Complete the steps to identify all potential rational roots of f(x) = 3x2 – x – 4.

The domain of the function is 0 ≤ t ≤ 3 and the greatest concentration of the medication is 2mg/L

The equation of the function is given as:

[tex]C(t) = \frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex]

Time can be 0 or greater but cannot be negative.

So, the domain of the function includes t ≥ 0

Set the function to 0 to determine the maximum value of t.

[tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10} = 0[/tex]

Cross multiply

[tex]-18t^2 + 54t = 0[/tex]

Factor out -18t

-18t(t - 3) = 0

Divide both sides by -18t

t - 3 = 0

Add 3 to both sides

t = 3

This means that the maximum value of t is 3

Hence, the domain of the function is 0 ≤ t ≤ 3

From the graph of the function (see attachment), we have the maximum value to be;

C(t) = 2

Hence, the greatest concentration of the medication is 2mg/L

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Answer:

the second picture shown

Step-by-step explanation:

it’s has on the x axis (-3,0) and on y axis (0,-2.26)

Answer:

Step-by-step explanation:

Givens

Formula

Linda's speed * t + martin's speed * t = 855

s1 * t + s2 *t = 855

Solution

35*t + 60*t = 855t                Combine the left

95t = 855                              Divide both sides by 95

95t/95 = 855/95

t = 9

Answer

They will meet in 9 hours.

Answer:

Option (D) is correct, 9 hours.

Answer:

The mean is 23

The median is 22

Step-by-step explanation:

To find the mean you have to do 2 steps:

Step 1: Add up all your numbers:

31 + 14 + 26 + 17 + 32 + 18

= 138

Step 2: Divide you answer by how many numbers there are(6):

138 ÷ 6

= 23

Now to find you median

First put the numbers in order:

14, 17, 18, 26, 31, 32

Now grab the middle number and since there are an even amount of numbers grab the 2 middle numbers:

14, 17, 18, 26, 31, 32

Now add the 2 numbers:

18 + 26

= 44

The last step is to divide your answer by 2:

44 ÷ 2

= 22

Answer:

  72 ft

Step-by-step explanation:

The perimeter of the concrete walk is the sum of the lengths of its outside edges. Each of those is two border-widths longer than the parallel pool dimension.

__

The border width is ...

  (10 ft) + 2(3 ft) = 16 ft

The border length is ...

  (14 ft) + 2(3 ft) = 20 ft

The perimeter is the sum of the lengths of the four sides. It can be found using the formula ...

  P = 2(L +W)

  P = 2(20 ft + 16 ft) = 2(36 ft) = 72 ft

The perimeter of the concrete walk is 72 feet.

_____

Additional comment

The term "perimeter of the concrete walk" is actually somewhat ambiguous. It could refer to the total length of all of the edges of the concrete walk. If that is the case, then the 48 foot length of the inside edge must be added to the length of the outside edge for a total of 120 feet. That is, if one were to mark the edges of the walk with tape, for example, 120 feet of tape would be needed.

The constant of proportionality of the proportional relationship between x and y is: 1.3.

The constant of proportionality, k = y/x, of a proportional relationship.

To find the constant of proportionality of the relationship between x and y, select any given pair from the table, say, (2.5, 3.25).

Constant of proportionality (k) = 3.25/2.5

Constant of proportionality (k) = 1.3

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Answer:

  11.57%

Step-by-step explanation:

The probability of rolling two 3s is the product of the probability of rolling two 3s and two not-3s, and the number of ways that combination of rolls can appear.

__

Of the four die rolls, we want two of them to be 3s. The 3s can appear anywhere in the sequence. For example, we could have 33xx, or xx33, or any of a number of other combinations (where x is a "not 3"). The total number of ways two 3s can appear an a sequence of 4 rolls is ...

  C(4, 2) = 4!/(2!(4 -2)!) = 4·3/(2·1) = 6

__

The probability of rolling a 3 on a fair 6-sided die with one face labeled 3 is presumed to be 1/6. Then the probability of rolling something else is ...

  1 -1/6 = 5/6

So, two 3s and two not-3s in a given sequence have a probability of ...

  (1/6)(1/6)(5/6)(5/6) = 25/1296

__

The probability that four rolls of the die will show exactly two 3s is the product of the probability it can happen and the number of ways it can happen:

  (25/1296) × 6 = 25/216 ≈ 11.57%

_____

The attachment shows the probability function of a calculator gives the same result.

Answer:

53500

Step-by-step explanation:

if we take 2,000 and multiply it by 0.07 the resulting percentage equates to 140, or $140, add 140 to 2,000 and multiply by 25 will yield 53500

(2, 8) and (-10, 2)

:)

Leticia made a mistake in her step 2. She did subtraction before multiplication.

The expression can be simplified as follows;

4.5 ÷ 0.25 + 2.5 - 0.75 × 8

Hence, using Pemdas rule,

4.5 ÷ 0.25 + 2.5 - 0.75 × 8

18 + 2.5 - 0.75 × 8

18 + 2.5 - 6 = 14.5

Therefore, she made mistake in her step 2 because she was suppose to solve the multiplication before subtraction.

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Answer:27?

Step-by-step explanation:

So since there needs to be 3 1/3ds in each cup you just multiply 3x9=27

The amount received by Ahmed is 168 gm.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

Here, let the amount received by Ahmed be 7x

          and amount received by Babar be 3x

       Total amount of sweets = 240 gm

Now, according to question,

           7x + 3x = 240

              10x = 240

               x = 240/10

              x = 24

Thus, the amount received by Ahmed is 7 X 24 = 168 gm and amount received by Babar = 3 X 24 = 72 gm.

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Answer:

9

Step-by-step explanation:

The information given can be written as:

So, x + x + 2 + x + 4 = 33. This simplified is 3x + 6 = 33

Subtract 6 from both sides: 3x = 27

Divide both sides by 3: x = 9

This means that the numbers are 9, 11, and 13, so 9 is the smallest number.

To check, we can add together 9, 11 and 13, which is 33.

Hope this helps!

The area of the sector shown in the diagram below is A = 136.8 cm²

The formula for calculating the area of a sector is expressed as:

A = r²Ф/2

Given the following

radius = 14cm

Ф = π/6

Substitute

A = (14)²π/12

A = 196(3.14)/2

A = 136.8 cm²

Hence the area of the sector shown in the diagram below is A = 136.8 cm²

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Answer:

A

Step-by-step explanation:

Consider the left triangle within the big triangle.

Identity :

sin θ = opposite side / hypotenuse

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

Taking the sine value of the angle to find h :

⇒ sin37° = h/6

⇒ h = 6sin37°

Opposite 37 is h

Angle opposite 6 is 90

Sine rule:

h/sin37 = 6/sin90

xsin37

h = 6 x sin37/ sin90

h = 3.6108....

h = 3.6 to 1dp

A) 6xsin37= 3.6108...

B) 10xsin37 =6.018...

C) 6x 10 xsin37 = 36.108...

D) 10 x 6 x sin37 = 36.108...

Thus, answer is A

Hope this helps!

Answer:

40

Step-by-step explanation:

14 = 35% of x

35% = 0.35

So lets make an equation and solve for x:

14 = 0.35x

x = 14÷0.35

x = 40

To check our answer let's put it back into the question :

35% of 40 = 14

10% = 4 , 30% = 12 , 5% = 2

35% = 12+2 = 14 ✅

Hope this helped and have a good day

The area of the arrow given in the figure is 610 square cm

The given figure is made up of rectangle and triangle. The area is expressed as:

Area = Area of rectangle + area of triangle

Substitute the given parameters

Area of the arrow = (15*20) + 0.5(31 * 20)

Area of the arrow = 300 + 310
Area of the arrow = 610 square cm

Hence the area of the arrow given in the figure is 610 square cm

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Answer:

8 minutes

Step-by-step explanation:

Jill jogs 3/4 of a mile in 1/10 hour.

⇒ 3/4 of a mile takes 6 minutes

For one mile :

1 mile she can run

8 mins

Maintain the same constraints on edge capacity, skew symmetry, and flow conservation in the ordinary maximum-flow problem on a flow network of comparable size.

A flow network is a directed graph with each edge having a capacity and each edge receiving a flow, according to graph theory. The amount of flow on an edge must not exceed the edge's capacity.

Let's suppose the network flow is given by;

G = (V, E)

With edge capacity:

c: E → R

And vertex capacity:

d: V → R

Maintain the same constraints on edge capacity, skew symmetry, and flow conservation.

Consider the new stipulation: for each:

v ∈V

So,

[tex]\rm \sum_{u \in v } \{ f(u,v)|f(u,v) > 0 \} \leq d(v)[/tex]

Thus, if maintain the same constraints on edge capacity, skew symmetry, and flow conservation the ordinary maximum-flow problem on a flow network of comparable size.

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because the x values are identical the radius would be found by subtracting the y values.

6-2 = 4

the radius is 4

Simplify (-2)² + 15 ÷ 3

Answer: 9

Hope this helps :))
P.s. Can you mark me as the brainliest? <3

Answer:  1/20

Step-by-step explanation:

Given: Number of red marbles in bag = 4

Number of blue marbles in bag = 3

Number of yellow marbles in bag = 3

Total marbles = 3+3+4=10

Hope this helps!!!!

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The correct option is B.

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

In the ΔGEF, the value of Sin(E) is,

Sin(E) = GF/GE

In the ΔDEF, the value of Sin(E) is,

Sin(E) = FD/FE

Hence, the correct option is B.

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Answer:

reflection

Step-by-step explanation:

its like a mirror, if it were rotated, they wouldnt line up as the same image. think of this like looking in a mirror! :)

1. Both triangles are congruent by: a. angle-angle-side congruence theorem.

Using the trigonometric ratios, we have:

2. C. 9

3. C. 4√3

4. B. sin C

The angle-angle-side congruence theorem states that two triangles are congruent to each other if they both have two pairs of corresponding congruent angles and a pair of non-included congruent side.

To solve any right triangle, the following Trigonometric ratios can be employed:

sin ∅ = opp/hyp

cos ∅ = adj/hyp

tan ∅ = opp/adj.

1. Both triangles can be proven to be congruent based on: a. angle-angle-side congruence theorem.

2. Given the points, A(-2, 6) and B(-2, -3), the distance between both points is:

AB = |6 - (-3)| = 9 units

The answer is: C. 9

3. Apply the sine ratio:

sin 60 = opp/hyp = m/8

m = (sin 60)(8)

m = (√3/2)(8) [sin 60 = √3/2]

m = 4√3

The answer is: C. 4√3

4. Using the sine ratio:

sin C = opp/hyp = 8/17

The answer is: B. sin C

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Answer:

C 33.52 cm³

Step-by-step explanation:

Here, we have Radius(r)=2(Given)

Volume = 4/3 πr³

= 4/3 · 22/7 · 2³

= 33.5238

Round to the nearest tenth:
C 33.52 cm³

Answer:

13.3787 m

Step-by-step explanation:

A = 3 × ( 2 + √3 ) × s2
If a is 2004 just do the reverse order and u get the answer