What are the common factors of 24 and 36?
O A. 1,2,4,6, 12
O B. 1,2,3,4,6,12
C. 1,2,3,4,6,8,12
O D. 1,3,4,9,18

Step-by-step explanation:

Marie had 160

Josh has 150

Trey has 600

When pH is 2, the hydrogen ion concentration in \(litre^{-1}\) is \(10^{-2}\)

The pH value of water indicates how acidic or basic it is. The negative log of the hydrogen ion concentration is defined as pH. The pH scale starts from 0 and ends at 14. A pH of 7 is considered neutral because pure water has a pH of exactly 7. Acidic values are less than 7; basic or alkaline values are greater than 7.

Given that,

pH = 2 for HCl acid

We know that,

The relation between concentration of acid and pH is,

pH = -log[\(H^{+}\)]

2 = -log[\(H^{+}\)]

\([H^{+} ]\)  = \(10^{-2}\)

Hence, the hydrogen ion concentration in a solution with a pH of 2 is \(10^{-2}\).

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the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Answer:

5b-5

Step-by-step explanation:

Replace a with a=5/6 * b

Applying the rule for the pattern, it is found that the numbers in the new pattern Q are given by: 8, 14, 20, 26, 32, 38.

To each term of P, 1 is added then 2 is multiplied, hence the rule is given by:

Q = 2(P + 1).

We do this for P = 3, 6, 9, 12, 15, 18, hence:

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Answer: You can have 7 different 2/3 Pieces

Step-by-step explanation:

The reason you can have more than the amount of feet is because each cut is less than one foot.

Answer:1.5

Step-by-step explanation:

Y=1/2 of x

Answer:

A. 28m^2

B. 32m^2

C. 72cm^3

Step-by-step explanation:

A. 7•4=28

B. 8•4= 32

C. 4•2= 8

8•9= 72

hope this helps <3

The solutions to this system of conics is; x = 6 and y = -4

We are given the system of equations as;

(x - 1)² + (y + 4)² = 25    ------(eq 1)

(x - 1)²/25 + (y + 4)²/100 = 1  ------(eq 2)

From eq 1, we can make (x - 1)² the subject to get;

(x - 1)² = 25 - (y + 4)²  ----(eq 3)

Plug in eq 3 into eq 2 to get;

(25 - (y + 4)²)/25 + (y + 4)²/100 = 1

Multiply through by 100 to get;

4(25 - (y + 4)²) + (y + 4)² = 100

100 - 4(y + 4)² +  (y + 4)² = 100

Solving for y gives y = -4

Plug in -4 for y into eq 1 to get;

(x - 1)² + (-4 + 4)² = 25

√(x - 1)² = √25

x - 1 = 5

x = 6

Now, a conic section is defined as the curve which is the intersection of cone and plane. There are three primary conic sections namely parabola, hyperbola, and ellipse. Thus, the solutions are x = 6 and y = -4.

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Answer:

= 34

Step-by-step explanation:

(32)-5+7

32 - 5 + 7

= 32 + 2

= 34.

The current population of Glen Cove is 5,000 people and in the long-run, the population of Glen Cove will approach 35,000 people.

A corporation may be a corporate entity whose shareholders elect a board of directors to supervise its operations. the dissimilarity between the business and an organization is that an organization may be a sort of business that's suitable for smaller businesses and organizations, whereas a corporation may be a kind of business that's appropriate for larger enterprises and entities.

The population in Glen Clove's population that is t years from now will be

P(t) = \(\frac{35t^2 + 125t + 200}{t^2 + 4t + 40}\)

The current population can be calculated by substituting t = 0 in P(t).

So,

P(0) = \(\frac{35(0)^2 + 125(0) + 200}{(0)^2 + 4(0) + 40}\)

P(0) = 5

Thus, the current population of Glen Clove is 5 thousand.

(b)For the long run, t tends to infinity. So, evaluate the infinite limit for the given function as follows:

\(\lim_{t \to \infty} P(t)= \lim_{t \to \infty}P(t)\frac{35t^2 + 125t + 200}{t^2 + 4t + 40}\)

                     =\(\lim_{t \to \infty}\frac{t^2(35+\frac{125}{t} +\frac{200}{t} )}{t^2(1+\frac{4}{t} +\frac{40}{t^2} )}\)

                    = \(\lim_{t \to \infty}\frac{(35+\frac{125}{t} +\frac{200}{t} )}{1+(\frac{4}{t} +\frac{40}{t^2} )}\)

Now, solve further by putting the limits as follows:

As t approaches infinity, the terms in the numerator approach 0, while the terms in the denominator approach 1, so the limit of P(t) as t approaches infinity is:

lim t -> infinity P(t) = 35 / 1 = 35

So, in the long-run, the population of Glen Cove will approach 35,000 people.

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Answer:

D

Step-by-step explanation:

I believe it's D but not 100%

Answer:

$16.92

Step-by-step explanation:

Just divide 42.30 by 2.5 and it will give you the answer

Answer:

We need 5 yards green felt and 4 yards blue felt for each quilt.

Step-wise:

Let length of green felt be 'x' , length of blue felt be 'y' and and number of quilts be z.

If Ivan has 15 yards of green felt and 12 yards of blue felt to make 3 quilts.

⇒15x+12y=3z15x+12y=3z

Now, divide both sides by 3 , we get

5x+4y=1z5x+4y=1z

Therefore, we need 5 yards green felt and 4 yards blue felt for each quilt.

Answer:

2.75c +3.59

Step-by-step explanation:

She only needs one bag of flour so it is a constant 3.59. She needs multiple bags of chocolate chips which is unknown so that will be c times the 2.75 for each bag

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

When 'a' is 10, 'c' is approximately 142.97. You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation

To use the elimination method to solve the equation 2a + c = 162.97, we need another equation with the same variables. However, as there is only one equation given, we cannot apply the elimination method directly.

The elimination method typically involves adding or subtracting equations to eliminate one of the variables, resulting in a new equation with only one variable. Since we have only one equation, we don't have the opportunity to eliminate variables using another equation.

In this case, we can solve the given equation directly by isolating one variable in terms of the other. Let's solve for 'c':

2a + c = 162.97

Rearrange the equation to isolate 'c':

c = 162.97 - 2a

Now, we have an expression for 'c' in terms of 'a'. This equation represents a line in the 'a-c' coordinate plane. We can choose any value for 'a', substitute it into the equation, and calculate the corresponding 'c' value.

For example, let's say we choose 'a' = 10:

c = 162.97 - 2(10)

c = 162.97 - 20

c = 142.97

So, when 'a' is 10, 'c' is approximately 142.97.

You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation since we have one equation and two variables.

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Answer:

1:1

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

500÷18=27.77778

but the remanding. 7777778 isnt a full bag so we don't count it.

therefore the answer is 27

Part (a)

The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.

\(C(x)=500+1.25x\)

Part (b)

The revenue is the number of slushies sold multiplied by the amount charged per slushie.

\(R(x)=3.50x\)

Answer:

Step-by-step explanation:

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

d=(−0.306)(1.67)+0.9979

Step 1: Simplify both sides of the equation.

d=(−0.306)(1.67)+0.9979

d=−0.51102+0.9979

d=(−0.51102+0.9979)    (Combine Like Terms)

d=0.48688  

Answer:

904.32

Step-by-step explanation:

i think this is correct

Answer:

n is 13

Step-by-step explanation:

\( {n}^{2} = {12}^{2} + {6}^{2} - (2 \times 12 \times 6) \cos(90 \degree) \\ {n}^{2} = 180 \\ n = 13.4\)

Answer:

n is 13

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

edge 2021

The ladder is 10 feet long, and the base of the ladder at least 3 feet away from the wall the ladder is leaning on.

So, By making a right triangle, the ladder will represent the hypotenuse of the triangle

So, we need to find how high will the ladder reach up?

So, using a Pythagorean theorem

which stated that at the right triangle, the sum of the squared of the sides adjacent to the right angle is equal to the squared of the hypotenuse

so, let the height = h , the length of the ladder = 10 ft

and the base is 3 feet away from the wall

The ladder will represents the hypotenuse of the triangle

So,

So, The height that can the ladder reach up is 9.54 feet

Answer:

\(thank \: you\)

Answer: x = 11

Step-by-step explanation:

Given

4 (x - 1) = 2 (x + 9)

Expand parentheses and apply the distributive property

4x - 4 = 2x + 18

Subtract 2x on both sides

4x - 4 - 2x = 2x + 18 - 2x

2x - 4 = 18

Add 4 on both sides

2x - 4 + 4 = 18 + 4

2x = 22

Divide 2 on both sides

2x / 2 = 22 / 2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

  a. 16.9 m

  b. 4.082 seconds

  c. no

  d. 2.041 seconds

  e. 21.41 m

Step-by-step explanation:

A graphing calculator can help you answer these questions quickly and easily. The graph is attached.

__

Evaluate the function at t=3.

  h(t) = -4.9t^2 +20t +1

  h(3) = (-4.9×3 +20)×3 +1 = 5.3×3 +2 = 16.9

The baton will be at a height of 16.9 meters after 3 seconds.

__

The axis of symmetry of quadratic ax^2+bx+c is located at x=-b/(2a). The point of release and the later point at the same height will be symmetrically located about the axis of symmetry. The peak height will be on the axis of symmetry of the graph. That value of time is ...

  tpeak = -20/(2(-4.9)) = 20/9.8 ≈ 2.041 . . . seconds

The baton will be at the release height again after 2×2.041 = 4.082 seconds.

__

As we saw in part (b), the maximum height will be when t=2.041 seconds. That height is found by evaluating the function for that value of t.

 h(2.041) = (-4.9(2.041) +20)(2.041) +1 = 21.41 . . . meters

The baton will not reach a height of 25 meters.

__

We found this answer in part (b): 2.041 seconds to reach the maximum height.

__

We found this answer in part (c): 21.41 meters is the maximum height.

_____

Additional comment

The time at maximum height is 20/9.8 seconds = 100/49 = 2 2/49 seconds. In general, the answer values shown here are rounded to 4 significant figures. The graphing calculator rounds to 3 decimal places.

Answer:

12.25

Step-by-step explanation:

3.5*3.5=12.25

Answer:

12.25m^2

Step-by-step explanation:

3 1/2 × 3 1/2

3 1/2 is equivalent to 7/2

7/2 × 7/2= 49/4

this simplifies to 12.25

answer: 12.25 m^2

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The base and height are perpendicular to each other. In each case, there is only one figure having a labeled h segment perpendicular to the labeled b.

Step-by-step explanation:

I solved it in my notebook