A particle is moving along the curve y= 4sqrt(5x+11) . As the particle passes through the point (5,24) , its -coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant

The correct statement is:

"She is not correct because she did not substitute the same number in both expressions in Step 1."

First, let's see if Sophia is correct.

She starts with the expression:

-(4x - 5) + 2*(x - 3) = -2x - 5

Expanding the left side:

-4x + 5 + 2x - 6 = -2x - 5

-2x -1 = -2x - 5

So the constant term is different.

Now, what Sophia does is evaluating in x = 1 and x = -1. You can't do that when finding equivalent expressions. (never evaluate in different numbers).

"She is not correct because she did not substitute the same number in both expressions in Step 1."

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236/100, 59/25, or 2 9/25

Step-by-step explanation:

There are 100 cents in a dollar, so 236/100 is your starting fraction. The simplest improper fraction would be 59/25. But if you're looking for a mixed number, you get 2 9/25.

236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.

To solve this problem,

We need to convert 236 cents into dollars.

Since there are 100 cents in one dollar,

we can divide 236 by 100 to get the equivalent dollar value.

⇒ 236 cents ÷ 100 cents per dollar = 2.36 dollars

Now that we know that 236 cents is equivalent to 2.36 dollars,

we can express it as a fraction of a dollar.

To do this, we'll use the fact that one dollar is equivalent to 100 cents, which means that one dollar can be expressed as the fraction 100/100.

To find the fraction of a dollar that 2.36 dollars represents,

we'll divide 2.36 by 1.

⇒ 2.36 ÷ 1 = 2.36/1

To express this as a fraction of a dollar,

Multiply both the numerator and denominator by 100 to get,

⇒ (2.36 x 100) / (1 x 100) = 236/100

Simplifying this fraction, we get,

⇒ 236/100 = 118/50

Therefore,

236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.

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Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

where:

Rewrite both equations into slope-intercept form:

a) 2x + 4y = 15

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

b) 6x + 12y = 45

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

New equations:

[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

No Solution: the same slope (both lines will be parallel)

One Solution: different slopes and different y-intercepts

Infinitely Many Solutions: the same slope and y-intercept

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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

Equation #1

Subtract 2x from both sides

Divide both sides by 4

Equation #2

Subtract 6x from both sides

Divide both sides by 12

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

70d+2-14d= 79+12d-20

70d-14d-12d= 79-20-2

44d= 57

d= 57/44

A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x) and g(x) can be plotted as shown in the below image.

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The triangle is an isosceles right triangle. Then the value of x will be 1.27 cm.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The right-angle triangle is given below.

The given triangle is an isosceles right triangle.

P = B = x

Then we have

1.8² = x² + x²

2x² = 3.24

 x² = 1.62

   x = 1.27 cm

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Answer:

angle M

Step-by-step explanation:

if you are using side angle side the two sides may be

line LK and NK

and angle M

Answer:

A

Step-by-step explanation:

Inflation decreases the amount of goods and services that can be purchased with a dollar.

Answer:

list five solution to the energy crisis of nepal

Answer: Heyaa!~

                  - Write 63 as the product of prime factors -

              - Write the prime factors in ascending order -

         -   what's the highest common factor of 63 and 105   -

             Hopefully this helps you! ^^^

Answer:

7 3/5

Step-by-step explanation:

2 x 3 4/5

2 x 19/5

2x19/1x5 = 38/5 = 7 3/5

[tex]~~~~~~2I_2 - A\\\\\\=2\begin{bmatrix}1&0\\0&1 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2&0\\0&2 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2-4&0-2\\0-3&2+3 \end{bmatrix}\\\\\\=\begin{bmatrix}-2&-2\\-3&5 \end{bmatrix}[/tex]

The equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The equation made by the given situation is:-

For kyle, there are g students attending 8 classes sp total number of students will be 8g similarly for h students there are 6 classes so the total number of h students will be 6h. The total number of students for both g and h students attending kyle's class is 62. So the equation will be given as:-

8g   +  6h  =  62

Now for Lauren, there are g students attending 5 classes so the total number of students will be 5g similarly for h students there are 10 classes so the total number of h students will be 10h. The total number of students for both g and h students attending Lauren's class is 70. So the equation will be given as:-

5g  +  10h  =  70

Therefore the equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

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A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.

Exponential decay obeys the equation

[tex]m(t) = m_0 e^{-kt}[/tex]

where t = time, days

Given:

Initial mass, m₀ = 8 g

Decay constant, k = 0.101

For half-life, the mass is m = m₀/2.

Therefore,

[tex]m(t) = m_0 e^{-kt}[/tex]

e^{-0.101t} = 1/2

-0.101t = ln 0.5

t = ln 0.5/-0.101

t = 2.98

Therefore, The half-life is 2.98 days.

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Answer:

 x = -2

Step-by-step explanation:

Prime factorize, 27 and 9

27 = 3 *3 * 3 = 3³

  9 = 3*3 = 3²

[tex]\sf \left(\dfrac{1}{27}\right)^{2-x}=9^{3x}\\\\[/tex]

 [tex]\left(\dfrac{1}{3^3}\right)^{2-x}=9^{3x}\\\\(3^{-3})^{2-x}=(3^2)^{3x}\\\\3^{(-3)*(2-x)}=3^{2*3x}\\\\3^{-6+3x} = 3^{6x}[/tex]

Bases are same, so now compare the exponents

     -6 + 3x = 6x

            3x = 6x + 6

       3x - 6x = 6

             -3x = 6

               x  = 6/(-3)

               [tex]\sf \boxed{\bf x = -2}[/tex]

         [tex](x^m)^n=x^{m*n}\\\\\left(\dfrac{1}{a^{m}}\right)=a^{-m}\\[/tex]

I think it's 12 because here it comes out

Answer:

the answer is 45

see the attachment photo!

Answer:

2/52 so the chance is unlikely.

Step-by-step explanation:

well I think I’m right because sometimes when my family has time we play blackjack in my house for fun or another card game so I should be right.

A parallelogram is a quadrilateral with four sides and the opposite sides of the parallelogram are equal and parallel.

In the given figure, AB||DC. AD is the transversal, such that:

∠A + ∠D = 180-degrees.

The parallelogram is a quadrilateral with equal such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees.

From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.

From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.

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Answer:

It always has an x coord of 0

The first step that we must take before attempting to solve a problem is to understand what it is asking for and what is given to us to help solve the problem.  Looking at the problem statement, we can see that they are asking what is true about the y-intercept.  We are given the information that the y-intercept is the place where a line crosses the y-axis.

Now that we have collected all that information, let us move onto understanding and solving the problem.  So first of all, using the information that was given to us, we know that the y-intercept is the place where a line crosses the y-axis.  The y-axis occurs where the x-coordinate is 0 and the x-axis occurs where the y-coordinate is 0.  Therefore, the option that would best fit the description that we have would be option A, it always has an x coordinate of 0.

no I dont feel like it is the answer

Answer:

the width is 59

Step-by-step explanation:

302/2-92=59

Answer:

f(x) = √x + 3

y = √x + 3

√x = y - 3

x = (y - 3)²

Hence inverse of f(x) = (x - 3)² and its domain is x >= 3.

Step-by-step explanation:

hope this helps

Answer:

See below

Step-by-step explanation:

Interest   3%   in decimal form is  .03

  interest in ONE year    7000 * .03

         interest in SEVEN years   7000 * .07 * 7

           this is added to the original deposit of 7000

              to become   7000 + 7000 * .03 * 7

                                        or  7000 ( 1 + .03*7 )

                                              or   7000 ( 1.21 ) = $ 8470

IF the interest is compounded

   the money in the account will be    7000 ( 1+.03)^7  

Answer: $7.40

Step-by-step explanation:

You can use $177.60 divide by 24 boxed lunches equals $7.40
Since you have to distribute 177.60 in 24 boxes.

Answer:

A.264

Step-by-step explanation:

((Area Of triangle*height)=Volume

Area of triangle is the base of the triangle multiplied by height of triangle divided by 2

((8*6)/2)*11=264

The study benefit from adding a control group as it would help in the correlation

A control group is s used to establish a cause-and-effect relationship by isolating the effect of an independent variable.

The best way to randomly place the bulls into the Therapy A, Therapy B, and control groups is random testing. The best blocking method will be breeding.

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