Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 8 times t squared plus 56 times t end quantity over the quantity t squared plus 3 times t plus 2 end quantity comma where the time, t, is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)

Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)

A store sold 22 colored shirts and 8 white shirts.

Let x be the number of colored shorts and y be the number of white shirts.

A store sold 14 more colored shirts than white shirts.

so, we get an equation,

x = y + 14                       ....................(1)

The white shirts cost $9.95, and the colored shirts cost $10.50. The store sold $310.60 worth of shirts.

So we get an equation,

10.50x + 9.95y = 310.60           .............(2)

Substitute above value of x in equation (2)

10.50(y + 14) + 9.95y = 310.60          

10.50y + 147 + 9.95y = 310.60          

20.45y = 310.60 - 147

20.45y = 163.6

y = 8

Substitute above value of y in equation (1)

So, x = 8 + 14

x = 22

Therefore, a store sold 22 colored shirts and 8 white shirts.

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Angle JKL has a measure of 24 degrees while angle LKM has a measure of 12 degrees

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following angles

From the attached figure, we can see that:

Angle 1 is twice the measure of angle 2

This is so because, the angle 1 is the vertex angle of an isosceles triangle

While the angle 2 is half of it

So, we have

Angle 1 = 2 * Angle 2

Substitute the known values in the above equation

So, we have

2 * 3x = 5x + 4

Evaluate the product

So, we have

6x = 5x + 4

Evaluate the like terms

x = 4

Substitute x = 4 in the equations JKL=5x+4 and LKM=3x

So, we have

JKL= 5 x 4 + 4

LKM = 3 x 4

Evaluate the equations

So, we have

JKL= 24

LKM = 12

Hence, the measures of the angles are JKL= 24 and LKM = 12, respectively

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Answer:

The smallest of the three integers is 17. (17, 19, 21)

the area of the pie that Carol will bake will be equal to 249.51 inches².

We are given the circumference of the pie as = 56 inches.

As pie is in the shape of a circle, we will use the formula for circumference to find the radius of the circle.

2 π r = 56 inches

2 × 22 / 7 × r = 56

r = 56 × 7 / ( 22 × 2)

r = 8.91 inches.

Area of circle is given by:

π r²

Substituting the values in the formula, we get that

A = 22 / 7 (8.91)²

A = 249.51 inches²

Therefore, we get that, the area of the pie that Carol will bake will be equal to 249.51 inches².

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Answer:

y = ± 13

Step-by-step explanation:

If y² = 169 then y = √169

√169 is either +13 or -13

This is usually written using the plus/minus sign

√169 = ± 13

Answer:

327 x 564

1648+2092+1685

190068

Step-by-step explanation:

im pretty sure that this is right. and the bold letter are the missing ones

commutative property

That's what you call the property 7x8 = 8x7

commutative property!

Answer: X1= 7 - sqrt{17} over 4

              X2= 7 + sqrt{17} over 4

Answer:

VERY

Step-by-step explanation:

VERY

If the cafeteria ordered 400 paper plates. They used 226 at breakfast. They bought 100 more. Then, they used some plates for lunch. Now there are 78 plates. The number of  plates that was used at lunch is 196.

Given :

Paper plates ordered = 400 plates

Plates used for breakfast = 226

Additional plate bought = 100

Plate used for lunch = ?

Hence,

Let calculate the plate left after breakfast

Number of plates = Paper plates ordered - Plates used for breakfast

Number of plates = 400 plates - 226 plates

Number of plates = 174 plates

Now let determine the plates that were used for lunch

Pates used for lunch :

Pates used for lunch = (174 + 100) -78

Pates used for lunch = 274 -78

Pates used for lunch = 196 plates

Therefore we can conclude that the number of  plates that was used at lunch is 196 plates .

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Answer: 1*5=5 is the counterexample.

Step-by-step explanation: The conjecture stated is that the product of two positive numbers is always greater than either number. We have to find certain values to check and see if this conjecture is false. We can use the numbers 1 and 5 to multiply. This would be the identity property of multiplication. 1 and 5 are both positive numbers and therefore that 1*5=5 is the counterexample.

Based on the equations given, the best comparison between them is that they are intersecting but not perpendicular.

When lines are perpendicular to each other, one line will have a slope that is the negative reciprocal of the other. For instance, if the slope of one line is 2, the slope of the perpendicular line will be -1/2.

Parallel lines will have the exact same slope.

The slope of the first line is:

2x - 7y = -5

(2x - 7y = -5) x 1/7

2/7x - y = -5/7

Slope = 2/7

The slope of the second line is:
x - 3y = 4

(x - 3y = 4) x 1/3

1/3x - y = 4/3

Slope = 1/3

The slopes are neither negative reciprocals nor the same so the lines must be intersecting but not perpendicular.

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The evaluated value of x from the line geometry given is 36.

An angle is the point where two lines meet. From the given diagram, the sum of the angles on the line is 180 degrees.

Take the sum to have

x + 3x + x = 180

Simplify

4x + x = 180

5x = 180

Divide both sides by 5

5x/5 = 180/5

x = 36

Hence the value of x from the diagram is 36

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we have

-2x+8y=-14 ------> equation A

-4x+y=-13 ------> equation B

solve the system

using the elimination method

step 1

multiply by -2 equation A

-2[-2x+8y=-14] -----> 4x-16y=28 -------> equation C

step 2

Adds equation B and equation C

-4x+y=-13

4x-16y=28

-----------------

-15y=15

solve for y

y=-1

Find the value of x

substitute the value of y in any equation

-4x+y=-13 ------> equation B

-4x+(-1)=-13

-4x=-13+1

-4x=-12

x=3

therefore the solution is

Answer: [tex]y=-((x-2)/\sqrt{2} )^{2} +4[/tex]

Step-by-step explanation:

This equation has it's parabola starting at (2,4)

So, we know that our equation will include (x-2) and +4

Next, we see the parabola is upside down, so we need a -

Next, we see the equation is wider than normal, so we need to divide x by something.

at x = -2, a normal graph would go through (0,0) , but this one goes through  (0,2)

at x = -2, [tex]2^{2} =4[/tex]

but we see at x = -2, [tex]x^{2} =2[/tex]

[tex]x=\sqrt{2}[/tex]

a) The distance that the bus traveled varies directly with time.

b) If the journey of 60 km takes 8 hours, the speed of the bus is 7.5 km/h.

The relationship between distance and speed can best be explained below:

For a constant speed, for example, 60 km/h, the distance traveled, 60 km, is proportional to the time used.

But if the distance is fixed at 60 km, the time it takes the bus, for example, 8 hours, is inversely proportional to the speed.

Total distance = 60 km

Steady speed = 60 km/h

Thus, for every kilometer, the bus takes one minute (60/60) and for every minute, the bus travels a kilometer.

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Answer:Explanation:

Option 1: Vertically compressed by a factor of 4, reflected across the x-axis, and shifted right 6 units and down 2 units.

iven the parent function:

If y is vertically compressed by a factor of 4, we have:

Next, a reflection across the x-axis will give:

If the result is shifted

Finally, a shift downwards by units gives:

Thus, the graph of g(x) is the graph of y vertically compressed by a factor of 4, reflected across the x-axis, and shifted right 6 units and down 2 units.

he firsyt option is correct.

Answer:

74.44

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]

The answer is 0.00650508866

Answer:

A

Step-by-step explanation:

The multiplicative inverse property states that any number multiplied by its multiplicative inverse (also called reciprocal) results in 1.

The required metric conversion is:

96 times 1/2 inch is equal to 4 feet

In this question, we need to find convert 1/2 inch to 4 feet

We need to convert metric unit.

We know that, 1 feet = 12 inches

So, 4 feet would be 48 inches

We can write 48 inches as,

48 inches

= 96 × (1/2) inches

This means, if we add 1/2inch 96 times then it is equal to 4 feet

Therefore, the required metric conversion is: 96 times 1/2 inch is equal to 4 feet

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Answer: Use the quotient rule to solve this problem (formula attached). g(x) would be -sqrt x and f(x) would be x^2 - 4x +5.

Charlie used 400 milliliters of Solution B if the resulting mixture is a 12% alcohol solution.

An algebraic equation is a declaration of the equality of two expressions created by applying the algebraic operations to a set of variables.

Monomial expressions, binomial expressions, and polynomial expressions are the three main categories of algebraic expressions.

Given : Solution A contains 20% alcohol, while Solution B contains 6% alcohol.

It is  also given that Charlie uses 300 milliliters of Solution A.

Let's say that the mixture contained x ml of the 6% solution B.

x + 300 = resulting mixture of 12 % alcohol.

20% (300) + 6% (x) = 12% (x+300)

60 + 0.06x = 0.12x + 36

0.06x = 24

x = 400 milliliters

As a result, if the resulting mixture is a 12% alcohol solution, he used 400 milliliters of Solution B.

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The angle x in the parallel line is 123 degrees.

In the diagram, l₁ and l₂ are parallel.

l₃ and l₄ are perpendicular to each other.

Since l₁ and l₂ are parallel lines, the line l₃ is a transversal that cut across the parallel lines.

Angle relationship are formed such as corresponding angles, alternate angles, vertically opposite angle etc.

Therefore,

57 + x  = 180°

x = 180 - 57

Therefore,

x = 123 degrees.

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The formula to obtain the future value (FV) is,

Where,

Therefore,

ence, there will be $6`166.13 in the account after 5years.

Blanks to be filled by 4,3,8 and 3.

Multiplication in mathematics is the same as adding equal groups. As we multiply, there are more items in the group. The product, the two factors, and the product are all components of a multiplication problem. The numbers 6 and 9 are the factors in the multiplication equation 6 x 9 = 54, and 54 is the result.

Given Data

           3 __ 8

×            7 8 4

_____________

       1 _    9 2

    2 7 __ 4

_   4 3  6

_____________

 2  7 2 8 __ 2

_____________

Solving

Multiplying and adding,

           3 _4_ 8

×            7 8 4

_____________

       1 3_    9 2

    2 7 _8_ 4

_   4 3  6

_____________

 2  7 2 8 _3_ 2

_____________

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a) 10.7

b) ΔABE~ΔACD | Angle Angle Similarity

1) Analyzing that triangle, and considering they are similar we can write out the following to find x

a) If they are similar their corresponding sides are proportional, therefore we can write a pair of ratios.

The smallest hypotenuse over the largest hypotenuse as well as there is a proportionality between those two corresponding legs 8 and 18.

b) In the last statement of that proof table, we can tell that the last line is well written as:

ΔABE~ΔACD | Angle Angle Similarity

The Angle Angle Similarity states that:

Note that in that table there are two instances in which there is a reference to two congruent angles.

Answer:

X = 1/5

Step-by-step explanation:

16 - 10X = 14

10X = 2

X = 0.2

Answer

x=0.2

-16+10x=-14

10x=-14+16

10x=2

10x÷10=2÷10

x=0.2