Flying against the wind, an airplane travels 7680 kilometers in 8 hours. Flying with the wind, the same plane travels 12,420 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?

1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.

2. 9(x + 3) = 9x + 12 ; This is true for no values of x.

3. 4(2x + 3) = 12 + 8x ; True for any values of x.

Given,

The equations;

1. 3x + 9 = -4.5x + 20

2. 9(x + 3) = 9x + 12

3. 4(2x + 3) = 12 + 8x

We have to find whether each equation is true for all, one or no values of x.

Here,

1. 3x + 9 = -4.5x + 20

Solve for x;

3x + 4.5x = 20 - 9

7.5x = 11

x = 11/7.5

x = 1.47

Then,

This is true for one value of x.

2. 9(x + 3) = 9x + 12

Solve using distributive property;

9x + 27 = 9x + 12

9x - 9x = 12 - 27

0 = -15

This is true for no values of x.

3. 4(2x + 3) = 12 + 8x

Use distributive property and solve;

8x + 12 = 12 + 8x

8x - 8x = 12 - 12

0 = 0

True for any values of x.

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The answer is

f(x) = (x - 1) 2(x +1)(x - 3 ).

Given equation

f(x) = (x − 2)2(x + 1)(x − 3)

f(x) = (x + 2)2(x − 1)(x + 3)

f(x) = (x + 2)2(x + 1)(x + 3)

f(x) = (x − 2)2(x − 1)(x − 3)

Factored form is a product of stayed and linear elements.

by checking of the red line cross the x-axis.it will give you the zero.

it passes at -1, touches at 1, and crosses again at 3.

This implies that the zeroes are -1, 1 and 3.

The factors 2(x+1), (x - 3), and (x - 1) must be evaluated.

Therefore the answer is

f(x) = (x - 1) 2(x +1)(x - 3 ).

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Answer:

B

Step-by-step explanation:

∠ ADB and ∠ AOB sum to 180° , that is

56° + ∠ AOB = 180° ( subtract 56° from both sides )

∠ AOB = 124°

An angle on the circle is half the central angle subtended on the same arc , so

∠ BCA = [tex]\frac{1}{2}[/tex] ∠ AOB = [tex]\frac{1}{2}[/tex] × 124° = 62°

Answer for No.2
Answer: 1/4

Step-by-step explanation:

Hits = 12

Misses = 60-12 = 48

Ratio of hits to misses = 12/48 = ¼

So the answer is 1/4.

The total number of athletes, the football club has is 180.

Given, In the football club, 36 footballers are Latvian, while there are 4 times the footballers of other nationalities.

as, footballers that are Latvian = 36

now, footballers of other nationalities = 4×36

footballers of other nationalities = 144

so the total number of footballers = 144 + 36 = 180

Therefore, the total number of athletes, the football club has is 180.

Hence, the total number of athletes, the football club has is 180.

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The quadratic function will be f(x) = 2[tex]x^{2}[/tex] + 4x + 15

General equation of quadratic is

f(x) = a[tex]x^{2}[/tex] + bx + c

and Standard form is

f(x) =a [tex](x-h)^{2}[/tex] + k

where h , k are coordinates of vertex

and x , y represent some point on the graph.

By replacing f(x) with y in standard equation we get

y = a[tex](x-h)^{2}[/tex] + k

Put value of x , y , h , k from the graph.

h = -2

k = 7

x = 0

y = 9

9 = a (4) + 7

a = 2

Now put value of a in standard equation

f(x) = 2 [tex](x + 2)^{2}[/tex] + 7

f(x) = 2[tex]x^{2}[/tex] + 4x + 15

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The height of the tower is 87.4870 feet

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The body of the calculation is contained in the attached file.

In conclusion, the height of the tower to the nearest ten thousandth is 87.4870 feet

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The area of the triangle is A. 17.5yd².

Using this formula to find the area

Area = 1/2 ( b × h)

Where:

b = base = 5

h = Height = 7

Hence,

Area = 1/2 (5 ×7)

Area = 1/2 (35)

Area = 1× 35/2

Area = 35/2

Area = 17.5yd²

Therefore the correct option is A.

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The value of c is 20.35 (approx).

The Pythagorean Theorem states that the hypotenuse, or side opposite the right angle, of a right triangle, which is represented by the square, is equal to the sum of the squares on the legs of the triangle (or, in popular algebraic notation, a2 + b2 = c2).

The following are some significant applications of the Pythagorean theorem in daily life: used in architecture and building, used to determine the shortest distance in two-dimensional navigation. used to measure how steep a mountain's or hill's slope is.

Let the other 2 sides of the triangle be named a and b

Given:- a = 15.5ft

            b = 13.2ft

According to the Pythagorean Theorem, We know that

[tex]a^{2}+b^{2}=c^{2}[/tex]

By substituting the values of a and b we get

[tex]15.5^{2}+13.2^{2}=c^{2}[/tex]

[tex]c^{2}= 414.5\\c=\sqrt{414.5}\\ c=20.35[/tex]

c is the hypotenuse of the triangle.

Hence the value of c is 20.35

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The probability that the sum of the 40 values is greater than 7,450 is 0.0239

Define Normal Distribution.

        Z  = (x - μ ) / (σ / √n )

We have given following info,

mean μ = 180

Standard deviation σ = 20

n = 40

σ(mean of x) = σ / √ n

                     = 20 / √40

                      = 3.16

Sample average  (mean of x) = 7450 / 40

                           = 186.25

P(x > 186.25) = 1 - P(x < 186.25)

                     = 1 - P( (x - μ ) / σ(mean of x) ) < ( [186.25 - 180] / 3.16) )

                     = 1 - P( Z < 1.98)

Using Normal distribution table,

                     = 1 - 0.9761

P(x > 186.25) = 0.0239

Therefore,the probability that the sum of the 40 values is greater than 7,450 is 0.0239

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Answer:

3.46

Step-by-step explanation:

[tex]\sqrt{21-9}[/tex]

[tex]\sqrt{12}[/tex]

3.46

Hopes this helps please mark brainliest

a. The slope of the line that is parallel to y = 5/8x + 9 is: 5/8.

b. The slope of the line that is perpendicular to y = 5/8x + 9 is: -8/5.

When two lines are parallel to each other, the lines will have the same slope value (m). However, if both lines are perpendicular to each other, they would have slope values that are negative reciprocals, meaning the product of their slope would be -1.

a. Given the equation, y = 5/8x + 9, the slope (m) of the line is 5/8.

Therefore, it implies that the line that is parallel to y = 5/8x + 9 will have a slope that is the same as 5/8.

Thus, the slope of the parallel line to the equation, y = 5/8x + 9, is: 5/8.

b. The negative reciprocal of 5/8 is -8/5.

Therefore, the slope of the line that is perpendicular to y = 5/8x + 9 would be: -8/5.

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Yes. The residuals' distribution pattern resembles a haphazard dispersion around the horizontal line at 0.

The horizontal plot in this instance comprises points that are unstructured and randomly dispersed around the horizontal mean line.

These are also points below the mean above the mean. This shows that some points in the distribution of data points are above and some are below the least square line, which crosses through the distribution.

The least-square line model would not produce adequate results if, in a residual plot, the majority of the data points are located roughly in a straight line or on either side of the horizontal line.

A residual plot must have data points randomly distributed on both sides of the horizontal mean line in order to produce good results.

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COMPLETE QUESTION:

if the least-squares line provides a reasonable model for the data, the pattern of points in the plot will seem random and unstructured about the horizontal line at 0. is this the case for the residual plot?

Answer:

There are 2 zeros. You know they are zeros because they are the only two points that intercept the x-axis. There is one touch zero and one bounce zero, meaning there are both even and odd multiplicities in the graph.

In the initial list, there were 4 integers.

We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:

m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).

The initial equation is x = mn.

Therefore, changing x in the other two equations:

m + 2 = (mn + 15) / (n + 1) ..............(1)

m + 1 = (mn + 16) / (n + 2)...............(2)

Based on equation (1):

(m + 2)(n + 1) =  mn + 15

mn + m + 2n + 2 = mn + 15

m + 2n + 2  = 15

m + 2n = 13

m = 13 - 2n.

Now change m in equation (2) to:

13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)

14 - 2n = (13n - 2n^2 + 16) / (n + 2)   Through-multiplication by n + 2:

(14 - 2n)(n + 2) =  13n - 2n^2 + 16

14n + 28 - 2n^2 - 4n =  13n - 2n^2 + 16

10n + 28 = 13n + 16

12 = 3n

n = 4.

Hence, there were 4 integers in the original list.

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The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.

A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.

The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;

d² = (x₂ - x₁)² + (y₂ - y₁)²

The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;

[tex]\overline{AB}^2[/tex] = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2

[tex]\overline{AC}^2[/tex] = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2

[tex]\overline{BC}^2[/tex] = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)

72 + 32 = 104

Therefore; [tex]\overline{AB}^2[/tex] + [tex]\overline{AC}^2[/tex] = [tex]\overline{BC}^2[/tex]

ΔABC is a right triangle

The slopes of the equation of the lines of the sides of the triangle are;

Slope of side AB = (5 - (-1))/(6 - 0) = 1

Slope of side BC = (3 - 5)/(-4 - 6) = 0.2

Slope of side AC = (3 - (-1))/(-4 - 0) = -1

Therefore;

[tex]\overline{AB}[/tex] ⊥ [tex]\overline{AC}[/tex]

Which gives;

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Answer:

Step-by-step explanation:

Let's break down the problem:

Quotient =  result obtained by dividing one quantity by another

So its division of x (a number implying variable) by 6

Then it says equal to 2 so we can piece together an equation like this

x/6 = 2

Then we use algebra to solve it

6(x/6)= (2)6

x = 12

So 12 is the unknown number

The area of the quadrilateral is determined as follows if the diagonal and the length of the perpendiculars from the vertices are known: The formula for calculating the area of a quadrilateral is (12) diagonal length the sum of the lengths of the perpendiculars drawn from the other two vertices.

A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words Quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above image as an example. quadrilateral pieces.

Quadrilaterals with four congruent sides, four right angles, and two sets of parallel sides are called squares. Quadrilaterals having two sets of parallel sides are known as parallelograms. All squares are parallelograms because squares must have quadrilaterals with two sets of parallel sides.

Four sides and four angles make up a quadrilateral. Any convex polygon's exterior angles (i.e., no interior angle is less than 180 degrees) sum up to 360 degrees ( 4 right angles).

In the quadrilateral, each point's coordinates change as follows:

(x, y) → (-x, -y)

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A graph of the given mathematical expression (x = -6) is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.

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Total cost includes initial charge for printer set up and material cost.

Average cost per T-shirt is

Average cost to print 25 T-shirts

Average cost to print 100 T-shirts

The average cost 4.25 + 35/x depends on the number of T-shirts printed.

The larger the x, the smaller is 35/x. It will be closer to but greater than $4.25.

She needs to complete 20 laps for a total distance of 0.5 kilometer.

1 kilometers = 1000 meters

0.5 kilometers = 500 meters

Length of swimming pool = 25 meters

That means, she covers 25 meters in 1 lap.

Laps to cover 500 meters = 500/25

                                            = 20

Hence, she needs to do 20 laps.

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The values of a, b and c from the given polynomial are a = -1 , b = 2 and, c= -35.

We are given the expression:-

[tex]x^2+2x-35[/tex]

We know that, the general form of a quadratic expression is :-

[tex]ax^2+bx+c[/tex]

We can rewrite the given expression as:-

[tex]-1x^2+2x+(-35)[/tex]

Comparing it with the given equation, we get:-

a = -1 , b = 2 , c= -35

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

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An artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.

What is a rectangle?

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Here, we have

FH ≅ GH

FH = EG = 22in

If diagonals bisect each other then, an artist connects stained glass pieces with lead strips

1/2(EG) = JG

1/2 (22) = JG

11 = JG

Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.  

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The ratio of dogs to birds at the second adoption center that are equivalent is 2:12.

Ratio demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

At the first adoption center, the ratio of dogs to birds was 4:24. The ratio will be:

= 4 / 24

= 1/6

= 1:6

Since the ratio of dogs to birds at the second adoption center is equivalent, this can be 2 to 12. This will be:

= 2/12.

= 1/6

= 1:6

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Answer:

[tex]^4\sqrt{2}[/tex]

Answer: Option C

Step-by-step explanation: just took the test.

The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

A golf ball is fabricated so that assuming it is dropped from A feet over the ground onto a hard surface, the most extreme level of each skip will be one portion of the level of the past bob.

Then the equation is given as,

h = a (1/2)ˣ

Where 'a' is the initial height.

The exponential equation that gives the height h the ball will attain during the nth bounce will be given as,

h = a (1/2)ⁿ

If the ball is dropped from 13 feet above the ground onto hard a surface. Then the height on the 5th bounce will be given as,

h = 13 (1/2)⁵

h = 13 x 1 / 32

h = 0.40625 feet

The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.

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Both  2/3m=-4 and -4m=24 have a solution of 1/6 and are equivalent

Algebraic expressions are described as expressions that contains terms, variables, coefficients, constants and factors.

They are also known to be made up of some arithmetic operations, such as;

We have the equations;

2/3m=4 and -4m=24

Let's solve for m in the first equation

12m = 2

Divide both side by coefficient of m

m = 2/ 12  = 1/ 6

For the second equation

-4m = 24

Divide both sides by - 4

m = 24/-4

m = 6/ -1

Take inverse

m = 1/6

Hence, the equations are equivalent

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It is true that WXY ≅ WZY.

What is a congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Properties of Congruence

Reflexive Property: An angle is congruent to itself.

Symmetric Property: The order of congruence does not matter.

Transitive Property: If two angles are both congruent to a third angle, then the first two angles are also congruent.

Here, It is given that

Angle ZWY is congruent to angle XWY

Segment WZ is congruent to Segment WX

Segment WY is congruent to Segment WY - Reflexive Property of Congruence (which states that one thing is congruent to itself.

Hence, Triangle WXY is congruent to Triangle WZY because of Side Angle Side (SAS) postulate.

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The expected value of the number of albino panthers is 5

The standard deviation of the number of albino panthers is 2.09

Given that albino panther is born once every 8 years, probability p, of one albino to be born in 8 years is 1/8

Expected value=n*p, where n is 40 years, and p=1/8

                        =40*1/8

                        =5 albino panthers

Hence, the expected value is 5 albino panthers

Standard deviation=(Expected value*(1-p))^1/2

                               =(5*(1-1/8))^1/2

                               =4.375^1/2

                               =2.09

Hence, standard deviation is 2.09

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The rules for the rotation and translation for the rectangle RSTU is:

Rotation: (x,y) ↔ (-y,x)

Translation : (x,y) ↔ (x+k , y)

Given,

we have rectangle R'S'T'U' which is the image of the rectangle RSTU under a rotation 90° counterclockwise about the origin followed by a translation.

we are asked to determine the rule of rotation and translation.

Rotation :

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x).

so the rule is:

Rotation: (x,y) ↔ (-y,x)

Translation:

When the shape is moved towards the right by k units, then replace x with x + k.

let's check:

R(-6,3) ↔ 90° counterclockwise rotation ↔ (-3,-6) ↔ translation↔R'(-3+9,-6) → R'(6,-6)

S(-4,7) ↔ 90° counterclockwise rotation ↔ (-7,-4) ↔ translation↔S'(-7+9,-4) → R'(2,-4)

Hence we get the required rules for sequences of congruence transformations.

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