Q2: How do you use the distance formula and slope formula to classify quadrilaterals

Answer:

Step-by-step explanation:

This is an easier way

\(-10p<-70\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-10p\right)\left(-1\right)>\left(-70\right)\left(-1\right)\\\\Simplify\\\left(-10p\right)\left(-1\right)>\left(-70\right)\left(-1\right)\\\\\mathrm{Divide\:both\:sides\:by\:}10\\\frac{10p}{10}>\frac{70}{10}\\\\Simplify\\p>7\)

I think this is what u meant

\(\frac{-10p}{-10} < \frac{-70}{-10} \\\\p > 7\)

To count the number of relations R on set A such that at least one ordered pair in R has element a as its first element, we can consider the total number of relations on A and subtract the number of relations that do not have a as the first element in any ordered pair.

Given:

- Set A has 6 elements.

- Element a is one of the elements in A.

- Element b is also an element in A, and it is distinct from element a.

The total number of relations on set A is given by 2^(n^2), where n is the number of elements in A. In this case, n = 6.

Total number of relations on A = 2^(6^2) = 2^36

Now, let's calculate the number of relations on A that do not have a as the first element in any ordered pair. For any ordered pair in a relation, the first element can be any of the remaining 5 elements in A (excluding a). Similarly, the second element can be any of the 6 elements in A.

Number of relations without a as the first element = 5 * 6^2 = 180

Therefore, the number of relations R on A such that at least one ordered pair in R has a as its first element is:

Number of relations with a as the first element = Total number of relations on A - Number of relations without a as the first element

Number of relations with a as the first element = 2^36 - 180

Please note that the resulting number is an extremely large number.

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a) The growth rate is, x = 23.89%

b)  A function that models the population P(t), for t months after my initial 6 mice.

⇒ P (t) = 6\(e^{rt}\)

c) The population of mice will I have after 1 year is, 105.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

I start out with 6 mice.

And, The population of mice triples every 2 months.

Here, The mice population is exponential.

Hence, We get;

The formula is,

P (n) = 3 eⁿˣ

Where, x is rate after n months.

Since,  The population of mice triples every 2 months.

Hence, We get;

18 = 6 e²ˣ

3 = e²ˣ

2x = log 3

x = 0.4772/2

x = 0.2389

x = 23.89%

And, A function that models the population P(t), for t months after my initial 6 mice.

⇒ P (t) = 6\(e^{rt}\)

And, The population of mice will I have after 1 year is,

⇒ P (t) = 6\(e^{rt}\)

⇒ P (t) = 6 × 17.46

⇒ P (t) = 105

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Given, Two vertical poles of length 6 feet and 8 feet, respectively, stand 10 feet apart.

A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. We need to express the amount of cable used, f, as a function of the distance from the 6-foot pole to the point where the cable touches the ground, x.

[asy]
size(200);
draw((0,0)--(8,0)--(8,10)--(0,6)--cycle);
draw((0,6)--(8,8));
label("$6$",(0,0)--(0,6),W);
label("$8$",(8,0)--(8,8),E);
label("$x$",(0,0)--(0,6),NW);
label("$10-x$",(0,6)--(0,10),W);
label("$y$",(8,0)--(8,8),NE);
label("$10$",(0,0)--(8,0),S);
[/asy]

Let the height of the point where the cable touches the ground be y. Then the distance from the 6-foot pole to the point where the cable touches the ground, x = 10 - y.

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Partial derivative with respect to\(X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ\)

Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)

The first partial derivatives of the function F(X,Y) = X2Y - 3Y2 + X/(X + Y)2 + XY2e-XZ can be found by taking the partial derivative with respect to each of the variables X and Y separately.
For the partial derivative with respect to X, we have:
Partial derivative with respect to X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ
For the partial derivative with respect to Y, we have:
Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)
This completes the calculation of the first partial derivatives of the function F(X,Y).
The first partial derivatives of the functions are given below:

\(F(x, y) = x^2y - 3y^2\)

The first partial derivative with respect to x,

Fx (x, y) = 2xy

The first partial derivative with respect to y,\(Fy (x, y) = x^2 - 6yW = xy^2 e^-xz\)

The first partial derivative with respect to x,

\(Wx (x, y, z) = y^2e^-xz - x^2y^2e^-xz\)

The first partial derivative with respect to y, Wy (x, y, z) = 2xye^-xz

The first partial derivative with respect to z, \(Wz (x, y, z) = -xy^2e^-xz\)

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Answer:

Green parachute

Explanation:

Orange parachute

• Distance = 12 feet

• Time = 5 seconds

Rate of descent = 12/5 =2.4 feet/seconds

Green parachute

• Distance = 14 feet

• Time = 7 seconds

Rate of descent = 14/7 =2 feet/seconds

Since 2 is less than 2.4, the green parachute has a slower descent.

Answer:

(a) 494₁₀ = 111101110₂

(b) 494₁₀ = 13232₄

(c) 494₁₀ = 3434₅

(d) 494₁₀ = 756₈

(e) 494₁₀ = 608₁₀

Step-by-step explanation:

494₁₀ means the number is to the base 10 and therefore a decimal number which we interpret in everyday terms as just 494

To convert a number from base 10 to another base, say b, we continuously divide by that base, noting the remainder at each operation. Then we read the remainders from the last to the first and that will give you the number in terms of that other base

This is a tedious operation and best done by a base conversion calculator.

I will demonstrate using base 9 as an example

494₁₀ = what in base 9

Keep dividing by 9 until you can divide no more. Keep track of the remainder at each division

operation        quotient    remainder

494 ÷  9             54                8
54  ÷  9               6                0
   6  ÷ 9               0                6

Read the remainders from the last to the first: 6 0 8
So 494₁₀ = 608₉

The others can be done in a similar manner

However this is tedious and a computer program is easy to write for this conversion

Search for number base conversion calculator - you will find several online.

I have provided the answers for you to verify

The required value of the sample standard deviation is 5.

The term" standard deviation" refers to the degree of dissipation of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Let's first review the information that has been provided: sample size m is 5, a total of x equals 20, and the sum of x squared equals 118 points. Discovering the sample standard deviation is the task.

First, let's review the formula for the sample standard deviation: it is equal to the root square sum of x square minus the sum of x in a square divided by n sample size divided by n minus 1 point.

Consequently, let's compute as follows: root square 118, minus 20 square, divided by 5, divided by 5, minus 1 point s, equals root square of 25 points, and the resultant value of s will be 5. We can now state that the requested sample standard deviation is equal to 5.

Hence, the requested sample standard deviation is equal to 5.

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Answer:

132.73228961417

Step-by-step explanation:

area = pi/4 * diameter^2(squared)

According to the question, the best estimate for the percentage of people who were affected by the outbreak is approximately 0.086%.

To estimate the percentage of people affected by the outbreak, we can use the following formula:

\(\[\text{Percentage} = \left(\frac{\text{Affected}}{\text{Total population}}\right) \times 100\]\)

Given that the number of affected people is 224,000 and the total population is 260,000,000, we can substitute these values into the formula:

\(\[\text{Percentage} = \left(\frac{224,000}{260,000,000}\right) \times 100\]\)

Calculating this expression, we find:

\(\[\text{Percentage} \approx 0.086 \%\]\)

Therefore, the best estimate for the percentage of people who were affected by the outbreak is approximately 0.086%.

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Answer:

g=11/12

Step-by-step explanation:

4g+8g=12-1

12g=11

g=11/12

Answer: 7%

(Hope this is right.)

Step-by-step explanation:

Let's solve this using the information we have and an equation.

Shane: $32,000 - (Given)

Theresa: 18,000+14x, if x=1,160 - (Given)

---------------------------------------------------------------

Step two: (Theresa) 14(1,160) =16,240 (Algebra)

Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.

---------------------------------------------------------------

Finally,

They're asking for how much more she paid for her car as a percentage of what Shane paid.

34,240-32,000=2,240 and

2,240/32,000=0.07

0.07x100=7

Answer 7% more than what Shane paid.

We need to find the general solution of the above PDE. Let's solve the above PDE by the method of characteristic. Let us first solve the PDE by using the method of characteristics.

The method of characteristics is a well-known method that provides a solution to the first-order partial differential equations. To use this method, we first need to find the characteristic curves of the given PDE. Thus, the characteristic curves are given by $x = t + c_1$.

Now, we need to eliminate $t$ from the above equations in order to obtain the general solution. By eliminating $t$, we get the general solution as:$$u(x,y) = f(2x - 3y) + 3(x - 2y)$$ where $f$ is an arbitrary function of one variable. Hence, the general solution of the PDE $u_{xx} - 2u_{xy} - 3u_{yy} = 0$ is given by the above equation. Thus, the main answer to the given question is $u(x,y) = f(2x - 3y) + 3(x - 2y)$. In order to find the general solution of the PDE $u_{xx} - 2u_{xy} - 3u_{yy} = 0$, we first used the method of characteristics. The method of characteristics is a well-known method that provides a solution to the first-order partial differential equations.

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The collection of outcomes for the event e of rolling a sum of 5 contains 4 possible outcomes: {1, 4}, {2, 3}, {3, 2}, {4, 1}.

To find the number of outcomes in the event of rolling a sum of 5, we need to determine all the possible ways to get a sum of 5 when rolling two number cubes.

There are several ways to get a sum of 5

The first cube lands on 1 and the second cube lands on 4.

The first cube lands on 2 and the second cube lands on 3.

The first cube lands on 3 and the second cube lands on 2.

The first cube lands on 4 and the second cube lands on 1.

Therefore, the collection of outcomes for the event e of rolling a sum of 5 contains 4 possible outcomes

{1, 4}, {2, 3}, {3, 2}, {4, 1}

So, there are 4 outcomes in the collection for event e.

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Answer: its (4f 5) ^3

Step-by-step explanation:

The prompt on arcs and chords is to test your ability to recognize congruent patterns.

G) Note that ∡AB = 82°

H) UV = 6; and

I) Secant QR = 15

G) Note that ∡ED = 82° and is given to be congruent to ∡AB hence, ∡AB = 82°. This is because the degree measure of a minor arc is equal to the measure of the central angle that intercepts it. Since the central angle here is 82°, hence, the arc AB is also 82°

H) UV is a chord. So is UT. They both are congruent, that is =67°.

Since the we know that the Chord UT = 6, then Line segment UV must also be 6.

I) In this case we are given two sets of diagrams.

The first indicates that the Secant is of length 15 and creates an arc of 120°.  If that is the case, and QR is also a secant creating an arc ∡QR of 120° then Secant QR must also be 15.

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x2−4x+3=0

For this equation: a=1, b=-4, c=3

1x2+−4x+3=0

Step 1: Use quadratic formula with a=1, b=-4, c=3.

x=

−b±√b2−4ac

2a

x=

−(−4)±√(−4)2−4(1)(3)

2(1)

x=

4±√4

2

x=3 or x=1

Answer:

x = 1, x = 3

Step-by-step explanation:

x² - 4x + 3 = 0

consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term (- 4)

the factors are - 1 and - 3 , since

- 1 × - 3 = + 3 and - 1 - 3 = - 4 , then

(x - 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 3 = 0 ⇒ x = 3

EXPLANATION

We are asked to describe the translation of the functions with respect to f(x) =x

To translate the function up and down, you simply add or subtract numbers from the whole function. If you add a positive number (or subtract a negative number), you translate the function up. If you subtract a positive number (or add a negative number), you translate the function down.

In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.

To do so, we will have to plot the graph of each function and compare it with f(x) represented by the red lines below

Part A

Thus, we will have

For part B

when

The translation here is

Part C

For the function

The graph is

Thus, we have the translation as A horizontal shift to the left by 2 units

Part D

The given function is

The transformed graph is

The translation is a shift to the right by 7.5 units

The turning point of the function in this problem is given as follows:

(-5,2).

The function for this problem is defined as follows:

\(f(x) = 2\sqrt[3]{x + 5} + 1\)

The parent function is the cube root function, which has a turning point at (0,0).

The transformations are given as follows:

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The cost described in the scenario is an example of a mixed cost.

A mixed cost consists of both fixed and variable components. In this case, the $10 per month base charge represents the fixed component of the cost. This charge remains constant regardless of the amount of electricity consumed. It covers the basic service and is not influenced by usage levels.

On the other hand, the additional charge of $0.08 per kilowatt-hour (kWh) of electricity used represents the variable component. This charge varies directly with the amount of electricity consumed. As more electricity is used, the variable cost increases proportionally.

By combining the fixed base charge and the variable charge per kWh, we get a mixed cost structure. The fixed component ensures a minimum cost for the service, while the variable component adds to the total cost based on actual usage. This combination of fixed and variable elements makes the cost a mixed cost.

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∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Given:

Three lines AD, CF, and BE are intersecting each other at the midpoint O.

To prove:

∠CFA ≅ ∠EDA

Proof:

Given that AD, CF, and BE intersect at the midpoint O.

By definition of a midpoint, OA ≅ OD, OB ≅ OE.

OA = OD and OB = OE.

Triangle OAD ≅ Triangle OBE (By Side-Side-Side congruence).

∠OAD ≅ ∠OBE (By Corresponding Parts of Congruent Triangles are Congruent).

∠CFA and ∠EDA are vertical angles.

∠OAD ≅ ∠CFA and ∠OBE ≅ ∠EDA (By Vertical Angles are Congruent).

Therefore, ∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Hence, it is proven that ∠CFA ≅ ∠EDA.

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Answer:

\(\huge\boxed{\sf 6xy-3x^2}\)

Step-by-step explanation:

Given Expression:

(x + y)² - (x - y)² + 2xy - 3x²​

Formulas used:

Expand the above expression according to the formulas

\(=x^2+2xy+y^2-(x^2-2xy+y^2)+2xy-3x^2\\\\= x^2+2xy+y^2-x^2+2xy-y^2+2xy-3x^2\\\\cancel \ out \ x^2 \ and \ y^2\\\\= 2xy+2xy+2xy-3x^2\\\\= 6xy-3x^2\\\\\rule[225]{225}{2}\)

the sum of the interior angles of a parallelogram is 360°,

we have the next angles equals

m

m

With this in mind, we can have the next equation

51+51+28x-11+28x-11=360

we sum similar terms

80+56x=360

we isolate the x

56x=360-80

56x=280

x=280/56

x=5

666    HELL HELL HELL HELL