I have a math's problem in polynomials. please help.

Answer: Add the 1/3 to look for the r

1. The constant of proportionality when Ana runs 3/4 mile in 6 minutes is 0.125.

2. The missing value in the table will be 7.5 miles and 8.75 miles.

It should be noted that the constant of proportionality simply illustrates the ratio of two given values that have a proportional relationship.

1. In this case, Ana runs 3/4 mile in 6 minutes. Therefore, the constant of proportionality will be:

y = kx

where y = distance

x = time

3/4 = 6x

0.75 = 6k

Divide

k = 0.75 / 6

k = 0.125

The constant of proportionality is 0.125.

2. The missing value in the table will be:

y = kx

when x = 60.

y = 60 × 0.125 = 7.5 miles.

y = kx

when x = 70

y = 70 × 0.125 =8.75 miles.

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19. The fourth option is correct, as the angle is bisected.

20. 7x - 8 = 6x + 11 (since they are vertically opposite angles)

Answer:

for 7 i believe its D

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The vector equation for a line segment that joins two points P and Q can be found by subtracting the position vectors of P and Q and representing the result as a vector from P.

The position vector of point P is given by [0, -4, 4] and the position vector of point Q is given by [1/2, 1/3, 1/4]. So, the direction vector of the line segment is found by subtracting the position vectors:

d = Q - P = [1/2, 1/3, 1/4] - [0, -4, 4] = [1/2, 5/3, -3/4]

The vector equation of the line segment can be written as:

r(t) = P + t * d = [0, -4, 4] + t * [1/2, 5/3, -3/4] = [t/2, -4 + 5t/3, 4 - 3t/4]

where t is a scalar parameter that varies from 0 to 1 to give the points on the line segment between P and Q.

The parametric equations of the line segment are:

x(t) = t/2

y(t) = -4 + 5t/3

z(t) = 4 - 3t/4

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Find a vector equation and parametric equations for the line segment that joins P to Q?

P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )

vector equation r(t)

parametric equations x(t), y(t), z(t)

Answer:

Range of the third side of a triangle

Step-by-step explanation:

Any one side of a triangle must be shorter than the sum of the other two sides. Therefore, the third side length x must be between 5 and 35, not including those endpoints: 5 < x < 35. All whole numbers satisfying this range would form a triangle.

20 is a possible value for a third side

Answer:

20 minutes

Step-by-step explanation:

Find the speed per km. 2km/8min. This is 4 minutes per km.

Next, multiply the minutes per km by km. 4 min x 5 km.

This equals 20 :)

Answer:

20

1

20 firsts

Answer:

y= -2x-2

Step-by-step explanation:

y=mx + b

y=-2x -2

slope -2 (m=-2) thats your slope

Points are (-3,4) (1,-4)

y2 -y2   -4 - 4 = -8

x2 -x1     1 - -3 =  4

-8/4    simplify

-2/1  

Answer: $25.85 assuming annual compounding.

Step-by-step explanation:

PV=470

I/Y=5.5

N=1

CPT_FV

A. 40

B. 40

C. both companies' means are equal so it does not matter which one you choose

Aisha complete 9/ 10 of a Paragraph in 1 minute.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Aisha types 3/5 of a paragraph in 2/3 minute.

So, In one minute she types

= 3/5 ÷ ( 2/3)

= 3/5 x 3/2

= 9/ 10 Paragraph

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so in the template above for a conic, the defining components are the coefficients A and C

If either A=0 or C=0, then the equation is a parabola

if A=C, then we have a Circle

if either A or C is negative, and A≠C, then we have a hyperbola

if A and C are both positive or both negative, and A≠C, then we have an ellipse.

The answer is -\(\frac{(a + 4) ( a +5) }{(a +2)( a - 5)}\)

Simplify is making something simple. In mathematics, simplification means reducing the expression/ fraction/problem in a simpler form by using different operations.  

In the process of simplification, some basic rules are needed to be used. The principle of BODMAS (B= Bracket, O = Of, D = Division, M = Multiplication, A = Addition, S = Subtraction)must be followed for solving the questions.

The equation is :

\(\frac{a^{2} - 16 }{ a^{2} - 25 }\)   ÷   \(\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}\)

=\(\frac{a^{2} - 4^{2} }{a^{2} - 5^{2} }\)  ÷   \(\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}\)

= \(\frac{ (a +4 ) ( a - 4 )}{ (a + 5) ( a - 5 )}\)    ÷   \(\frac{a^{2} - 4a + 2a - 8}{a^{2} + 5a + 5a + 25}\) ( by applying middle term factor method)

(using \(a^{2} - b^{2}\) formula )

=  \(\frac{ (a+4) ( a-4 )}{(a +5 ) (a - 5)}\)     ÷      \(\frac{a(a -4) + 2 (a - 4)}{a (a + 5) + a (a + 5)}\) ( by applying middle term factor method)

=\(\frac{( a + 4) ( a - 4)}{( a + 5) ( a - 5)}\)     ÷  \(\frac{(a + 2) ( a -4)}{( a +5) (a+5)}\)

= \(\frac{( a +4)(a-4)}{(a + 5)(a - 5)\\}\)  *   \(\frac{(a + 5) ( a + 5)}{(a + 2) ( a - 4)}\)

=\(\frac{( a + 4) ( a + 5)}{(a + 2) ( a - 5)}\)

so, the answer is - \(\frac{( a + 4 ) ( a +5) }{( a + 2) ( a - 5)}\)

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We need to find an exponential regression for the data of the \(form y = ab^x\) where a is the initial amount, b is the base, and x is the time elapsed. Let's make a table of values to solve the given problem.

Table:

March 1, 2020 (day 0)10,000

March 4, 2020 (day 3)12,000

March 7, 2020 (day 6)15,000

March 10, 2020 (day 9)20,000

March 13, 2020 (day 12)25,000

March 16, 2020 (day 15)30,000

March 19, 2020 (day 18)40,000

March 22, 2020 (day 21)50,000

March 25, 2020 (day 24)65,000

March 28, 2020 (day 27)90,000

April 1, 2020 (day 31)240,000

Let's use the table to find the values of a and b. From the table, we can see that when \(x = 0, y = 10,000.\) So, the initial amount, a = 10,000.Let's use the points (3, 12,000) and (6, 15,000) to find b. Substituting these values in the equation:\(12,000 = 10,000b^315,000 = 10,000b^6\)

Taking the ratio of the above equations, we get:\(b^3 = 5/4 = > b = 1.118.\)

Now that we have found the values of a and b, we can write the equation:\(y = ab^x = > y = 10,000(1.118)^x\\\).

Now, let's move onto part (e) and explain the steps for finding the value of y for day 33 using the regression model found in part (a).

Step 1: Substitute the value of x = 33 in the regression model found in part (a).\(y = 10,000(1.118)^33\)

Step 2: Using a calculator, evaluate the value of y.\(y = 10,000(1.118)^33 = 2,036,782.35.\)

Hence, the predicted number of Total COVID-19 cases in the US on day 33 is approximately 2,036,782.35.

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The arc length covered by the central angle equal to 72° is 12.56°

Arc length is the distance between two points along a section of a curve.

Given that, a circle with radius 10 units and a central angle equals 72°, we need to find the arc length covered by the central angle = 72°

We know that,

Arc length = 2π × radius × (θ / 360°), where θ is the central angle

Arc length = 2 × 3.14 × 10 × 72°/360°

= 12.56°

Hence, the arc length covered by the central angle equal 72° is 12.56°

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Answer: Option C is correct

11.1 feet

Step-by-step explanation: Area of the square(A) is given by:

The solution to the differential equation Y"-y'-6y=0 with the initial conditions y(0)=1 and y'(0)=-1 is y(t) = 1/5 e^3t + 1/5 e^(-2t).

To solve the differential equation Y"-y'-6y=0 with the initial conditions y(0)=1 and y'(0)=-1 using Laplace transforms, we follow these steps,

Take the Laplace transform of both sides of the differential equation, using the property that the Laplace transform of a derivative is s times the Laplace transform of the function minus the initial value of the function,

L{Y''} - L{y'} - 6L{y} = 0

s^2 Y(s) - s y(0) - y'(0) - s Y(s) + y(0) - 6 Y(s) = 0

Substitute the initial conditions and solve for Y(s),

s^2 Y(s) - s - 1 - s Y(s) + 1 - 6 Y(s) = 0

Y(s) = (s-1) / (s^2 - s - 6)

Y(s) = (s-1) / ((s-3)(s+2))

Use partial fraction decomposition to express Y(s) as a sum of simpler fractions,

Y(s) = A / (s-3) + B / (s+2)

(s-1) / ((s-3)(s+2)) = A / (s-3) + B / (s+2)

s - 1 = A (s+2) + B (s-3)

satisfying this equation for s = 3 and s = -2, we have,

1 = 5A

-1 = -5B

Thus, A = 1/5 and B = 1/5.

So, we can write,

Y(s) = 1/5 * 1/(s-3) + 1/5 * 1/(s+2)

Take the inverse Laplace transform of Y(s) to obtain y(t),

y(t) = L^-1 {Y(s)}

y(t) = L^-1 {1/5 * 1/(s-3)} + L^-1 {1/5 * 1/(s+2)}

y(t) = 1/5 e^3t + 1/5 e^(-2t)

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Answer:

7,295.16

Step-by-step explanation:

A=p(1+i/m)^mn

A=9,500×(1+0.04÷4)^(4×3)

A=10,704.84

The balance she needs

18,000−10,704.84

=7,295.16

The class that lost the fewer pencils overall is Mr. Johnson's class. It had a median of 11.

A box plot is a graph used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers.

The whiskers represent the minimum and maximum values. In order to determine the class that lost fewer pencils, find the range of the data and the median. The class that has the smaller number lost fewer pencils.

The range is the difference between the highest and smallest number. Range of Mr. Johnson's class = 45 - 7 = 38

Range of Mrs Cheng's class = 50 - 5 = 45

Median is the number at the center of a dataset. The line in the middle of the box in the box plot represents the median.

The median of Mr. Johnson's class = 11

Median of Mrs. Cheng's class = 16

To determine the median, the initial step involves arranging the dataset in ascending order. When the number of data points is odd, the median can be determined by identifying the midpoint.

Given the data values, the median is calculated and it can be seen that the class that lost the fewer pencils overall is Mr. Johnson's class. It had a median of 11.

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Answer:

Step-by-step explanation:

Given:

MO bisects ∠KMN and LO bisects ∠KLN

To prove:

LK ≅ LN

             Statements                                                   Reasons

1). MO bisects ∠KMN                               1). Given

2). LO bisects ∠KLN                                2). Given

3). ∠KLM ≅ ∠NLM                                    3). Definition of angle bisector

4). ∠KMO ≅∠NMO                                   4). Definition of angle bisector

5). ∠KMO + ∠KML = 180°                         5). Linear pair postulate

6). ∠NMO + ∠NML = 180°                        6). Linear pair postulate

7). ∠KMO + ∠KML = ∠NMO + ∠NML       7). Transitive property of equality

8). ∠KMO + ∠KML = ∠KMO + ∠NML       8). Substitution property

9). ∠KML = ∠NML                                     9). Subtraction property of equaity

10).  LM ≅ LM                                           10). Reflexive property

11). ΔLKM ≅ ΔLNM                                   11). ASA property of congruence

12). LK ≅ LN                                              12). CPCTC

The length of the legs of the right triangle are 2.83 units.

A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the legs of the triangle can be found using trigonometric ratios.

Hence,

sin 45 = opposite / hypotenuse

sin 45 = a / 4

cross multiply

a = 4 × 0.70710678118

a = 2.83 units

Therefore,

cos 45 = b / 4

cross multiply

b = 0.70710678118 × 4

b = 2.82842712475

b = 2.83 units

Therefore, the legs are 2,83 units

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The total cost of each utility eliminating 450 tons of pollution is $180,000.

To calculate the total cost for each utility to eliminate 450 tons of pollution, we need to multiply the cost per ton of pollution elimination by the number of tons each utility needs to eliminate.

For People's Electric, the cost of eliminating one ton of pollution is $400. So, to eliminate 450 tons, the total cost would be 450 tons * $400/ton = $180,000.

For Municipal Energy, the cost of eliminating one ton of pollution is $350. Again, to eliminate 450 tons, the total cost would be 450 tons * $350/ton = $157,500.

Therefore, the total cost for each utility to eliminate 450 tons of pollution is $180,000 for People's Electric and $157,500 for Municipal Energy.

The cost calculation is based on the given information that each utility is provided with 450 pollution permits by the government. These permits allow them to legally produce a ton of pollution. By setting a limit on the number of permits, the government aims to reduce pollution by half. The utilities have the option to trade permits with each other.

In this scenario, People's Electric has a higher cost of eliminating pollution per ton compared to Municipal Energy ($400 vs. $350). It means that People's Electric would find it more expensive to reduce pollution through internal measures like investing in cleaner technology or implementing environmental initiatives. On the other hand, Municipal Energy has a lower cost, indicating that they have relatively more cost-effective methods for pollution reduction.

Given these costs, it is more beneficial for People's Electric to purchase permits from Municipal Energy rather than eliminating the pollution themselves. By purchasing permits, People's Electric can meet the pollution reduction target at a lower cost. Conversely, Municipal Energy can generate additional revenue by selling their permits.

This permit trading mechanism allows for cost efficiency in achieving the government's pollution reduction goal. The total cost for each utility is determined by multiplying the cost per ton of pollution elimination with the number of tons they need to eliminate.

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dy/dx at (1,7/13) = -32/169. To find dy/dx at (1,7/13), we need to take the derivative of both sides of the equation y/x-6y = x^5 + 4 with respect to x. Using the quotient rule and simplifying, we get:

The first step to evaluate dx/dx is to realize that dx/dx is simply equal to 1. This is because we are taking the derivative of x with respect to x, which is the same as saying "how much does x change when x changes?" and the answer is always 1. Therefore, dx/dx = 1.
dy/dx = (6y - x(x^5 + 4))/(x-6y)^2
Substituting (1,7/13) into this equation, we get:
dy/dx at (1,7/13) = (6(7/13) - 1(1^5 + 4))/(1-6(7/13))^2
Simplifying, we get:
dy/dx at (1,7/13) = (35/13 - 5)/(1 - 42/13)^2 = (-32/169)
Therefore, the answer is:
dx/dx = 1
dy/dx at (1,7/13) = -32/169
Overall, it is important to remember the basic rules of derivatives and to carefully plug in the given point when evaluating dy/dx.

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Answer:

x = -2

Step-by-step explanation:

3/2 (x-5) - 3/2 = 9x/2

3x/2 - 15/2 - 3/2 = 9x/2 ... alldenominator

are 2 so we can multiply all term by 2

2(3x/2 - 15/2 - 3/2 = 9x/2)

3x - 15 - 3 = 9x ... simplify it

3x - 12 = 9x

-12 = 9x - 3x ... take 3x to the left

-12 = 6x ... simplify

6x/6 = -12/6 ... dividing both side by 6

x = -2 ... simplify and solve x

The probability of Margo being paired with Irma will be = 1/29

As per the data given,

Total number of students participated in the quiz = 30

Since each student must be paired with exactly one other student, there are 29 possible students that Margo could be paired with.

Since Irma is Margo's best friend, there is only one possibility for Margo's pairing that would result in her being paired with Irma.

The probability of Margo being paired with Irma is 1 out of 29 possible pairings, so the answer is = 1/29

This is the exact probability, expressed as a common fraction.

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Answer:

Below

Step-by-step explanation:

Slope of BLACK line = rise/run =   9  / 3 = m =  3  

  y intercept = b = 2       Line eq =  y = mx+ b    y = 3x +2

Slope of BLUE line   similarly is  9 / -3  = m = -3

   and b = 8

     y = mx + b      y = -3x + 8