors

[tex]4(2x^2 - 4x + 1x - 2)[/tex]

Group first two terms and last two terms

[tex]4[(2x^2 - 4x) + (1x - 2)][/tex]

Factor out GCF from each group

[tex]4[2x(x - 2) + 1(x - 2)[/tex]

4(2x+1)(x-2)

Tony factored it correctly

Mike factored it as (x − 2)(8x + 4)

Mike factor 8x+4 further. GCF of 8 and 4 is 4

So it becomes 4(2x+1)

Mike not factored it completely

note that +(-) is equivalent to -

thus the equation can be written as

n - 11 = 24 ( add 11 to both sides )

n = 24 + 11 = 35