the equation of a straight line L1 is given as 3x plus 2y is equal to 12. Another line L2 is perpendicular to L1 at (2,9).

(a) Find the equation of L2 in the fom y is equal to mx plus c where m and c are constants
(b) Another line L3 is parallel to L1 and passes through point (-4,-1). Find
(i) The equation of L2 in the form ax plus by is equal to c where m and c are intergers
(ii) The x and y intercepts of L3
(iii) The point of intersception between L2 and L3

The Earth's human population, approximately 7,900,000,000 people, can be expressed using scientific notation as 7.9 x 10^9.

Scientific notation is used to express extremely large numbers using a number between 1 and 10.

In this case, that number is 7.9

We need to move that decimal spot 9 places to the right to get 7,900,000,000. Therfore, to state that number in scientific notation, we would write it as:

7.9 * 10^9

~~~Harsha~~~

The equivalent statement using parenthesis using the de Morgan laws would be (not q) or (not p).

De Morgan's Laws. To write an equivalent statement using parentheses for P and not Q (P ∧ ¬Q), we'll apply De Morgan's Law:
De Morgan's Law states that:
1. ¬(P ∧ Q) ≡ ¬P ∨ ¬Q
2. ¬(P ∨ Q) ≡ ¬P ∧ ¬Q
In your case, you have P ∧ ¬Q, which doesn't directly match either of these forms. However, we can manipulate it to apply De Morgan's Law by taking the negation of both sides and then applying De Morgan's Law:
Original statement: P ∧ ¬Q
Negate both sides: ¬(P ∧ ¬Q)
Now, we can apply De Morgan's Law to the negated statement:
¬(P ∧ ¬Q) ≡ ¬P ∨ ¬¬Q
Since ¬¬Q is equivalent to Q, we have:
¬(P ∧ ¬Q) ≡ ¬P ∨ Q
Now we have an equivalent statement with parentheses:
Your answer: ¬(P ∧ ¬Q) ≡ ¬P ∨ Q

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patterns a and d have a constant difference, pattern c has a constant difference, and patterns b, e, and f do not have a constant difference or a constant ratio.

a. The pattern has a constant difference. The first term is 1, the second term is 4, which is 3 more than 1, the third term is 10, which is 6 more than 4, and the fourth term is 19, which is 9 more than 10.

b. The pattern does not have a constant difference or a constant ratio. The differences between consecutive terms are 3, 2, and 4, respectively, which are not constant. The ratios between consecutive terms are 2.5/2, 1.4/2.5, and 11/1.4, respectively, which are also not constant.

c. The pattern has a constant difference. The first term is 3, the second term is 7, which is 4 more than 3, the third term is 13, which is 6 more than 7, and the fourth term is 21, which is 8 more than 13.

d. The pattern has a constant difference. The first term is 12, the second term is 10, which is 2 less than 12, the third term is 6, which is 4 less than 10, and the fourth term is 0, which is 6 less than 6.

e. The pattern does not have a constant difference or a constant ratio. The differences between consecutive terms are 4, 7, and 10, respectively, which are not constant. The ratios between consecutive terms are 2.5/2, 13/2.5, and 23/13, respectively, which are also not constant.

f. The pattern does not have a constant difference or a constant ratio. The differences between consecutive terms are 6, 12, and 18, respectively, which are not constant.

The ratios between consecutive terms are 13/7, 25/13, and 43/25, respectively, which are also not constant.

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The measure of arc MN is 144 degrees

measure of POQ is 322 degrees

The measure of arc PQ  is 132 degrees

The measure of arc MN is 72×2 = 144 degrees

The measure of arc NQR is 180 degrees

We have to find measure of NQ

First we have to measure of POQ

92+22+POQ=180

POQ=180-114

POQ=66 degrees

Now measure of arc POQ is (95+66)×2 which is 322 degrees

Measure of arc QR is 72×2 = 114 degrees

The measure of MOR is 108×2 =216 degrees

The measure of PQ is 66×2 which is 132 degrees

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The median number of pages of the 9 books that Mary read during the summer reading program is  195 pages .

To find the median number of pages of the 9 books that Mary read during the summer reading program, we first need to arrange the pages in ascending order:

112 pages, 138 pages, 138 pages, 159 pages, 195 pages, 210 pages, 217 pages, 270 pages, 356 pages

The median is the middle value in this ordered list. Since there are an odd number of values, the middle value is the fifth one, which is 195 pages.

The median is a measure of central tendency that divides a dataset into two equal halves. In this case, it represents the number of pages that is halfway between the smallest and largest values. It is a useful measure because it is less affected by outliers or extreme values than the mean.

In Mary's case, the median number of pages of the 9 books she read during the summer reading program is 195 pages. This means that half of the books she read had fewer than 195 pages and half had more than 195 pages. It gives us a good idea of what to expect in terms of the length of the books she read.

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Answer:

Step-by-step explanation:

Use Pythagorean Theorem to find the missing hypotenuse x:

The matching choice is C.

if its constant rate or unit rate its just multiple 6 until u get 30

Hello !

total = $375,42 + $24,95 = $400,37

in cash = $45

the remaining amount = $400,37 - $45 = $355,37

I recommend use of simple random sampling to determine the three possible toppings to be used for the vegetarian pizza.

It is a sampling technique in which each member of the population has an equal chance of being selected for the sample. Here, the population would be students who regularly eat at the school cafeteria.

By using the sampling, we make sure that each student has an equal chance of being selected to taste test the different pizza toppings. This will help to eliminate bias and provide a representative sample of the population's preferences. They will provide feedback which will be used to determine which topping should be used for the vegetarian pizza.

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[tex] \qquad\longrightarrow \sf f(x) = sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]

The Derivative of f(x) with respect to x-

[tex] \qquad\longrightarrow \sf \dfrac{d}{dx} \:sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x}{2}\bigg)^2}}\;\times \dfrac{d}{dx}\:\dfrac{x}{2}\\[/tex]

[tex]\qquad\sf\because\boxed{\sf{ \: \dfrac{d}{dx} sin^{-1}x = \dfrac{1}{\sqrt{1-x^2}}}}\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \:x^{1-1}\\[/tex]

[tex]\qquad \sf\because\boxed{\sf{ \dfrac{d}{dx }x^n = nx^{n-1}}}\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \times 1\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \\[/tex]

[tex] \qquad\longrightarrow \sf\dfrac{1}{2}\: \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\\[/tex]

[tex] \qquad\longrightarrow \underline{\sf\: \dfrac{1}{2\:\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}}\\[/tex]

Henceforth, Option C) is the correct answer.

(4, -2) is the solution of the given system of equations

The given system of linear equations are

2x-12y=16

4x-19y=22

The missing number in 1st step is 1/2

The missing number in 2nd step is -4

The missing number in 3rd step is 1/5

The missing number in 4th  step is 6

The solution of the equation is 4 and -2

Hence, (4, -2) is the solution of the given system of equations

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Answer:

midsegment = 20

Step-by-step explanation:

the midsegment is half the sum of the bases, that is

midsegment = [tex]\frac{12+28}{2}[/tex] = [tex]\frac{40}{2}[/tex] = 20

The elevator and the worker both did the same amount of work, but the elevator provided more power. a.

The object is lifted to the same height the elevator and the worker both did the same amount of work against gravity is given by the formula W = mgh

m is the mass of the object, g is the acceleration due to gravity, and h is the height lifted.

The work done by both the elevator and the worker is W = (100 kg) x (9.8 m/s²) x (10 m)

= 9800 J.

Power is defined as the rate at which work is done, given by the formula P = W/t

t is the time taken to do the work.

Since the elevator reached floor 4 before the worker took less time for the elevator to do the work.

The elevator provided more power than the worker.

The formula states that when an object is raised to a specific height using a lift and a worker they both exerted an equal amount of effort against gravity.

W = mgh where m is the object's mass, g is its gravitational acceleration, and h is the height raised.

The lift's and the worker's combined work is given by W = (100 kg) x (9.8 m/s²) x (10 m)

= 9800 J.

According to the formula P = W/t power is the pace at which work is completed t is the amount of time required to complete the task.

Since the lift arrived at level 4 prior to the worker the lift's work was completed more quickly.

The lift was more powerful than the employee.

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The step with the proof that has a flaw is Step 2, AB ≅ BC, Symmetric Property.

Step 2 is the flaw in the proof. The symmetric property states that if AB = BC, then BC = AB. It does not justify that AB = BC in the first place.

Therefore, the proof needs additional steps to justify that AB and BC are congruent. One possible way to do this is to use the definition of a midpoint and the segment addition postulate as follows:

Step 1 | B is the midpoint of AC | Given

Step 2 | AB + BC = AC | Segment Addition Postulate

Step 3 | AB + AB = AC | Definition of midpoint (since B is the midpoint of AC)

Step 4 | 2AB = AC | Simplification

Step 5 | AB = AC/2 | Division Property of Equality

Step 6 | AB = BC | Substitution Property of Equality

Step 7 | _____ | Q.E.D.

Step 6 follows from the fact that B is the midpoint of AC, so AC = 2AB. Substituting AC/2 for AB in Step 2 gives AB + BC = AC/2 + BC, which simplifies to AB = BC. Therefore, Step 6 uses the transitive property of equality, which is a valid property of equality.

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Answer:8

Step-by-step explanation:

3. To find the number of ways to choose the winners, you use combinations.

n = 100 (total number of people)

k = 10 (number of winners to be chosen)

The formula for combinations is:

C(n,k) = n! / (k! * (n-k)!)

Substituting n and k into the formula, we get:

C(100,10) = 100! / (10! * (100-10)!)

We do not need to simplify this expression.

For the club with 30 students, the number of ways to choose the officers is given by permutations because the order in which the officers are chosen matters.

n = 30 (total number of students)

k = 3 (number of officers to be chosen)

The formula for permutations is:

P(n,k) = n! / (n-k)!

Substituting n and k into the formula, we get:

P(30,3) = 30! / (30-3)!

We do not need to simplify this expression.

Answer:

This quadratic function has no roots.

There are no roots of the quadratic function shown in the graph

We we consider the quadratic equation given be of the form ax^2 + bx + c = 0, then

The quantity b^2 - 4ac is known its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

Therefore, it has to be two roots of a quadratic equation always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solutions if roots are distinct, and have 1 solution when both roots are the same.

Hence, we can conclude that there are no roots. so option D is correct.

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The solution to the system of equations, using the Gauss-Jordan method, is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]

The matrix representing the system of equations is given as follows:

[tex]\left[\begin{array}{cccc}-5&-3&-4&-12\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]

First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1/5, that is:

R1 -> -1/5R1

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]

First we want a value of 1 at line 2, column 2, hence we multiply the second line by -1/2, that is:

R2 -> -1/2R2

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&1&4&-22\end{array}\right][/tex]

We want an element of zero at line 3, column 2, hence:

R3 -> R3 - R2

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&2.5&-3\end{array}\right][/tex]

First we want a value of 1 at line 3, column 3, hence we multiply the third line by 2.5, that is:

R3 -> 1/2.5R3

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&1&1.2\end{array}\right][/tex]

Then the solution to the system of equations is given as follows:

Hence the row-echelon form is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]

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The value of missing side length is, 51.11

We have to given that;

A triangle is shown.

And, To find the missing side of triangle.

Since, An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

And, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, By using trigonometry formula, we get;

⇒ cos 63° = Hypotenuse / Base

⇒ cos 63° = 23 / x

⇒ 0.45 = 23 / x

⇒ x = 23 / 0.45

⇒ x = 51.11

Therefore, The value of missing side in the triangle is,

⇒ x = 51.11

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The equation to represent A, the area in square feet, as a function of w, the width in feet, would be A = w x L

To represent the area (A) in square feet as a function of the width (w) in feet, you will also need to consider the length (l) of the rectangle. The formula for the area of a rectangle is:
A = l * w
However, since you want A to be a function of w, we can rewrite the equation as:
A(w) = l * w
In this equation, A(w) represents the area as a function of the width, and l is a constant value representing the length of the rectangle in feet.

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To have an infinite number of solutions the value of a would be

D. 20

Information given in the problem includes

5(x - 3) + a = 5(x + 1)

To have an infinite number of solutions we can simplify as follows

5(x - 3) + a = 5(x + 1)

opening the parenthesis

5x - 15 + a = 5x + 5

collecting like terms

-15 + a = 5

Adding 15 to both sides, we get:

a = 20

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Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

[tex] A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} [/tex]

The initial amount occurs at t = 0.

[tex] A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} [/tex]

[tex] A(0) = 934 (\dfrac{1}{2})^0 [/tex]

[tex] A(0) = 934 \times 1 [/tex]

[tex] A(0) = 934 [/tex]

After 80 years, t = 80.

[tex] A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} [/tex]

[tex] A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} [/tex]

[tex] A(80) = 934 (0.15749) [/tex]

[tex] A(80) = 147 [/tex]

In the given diagram, the area of the shape is 2π units²

From the question, we are to calculate the area of the given shape.

In the given diagram, the shape is a quadrant.

The area of a quadrant is given by the formula

Area = 1/4 πr²

Where r is the radius

From the given information,

Radius = 8

Thus,

Area of the quadrant = 1/4 × π × 8

Area of the quadrant = 2π units²

OR

Area of the quadrant = 2 × 3.14 units²

Area of the quadrant = 6.28 units²

Hence,

The area of the shape is 2π units² OR 6.28 units².

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The coefficients and degree of each term are:

Second term:

degree = 4, coefficient = -8

Third term:

degree = 3, coefficient = 6

Fourth term:

degree = 0, coefficient = -1 (constant term)

Fifth term:

degree = 1, coefficient = -1

To find the leading coefficient, degree of the leading term, and degree of the polynomial, we need to identify the term with the highest degree:

The leading term has the highest degree: -8x^4

Leading coefficient = -8

Degree of the leading term = 4

Degree of the polynomial = 4

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Answer:

936 cubic feet

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the volume of the prism next to the pyramid, we need to determine its height. Since the prism has the same base area as the pyramid, we can infer that its height is also the same as the height of the pyramid.

Given that the volume of the pyramid is 312 cubic feet, we can use the formula for the volume of a pyramid:

Volume = (1/3) * Base Area * Height

Let's assume the base area of both the pyramid and the prism is represented by "A" and the height is represented by "h".

For the pyramid:

Volume of pyramid = (1/3) * A * h_p

Given that the volume of the pyramid is 312 cubic feet:

312 = (1/3) * A * h_p

Simplifying the equation, we have:

936 = A * h_p

Now, since the prism has the same base area and height, we can use the same values for "A" and "h_p" to find the volume of the prism.

Volume of prism = A * h_p

Substituting the known values, we have:

Volume of prism = 936 cubic feet

Therefore, the volume of the prism next to the pyramid is 936 cubic feet. This is because the prism has the same base area and height as the pyramid, so their volumes will be equal.

If Angle 2 Is-congruent-to Angle 6, then the statement which must be true about Angle 2 is that Angle 2 is supplementary to Angle 8.

We, have,

This refers to the type of angle where two different angles are said to have equal measure on their corresponding sides.

With this in mind, we can see that based on the two horizontal parallel lines are intersected by a third line, there is a third line that intersects the top line and forms four angles.

Hence, if If Angle 2 Is-congruent-to Angle 6, then the statement which must be true about Angle 2 is that Angle 2 is supplementary to Angle 8 because the sum of either angles is 180 degrees.

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complete queston:

Two lines are intersected by a third line.

Two horizontal parallel lines are intersected by a third line. The third line intersects the top line and forms 4 angles. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. The third line intersects the bottom line and forms 4 angles. Labeled clockwise, from uppercase left, the angles are 5, 6, 8, 7.

If Angle2 Is-congruent-to Angle6, which must be true about Angle2?

Angle2 Is-congruent-to Angle5

Angle2 is complementary to Angle5.

mAngle2 = mAngle8

Angle2 is supplementary to Angle8.

The outcomes in set A U B are 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 (the odd sums) 4, 8, 12 (the sums divisible by 4)

The sum of the number cubes is odd if one die shows an even number and the other shows an odd number, or vice versa.

There are 3 even numbers and 3 odd numbers on a number cube, so there are 3 x 3 = 9 ways to get an odd sum.

The sum of the number cubes is divisible by 4 if both dice show either 2 or 4.

There are 2 ways to get a 2 on a number cube and 2 ways to get a 4, so there are 2 x 2 = 4 ways to get a sum of 4.

Therefore, the outcomes in A U B are 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 (the odd sums) 4, 8, 12 (the sums divisible by 4)

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Answer:

-0.91 = strong, as it is close to -1 and if it's close to -1 that means it is linear.

0.82 = strong. Again, it's approaching 1 and is, therefore, approaching linearity.

-0.49 = moderate

0.26= weak

0.54 = moderate

-0.18 = weak

Step-by-step explanation:

Answer:

Not rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Anything with a square root is automatically not a rational number.

have a great day and thx for your inquiry :)