Write a line in slope-intercept from that goes through the point (2, 5) with a slope of 1/2​

The volume of the snowball is decreasing at a rate of 10.24π cm³/min when the diameter is 8 cm.

The diameter of the spherical snowball is decreasing at a rate of -0.2 cm/min. The rate of decrease of diameter is a sign of negative. Let us first find the radius of the spherical snowball using the diameter equation.The diameter of a sphere = 2r, therefore,2r = diameter = 8 cm ⇒ r = 4 cmNow, we need to find the rate of decrease in volume of the snowball when the diameter is 8 cm. The volume of a sphere is given by the formula V = 4/3πr³Differentiating V with respect to time, we getdV/dt = 4πr² × dr/dtPut the values of r and dr/dt,dV/dt = 4π(4)² × (-0.2) = -10.24π cm³/min.

Therefore, the volume of the snowball is decreasing at a rate of 10.24π cm³/min when the diameter is 8 cm.

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The correct expression representing the value stored in the variable x after executing the given program is: a. 2*3*3*3 This is because the program starts with x having a value of 2 and then multiplies x by 3 four times in a row.

The expression that represents the value stored in the variable x as a result of executing the program is option D: 24*4*4*4. This is because the program starts with the x being assigned the value 2, and then the instruction "XX * 3" is executed 4 times.

This means that the value of x is multiplied by 3, four times in a row. So, the final value of x will be 2 * 3 * 3 * 3 * 3, which simplifies to 24 * 4 * 4 * 4.

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Answer:

His savings be $32 and spendings be $112.

Step-by-step explanation:

Let her savings and spending be 2x and 7x.

Total earning is equal to the sum of savings and spending.

ATQ,

2x+7x=144

9x=144

x = 16

Savings = 2x = 2(16) = $32

Spendings = 7x = 7(16) = $112

Hence, his savings be $32 and spendings be $112.

The example that meets the given specific conditions that 3 × 3 nonzero matrices and ab = 033 are a = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\1&0&0\end{array}\right]\) and b = \(\left[\begin{array}{ccc}0&1&1\\0&0&0\\0&0&0\end{array}\right]\).

To get such examples where matrix's configuration is 3 x 3 and the multiplication of the matrix is equal to zero, we need to take such values on a specific position so that the multiplication results in zero. We have been given certain conditions, which needs to be taken care of.

According to the question given, a and b are 3 × 3 nonzero matrices:

a = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\1&0&0\end{array}\right]\)

b = \(\left[\begin{array}{ccc}0&1&1\\0&0&0\\0&0&0\end{array}\right]\)

Now, multiplication of a and b results:

ab = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\1&0&0\end{array}\right] * \left[\begin{array}{ccc}0&1&1\\0&0&0\\0&0&0\end{array}\right]\)

ab = \(\left[\begin{array}{ccc}0*0 + 0*0 + 0*0& 0*1 + 0*0 + 0*0&0*1 + 0*0 + 0*0\\0*0 + 0*0 + 0*0&0*1 + 0*0 + 0*0&0*1 + 0*0 + 0*0\\0*0 + 0*0 + 1*0&0*1 + 0*0 + 0*0&0*1 + 0*0 + 1*0\end{array}\right]\)

ab = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right]\)

Therefore, the example that meets all the given specific conditions in the question are a = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\1&0&0\end{array}\right]\) and b = \(\left[\begin{array}{ccc}0&1&1\\0&0&0\\0&0&0\end{array}\right]\).

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Answer:

By the vertical Angles Theorem , < 1 = <2 and < 4 = <3.  <1 = <4 is given , so <2 = <3 by the transitive property of Congruence.

Step-by-step explanation:

By the vertical Angles Theorem , < 1 = <2 and < 4 = <3.  <1 = <4 is given , so <2 = <3 by the transitive property of Congruence.

The transitive property of congruence states that two objects that are congruent to a third object are also congruent to each other

1 =4

and 4=3

and 1=2

so 2=3

Answer:

Step-by-step explanation:

The equation that Dimitri and Jillian were trying to solve is expressed as

(x+1)(x+3) = 12. They are both solving this equation to get the value of x.

Based on the their suggestion, Jillian strategy would have been the best and the only one that will work for us in solving the equation but he didn't take cognizance of 12 when using the formula in his second step hence None of them are correct. The following steps should have been taken;

Step 1: Multiply out the expression (x+1)(x+3)

= (x+1)(x+3)

= x(x)+ 3x+x+1(3)

= x² + 3x + x + 3

= x² + 4x + 3

He got x² + 4x + 3 on expansion

Step 2: He should have rewrote the equation as shown;

x² + 4x + 3 = 12

x² + 4x + 3 -12 = 0

x² + 4x -9 = 0

Step 3: He used the quadratic formula to factorize the expression x² + 4x + 3 where a = 1, b = 4 anad c = -9

x = (-b±√b²-4ac)/2a

x = (-4±√(4)²-4(1)(-9))/2(1)

x = -4±√16+36/2

x = (-4±2√13)/2

x = (-4+2√13)/2 or  (-4-2√13)/2

x = -2+√13 or -2-√13

Hence Neither of them is correct. Jillian is almost correct but he should have equated the equation to zero by taking 12 into consideration before factorizing.

soln,

2x+3x+x=180[Being angle on a line]

or,6x=180

or,x=180/6

or,x=30

Please give me brainliest answer

a. The first equation for x2 and substitute the result into the second equation obtaining a second order IVP in terms of X1 can be solved as  x1(0) = -2, x1'(0) = 4

b. The second order IVP found in part (a) can be solve as x1(t) = 2e^(-0.25t)sin(1.984t)

c. Using answer from part b we get  22 = -3.968e^(0.25t)sin(1.984t)

d.  The solution of the system in vector form is x(t) = [x1(t), x2(t)]^T = [2e^(-0.25t)sin(1.984t), 0.5x1(t) + x1'(t)]^T

(a) Solving the first equation for x2, we have:

x2 = 0.5x1 + x1'

Substituting this expression for x2 into the second equation, we get:

x1'' + 0.5x1' + 2.5x1 = 0, x1(0) = -2, x1'(0) = 4

This is a second order linear homogeneous differential equation with constant coefficients.

(b) The characteristic equation is:

r^2 + 0.5r + 2.5 = 0

Using the quadratic formula, we find the roots:

r1 = -0.25 + 1.984i, r2 = -0.25 - 1.984i

The general solution is:

x1(t) = e^(-0.25t)(c1cos(1.984t) + c2sin(1.984t))

Using the initial conditions, we get:

x1(t) = 2e^(-0.25t)sin(1.984t)

(c) Using the first equation from the system of differential equations, we have:

x1' = 0.5x1 + 2x2

Substituting x2 = 0.5x1 + x1', we get:

x1' = 0.5x1 + 2(0.5x1 + x1') = 2x1' + 1.5x1

Rearranging terms, we get:

x1' + 0.5x1 = 0

Taking the derivative of x1'(t) = 2e^(-0.25t)cos(1.984t) and substituting into the above equation, we get:

2e^(-0.25t)(-0.25sin(1.984t) - 1.984cos(1.984t)) + 0.5(2e^(-0.25t)sin(1.984t)) = 0

Simplifying, we get:

22 = -3.968e^(0.25t)sin(1.984t)

(d) The solution of the system in vector form is:

x(t) = [x1(t), x2(t)]^T = [2e^(-0.25t)sin(1.984t), 0.5x1(t) + x1'(t)]^T

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Answer:

Value  of the car after depreciation = $800.

Step-by-step explanation:

Formula to get the final value of the car after depreciation of the car price,

Final value = \(\text{Initial value}(1-\frac{r}{100})^{\frac{t}{n} }\)

Here, t = Number of years after the purchase

n = Number of years for the depreciation of price by half

By substituting values in the formula,

Final value = \(40000(1-\frac{50}{100})^{\frac{17}{3}}\)

                  = \(40000(0.5)^{\frac{17}{3}}\)

                  = $787.451

                  ≈ $800 [Nearest hundred dollars]

Therefore, after 17 years value of the new car will be $800.

Answer:

21 male students

Step-by-step explanation:

For every teacher on the trip, 3 male students and 5 female students are there

If there are 35 female students, we have to divide that by 5 to find the number of teachers

35 divided by 5 is 7

There are seven teachers, so we multiply by 3 to find the number of male students

7 x 3 = 21

There are 21 male students on the school field trip

Answer:

no

Step-by-step explanation:

Order of operations

18/2=9

9/3=3

5-2=3

3/3

1 (simplified)

The outcome is still the same but since you have to show your work.....That's the correct way to do it

Hope this helps. Have a nice day.

Answer:

the answer is D) 300 π

Step-by-step explanation:

Formula for Area of sector is:

θ/360° * π * (r)^2

here,

θ= 30° and radius= 60 in

so, after we substitute, we get:

30/360* π* 60*60       after simplifying we get:

= 1/12* π* 5*60

=300π

Hope it helps.

Answer:

D

Step-by-step explanation:

area of sector=

\( \frac{theta}{360} \times \pi \: r {}^{2} \\ \\ \frac{30}{360} \times \pi \: (60) {}^{2} \\ \\ 300\pi\)

360

The experimental and theoretical probabilities for the given experiment are:

i) The experimental probability of rolling a 2 is equal to the quotient between the number of times that the outcome was a 2 and the total number of times that the number cube was rolled, so the probability is:

P = 8/50 = 0.16

ii) The theoretical probability assumes that all the numbers (6) have the same probability of rolling up.

Then all the numbers have a probability of 1/6.

This means that the theoretical probability of rolling a 2 is:

P(2) = 1/6 = 0.167

iii) The experimental probability of NOT rolling a 2 is computed in a similar way than the first one, if out of 50 rolls, in 8 we rolled a 2, then in 42 we did not rolled a 2.

So the probability is:

P = 42/50 = 0.84

iv) The theoretical probability of not rolling a 2 is equal to 1 minus the theoretical probability of rolling a 2.

P = 1 - 1/6 = 5/6 = 0.833...

v) For the experimental probability of getting a 1, we see that out of 50 rolls, in 10 we rolled a 1, so the probability is:

P = 10/50 = 1/5 = 0.2

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The integral of \(\int {x(25x^2 + 1)} \, dx\) is \(\frac{25}{4}x^4 + \frac{x^2}{2} + C\)

The integral expression is given as:

\(\int {x(25x^2 + 1)} \, dx\)

Start by expanding the bracket

\(\int {25x^3 + x} \, dx\)

Next, we integrate each term in the expression

\(\frac{25}{4}x^4 + \frac{x^2}{2} + C\)

Hence, the integral of \(\int {x(25x^2 + 1)} \, dx\) is \(\frac{25}{4}x^4 + \frac{x^2}{2} + C\)

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Answer:

Hey there!

The answer is -12

They are using the foil method, First, Outer, Inner, Last.

Let me know if this helps :)

The missing term is -12 in the given equation. which is the correct answer would be option (A).

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.

The two factors are given in the question.

⇒ (2x - 3)(7x + 4)

We have to determine the polynomial of the given factors

⇒ (2x - 3)(7x + 4)

⇒ 2x (7x + 4) - 3(7x + 4)

Apply the distributive property of multiplication,

⇒ 2x × 7x + 2x × 4 - 3 × 7x - 3 × 4

⇒ 14x² + 8x -21x - 12

Comparing to the given equation, then we find the missing term is -12.

Therefore, the correct answer would be an option (A).

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The matrix A representing the linear transformation T is [5 -2; 0 6].

To find the matrix A that represents a linear transformation T, we need to determine the images of the standard basis vectors under T and use them to form the columns of A. In this case, we are given that T(1,0) = (5,0) and T(0,1) = (-2,6). These correspond to the first and second columns of A, respectively. Therefore, the matrix A is:

A = [5 -2]

[0 6]

To apply T to any vector x, we simply multiply it by A:

T(x) = Ax

So, if we have a vector x = [x1, x2], we can calculate T(x) as follows:

T(x) = [5x1 - 2x2, 6x2]

Thus, A fully characterizes the transformation T and enables the computation of T(x) for any given vector x.

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The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as = 2 * 10^-7

A canonical, normal, or standard form of a mathematical object is a conventional manner of presenting that item as a mathematical expression in mathematics and computer science. It is frequently the one that gives the simplest representation of an item and allows it to be identified in a unique fashion.

A quantity is said to be stated in standard form if it is written as the product of a power of ten and a number higher than or equal to one but less than ten (or scientific notation).

The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as follows:

=3.6 * 10^-5 / (1.8 * 10^2)

= (3.6 / 1.8) * (10^-5 / 10^2)

= 2 * 10^-7

Therefore, the answer in standard form is 2 * 10^-7.

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The advantages of the 'Monthly Reporting Form' are given below:a) Reduced administrative hassle compared to single shot: Monthly reporting forms reduce the workload of administrative work that may have been required if it was a single-shot.

For instance, when it comes to accounting and finance, monthly reporting can help to reduce the administrative burden that comes with running a business. This is because monthly reporting makes it easier to keep track of financial data, ensuring that records are updated on a more frequent basis.

There is a lower rate associated with monthly reporting forms as they can offer a reduction in cost compared to single-shot options. This is because they can save time and money in the long run, reducing the amount of work and administration required to keep track of things.

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Answer: yes Jim is correct

Each side of the quadrilateral is congruent. Then the quadrilateral is known as the rhombus.

The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.

If all the sides of the quadrilateral are congruent then the quadrilateral may be a square or rhombus.

If none of the angles of that quadrilateral is equal to 90 degrees. Then the quadrilateral is known as a rhombus.

Jim is experimenting with a new drawing program on his computer. He created quadrilateral TEAM with coordinates T(- 2, 3), E(- 5, - 4), A(2, - 1) , and M(5, 6) .

The diagram is given below.

From the diagram, each side of the quadrilateral is congruent. Then the quadrilateral is known as the rhombus.

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Answer:

is the line or line segment that divides the angle into two equal parts

Step-by-step explanation:

The required coordinates of E is [150/13,50/13].

Given,

A=[3,3], B=[-3,5], C=[-1,-2] and D=[3,-1]

The points A, B, C and D form a quadrangle in the xy-plane.

Line segments AC and BD intersect each other in a point E.

We have to find the coordinates of E.

To find the coordinates of E, we will first find the equations of line segments AC and BD.AC: A[3,3] and C[-1,-2]

So, the equation of line segment AC is given by(3,3) and (-1,-2) will satisfy the equation y = mx + c,

where

m is the slope and c is the y-intercept.

Substituting (3,3) in y = mx + c, we have

3 = 3m + c

Substituting (-1,-2) in y = mx + c,

we have

-2 = -m + c

Solving these equations, we get the value of m and c as:

m = -1/2 and c = 5/2

The equation of line segment AC is

y = -1/2 x + 5/2BD: B[-3,5] and D[3,-1]

So, the equation of line segment BD is given by (-3,5) and (3,-1) will satisfy the equation y = mx + c, where m is the slope and c is the y-intercept.

Substituting (-3,5) in y = mx + c, we have5 = -3m + c

Substituting (3,-1) in y = mx + c, we have-1 = 3m + c

Solving these equations, we get the value of m and c as:

m = -2/3 and c = 7/3

The equation of line segment BD is

y = -2/3 x + 7/3

We will now equate these two equations to find the point of intersection (x,y) of the two line segments.

AC : y = -1/2 x + 5/2...equation(1)

BD: y = -2/3 x + 7/3...equation(2)

Equating (1) and (2),

we get

-1/2 x + 5/2 = -2/3 x + 7/3

Simplifying this equation, we get

x = 150/13

Substituting this value of x in equation (1), we get

y = 50/13

So, the coordinates of E are (150/13, 50/13).

Therefore, the required coordinates of E is [150/13,50/13].

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Answer:

.25 kilometers

Step-by-step explanation:

Divide the length value by 1000 when going from meters to kilometers

Answer:

Step-by-step explanation:

The price is x

50% of the price is $35

Answer is $70

Answer:

Step-by-step explanation:

50% off the price of $35

= $35 ( 0.50)

= $17.50 (price now)

The cost to ship 2000 lbs of goods from Atlanta to New Orleans using overnight shipping is $8000 option (A).

To calculate the cost of shipping 2000 lbs of goods from Atlanta to New Orleans (470 miles) using overnight shipping, we need to determine the appropriate price per 100 lbs based on the given distance and then apply the 100% premium for overnight shipping.

First, we need to determine the price per 100 lbs based on the distance of 470 miles. Looking at the given table, the distance falls into the range of 401-600 miles, which has a price of $200 per 100 lbs.

Since we have 2000 lbs of goods, we need to calculate the number of 100 lb units: 2000 lbs / 100 lbs = 20 units.

Now, we can calculate the cost of shipping without the overnight premium: 20 units * $200 per unit = $4000.

As the premium for overnight shipping is 100%, we need to double the cost: $4000 * 2 = $8000.

Hence, the correct answer is A) $8,000.

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Answer:

There are 3 roses in the garden.

Step-by-step explanation:

If there are 5 times as man tulips in the garden as the roses, you would have to count 3, 5 times in order to get 15 which brings us to the answer of 3 roses in the garden.

Complete question:

Joelwants to buy a new tablet computer from a store having a 20% off sale on all tablet. The tablet he wants has an original cost of $190. He also wants to make sure he has enough money to pay the 5% sales tax.

Answer:

$159.60

Step-by-step explanation:

Given the following :

Sales tax = 5%

Percentage discount = 20%

Original cost = $190

Joel's incorrect expression : 0.95(190)(0.8)

Joel's mistake is the 0.95 which is equivalent to 95% used in Calculating the total cost of the computer. The sales tax increases the total cost of the computer and instead of subtracting 5% sales tax, it should be added.

B.) 20% discount = 0.2 will be deducted from 100%(1)

1 - 0.2 = 0.8

5% sales tax = 0.05 will be added :

1 + 0.05 = 1.05

Original cost = $190

Therefore,

Total cost : Original cost * sales tax * discount

Total cost = $190 * 1.05 * 0.8

Total cost = $159.60

Answer:

706.5

(there is no hundredths place)

Step-by-step explanation:

r=15

a= pi × r²

3.14×15²

15²=225

3.14×225=706.5

Answer:

We can make 120 three digit distinct numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the number is xyz, we have:

Total number of possible 3-digit numbers: