A pharmacy claims that the average medication costs $32 but it could differ as much as $8. Write and solve an absolute value inequality to determine the range of medication costs at this pharmacy.

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf y+2=\cfrac{1}{2}(x-4)\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( y+2 \right)=2\left( \cfrac{1}{2}(x-4) \right)}\implies 2y+4=2(x-4) \\\\\\ 2y+4=2x-8\implies 2y=4x-12\implies -4x+2y=-12\implies 4x-2y=12[/tex]

Answer:A

Step-by-step explanation:

Y varies directly as x

Y = kx

When y = 2.5, x = 5

Substitute the value of y and x

2.5 = k * 5

Make k the subject of the formula

k = 2.5/5

k = 1/2

:. The equation connectin y and x is

Y = 1/2x

When x = 10

Y = 1/2*10

Y = 10/2

Y = 5

Answer:

127%

Step-by-step explanation:

All you have to do is multiply both numerator and denominator by 100.

Hello There!

1.27 to a percent would be 127%

"Percent" means "per 100" or "over 100". So, to convert 1.27 to percent we rewrite 1.27 in terms of "per 100" or over 100.

Multiply 1.27 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.

Therefore, we have shown that

1.27 = 127%

Answer:

1.) 8 = 8

2.) -12 = -12

3.) -3y² = -3y²

4.) 6x² + 36x = 6x(x + 6)

5.) 7x - 14x² = 7x(1 - 2x)

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Answer:

The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.

Step-by-step explanation:

1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

6x - 5y = 8

y = 8 - 6x

        -5

Step 2 : Substitute y in terms of x from step 1 in the second equation.

16x - 6y = 22

16x - 6 (8 - 6x) = 22

              -5

80x - 48 + 36x = 22 x -5

94x = 43

x = 0.457

This statement is incorrect as it does have a solution.

2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

7x + 2y = 6

y = 6 - 7x

        2

Step 2 : Substitute y in terms of x from step 1 in the second equation.

14x + 4y = 16

14x + 4(6 - 7x) = 16

              2

14x + 12 - 14x = 16

0 ≠ 4

This statement is not true as there are no solutions.

3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

8x - 3y = 10

x = 10 + 3y

        8

Step 2 : Substitute x in terms of y from step 1 in the second equation.

16x - 6y = 22

16(10 + 3y) - 6y = 22

       8

20 + 6y - 6y = 2

0 ≠ -18

This statement is true because there are no solutions

4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

9x + 6y = 14

x = 14 - 6y

        9

Step 2 : Substitute x in terms of y from step 1 in the second equation.

18x + 12y = 26

18 (14 - 6y) + 12y = 26

        9

8 - 12y + 12y = 26

0 ≠ 18

This statement is incorrect because there are no solutions. It does not have infinite number of solutions.

!!

Answer:

Step-by-step explanation:

The true statement is the third one, because that system of equations has no solutions. This is because those lines are parallel, see image attached.

We can demonstrate this by solving the system:

[tex]\left \{ {{8x-3y=10} \atop {16x-6y=22}} \right.[/tex]

If we multiply the first equation by -2, we would have

[tex]\left \{ {{-16x+6y=-20} \atop {16x-6y=22}} \right\\0x+0y=2\\0=2[/tex]

When this happens, means that the system has no solution, that is, the lines that represents those linear equations, are parallel.

Therefore, the right answer is the third option.

The smallest possible value for the sum of the squares of two numbers differing by 1 is 0.5. This is obtained by setting one number as x and the other as x + 1, and then minimizing the function f(x) = x² + (x + 1)².

The difference of two numbers is 1 implies that if we set one number as x, then the other would be x + 1. To find the smallest possible value for the sum of their squares, you need to minimize the function f(x) = x² + (x + 1)².

Completing the square, this simplifies to 2(x² + 1)². Setting the derivative of this expression, 4x(x² + 1), equal to zero and solving for x, we obtain x = 0 or x = -1. Testing these values within the function f(x), we find that the minimum value is when x = -0.5 and x + 1 = 0.5 and the sum of their squares equals 0.5.

Although one can handle an equation containing an unknown square which produces two solutions, in this problem, the meaningful solution is that the smallest possible value for the sum of their squares is 0.5.

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Answer:

32

Step-by-step explanation:

Plug in 4 for c.

(c³)/2 = (4³)/2

First, solve the parenthesis, then divide. Multiply:

4³ = 4 * 4 * 4 = 16 * 4 = 64

Next, divide:

64/2 = 32

32 is your answer.

~

Answer:

1.5

Step-by-step explanation:

m=80-65/84-74

=15/10

1.5

*Since this is an application problem, we can use decimals.*

Answer:

The slope of the line is 1.5

Step-by-step explanation:

To know the slope of a line we can have the equation or to know points of the line. In this case from the graph we have to points (84,80) and (74,65). Having this and using the equation to calculate the slope, we have:

[tex]m=\frac{y2-y1}{x2-x1} \\[/tex]

Defining:

[tex](x1=84,y1=80)[/tex] and [tex](x2=74,y2=65)[/tex]

Now using the equation:

[tex]m=\frac{65-80}{74-84}[/tex]

[tex]m=\frac{-15}{-10} \\m=\frac{15}{10} =1.5[/tex]

The slope of the line is 1.5

Answer:

m = -6

Step-by-step explanation:

Put this given equation into slope-intercept form:

y−15=−6(x+7)  becomes y - 15 = -6x - 42.

Adding 15 to both sides results in y = -6x - 27,

and so the slope is -6.  The y-intercept is -27, or (0, -27).

Answer:

slope m = -6

Step-by-step explanation:

y−15=−6(x+7)

y =−6(x+7) + 15

y =−6x +7(-6) + 15

y =−6x -42 + 15

y =−6x - 27

THis is in slope intercept form where slope m = -6

[tex]x- 13 =25\\x=38[/tex]

Answer:

[tex]x = 38[/tex]

Step-by-step explanation:

We have the following equation

[tex]x- 13 =25[/tex]

We must solve the equation for the variable x

Add 13 on both sides of the equation

[tex]x- 13 +13 =25+ 13[/tex]

[tex]x=25+ 13[/tex]

[tex]x=38[/tex]

So the solution to the equation is [tex]x = 38[/tex]

Answer:

x = 3

Step-by-step explanation:

Given

7x - 4 = 2x + 11 ( subtract 2x from both sides )

5x - 4 = 11 ( add 4 to both sides )

5x = 15 ( divide both sides by 5 )

x = 3

Answer:

$16.75

Step-by-step explanation:

$25×.33=$8.25

$25-$8.25=$16.75

Answer:

77 inches

Step-by-step explanation:

1 foot=12 inches so what you have to do is 12x6=72 and since he is 6 foot 5 inches you add 5 to get 77.

Please mark brainliest and have a great day!

Answer:

8^5

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

10-7=3

2*3=6

Answer:

6

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

[tex]2(10-b)[/tex]

[tex]2(10-7)[/tex]

First, do parenthesis.

[tex]2(10-7)[/tex]

[tex]10-7=3[/tex]

[tex]2(3)[/tex]

Then, multiply to find the answer.

[tex]2*3=6[/tex]

6 is the correct answer.

Answer:

3.10 * 72

Step-by-step explanation:

To find 310% of 72

Of means multiply and is means equal

310% * 72 = answer

Change to decimal form

3.10 * 72 = answer

223.20

Answer: (3.10)(72) is the correct answer

Step-by-step explanation:

Answer:

f(x) = x

Step-by-step explanation:

note : slope is positive 1, so the x term must be positive

also note the graph intersects the curve at y = 0, which means that they y-intercept is zero .

if we substitute this into the general equation for a line

y = mx + b, where m = +1 and b = 0,

we get y = x

or f(x) = x (in function form)

Answer:

36π cubic inches

Step-by-step explanation:

Volume of sphere:

V = 4/3 πr^3

Given: r = 3 in.

Plug in

V = 4/3 π (3^3)

V = 4/3 π (27)

V = 36 π

Answer

36π cubic inches

Answer with explanation:

 Radius of the Sphere (r)= 3 inches

Volume of the sphere

                  [tex]=\frac{4*\pi *r^3}{3}\\\\\rightarrow \frac{4*\pi *3^3}{3}\\\\\rightarrow 4*\pi *3^2\\\\=36\pi \text{Cubic inches}[/tex]  

→→→Option B: 36 π Cubic inches          

Answer:

[tex]\boxed{2.7 \times 10^{3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}}[/tex]

1. Divide the coefficients and the exponentials separately

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}} = \dfrac{4}{1.5} \times \dfrac{10^{9}}{10^{6}}[/tex]

2. Divide the coefficients

[tex]\dfrac{4}{1.5} \approx 2.7[/tex]

3. Divide the exponential terms

Subtract the exponent in the denominator from the exponent in the numerator.

[tex]\dfrac{10^{9}}{10^{6}} = 10^{(9 - 6)} = 10 ^{3}[/tex]

4. Rejoin the new coefficient and the new exponential

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}} \approx \boxed{\mathbf{2.7 \times 10^{3}}}[/tex]

Answer:

2.7 x 10(3)

Step-by-step explanation:

The probability of getting heads on a coin toss is 1/2

The probability of getting an even number rolling a number cube is 1/2 ( 3 even numbers out of 6 total numbers).

To find the probability of both happening, multiply each probability by each other:

1/2 x 1/2 = 1/4

Answer:

The length is 39.6 feet.

Step-by-step explanation:

Since the area is lw, we make this an equation. The width is already known, it's 26.2. So make a single variable equation: 26.2w=1037.52

dividing both sides by 26.2 gives you the answer of 39.6.

Hope this helps!

We know that - Area of a Rectangle is given by : Length × Width

Here : Length = u  and  Width = 26.2 ft

Given : Area of the Rectangle = 1037.52 ft²

[tex]:\implies[/tex]  u × 26.2 = 1037.52

[tex]\mathsf{\implies u = \dfrac{1037.52}{26.2}}[/tex]

[tex]:\implies[/tex]  u = 39.6 ft

Answer: 348 kiwis.

Step-by-step explanation:

You need to analize the information provided in the exercise.

First: You know that you can put 6 trays in crates.

Second: Each one of these trays holds 58 kiwis.

Therefore, in order to calculate the number of kiwis that the crates contain when it is full, you need to multiply the total number of trays you can put in crates by the number of kiwis each tray can hold.

Then:

[tex]number\ of\ kiwis=(6)(58\ kiwis)\\\\number\ of\ kiwis=348\ kiwis[/tex]

Answer:

10°

Step-by-step explanation:

i did it in my brain maybe not the best but can help u 75°(180°-115°)+4k+5°+6k+10°=180

Answer:

k=10

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of the opposite interior angles

115 = 4k+5 + (6k+10)

Combine like terms

115 = 10k +15

Subtract 15 from each side

115-15 =10k+15-15

100 = 10k

Divide by 10

100/10= 10k/10

10 =k

Answer:

The first answer :)

Step-by-step explanation:

That is because N represents the amount of hours that the other person studied.

Answer:

The equation is y = 15(2)^x , the graph is X

Step-by-step explanation:

* Lets talk about the exponential graph

- The form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

 b ≠ 1, and x is any real number

- It has a constant base b

- It has a variable exponent x

- The constant a is the beginning value

* Lets solve the problem

- The sample containing 15 cells

∴ a = 15

- The cells double with each cycle ⇒ means × 2 each cycle

∴ b = 2

- x is the number of cycles

- y is the number of cells

∴ The equation is y = 15(2)^x

- From the graphs the answer could be X or Y

* To know which one substitute the values of x to find the value of y

# Figure X

∵ y = 15(2)^x

∵ x = 0

∴ y = 15(2)^0

∵ (2)^0 = 1 ⇒ any number to the power of 0 = 1 except the zero

∴ y = 15(1) = 15

∵ x = 1

∴ y = 15(2)^1 = 15(2) 30

- The graph has y = 30 when x = 1

# In the Figure Y the value of y not equal 30 at x = 1

∴ The answer is graph X

* The equation is y = 15(2)^x , the graph is X

Final answer:

The number of cells after each cycle of mitosis can be represented by an exponential growth model with the equation N = 15 × 2ⁿ. Graphically, this will be a rapidly ascending curve, starting with 15 cells at cycle 0 and doubling each cycle.

Explanation:

The question is asking us to determine the number of cells after each cycle of mitosis given an initial count of 15 cells. When a cell undergoes mitosis, it produces two genetically identical daughter cells, effectively doubling the number of cells with each cycle. To represent the number of cells after each cycle, we will need to use an exponential growth model as each cell division results in doubling the number of cells present.

The general equation representing the growth of cells through mitosis is given by N = N0 × 2ⁿ, where N is the number of cells after n cycles, N0 is the initial number of cells, and n is the number of cycles of mitosis. For the given initial condition of 15 cells (N0 = 15), the equation becomes N = 15 × 2ⁿ.

The corresponding graph to this equation would show a curve that rises sharply upward, reflecting the exponential increase in the number of cells after each cycle. The graph starts at 15 cells when n = 0 (no cycles have occurred) and doubles with each subsequent cycle.

Answer:

x =5

Step-by-step explanation:

3.1x−16.3=−0.8

Add 16.3 to each side

3.1x−16.3+16.3=−0.8+16.3

3.1x = 15.5

Divide each side by 3.1

3.1x = 15.5/3.1

x =5

Answer:

20 minutes

Step-by-step explanation:

Both will meet again at start point after LCM(60,80) seconds.

That is 240 seconds.

in time slower car completes one lap, faster one covers 1 +20/80 lap, that is 1.25 laps. After 20 laps faster by slower car car will be 5 laps ahead, time =20*60 = 1200s = 20 minutes