graph a linear function is shown.
Which word describes the slope of the line?
O positive
O negative
O zero
O undefined

Let:

x = Speed of the jet

y = Speed of jetstream

so:

and

Solve the system using elimination method:

Replace x into (1)

Answer:

Rate of the jet in still air: 726 mph

Rate of the jetstream: 65mph

We can conclude that after the construction of line PX perpendicular to line l, which creates a square, the correct statement about the construction will be (E) none of these.

So, after drawing line PX⊥L (AB), and extending PX to the other side to point C.

(A) PA = PB

(B) AX = BX

(C) PX = CX

(D) AC = BC

Therefore, we can conclude that after the construction of line PX perpendicular to line l, which creates a square, the correct statement about the construction will be (E) none of these.

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The complete question is given below:
The diagram shows the construction of line PX perpendicular to line l.

Which statement is not always true about this construction?

A) PA = PB

B) AX = BX

C) PX = CX

D) AC = BC

E) Non of these

Writing 1 trillion in scientific notation is 1 × 10^12.

A scientific notation simply means the way of expressing numbers that are either too large of too small. Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format. As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation.

In this case, I trillion is written as 1,000,000,000,000.

Therefore, it has 12 zeros.

The scientific notation is 1 × 10^12.

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Answer:

Step-by-step explanation:

The total for 12 oranges would be $8.28

Step-by-step explanation:

can we become friends???

Answer:

6.17

Step-by-step explanation:

add the pepsi wich is 2.19 then do 1.99 x 2 wich would be 3.98 then add them all together

The amount of time it takes to reach the beam of sum from sun to earth is 200 seconds approximately

What is division?

Division is one of the basic arithmetic operation in which we find a number such the product of the number with the denominator is equal to the numerator.

We are given that the distant of earth from sun is 9.3 ×10^7

And the speed of light is 1.86×10^5

We divide the distance by the speed to get the value of time

[tex]\frac{9.3}{1.86}[/tex]×[tex]\frac{10^7}{10^5}[/tex]

On simplifying we get

200 seconds

Hence, The approximate time require to reach the beam of sun from sun to earth is 200 seconds

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The relation is the relationship between two or more sets of values. Suppose, x and y are two sets of ordered pairs. If set x has a relation with set y, then the values of set x are called domain whereas the values of set y are called range. A relation from a set A to a set B is a subset of A×B. Hence, a relation R consists of ordered pairs (a,b), where a∈A and b∈B. If (a,b)∈R, we say that is related to, and we also write aRb. A connection between the elements of two or more sets is a relation. The sets must be non-empty. A subset of the Cartesian product also forms a relation R. A relation may be represented either by the Roster method or by the Set-builder method.

The quadratic function of best fit for the data is given as follows:

h(t) = -0.004t² +1.032t + 5.667.

Using this function, the initial height of the shot is of 5.67 feet.

The input and the output of the data are given as follows:

As the input increases, the output increases and then it decreases. Since this behavior of increase/decrease is not uniform over the entire domain of the relation, a quadratic function best models this data.

To find the quadratic function of best fit, we insert the points (input,output) into a calculator, from point (20, 25) to point (200,64).

Inserting the points into the calculator, the function is defined as follows:

h(t) = -0.004t² +1.032t + 5.667

The height in which the shot started its flight is given by the height when t = 0, hence:

h(0) = -0.004(0)² + 1.032(0) + 5.667 = 5.667 feet = 5.67 feet (rounded to the hundredths place).

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Based on the straight line being parallel to the line, L1, and the gradient, the equation of the straight line L2 is y = 2x - 5

The equation of a straight line takes the form:

y = mx + b

Where:

m = slope

b = y - intercept

The slope is the same as the gradient and parallel lines have the same gradient. The gradient of L2 is therefore 2 as well.

Use this gradient and the point (0, -5) to find the y - intercept:

-5 = 2(0) + y - intercept

y - intercept = -5

The equation of the line is:

y = 2x - 5

Full question is:

A straight line, L2, is parallel to the straight line L1 and passes through the point (0,-5). L1 has a gradient, 2.

Find an equation of the straight line L2.

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Answer:

Dilation

Step-by-step explanation:

A dilation is a transformation that will shrink or expand a figure, so the area will change.

The probability that precisely two of the sampled people utilized a discount broker is 0.2668.

A discount broker was employed by 30% of individual investors.

p = 30 ÷ 100 = 0.3

q = 1 - p

q = 1 - 0.3

q = 0.7

n = 9

P(x) = [tex]{}^{n}C_{x}p^{x}q^{n - x}[/tex]

Only two of the people polled had utilized a broker.

x = 2

P(2) = [tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex]= 0.2668

Only three persons have used a deal broker.

= P(3) + P(2) + P(1) + P(0)

= [tex]{}^{9}C_{3}[/tex](0.3)³[tex](0.7)^{6}[/tex] +  [tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex] + [tex]{}^{9}C_{1}[/tex](0.3)¹[tex](0.7)^{8}[/tex] + [tex]{}^{9}C_{0}[/tex](0.3)⁰[tex](0.7)^9[/tex]

= (84 × 0.027 × 0.1176) + (36 × 0.09 × 0.0823) + (9 × 0.3 × 0.0576) + (1 × 1 × 0.0403)

= 0.7291

Probability of a broker has been employed by at least three of them.

= P(2) - P(1) - P(0) - 1

= -([tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex] -  [tex]{}^{9}C_{1}[/tex](0.3)¹[tex](0.7)^{8}[/tex] -  [tex]{}^{9}C_{0}[/tex](0.3)⁰[tex](0.7)^9[/tex]  - 1)

= -((36 × 0.09 × 0.0823) - (9 × 0.3 × 0.0576) - (1 × 1 × 0.0403) - 1)

= 0.9291

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Answer:h

Step-by-step explanation:

Answer:

6/4

Step-by-step explanation:

For a RIGHT triangle, Tan = opposite leg / adjacent leg  =  6/4 for angle F in this example

Using integer numbers, it is found that the expressions that will also be integers are given as follows:

1.75kx, in which k is an integer.

Integer numbers are numbers that have a decimal part of zero, that is, they are whole numbers, either positive or negative.

In the context of this problem, the relevant property is that the multiplication of two integer numbers will always result in an integer number.

We have that the term 1.75x represents an integer number, hence any integer number multiplying 1.75x will result in an integer number.

Symbolically, any integer number can be represented by the variable k,  hence the expressions that will also be integers are given as follows:

1.75kx, in which k is an integer.

This problem could not be found on any search engine, hence the expression is given in general terms.

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Answer:2.10971436E14

Step-by-step explanation:

Answer:

Step-by-step explanation:

1,747,544,165,078,382 is the answer.

Answer: length 20

width 10

Step-by-step explanation:

L = 2W

W+W+L+L=60

2W+2W+2W=60

6W=60

•1/6 to both sides

W=10

L=20

Answer:

Length = 20 in

Width = 10 in

Step-by-step explanation:

Given information:

Define the variables:

Perimeter of a rectangle

[tex]P = 2(w + l)[/tex]

where:

Substitute the given values into the formula and solve for x:

[tex]\begin{aligned}\textsf{Perimeter of rectangle}&=\sf 2(width + length)\\\implies 60&=2(x+2x)\\60&=2(3x)\\60&=6x\\x&=10\end{aligned}[/tex]

Substitute the found value of x into the expressions for width and length.

Solution

IN THE PLACE OF Y PLUG IN 0

[tex] = \frac{( {0})^{2}}{5} \\ = \frac{0}{5} \\ = 0[/tex]

The answer is 0

Answer: b + 24 = 68

Step-by-step explanation:

we are told the zoo has 68 different species of birds so the equation will be = 28. The answers showing = 24 are already wrong.

transported means they are taken away, so we have to subtract 24 (animals that stayed in the zoo) to find b which are the remaining species moved to the barn.

b + 24 = 68
  -  24    -24

b = 44 (transported to the barn)
     24 ( stayed in the zoo)
    68 ( total number of species of birds)

The correct expression to show the species of transported birds will be;

⇒ b + 24 = 68

Where, b is the number of transported birds.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Total number of birds in Roaring Zoo = 68

Number of stayed birds in Zoo = 24

Let number of transported birds = b

Then, We can formulate;

Total number of birds = Stayed birds + Transported birds

Substitute all the values, we get;

⇒ 68 = 24 + b

Therefore,

The correct expression to show the species of transported birds will be;

⇒ b + 24 = 68

Where, b is the number of transported birds.

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Answer:

X = $250.16

Step-by-step explanation:

22( +150) + 71 = 26,565  

22 + 3300 + 71 = 26,565

93 = 23,565  

= 250.16  

Each support staff is paid $250.16 per shift.

The balloon that was farther from the town at the beginning, and which traveled more quickly is Henry's balloon.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Henry's balloon is 48 miles after 2 hours.

Tasha's balloon after 2 hours will be:

= 8x + 20

= 8(2) + 20

= 32 miles

In this case, Henry's balloon is farther.

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If the values of x are -15, -20 and -25, then the solutions are -3, -4 and -5

The statement is given as

The quotient x divided by 5 is a negative integer

This means that:

x is a negative integer and it is a multiple of 5

Represent the statement as an expression

So, we have

x/5

Take for instance:

x = -15, -20 and -25

So, we have

-15/5 = -3

-20/5 = -4

-25/5 = -5

Hence, the possible values of x are -15, -20 and -25

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The correct answer is B

Answer:

2

Step-by-step explanation:

The true statement is Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Given:

MATH is congruent to quadrilateral WXYZ.

Then congruent sides are

MA= WX

AT = XY

TH = YZ

and, congruent angles are

<M = <W

<A = <X

<T= <Y

<H = <Z

So, if the quadrilateral is congruent then they equal in measure.

Hence, the true statement is  Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.

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Because we have a closed dot at (4, 17), we conclude that when x = 4 the value of the function is 17, so the correct option is the third one.

Here we have the graph of a piecewise function, and we want to see which value the function takes when x = 4.

To do so, we need to find x = 4 on the horizontal axis, and then move until we hit the graph.

For x = 4 we can see two points on the graph.

One open point at y = 7, where the open dot means that this value does not belong to the function.

A closed point at y = 17, where the closed dot means that this value belongs to the function.

From this, we conclude that when x = 4, the value of the function is 17.

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If a given point, P, exists on a great circle on the surface of a sphere, no line can be drawn on the sphere that is parallel to the great circle because each pair of great circles(parallel lines) will always intersect, regardless of how they are drawn.

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The arc marked in red is a quarter of the circle's circumference.

Hence the arc marked red subtends an angle of 90degrees.

In our case

19x/3+2/9 is the quotient and 50 is the remainder for the given equation (6x³+13x²-12x-6)÷(3x+2).

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three. Latin's "how many times" is the meaning of the word "quotient." That makes perfect sense: by dividing two numbers, you can determine "how many times" the second number enters the first.

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remainder is the name for this amount.

On dividing the equation,

The quotient will be 19x/3+2/9 and the remainder will be 50.

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Answer:

Step-by-step explanation:

[tex]\sf -3\left(33b+65\right)=-95b-6b-87[/tex]

Combine like terms:

[tex]\sf -3\left(33b+65\right)=-101b-87[/tex]

Expand:-

[tex]\sf -99b-195=-101b-87[/tex]

Add 195 to both sides:-

[tex]\sf -99b-195+195=-101b-87+195[/tex]

Simplify:-

[tex]\sf -99b=-101b+108[/tex]

Add 101b to both sides:-

[tex]\sf -99b+101b=-101b+108+101b[/tex]

Simplify:-

[tex]\sf 2b=108[/tex]

Divide both sides by 2:-

[tex]\sf \cfrac{2b}{2}=\cfrac{108}{2}[/tex]

Simplify:-

[tex]\sf b=54[/tex]

Therefore, your answer is b = 54!!

___________________________

Hope this helps you!

Have a great day! :)

The polynomial factors are (x -2)(x+ i)(x - i)

In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

To find the factors of the given polynomial, we can proceed as

[tex]x^3 -2x^2 + x - 2[/tex]

Let's factor out a common term

[tex]x^3 - 2x^2 + x - 2 = x^2(x-2) + (x-2)\\x^2(x-2)+(x-2)\\(x-2)(x^2+1) = (x-2)(x+i)(x-i)[/tex]

The factors of the given polynomial is (x-2)(x+ i)(x- i)

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