what is the slope of this line?

Using the decay formula, the particular antibiotic with half-life of 16 hours, will decrease to 30-milligrams in the blood after 27.79 hours.

We can use the decay formula to solve the problem:

A(t) = A(0) . (0.5)^(t/T)

Where:

A(t) is the remaining quantity at time t

A(o) is the initial quantity

t  is the time interval

T is the half-life rate

In the given problem:

A(0) = 100 milligram

T = 16 hours

A(t) = 30 milligram

We need to find t such that the remaining quantity of this antibiotic is 30 mg.

Substitute the given parameters into the formula:

A(t) = A(0) . (0.5)^(t/T)

30 = 100 . (0.5) ^(t/16)

Taking the logarithm:

log (30) = log [100 . (0.5) ^(t/16)]

Use the logarithm property, log(A.B) = log A + log B

log (30) = log (100) + log [(0.5) ^(t/16)]

Use the logarithm property, log(Aⁿ) = n.log A

log (30) = log (100) + (t/16) . log (0.5)

log (30) = 2 + (t/16) . log (0.5)

(t/16) . log (0.5)  = log (30) - 2

t/16 = 1.737

t = 1.737 . (16) = 27.79 hours

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The perimeter of the polygon will be 20 units and the area will be 21 square units.

From the given vertices a rectangle will be formed. A rectangle is a closed figure in which each interior angle is a right angle. The Perimeter of the rectangle can be given by formula 2(l + b) and the area is given by l×b where l is the length and b is breadth of rectangle. Now from the given points the dimensions of rectangle will follow the order W (5, -1), X (5, 6), Z (2, 6) and Y (2, -1).

The length of the rectangle is given by l = √ (6 + 1) ² + (5 - 5) ²

l = √49

l = 7 units

The breadth of the rectangle is given by b = √ (6 - 6) ² + (2 - 5) ²

b = √9

b = 3 units

Now, the perimeter of rectangle = 2 (l + b)

P = 2(7 + 3)

P = 20 units

Area of the rectangle = l×b

A = 7×3

A = 21 square units.

Thus, the perimeter and area are 20 units and 21 square units respectively.

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The equation of the line is y+x+1=0.

It is required to find the equation of the line.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

The given line is

y=-x-5.

Slope of line

y+x-5=0

We have to find the  equation of the line.

According to given question we have

Slope =-1

Thus the slope of the required line is

-1

The point (5, -6)

The equation of the line is

  y+6=-1​(x−5)

=>y+6=-x+5

=>y+x+1=0

Therefore, the equation of the line is y+x+1=0.

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The measures of angles q, r and s are 100°, 135° and 125° and the sum of the three angles equals 360°.

In this problem we find a geometric system generated by three lines no collinear to each other, which generate the triangle DEF. In accordance with the Euclidean geometry, the sum of the measures of internal angles in a triangle equals 180°:

m ∠ FDE + m ∠ DEF + m ∠ DFE = 180°            (1)

If m ∠ FDE = 80° and m ∠ DEF = 45°, then the measure of the angle DFE is:

m ∠ DFE = 55°

Finally, we find the values of the angles q, r and s by definition of supplementary angles:

q = 180° - 80°

q = 100°

r = 180° - 45°

r = 135°

s = 180° - 55°

s = 125°

The sum of the measures of angles q, r and s is:

q + r + s = 360°

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Answer:if it is division it is:

Divide

233.91

by

3.45

=

67.8

Step-by-step explanation:

Answer: a. y=0.03x+29.99

b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.

y-int: (0, 29.99). Total cost per month when phone isn't being used.

c. $34.07

Step-by-step explanation:

a. p=Cell phone plan. m=minutes used for phone.

3¢=$0.03

p=29.99+0.03m

y=0.03x+29.99

b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.

y=0.03(0)+29.99

p=29.99 ==> y-int: (0, 29.99). Total cost per month when phone isn't being used.

c. y=0.03(136)+29.99

y=4.08+29.99

y=$34.07

The principal amount is calculated as $720.

Simple interest is a simple and quick method to calculate the interest on a loan.

The formula for calculating the simple interest is;

SI = PRT/100

Where,

SI = simple interest

P = principal amount

R = rate of interest (%)

T = time period in years

For the given values in the question

Substitute the given values in the question;

39.60 = (P×11×0.5)/100

P = 39.60×100/(11×0.5)

P = 720

Therefore, the value of the principal amount is estimated as $720.

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Answer:

Step-by-step explanation:

The variable here is u, and the highest power of u is u^8.  The first term is thus -u^8, and the coefficient of this is -1.  Thus, the leading coefficient of the polynomial is -1.  The degree is 8.

Answer:

{-9, 3, 10}

Step-by-step explanation:

Place the elements (the numbers marked by red) within curly brackets.

Answer:

659

Step-by-step explanation: Divishion of practice

Answer:

Area : 63.6 square inches.

Cost: Cost per square inch = 18.60 / 63.6 = $0.29 (rounded to the nearest cent)

Step-by-step explanation:

Answer:

========================

In order to find the distance you run each month you need to divide the total distance by the number of months:

The number of answers that each school got correct in the final round is 18.

School A point = 128

School B point = 56

Let x = the number of correct answers given by School A in the final round.

Therefore, the equation for A will be:

128 + 9x - 4x = 128 + 5x

The equation for B will be:

= 56 + 9x.

We will equate the equations.

128 + 5x = 56 + 9x

9x - 5x = 128 - 56

4x = 72

x = 72/4

x = 18

School A and B gave 18 correct answers

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160 boxes needed to pack these items

Therefore contents in each box have 4 bags of groceries, 2 cases of bottled water, and 5 toys.

Given no of groceries bags = 640

number of cases of bottled water = 320

number of small toys = 800

We have to find out how many boxes are needed and the contents of each box.

(i) How many boxes are needed:

To do this we need to find the greatest common factor of these three items

as

640 - 2⁷ * 5

320 - 2⁶ * 5

800 - 2³ * 5²

GCF = 2⁵ * 5 = 160

Therefore 160 boxes needed to pack these items

(ii) Contents of each box:

No of bags of groceries in each box = 640 / 160 = 4

No of cases of bottled water = 320 / 160 = 2

No of toys in each box = 800 / 160 = 5

Therefore, contents in each box have 4 bags of groceries, 2 cases of bottled water, and 5 toys.

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The Probability that Outcome B is drawing a green marble on the second draw without replacing the first marble is

P(B|A) = 3/7.

The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

Probability is another word for possibility. It is a field of mathematics that examines the occurrence of a random event. The value is given as a number between 0 and 1. To determine how likely an event is to occur, probability has been introduced in mathematics.

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Answer:

Step-by-step explanation:

Answer:

c) -66%, -0.45, -1/3, 1.8

Step-by-step explanation:

Numbers provided:

Rewrite them in decimals:

In ascending order (from least to greatest):

Solution: -66%, -0.45, -1/3, 1.8

the height of pyramid vabcdef gh is 45.2º.

A polygon is a closed polygonal chain made up of a limited number of straight line segments that are joined to form a planar figure in geometry (or polygonal circuit). A polygon can be defined as the region that is circumscribed by a bounding circuit, the bounded plane, or both.

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In reality, the lateral face VAB is an isosceles triangle with a 14-length base and 25-length legs. This triangle's altitude must cut over angle V and the base, forming a right triangle with a hypotenuse that is 25 inches long and a short leg that is 7 inches long. We can calculate the altitude, which is also the slant height of the pyramid, using the Pythagorean theorem.

s.h. = alt. = √(252 - 72) = 24

Now, by adding the pyramid's height and half of its base, we may utilize this slant height as the hypotenuse of another right triangle.

We look at a regular octagon to identify half the base. You'll see that four of the sides are horizontal or vertical, while the other four are at an angle of 45 degrees to the first four. So, in this example, 14 + 28/2 = 14 + 142, the distance between parallel sides of a regular octagon would be equal to s + 2s/2.

hence, the base's half would equal 7 + 72.

The height of the pyramid and the dihedral angle with the base are both provided by this right triangle.

h = √(242 - (7 + 7√2)2) = 17.0"

θ = cos-1((7 + 7√2)/24) = 45.2º

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Answer:

0.32×0.5=0.16

Answer: n=24

Step-by-step explanation:

n=number

2/3 * n - 5=11

2n/3=16

2n=48

n=24

Answer:

x = 3

Step-by-step explanation:

AB is the line segment and is 20 cm

Since M is the midpoint, AM = MB = 20/2 = 10

3x + 1 = 10

==> 3x = 10- 1 = 9

==> x = 9/3 = 3

Answer:

AB=20 then AM =10

now,

[tex]3x + 1 = 10 \\ 3x = 10 - 1 \\ 3x = 9 \\ x = 3 [/tex]

Answer: c. P=43

d. P=3x^2+5x+8

Step-by-step explanation:

c. P=12x+19 ==> See how I got this formula in my previous answer to parts a and b

P=12(2)+19

P=24+19

P=43

d. P=a+b+c+d

P=x^2 +4x+8+2x^2 +x

P=x^2 +2x^2 +4x+x+8

P=3x^2+5x+8

Answer:

x > 2 or x < −4

Step-by-step explanation:

Let's solve your inequality step-by-step.

|3x + 3| −5 > 4

Step 1: Add 5 to both sides.

|3x + 3| −5 + 5 > 4 + 5

|3x + 3| > 9

Step 2: Solve Absolute Value.

|3x + 3| > 9

We know either3x + 3 > 9 or 3x + 3 < −9

3x + 3 > 9(Possibility 1)

3x + 3 −3 > 9 −3(Subtract 3 from both sides)

3x > 6

3x > 6    (Divide both sides by 3)

3      3

x > 2

3x + 3 < −9(Possibility 2)

3x + 3 −3 < −9 −3(Subtract 3 from both sides)

3x < −12

3x < -12  (Divide both sides by 3)

3       3

x < −4

Solution:

B. [tex](-6-\sqrt{29},-6+\sqrt{29})[/tex]

Hope this helps! If so, lmk! Thanks and good luck!

Answer: (-6-[tex]\sqrt{29}[/tex], -6+[tex]\sqrt{29}[/tex]) ==> D

Step-by-step explanation:

x^2 + 12x +7 < 0

x^2+12x+36-29<0

(x+6)^2-29<0

(x+6)^2<29

x+6<[tex]\sqrt{29}[/tex]

x<-6+[tex]\sqrt{29}[/tex]

x+6>-[tex]\sqrt{29}[/tex]

x>-6-[tex]\sqrt{29}[/tex]

(-6-[tex]\sqrt{29}[/tex], -6+[tex]\sqrt{29}[/tex]) ==> D

-6-[tex]\sqrt{29}[/tex] and -6+[tex]\sqrt{29}[/tex] aren't included in the solution since if these values are plugged in to x^2 + 12x +7, the expression will equal 0. That's not supposed to happen. The expression is supposed to be LESS than 0.

Answer:

When multiplying the tens, the student didn't use the 0 place holder for the ones place.

Step-by-step explanation:

When using or doing long multiplication the answer was correct (2871) BUT before multiplying the tens, a zero should be placed in the ones place of the results. So, the tens should be 19140

2871+19140=22011

Answer: 1) When multiplying the ones, the student did not carry over a ten to the next place in the first multiplication.

2) When multiplying the ones, the student should have calculated 3 times 2 plus 5 as 11 and placed a 1 in the tens place.

3) When multiplying the tens, the student did not use the 0 place holder for the ones place.

4) When multiplying the tens, the student should have calculated 2 times 1 plus 9 as 11 and used a 1 should in the hundreds place.

Answer:

The correct option is;

4) When multiplying the tens, the student did not use the 0 place holder for the ones place

Step-by-step explanation:

Here we have when doing long multiplication, the student correctly multiplies the ones as 2871, however, before commencing multiplication of the tens, a 0 should be placed in the ones place of the result as a place holder such that the outcome of the multiplication of the tens should be;

19140

Hence, the correct result should be 2871 + 19140 = 22011

The correct option is therefore, that "When multiplying the tens, the student did not use the 0 place holder for the ones place."

Step-by-step explanation:

If she starts with 6 miles today and add 2 miles each day to her distance until she achieves her goal and  then she has to run 176 miles in total to achieve her 26 miles goal.

Given,

Total distance for the marathon = 26 miles

Distance she add each day =2

She starts with 6 miles

Then,

Equation of nth term in the arithmetic sequence

[tex]t_{n}=a+(n-1)d[/tex]

Substitute the values and find the value of n

26=6+(n-1)2

26=6+2n-2

26=4+2n

2n=22

n=11

To find the total distance she run to achieve her 26 miles goal, we have to apply the sum of n terms of arithmetic sequence,

[tex]S=\frac{n}{2}[2a+(n-1)d]\\ S=\frac{11}{2}[2(6)+(11-1)2]\\ S=\frac{11}{2}[12+20]\\ S=\frac{11}{2}[32]\\ S=176[/tex]

If she starts with 6 miles today and add 2 miles each day to her distance until she achieves her goal and  then she has to run 176 miles in total to achieve her 26 miles goal.

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Answer:

75% of 48 = 36 oranges used on M. 36/12=3, 3 is 1/12 of 36, so he sold 33 more oranges on M then on T when he only sold 3.

Answer:

0.5

Step-by-step explanation:

7 1/2 • 2 = 15

7 times 2 is equal to 14

1/2 times 2 is equal to 1

14 plus 1 is equal to 15

The average time of Lynden's first two, 100-meter-dash is 12.813 seconds.

We are given the 100-meter-dash times of Lynden in first two races. So, the average time for first two races will be calculated using the formula -

Average = sum of all observations ÷ total number of observations

Sum of all observations here will be the sum of time of race.

Sum of observations = 13.075 + 12.55

Performing addition

Sum of observations = 25.625 seconds

Number of observations is the number of races whose time is taken in calculation.

Number of observations = 2

Keep the values in formula to find the average time.

Average time = 25.625 ÷ 2

Average time = 12.8125 seconds.

Rounding to nearest thousands place : 12.813 seconds

Hence, the average time of Lynden's first two, 100-meter-dash is 12.813 seconds.

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Answer:

Grace's work was done correctly.

Step-by-step explanation:

She expanded the equation and grouped the like terms, then added them together to get the answer.

[tex]6-3x-2\left(6x-8\right)\\=6-3x-12x+16\\3x - 12x = -15x\\= -15x + 6 + 16\\6 + 16 = 22\\= -15x + 22[/tex]

Hope this helps!