Solve the system of equations in three variables

Answer: Full price of Drug Y = $98.793

Step-by-step explanation:

Cost of 500 tablet = $425

28% markup = 425 * 28/100

= $119

Cost + markup = $425 + $119 = $544

Cost + markup + dispensing fee = $544 + $4.85 = $548.85

Full price of 500 tablet = $548.85

Full price of 1 tablet = $548.85/500

=$1.0977

Full price of 90 tablet = $1.0977 * 90

= $98.793

6x+y=4x+11

y=4x+11-6x

y=-2x+11

[tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.

To rearrange the equation [tex]\(6x + y = 4x + 11\)[/tex] so that (x\) is the independent variable and (y) is dependent, we need to isolate (y) on one side of the equation.

Start with the given equation: [tex]\(6x + y = 4x + 11\)[/tex].

Subtract (4x) from both sides to move all terms involving (y) to one side: [tex]\(6x - 4x + y = 11\).[/tex]

Simplify the left side by combining like terms: 2x + y = 11.

To isolate y, subtract 2x from both sides: 2x + y - 2x = 11 - 2x.

Simplify: [tex]\(y = 11 - 2x\)[/tex].

So, the rearranged equation with (x) as the independent variable is y = 11 - 2x.

Detailed calculation:

Starting equation: (6x + y = 4x + 11)

Subtract (4x) from both sides:

[tex]\(6x - 4x + y = 4x - 4x + 11\)[/tex]

[tex]\(2x + y = 11\)[/tex]

Subtract (2x) from both sides:

[tex]\(2x + y - 2x = 11 - 2x\)[/tex]

[tex]\(y = 11 - 2x\)[/tex]

Therefore, [tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.

Answer:

35 percent

Step-by-step explanation:

To solve this problem we multiply the amount by the percent and add them up to get the total amount times the percent

amount * percent + amount * percent = total amount * percent

4  * .20 + 12  * .40 = (4+12) * x

.8 + 4.8 = 16 x

Combine like terms

5.6 = 16x

Divide by 16

5.6/16 = 16x/16

.35 =x

35 percent

Answer:

$9,936.47

Step-by-step explanation:

Similarly to the other problem I helped you with we have:

[tex]A_{final}=A_{initial}(1+r)^t[/tex]

Where A is amount, r is rate and t is time.

In this case A=12000, r=9%=0.09 and 9% in decimals is 0.09 (9÷100=0.09), and t=7 since 2025 -2018 = 7 years. So how much is this investment worth in 7 years? Let's plug those values in and we obtain:

[tex]A_{final}=12000(1+0.09)^7=12000(1.09)^7=21936.47[/tex]

So the investment will be worth $21,936.47.  Now we must calculate how much more will this precious mineral be worth so we get the difference of the final amount and the initial amount the mineral was worth and so:

[tex]A_{final}-A_{initial}=21936.47-12000=9936.47[/tex]

And so the mineral will be worth $9,936.47 more than it originally was worth after 7 years.

Answer:

A triangle with angles less than 90°

Step-by-step explanation:

An acute triangle is a triangle where all its interior angles are less than 90 degrees, distinguishing it from other types of triangles.

In mathematics, an acute triangle is a type of triangle where all three of its interior angles are less than 90 degrees. This is what distinguishes it from other types of triangles such as right triangles, which have one angle of exactly 90 degrees, or obtuse triangles, where one angle is larger than 90 degrees. For example, a triangle with angles of 30, 60, and 90 degrees would be considered an acute triangle because all the angles are less than 90 degrees.

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Answer:

15 4/9 inches long

Step-by-step explanation:

5 4/9 × 3

When lining them vertically the 3 ends up under 5 in which you multiply and transfer the 4/9 next to the product of 15. Hope that helped!

The king size chocolate bar is three times as long as the regular bar, so given that the regular bar is 5 4/9 inches long, the king size bar is 16 1/3 inches long.

The problem involves a regular size chocolate bar that is 5 4/9 inches long and a king size bar that is three times as long. Given the length of the regular bar, our objective is to find out how long the king size bar is.

We start by converting the mixed number 5 4/9 into an improper fraction which gives us 49/9 inches. We then multiply 49/9 by 3 to get the length of the king size bar which is 147/9 inches. Converting this improper fraction back into a mixed number, we get 16 1/3 inches. Therefore, the king size bar is 16 1/3 inches long.

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Answer:

x^2=12y

**C on edge

The equation of a parabola with its vertex at (0,0) and directrix at y=-3 is y = 1/12 x².

To write the equation of a parabola, we are given that its vertex is at (0,0) and its directrix is y=-3. The equation of a parabola with the vertex at (0,0) and the focus at (0,p) or a directrix at y=-p is given as y = 1/4p x². Considering the distance from the vertex to the directrix is the same as the distance from the vertex to the focus, the value of p in this case will be 3. Therefore, the equation of this parabola is y = 1/12 x².

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Answer:

6400 people.

Step-by-step explanation:

If 640 is 10%. You multiply 640 by 10 to get 6400 or 100% of the people.

Answer:

$192.20

Step-by-step explanation:

8 x 5=40  48.32x40=192.20                                                                                                          

Answer:

You will make $1929.20 this summer.

Step-by-step explanation:

You have just accepted a jab at Wonders Day Camp for the summer.

The camp will pay for each day for 8 weeks = $48.23

You work 5 days each week.

So total days of work = 8 × 5 = 40 days

You earn $48.23 for one day.

For 40 days you will earn = 40 × 48.23 = $1,929.20

You will make $1929.20 this summer.

[tex]\dfrac{b}{2q}=h+7\qquad\text{multiply both sides by 2q}\neq0\\\\b=2q(h+7)\qquad\text{use distributive property}\\\\b=(2q)(h)+(2q)(7)\\\\\boxed{b=2hq+14q}[/tex]

Johnny needs to buy an amount of small bags of flour at the store for making cookies. One bag of flour is $7.50. Y represents the amount of bags he buys.

At the checkout, the cashier asks if he wants to donate 9 dollars to charity, and he says yes.

How much money did Johnny spend?

Answer:

(x - 2)² + (y + 8)² = 121

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (2, - 8) and r = 11, hence

(x - 2)² + (y + 8)² = 121

The equation [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex] represents a circle with a center at (2, -8) and a radius of 11. This is derived from the general circle equation [tex]\((x - h)^2 + (y - k)^2 = r^2\).[/tex]

The correct equation representing a circle with a center at (2, -8) and a radius of 11 is option (b) [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex].

The general equation of a circle is [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], where (h, k) is the center and r is the radius.

In option (b), [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex], the values match the given center (2, -8) and radius of 11. The squared terms with (x-2) and (y+8) are in the correct form, and the radius squared [tex](\(11^2 = 121\))[/tex] is on the right side.

Options (a), (c), and (d) do not represent the given circle because they have incorrect signs, centers, or radius values. Therefore, the correct equation is option (b).

Answer: hope this helps. it's 130.

Answer:

a and e

Step-by-step explanation:

Answer:

Length = 6 cm and width = 4 cm.

Step-by-step explanation:

Let the width be x, then the length is x + 2 cm and its area = x(x + 2).

The new width and length are x + 4 and x + 6, and the new area is

(x + 4)(x + 6).

So we have the equation:-

(x + 6)(x + 4) = x(x + 2) + 56

x^2 + 10x + 24 = x^2 + 2x + 56

10x - 2x = 56 - 24

8x = 32

x = 4 cm = width

and length = 4 + 2 = 6 cm

Answer:

There are four different possible outcomes: both coins are heads, the red coin is heads and the blue coin is tails, the red coin is tails and the blue coin is heads, or both coins are tails. Each outcome has equal probability. So the probability of both being heads is 1/4.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

if you reduce 2/4 and divid both sides by  u get 1/2

and 1/2 = 1/2

Answer:

Plug in x=0 and plot the point, then plug in y = 0 and plot the point.

Answer:

y=-2x+8

Step-by-step explanation:

first you have to -18x on both sides because you want to get y by itself

9y=-18x+72

then divide 9 by both sides

9y/9=-18x+72/9.....-18/9=-2 and 72/9=8

y=-2x+8

-2x is your slope and 8 is your y intercept

Answer: x = -11   ∠FGK = 30°   ∠KGH = 150°

Step-by-step explanation:

∠FGK + ∠KGH = ∠FGH    Segment Addition Postulate

x + 41 + x + 161 = 180       Substitution

2x + 202 = 180                 Simplify (added like terms)

2x = -22                            Subtraction Property of Equality

x = -11                               Division Property of Equality

∠FGK = x + 41     = (-11) + 41    = 30

∠KGH = x + 161   = (-11) + 161   = 150

Answer:

B

Step-by-step explanation:

There isn't any number that x can't be. Start with a graph to show how this could be so.

It is easy to see that x > 0 gives a line that goes very near the x axis. It is not quite so easy to see that it never touches the x axis. But if you recreate the graph in  Desmos, you will see that is true if you spread the x's out.

It is not quite so easy to see that when x<0 the graph tips upward very quickly but again if you move the values of the axis around you will see there is no value that x cannot be.

Answer:

B:All real numbers

B. 72 + 78 + 70 + x > 289

Answer:

(-4.0,-6.2) and (0.6,5)

Step-by-step explanation:

We have been given the system of equations

[tex]

2.4x-y=-3.5........(1)\\x^2+x+y=6 .....(2)[/tex]

Let us graph these equation on the xy-plane.

The intersection point of these two curves will give us the solution of the system of equations.

Equation 1 represents a parabola and equation (2) represents a straight line.

The graph is shown in the attached file.

The intersection points of the parabola and the line are (0.622,4.992) and (-4.022, -6.152)

Therefore, the solutions rounded to nearest tenth are

(-4.0,-6.2) and (0.6,5)

Answer:

B.  (–4, –6.2) and (0.6, 5)

Step-by-step explanation:

Hope this helps!! Have a great day!!   : )

Answer:

x = 10

Step-by-step explanation:

the area of a square = s² ( s is the side length )

s² = (4x + 3)² ( take the square root of both sides )

s = [tex]\sqrt{(4x+3)^2}[/tex] = 4x + 3

perimeter = 4s = 172, that is

4(4x + 3) = 172 ( distribute left side )

16x + 12 = 172 ( subtract 12 from both sides )

16x = 160 ( divide both sides by 16 )

x = 10

Answer

The answer is C=(4,2). Let me know if you need an explanation.

Step-by-step explanation:

Answer:

D[tex]_o[/tex] of Y = (-3/2, -1)

Step-by-step explanation:

We are given three points on the graph:

X (4, 0)

Y (3, 2)

Z (2, 2)

and the scale factor of dilation which is [tex]-\frac{1}{2}[/tex].

Given that, we are to find the coordinates of Y after dilation. To find that, we will multiply the coordinates of the point Y with the scale factor.

Y =  [tex](-\frac{1}{2}[/tex] × [tex]3[/tex] , (-\frac{1}{2}[/tex] × [tex]2)[/tex]

Y = [tex](-\frac{3}{2} , -1)[/tex]

Answer:

l = 2.5 feet

Step-by-step explanation:

A = lb

8.5 = l * 3 2/5

8.5 = l * 3.4

l = 8.5 / 3.4

l = 2.5 feet (Always remember to put the units, otherwise you may not get points.)

Please give a rating and a thanks.

Thank you.

Answer:

l = 2 1/2 ft

Step-by-step explanation:

Area is given by the formula

A = l*w

We know the area is 8 1/2  

Changing this to an improper fraction  8 1/2 = (2*8 +1)/2 = 17/2

The width is 3 2/5  as an improper fraction  = (5*3+2)/5 = 17/5

A = l*w

17/2 = l* 17/5

Multiply each side by 5/17

17/2 * 5/17 = l* 17/5 * 5/17

5/2 = l

2 1/2 = l

Answer:

y = 15x + 85

Step-by-step explanation:

Let:

x = amount of months ; y = total amount

The constant is 85, meaning that this number will not change (for he would have at least 85 no matter how much time has passed).

15 is next to a variable, for depending on the amount of time passed, you will add a certain amount of "15" to the answer.

y is your total, and is also a variable, because it also depends on the amount of time that passes.

~

[tex]\left\{\begin{array}{ccc}2x+y=1&|\text{subtract 2x from both sides}\\4x+2y=-1\end{array}\right\\\\\left\{\begin{array}{ccc}y=-2x+1&(*)\\4x+2y=-1&(**)\end{array}\right\\\\\text{substitute}\ (*)\ \text{to}\ (**):\\\\4x+2(-2x+1)=-1\qquad\text{use distributive property}\\\\4x+(2)(-2x)+(2)(1)=-1\\\\4x-4x+2=-1\\\\2=-1\qquad\text{FALSE}\\\\Answer:\ \boxed{NO\ SOLUTION}[/tex]

none of the above

This question wants you to see that the radical can be simplified because it is ...

[tex]f(x)=\sqrt{(x+6)^2}[/tex]

The answer choices show you are expected to simplify this to ...

... f(x) = x +6

Then

... f(x)·g(x) = (x+6)(x³ -12) = x⁴ +6x³ -12x -72 . . . . . matches choice C

_____

However,

... f(x) = |x+6| . . . . . . . √(x^2) = |x|, the positive root regardless of sign of x

so the product f(x)·g(x) only matches selection C for x≥ -6. It matches the opposite of selection C for x ≤ -6.

The attached graph shows this. It graphs f(x), g(x), f(x)·g(x) (as a purple curve), and selection C (as orange dots).