Descartes decides to plot the runways at the Regina airport on a grid. Runway AB passes through the points A(-5, -24) and B(6, 9). Being the father of analytic geometry, he notices right away that he can describe
Runway CD with the equation 2x + y - 11 = 0.
Find the intersection point of Runways AB and CD analytically.

The equation for the parabola is: (x - 1)^2 = 4(y - 5). The vertex of the parabola is located at (1, 5) and the focus is at (1, 1). The equation describes a parabola that opens upward, and is symmetrical about the y-axis.

The equation for the parabola is: (x - 1)^2 = 4(y - 5). This equation describes a parabola with its vertex located at (1, 5) and its focus at (1, 1). The parabola is symmetrical about the y-axis and opens upward. This means that the base of the bulb is at (1, 5) and the top of the bulb is at (1, 1). To get the equation for the parabola, we need to subtract the x-coordinate of the vertex from the x-coordinate of the focus, which gives us 1. We then square this number, giving us 1. We then subtract the y-coordinate of the vertex from the y-coordinate of the focus, giving us 4. We then multiply this number by the squared number from before, giving us 4. The final equation is then (x - 1)^2 = 4(y - 5).

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5329 Sq meters  is the maximum area that can be enclosed.

What is a rectangle, exactly?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. It is also known as an equiangular quadrilateral for this reason.

                          The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

Perimeter of Rectangle: 2W + 2L

One L is the river so we have 3 sides

220m/3 = 73m

Area of Rectangle is WL

73 × 73 =  5329 Sq meters

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The length of side LN is equal to 44 units. (Correct choice: A)

Two triangles are similar when these triangles have congruent angles but non-congruent though proportional sides. Triangles LMN and NUV are similar. Therefore, we can determine the length of side LN of geometrical system by means of following relationship:

NV / LN = NU / MN

LN = NV × MN / NU

If we know that NV = 11, MN = 32 and NU = 8, then the length of side LN is:

LN = 11 ×  (32 / 8)

LN = 11 × 4

LN = 44

The side LN has a length of 44 units.

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X = 88.1. The total of all interest, dividends, or other income that an investment provides divided by the age of the investment or the period over which the investor has held it is the average yield on an investment.

What is average yield?

The average yield on an investment or a portfolio is calculated by dividing the total interest, dividends, or other income received by an investment by the investment's age or the period over which the investor has held it. In particular, it alludes to yield, or the total revenue from an investment divided by the number of years kept.

There are numerous yield kinds, and the calculating process varies depending on the specific yield type and the type of security. Because of these variations, comparisons of yields between other financial product categories should be used with caution.

In the case of stocks, yield is determined by dividing the price rise plus dividends by the original purchase price. Both cost yield and current yield can be used to examine bond yield.

Given data :

Let x be the number of trees in the orchard and N the yield per tree.

No of trees = 70

yield = 10

formula for N in terms of the unknown x :

(10+(70-x)0.55)

10 + 38.5 - 0.55x

-0.55x = 48.5

x = 48.5/ 0.55 = 88.1

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The point (2, 48) means in this context: Cesar and Camden are both 48 kilometers away from home after 2 hours.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Cesar and Camden are brothers and live at the same house.

Cesar is 80 kilometers away from home and bikes towards home at a rate of 16 kilometers per hour.

Camden is 20 kilometers away from home and keeps walking away from home at a rate of 14 kilometers per hour.

You found that the point of intersection on the graph is (2, 48),

and you solved algebraically to find that x=2 and y = 48.

Cesar and Camden are both 48 kilometers away from home after 2 hours.

Therefore, Cesar and Camden are both 48 kilometers away from home after 2 hours.

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The least common denominator to both fraction expressions is; (x - 3)

The least common denominator simply means the least number or expression that is common to both denominators of a given fraction.

Now, the given denominators of the fraction expression are;

(2x - 6) and (7x - 21)

To find the least common denominator here, we will just factoriuze each algebraic expression to getl

(2x - 6)  = 2(x - 3)

(7x - 21) = 7(x - 3)

Thus, we see that the common expression is (x - 3) which we will conclude will be the least common denominator

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The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.

When two quantities are inversely related, that is, when an increase in one quantity causes a decrease in the other and vice versa, they are said to be in inverse proportion. The product of the given two quantities is equal to a constant value in inverse proportion.

Given that the two ratios are 96:38 and 38:96. The value of the two ratios will not be the same because both the ratios are inverse of each other or are reciprocals of each other.

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Answer:

The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.

Step-by-step explanation:

I took the quiz.

A coda ulna de las personas le Toccara ulna porcino de 2/3 de Dona

Si mi tía ha legato a la casa y trae consigo 4 Donas de azúcar, pero no se ha percatado que la cantidad de personas en la casa es de 6 contándose, entonces decide repartir en partes iguales, para esta operation deems divider la candida de donnas entre la cantidad de personas

4 donnas / 6 personas = 2 /3 ester 2/3 es la porcino de coda uno es décor coda Dona se picara eon tress torsos y dos torsos para coda persona de 2/3

Respuesta:

para que alkanes les tocaria

a 4 personas la mated de una dona

(osea 2 donas las partes a la mated)

y a las okras 2 personas la Dona entera

Explication paso a paso:

esparto hiver aoudad:)

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The required values are for the given angle, as follows: a. sin α is positive. b. sin(π + α) = -sin α. c. cos(2π - α) = cos α.

A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.

a. For an angle α in the first quadrant, sin α is positive.

Since the first quadrant is between 0 and 90 degrees, sin α is equal to the opposite side divided by the hypotenuse, where the opposite side is the y-coordinate and the hypotenuse is the distance from the origin to the point on the unit circle corresponding to the angle α.

b. sin(π + α) = sin (π - α). In the second quadrant (90 < α < 180), sine is negative, so sin(π + α) = -sin α.

c. cos(2π - α) = cos α. The cosine function has period 2π, so cos(2π - α) = cos α.

Since the first quadrant is between 0 and 90 degrees, cos α is positive.

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[tex] \large \frak{ \green 5 + \red{w }= \green 8}[/tex]

[tex] \: [/tex]

[tex] \ \: \large \frak{ \red{w }= \green 8 { -} \green5}[/tex]

[tex] \: [/tex]

[tex] \underline{ \boxed{ \large \frak{ \: \red{w }= \green 3 \: }}}[/tex]

[tex] \: [/tex]

hope it helps!

Answer:

see below & attached

Step-by-step explanation:

red line length call it a² = (8√3)²- 12²  = 192-144 =48

so look at the graph we know x is longer than 12,

the portion that's longer than 12 call it c = x-12

top short line call it b

because it's all right angle you are looking at 3 right angle triangles

the big one that's cut into 2 by the red line

the larger one & the smaller one

each will have this property: short side 1 ²+short side 2 ²= long side ²

so for the largest one:

(8√3)² +b² = (12+c)² = x²

second largest triangle we already know all 3 sides: (8√3), 12, √48

now look at the smallest

48+c² =b²

once you have all equations listed , you can solve for c.

see attached.

Answer:

5 committees can be formed

Step-by-step explanation:

number of teachers=11

number of students=50

number of teachers in a committee=2

number of students in a committee=2

Answer:

2x + 3

Step-by-step explanation:

1/2(6x - 10) - x

3x -5 -x

2x -5

We would need the structure of the equation to be 2x plus or minus anything other than 15.

For example:

2x - 5 = 2x + 3  if we subtract 2x from both sides we are left with

-5 = 3  This is a false statement and their will be no solution.

Answer:

63

Step-by-step explanation:

Consecutive odd integers increase by the addition of 2 therefore if the smallest value is x then the next odd number is x + 2

So therefore; x + x + 2 + x + 4 + x + 6 = 264

Collect like terms

x + x + x + x + 2 + 4 + 6 = 264

4x + 12 = 264

4x = 264 - 12

4x = 252

Divide both sides by 4

x = 63

Therefore the smallest of the four consecutive integers is 63

a. 17, 15, 8 this can be a right triangle, while b. 7 25 19 is not a right a triangle

There are an endless number of triangles produced when no side is specified.

The three angles produce an unlimited number of distinct triangles if side lengths are not provided.

When the three sides are specified the sides will be such that addition of the two smaller sides will be greater than the third side

For a. 17, 15, 8

the two smaller sides are:15 and 8

15 + 8 > 17

this can be a triangle

For b. 7, 25, 19

the two smaller sides are:7 and 19

7 + 19 > 25

this can be a triangle

For a right triangle the Pythagoras rule should be observe: the squire of the smaller sides will be equal to the square of the longer side. let the longer side be x

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17

this is a right triangle

x² = 7² + 19²

x ² = 49 + 361

x² = 410

x = √410

x = 20.25

this is not a right triangle

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a. (3, 4, 5) will create a triangle.

b. (10, 20, 30) will not create a triangle

c. (15.5, 45, 20.5) will not create a triangle.

What is a triangle?

A triangle is a polygon with three sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their sides (such as equilateral, isosceles, or scalene) or by their angles (such as acute, right, or obtuse).

The set of lengths (3,4,5) will create a triangle. This is because it follows the "triangle inequality theorem" which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

The set of lengths (10, 20, 30) will not create a triangle. This is because 10 + 20 is less than 30, so it does not satisfy the triangle inequality theorem.

The set of lengths (15.5, 45, 20.5) will not create a triangle. This is because 15.5 + 20.5 is less than 45, so it does not satisfy the triangle inequality theorem.

Hence,

a. (3, 4, 5) will create a triangle.

b. (10, 20, 30) will not create a triangle

c. (15.5, 45, 20.5) will not create a triangle.

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Answer:

see below

Step-by-step explanation:

b = √3

then move t to the end you'll see

m= -0.4√13

Answer:

£362.1

Step-by-step explanation:

6.5% =

6.5 / 100 =

65 / 1000 = 0.065

£340 * 0.065 = £22.1  => £22.1 is the pay raise in terms of English pounds(£)

Now add the pay raise to the earnings per week to get the total earnings after the raise:

£22.1 + £340 =

£22.1 + £340.0 = £362.1

The number of quarters in the bowl is 14.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x+ 3 = 9 is an equation.

We have,

Dimes = x

Quarters = y

10 dimes = $1

1 dime = $0.1

4 quarters = $1

1 quarter = $0.25

Now,

0.1x + 0.25y = 5 _____(1)

x + y = 29 _____(2)

Solve for y from (1) and (2),

x = 29 - y

Substitute in (1) we get,

0.1 (29 - y) + 0.25y = 5

2.9 - 0.1y + 0.25y = 5

2.9 + 0.15y = 5

0.15y = 5 - 2.9

y = 2.1/0.15

y = 14

Thus,

There are 14 quarters in the bowl.

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On solving the equation, it is seen that about 12 ounces of the 15% solution must be mixed with about 6 ounces of the 6% solution to get 18 ounces of the 12% perfume.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let x = number of liters of the 15% solution

Let 18 − x = number of liters of the 6% solution

Solution Ounces Strength Amount of Perfume

15%         x            15            15x

6%          18 - x      6             6(18 - x)

Mixture   18           12            (18)(12)

So, the equation will be -

(amount of perfume in 15% solution) + (amount of perfume in 6% solution) = (amount of perfume in mixture)

15x + 6(18 − x) = (18)(12)

Solve the equation using distributive property -

15x + 108 - 6x = 216

Combine the like terms -

15x - 6x = 216 - 108

Simplify the equation further -

9x = 108

x = 108/9

x = 12

Now, substituting the value of x in 18 − x = 18 - 12 = 6.

Therefore, the amount in ounces is obtained as 12 ounces and 6 ounces.

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In the parallelogram ABCD it is proved that AC ≅ BD, which proves that AC = BD.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

It is given that the parallelogram is ABCD.

In this parallelogram AX ≅ DX, XB ≅ XC.

Now, according to the properties of parallelogram the segment addition can be done.

AC = AX + XC

Similarly, the segment addition for line BD is -

BD = DX + BX

Now if AX ≅ DX and XB ≅ XC, then substitution of  DX and XC can be done -

AC = AX + BX

BD = AX + BX

This proves that AC = BD by the transitive or substitution method.

Therefore, it is proved that AC = BD and also that AC ≅ BD.

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Answer:

vertex point is (4,-6)

and it opens upwards as the coefficient of x is positive.

I assume B is the correct answer, good luck!

Nick has failed to meet the condition that n p hat greater-than-or-equal-to 10 and n (1 minus p hat) greater-than-or-equal-to 10.

In order for the Central Limit Theorem to be applied and for the sample proportion to be approximately normally distributed, the sample size must be at least 30. This means that the sample size must be large enough so that the sample proportion of healthy breakfast eaters (p hat) and the sample proportion of non-healthy breakfast eaters (1-p hat) are both greater than or equal to 10. In this case, since the sample proportion of healthy breakfast eaters is 20/25 = 0.8, the sample proportion of non-healthy breakfast eaters is 5/25 = 0.2. Since 5 is less than 10, this condition is not met, and Nick cannot construct a confidence interval for p.

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the two possible values for the third side of the triangle are 22.5 and 24.00.

We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, the third side must be greater than 10.25 and less than 19.75.

From this, we can conclude that the third side of the triangle must be either 22.5 or 24.00.

We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given that two sides of the triangle measure 19.75 and 10.25, the third side must be greater than 10.25 and less than 19.75. Therefore, the only two possible lengths for the third side of the triangle are 22.5 and 24.00. Any length greater than 19.75 or less than 10.25 would not satisfy the triangle inequality and would not be a valid third side for the triangle. Thus, We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

the two possible values for the third side of the triangle are 22.5 and 24.00.

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the angle between the diagonal of a cube and its edge is equal to 35.2 degrees.

Let us consider a cube with side length = a.

Length of diagonal of cube on one of its faces = a√2

Length of diagonal of cube = a√3

To find the angle between the, use law of cosines.

The law of cosines is given by.

⇒ [tex]c^2=a^2+b^2-2abcosC[/tex]

Where c = length of side c, b = length of side b, a = length of side a

C = angle opposite to c

⇒ [tex]c^2=(a\sqrt{2})^2+(a\sqrt{3})^2-2a\sqrt{2}a\sqrt{3}[/tex]

On simplification,

[tex]cosC=\frac{2a^2}{a^2\sqrt{2}\sqrt{3}} \\cosC=\sqrt\frac{2}{3} \\[/tex]

C=35.2 degree

Therefore, the angle between the diagonals is 35.2°

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Answer: B

Step-by-step explanation:

[tex]3 \frac{5}{8} \div 4=\frac{29}{8} \div 4=\frac{29}{32}[/tex]

The measure of the missing angle in a triangle is C = 18°.

An acute angle is one that is 45 degrees. It is a 90-degree angle or half of a right angle. Look at the illustration of the 45-degree angle. Angles are expressed in degrees or radians.

A straight angle is one in which the two arms extend in precise opposition to one another. A 180° angle is a straight angle. A protractor can be used to measure angles; a straight angle is an angle that is measured at 90 degrees.

The two arms are perpendicular to one another at a right angle. Each angle measures 45° when the right angle is divided into two equal pieces. An acute angle is one that is 45 degrees. It is a 90-degree angle or half of a right angle.

Given one of the angles A = 45°

And B is 65% of the total angle sum = 65/100 × 180

                                                             = 117°

For angle C, using angle sum property

⇒ A + B + C = 180°

⇒ 45° + 117° + C = 180°

⇒ C = 180° - (45° + 117°)

⇒ C = 180° - 162°

⇒ C = 18°

Thus, The measure of the missing angle in a triangle is C = 18°.

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Complete question:

What is the size, in degrees, of the missing angle of a triangle?

A = 45°

B = 65%

C = x

To find out how many bricks are needed to make the wall, we need to find the total area of the wall and divide it by the area of one brick.

The area of the wall is:

length x height x width = 10 m x 1 m x 0.5 m = 5 m^2

The area of one brick is:

10 cm x 10 cm x 20 cm = 2000 cm^3

To convert the area of the wall from square meter to cubic centimeter, we need to multiply it by 100*100 = 10000.

5 m^2 x 10000 = 50000 cm^2

Now we can divide the total area of the wall by the area of one brick to find out how many bricks are needed:

50000 cm^2 / 2000 cm^2/ brick = 25 bricks

So, 25 bricks will be needed to make the wall.

The ODE's general solution has real solution and complex eigen functions. Typical trajectories are sinusoidal curves.

The general solution of the ODE involves complex eigenfunctions, which are solutions of the form e^(ikx), where k is a real number and i is the imaginary unit. By combining these complex eigenfunctions with real coefficients, a general real solution can be obtained. Typically, these solutions will take the form of sinusoidal curves, with the amplitude and period determined by the coefficients of the eigenfunctions. The coefficients can be determined using initial conditions, allowing for more specific trajectories to be determined. For example, if the initial condition is known, then the coefficients of the eigenfunctions can be determined using Fourier analysis, allowing for the trajectory of the system to be determined.

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