A new health drink has 130% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 45 mg. How many milligrams of the vitamin are in the drink?

Step-by-step explanation:

so, if I understand your text correctly, we need to bring

2 - (x+2)/(x-3) - (x-6)/(x+3)

into a form

(ax + b)/(x² - 9)

what we notice immediately is

(x+3)(x-3) = x² - 9

that makes sense, as we want to transform all terms into fractions with the same denominator.

and the necessary "criss-cross" multiplication leads to (x² -9) as denominator.

so, let's transform every term to a fraction with that denominator, and then we add or subtract them all up as per the original expression.

2 :

multiply by (x²-9)/(x²-9)

2(x²-9)/(x²-9) = (2x²-18)/(x²-9)

(x+2)/(x-3) :

multiply by (x+3)/(x+3)

(x+2)(x+3)/(x²-9) = (x²+3x+2x+6)/(x²-9) =

= (x²+5x+6)/(x²-9)

(x-6)/(x+3) :

multiply by (x-3)/(x-3)

(x-6)(x-3)/(x²-9) = (x²-3x-6x+18)/(x²-9) =

= (x²-9x+18)/(x²-9)

for the whole expression we get then

(2x²-18)/(x²-9) - (x²+5x+6)/(x²-9) - (x²-9x+18)/(x²-9) =

= (2x²-x²-x² -5x+9x -18-6-18)/(x²-9) =

= ( 0 + 4x - 42 )/(x²-9)

a = 4

b = -42

Given, (1, 3), (6,3), (6, 6) and (1, 6) are the vertices of a rectangle, the width is 1 unit shorter.

A rectangle is a quadrilateral with the four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with the four equally long sides. Oblong is occasionally used to describe a rectangle that isn't square. Rectanglen is the symbol for a rectangle having the vertices ABCD. ABCD in PNG.

Rectangulus, a combination of rectus (as an adjective, right, proper), and angulus, is the source of the English word rectangle (angle).

A crossed rectangle is a quadrilateral that is formed by the intersection of two diagonals and the two opposite sides of a rectangle (therefore only two sides are parallel). Although opposite angles are equal, it is a specific example of an antiparallelogram in which the angles are not all right angles and equal. There exist so-called rectangles in other geometries, including spherical, elliptic, and hyperbolic ones, with opposite sides of equal length and equal angles that are not right angles.

Many tiling issues use rectangles, like tiling the plane with rectangles or tiling a rectangle with polygons.

By plotting given points in the coordinate plane,

We get rectangle ABCD having vertices,

A(-1,6), B (3,6), C (3,1), D (-1,1)

By distance formula,

Shorter side or width of rectangle,

AB= [tex]\sqrt{ [3-(-1)]^{2}+ (6-6)^{2}} = \sqrt{4^{2}+0 } = 4 units[/tex]

Longer side or length of rectangle,

BC= [tex]\sqrt{(3-3)^{2}+(1-6)^{2}}=\sqrt{5^{2} } = 5 units[/tex]

The difference between length and width,

BC-AB= 5-4= 1units

Hence, width of rectangle is 1 unit less than the length.

active attachment

To know more about rectangle visit: https://brainly.com/question/15019502

#SPJ9

it is possible to make a triangle with the sides 3, 3 and 9

true

Answer: £900

Step-by-step explanation:

The greatest common factor (GCF) of the given expression 48x^4 and 44x^5 is  4x^4.

Greatest common factor, as the name implies, is greatest among all common factors among the quantities given. We can factorize the quantities in smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could. Those will together compose GCF(Greatest common factor).

To find the GCF of [tex]48x^4[/tex] and [tex]44x^5[/tex]. we have to write the prime factorization of both the terms;

Prime Factorization of   [tex]48x^4[/tex]= 2 × 2 × 2 × 2 × 2 × 2 × x × x × x× x

Prime factorization of  [tex]44x^5[/tex] = 2 × 2 × 11  × x × x × x × x × x

Thus the common factors are 2 × 2x × x × x× x

Therefore The greatest common factor (GCF) of the given expression 48x^4 and 44x^5 is  4x^4.

Learn more about greatest common factor here:

https://brainly.com/question/207329

#SPJ1

Answer:

The answer is x=16

Step-by-step explanation:

63=3x+15

63-15=3x     Put like terms together and subtract

48=3x          

x=48/3        isolate the variable

x=16

Answer:

Given that,

Calvin has three alarm clocks which sound at different intervals.

Clock A goes off every 10 minutes

Clock B every 15 minutes

Clock C every 20 minutes.

To find: the three clocks sound together every _minutes

The three clock sounds together for every least common minutes of the 3 clocks (A,B,C)

To find LCM of 10,15,20.

we get,

LCM of 10,15,20 is 60

Therefore we get that,

The three clock sounds together for every 60 minutes.

Answer is:

The three clock sounds together for every 60 minutes.

The sales director is conducting a experiment study.

There are different types of studies related to researches. The researchers may conduct simply, a survey, more thoroughly, an observational study or an experiment to get more details of things of their research.

An observational study is based on observations and analysis of different comparable situations. A survey is actually a method to study about things directly through personally involving into the situations.

Experiments are mostly used in situations which asks for a solution to certain issue. An experiment is implementing new measures first and then check if it works and get on conclusions about it. Such experiments leads to new inventions.

So here, the sales director conducted an additional training program for the sales representatives to increase the sales in Midwest and Northeast regions.

Then he studied the effectiveness of this implementation by comparing the sales from trained and non-trained representatives.

Thus the sales director conducted an experiment based study here.

Learn more about experimental study at https://brainly.com/question/17274244

#SPJ1

The value that makes the inequality true for the first inequality is x < 4 and x >4 for the second inequality

To solve this problem, we have to solve each of the inequality and find the missing values that holds them true.

For the first inequality,

Let x represent the unknown value

[tex]8 * \frac{x}{4} < 8\\\frac{8x}{4} < 8\\x < 4[/tex]

For the second inequality;

Let x represents the unknown value.

[tex]8 * \frac{x}{4} > 8\\ x > 4[/tex]

In the first inequality, x < 4 and the second inequality, x > 4.

Learn more on inequality here;

https://brainly.com/question/25275758

#SPJ1

Answer:56.52

Step-by-step explanation:

Answer:

X = 8?

Step-by-step explanation:

I'm not sure if I'm correct but I used this solution of since 4x + 1.

Usually if its + something then you subtract it so 33-1 is 32 then

4x= 32

x=8

If I'm wrong, I apologise.

Answer:

its 40

Step-by-step explanation:

200 and 240 have an HCF of 40.

Finding all common factors between two numbers and choosing the biggest one yields the highest common factor (HCF).

So, let's determine factors of 200

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200 are all factors of 200.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240 they are all factors of 240.

now, we will select the highest common factors of 200 and 240.

the highest common factors of 200 and 240 is 40.

Hence, the HCF of 200 and 240 is 40.

To learn more about HCF click at https://brainly.com/question/17240111

The domain of the function in this situation as required in the task content is; Choice C; {0, 1, 2, 3, 4, 5, 6}

It follows from the task content that the domain of the function described by the situation is to be determined.

Since the domain is the set of all possible input values, otherwise termed the independent variable, x.

It follows that since the carton can hold from 0 to 6 books; the domain is; Choice C ; {0, 1, 2, 3, 4, 5, 6}

Please Note: The set of all possible output values of a function, otherwise termed the dependent variable, y is called the Range.

Read more on domain of a function ;

https://brainly.com/question/1369616

#SPJ1

The value of x is either 2 or -7/3.

Given expression:-

(x/x+1)+((x-1)/4)=(11/12)

We have to find the value of x.

The LCM of (x + 1) and 4 is 4(x - 1).

We can write,

[4x + (x + 1)(x - 1)]/4(x + 1) = 11/12

[tex]\frac{4x+x^2-1}{4(x+1)}=\frac{11}{12}[/tex]

We can multiply 4 to the given equation, and get,

[tex]\frac{4x+x^2-1}{(x+1)}=\frac{11}{3}[/tex]

By cross multiplying, we can write,

[tex]12(4x+x^2-1)=11(4(x+1))[/tex]

12x + [tex]3x^2[/tex] -3 = 11x + 11

[tex]3x^2[/tex] + 12x - 11x -3-11 = 0

[tex]3x^2[/tex] + x-14 = 0

Using the middle-term split theorem, we can write,

[tex]3x^2[/tex] + 7x - 6x -14 = 0

x(3x + 7) - 2(3x + 7) = 0

(3x + 7)(x - 2) = 0

x = -7/3, 2.

To learn more about equation, here:-

https://brainly.com/question/10413253

#SPJ1

The graph of g will differ from the graph of f as the graph of g is the graph of f shifted 2 units to the right. Option C

This is further explained below.

A relation between a collection of inputs and one output for each of those inputs is the definition of a function.

A function is a connection between inputs in which each input is associated with precisely one output.

To put it another way, a function is a relationship between inputs. Each function has both a domain and a codomain or range that it operates inside.

Generally, The progression towards

g(x) = f(x -h) +k

depicts a translation with k units added on top and h units added to the right.

Since you have h equal to 0 and k equal to -2, this means that the graph is moved 0 units to the right and 2 units in the opposite direction of up.

The graph of g may be found by shifting f's graph down by two units.

Read more about graph

https://brainly.com/question/17267403

#SPJ1

Answer:

Y=3X-4

Step-by-step explanation:

1. Find the slope using matching (x,y) values. (5,11) and (2,2) for example. (Change in Y)/(Change in X) [tex]\frac{11-2}{5-2}[/tex] = [tex]\frac{9}{3}[/tex] = 3

2. Use the point-slope form to find the equation. Pick a matching (x,y) value. (2,2) for example. and plug it in for Y₁ and X₁ in the equation Y-Y₁=M(X-X₁)

with M as the slope. Y-2=3(X-2).

3. Simplify

Y-2=3X-6

Y=3X-4

Answer:

Answer down below!

Step-by-step explanation:

Let's find a point on the graph that we can start off on

We can use (2,-1)

From there, we can use rise/run to find our answer

We go up 3 and over -2

So, our slope is -3/2 because we cannot simply it any further

Answer:

w > 6

Step-by-step explanation:

48 < 8w

48 ÷ 8 < w

w > 6

I switched the sign if you dont want that you can write 6 < w

Answer:

3

Step-by-step explanation:

Use the slope formula

y2-y1/x2-x1

Answer:x=2(-y+2)

Step-by-step explanation:easy

Answer:

Domain(X-value): {-5,-4,-3,-2,-1,0,1,2,3,4,5}

Range (Y-value): {-2,-1,0,1,2}

Step-by-step explanation:

The domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

a formula for the surface area of the box in terms of only x , the length of one side of the square base is A =  x² + 170368 cm³/x

The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.

Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are

A = 2lh + lw + 2wh

Now for a box of square base, l = w = x.

So, A = 2xh + x² + 2xh

A = x² + 4xh

Since V = x²h and V = 42592 cm³,

h = V/x² = 42592/x²

substituting h into A, we have

A =   x² + 4xh

A =  x² + 4x(42592 cm³/x²)

A =  x² + 4 × 42592 cm³/x

A =  x² + 170368 cm³/x

learn more about of surface area here

https://brainly.com/question/24126177

#SPJ4

The slope of the line is 2 for the equation that is perpendicular.

Slope of the line:

Slope of the line refers the change in y coordinate with respect to the change in x coordinate.

Given,

Here we have the equation 3x + 6y = - 72 that is perpendicular to the line.

Now, we need to find the slope of the line from it.

First we have to convert the given equation of line into standard form,

Then we get,

3x + 6y + 72 = 0

Now we know that the slope of the line for this type of equation is,

m = -a/b

Whlie we compare the equation with the standard form ax + by + c = 0,

Then we get the value of a = 3 and b = 6

Therefore, the slope of the line is

m1 = -3/6

m1 =-1/2

Here we need to find the slope of a line which is perpendicular to the given line.

Through the definition we know that product of two perpendicular line is -1.

So,

m1 x m2 = -1

(-1/2) x m2 = -1

m2 = 2

Therefore, the slope of perpendicular line is 2

To know more about Slope of the line here.

https://brainly.com/question/16180119

#SPJ1

Answer:

y = -1/3x -3.5

Step-by-step explanation:

line interesects y axis at -3.5, distance between dots is down 1 and forward 3

Answer:

Step-by-step explanation:

model2 is times and model on is 432

let's recall that for a synthetic division, or even a long division as well, the dividend and divisor must be in descending order from left-to-right.  Check the picture below.

1/2 + 1/4 =

2/4 + 1/4 = = 3/4 = 0.75