Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The differentiation of the given function x² + xy + y² + 1 = 0 will be 2x + y + dy/dx(x + 2y) = 0.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

As per the given,

x² + xy + y² + 1 = 0

Take the first derivative on both sides with respect to x as,

d/dx(x² + xy + y² + 1) = d/dx(0)

2x + xdy/dx + ydx/dx + 2ydy/dx + 0 = 0

2x + x(dy/dx) + y + 2y (dy/dx) = 0

2x + y + dy/dx(x + 2y) = 0

Hence "The provided function x2 + xy + y2 + 1 = 0 will be differentiated as 2x + y + dy/dx(x + 2y) = 0.".

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Answer: S wanted points I

Step-by-step explanation:

The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that the selling price of strawberries each pound = $2.50,

The selling price of grapes each pound = $2

The total earning = $160

Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,

x = y + 12 and 2.50x + 2y= 160

Solve the equation by substitution method;

x = 32 and  y = 20

Therefore, the number of pounds of strawberries sold is 32

the number of pounds of grapes sold is 20.

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A linear function gives us the following:

a) At 0 seconds, there are 300 liters of water in the aquarium.

b) The amount of water is losing volume at a rate of 60 liters per minute as time goes on.

Given,

Linear function;-

Modeling a linear function involves:

y = ax + b

That where:

The y-intercept in this problem is 300, hence 300 liters of water are present in the tank at 0 seconds.

The quantity drops by 60 liters each minute, so:

Water is losing volume at a rate of 60 liters per minute as time goes on.

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Answer:

Step-by-step explanation:

You want two transformations that will map segment AB to segment A"B", where the points are A(1, 1), B(5, 3), A"(-5, -2), B"(-9, 0).

We notice that the difference B-A is (5 -1, 3 -1) = (4, 2), and the difference B"-A" is (-9 -(-5), 0 -(-2)) = (-4, 2). These values have the same magnitudes, so we know no dilation is involved. The sign of the x direction of the segment has been reversed, which means the segment has been reflected horizontally. (B" is left of A", where B is right of A.)

Reflection over any vertical line will do, but the simplest is reflection over the y-axis.

The first transformation can be reflection over the y-axis.

The reflected line segment will be ...

  (x, y) ⇒ (-x, y)

  A(1, 1) ⇒ A'(-1, 1)

  B(5, 3) ⇒ B'(-5, 3)

The value that must be added to A' to move it to A" is ...

  A" -A' = (-5, -2) -(-1, 1) = (-5 -(-1), -2-1) = (-4, -3) . . . . . . left 4, down 3

Similarly, the value that must be added to B' to move it to B" is ...

  B" -B' = (-9, 0) -(-5, 3) = (-9 -(-5), 0 -3) = (-4, -3) . . . . . . left 4, down 3

That is, the entire segment A'B' can be moved to A"B" by a translation left 4 and down 3.

The second transformation can be translation left 4 and down 3.

__

Additional comment

The translation left could be accomplished by reflection over the line x = -2 instead of the y-axis.

The movement of the line segment could be accomplished in one transformation by rotation 126.87° clockwise about the point (-1.25, -2). The exact angle is arctan(-4/3) in the second quadrant.

The value of the numbers 'x' and 'y' will be 6 and 17, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

One number is 5 more than twice another and their sum is 23.

Let the two numbers be 'x' and 'y'. Then the equations are given as,

y = 2x + 5            ...1

x + y = 23           ...2

From equations 1 and 2, then we have

x + 2x + 5 = 23

3x + 5 = 23

3x = 23 - 5

3x = 18

x = 6

Then the value of the variable 'y' will be given as,

6 + y = 23

y = 23 - 6

y = 17

The value of the numbers 'x' and 'y' will be 6 and 17, respectively.

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Answer:

a) 9/5

Step-by-step explanation:

Formula we use,

→ Slope (m) = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (-16 - 2)/(-10 - 0)

→ m = (-18)/(-10)

→ m = 18/10

→ [ m = 9/5 ]

Hence, the slope is 9/5.

When x = 10 the equations are equal and when x gets any value the two equations are equal.

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

The equals sign is a part of mathematical expressions known as equations. Often, algebra is used in equations. When a calculation requires an exact number but you don't know it, algebra is utilized.

When x = 10 the equation becomes

6x³ + 9x² + 4x + 7

6(10)³ + 9(10)² + 4(10) + 7

= 6000 + 900 + 40 + 7

= 6947

6x³ + 3x² + 6x² + 4x + 5 + 2

= 6x³ + 9x² + 4x + 7

= 6(10)³ + 9(10)² + 4(10) + 7

= 6000 + 900 + 40 + 7

= 6947

Both the equations are equal when x = 10

When x = -3/2 the equation becomes

6x³ + 9x² + 4x + 7

6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7

= -20.25 + 20.25 + 6 + 7

= 13

6x³ + 3x² + 6x² + 4x + 5 + 2

= 6x³ + 9x² + 4x + 7

= 6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7

= -20.25 + 20.25 + 6 + 7

= 13

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Answer:

I'm not to sure what the answer is

Lupe's statement seems quite fair

When multiplied by 4, any number's pair

An even product will be produced

By this rule, we are not reduced

For example, take the number 6

Multiply it by 4, and what do you get?

The answer is 24, a multiple of 2

This confirms Lupe's statement is true

In conclusion, Lupe's statement rings true

It makes perfect sense, through and through

The product of 4 and any number

Will always be an even number.

Answer:

36

Step-by-step explanation:

Answer: 7/8

Step-by-step explanation:

slpoe is -1/2 and y-intercept is 2

Answer:

18w-24y

Step-by-step explanation:

distribute

6(3w-4y)

18w-24y

Answer:

88 cm²

Step-by-step explanation:

Area of trapezium = [tex]\frac{1}{2}[/tex](a + b)h

12 * 2 = 24

68 -24 = 44

44 is (a + b) as they are the sum of the parallel sides of the trapezium.

h (altitude) = 4

[tex]\frac{1}{2}[/tex](44)(4) = 88 cm²

Answer:

88 cm², hope it helps.

The bisector of the angle TUV is attached below.

What is an angle?

In Euclidean geometry, an angle is the shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The steps to draw a bisector of an angle:

1) Cross both rays with an arc. Place the compass point at the vertex of the angle after opening it to any width. Swing the compass so the pencil creates an arc that spans the angle's two rays.

2) Make a vertical arc inside. Place the compass such that the point is at the spot where the first ray and the first arc connect. Swing the compass to create an arc that fits inside the angle.

3) To intersect the first interior arc, draw a second interior arc. Move the point to the spot where the first arc crosses the second ray without altering the compass's breadth. Draw an internal arc by swinging the compass and intersecting it with the initial interior arc you drew.

4) From the vertex to the spot where the arcs meet, draw a line. To make sure the line is exact, use a straightedge. This line cuts the angle in half.

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In 2401  meters will sound travel in 7 seconds if In dry air at 20° Celsius, sound travels about 343 meters in one second.

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line. Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Given

Speed = 343 m

Time = 7 seconds

For distance,

Distance = Time × Speed

Distance = 343 × 7

Distance = 2401

In 2401 meters sound will travel in 7 seconds if In dry air at 20° Celsius, sound travels about 343 meters in one second.

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Answer:

Step-by-step explanation:

turn percentage into decimal :

60/100 = 0.6

Then times it by how many flowers there are :

0.6×25 = 15

And your answer should be 15.

Answer:

a walked x feet then half that length again-step explanation:

Answer:

14,641

Step-by-step explanation:

11^4 = 11 × 11 × 11 × 11 = 121 × 11 × 11 = 1331 × 11 = 14,641

Answer:

14,641

Step-by-step explanation:

10^4 = 10000

11^4 > 10 ^4 so A is the answer

Answer:

To find the five-number summary for a set of data, we need to find the minimum, first quartile, median, third quartile, and maximum of the data. To find the interquartile range, we subtract the first quartile from the third quartile.

The minimum temperature in the list is 50 degrees Fahrenheit. The maximum temperature is 80 degrees Fahrenheit. To find the median, we need to first find the middle value in the list. Since there are 13 temperatures in the list, the middle value is the seventh temperature, which is 64 degrees Fahrenheit.

To find the first and third quartiles, we need to divide the list into two halves at the median. The first half of the list contains the first six temperatures, and the second half contains the last six temperatures. The median of the first half of the list is the average of the third and fourth temperatures, which is 55 degrees Fahrenheit. The median of the second half of the list is the average of the sixth and seventh temperatures, which is 61.5 degrees Fahrenheit.

Therefore, the five-number summary for this data set is:

Minimum: 50

Lower quartile: 55

Median: 64

Upper quartile: 61.5

Maximum: 80

The interquartile range is the difference between the upper and lower quartiles, which is 61.5 - 55 = 6.5.

Answer:

a.) Constant Rate of Change - yes

b.) origin - yes

c.) Change in y / Change in x - yes

d.) rise/run - yes

e.) inverse - Not apply

What is the difference between rate of change and slope coefficient?

The terms rate of change, gradient, slope coefficient, and rise over run are all equivalent to the slope in a proportional relationship. The slope of a line describes the rate at which a variable changes in relation to another variable. Rate of change is the same concept, but it is more general and can be applied to any relationship, not just linear. Gradient is another term for the slope of a line, which is the change in one variable compared to the change in another variable. Slope coefficient is a mathematical term for the slope of a line, which is the ratio of the vertical change to the horizontal change. Rise over run is another term for the slope of a line, which describes the rate of change by measuring the vertical change (rise) over the horizontal change (run). All of these terms describe the same concept, which is the rate of change in a proportional relationship.

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According to the given sets, A ⋂ B = {blue, green, yellow}.

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.

A set is a mathematical model for a collection of various things.

A ⋂ B:

A set called an intersection B has components that are found in both sets A and B.

The intersection of sets A and B is shown by the symbol, which is interpreted as "An intersection B" and written as A⋂B.

The set of components shared by all sets is the intersection of two or more sets.

So, we have:

A = {red, blue, green, yellow, orange}

B = {pink, blue, purple, yellow, green}

A ⋂ B which means common elements:

A ⋂ B = {blue, green, yellow}

Therefore, according to the given sets, A ⋂ B = {blue, green, yellow}.

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Answer:

<B, <C, <A

Step-by-step explanation:

The order from smallest to largest angle is the same as the order from shortest to longest opposite side.

Sides from shortest to longest:

120, 130, 180

Angles from smallest to largest:

<B, <C, <A

Answer:

9.16

Step-by-step explanation:

formula for Geometric mean is

b = √a × √c

a = 7 and c = 12

b = √ 7×12

b = √84

b = 9.16

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The diameter of the plate. show all work. will be 9.24 inches. The diameter is double of the hypotenuse.

What is the diameter?

A diameter is a line that travels through the center of an object and intersects the circumference at opposing ends. It measures twice as long as the object's radius.

The radius of the circle becomes the hypotenuse when a right triangle is formed by joining the edge of the knife to the center of the circle and the center of the knife to the center of the circle.

With the help of the trigonometric function, the value of the hypotenuse is found as;

sin60 = 8/h

h = 4.62 inches

The diameter of the plate is double the hypotenuse in the given figure;

D = 2 X h

D = 2 X 4.6

D = 9.8

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27 kilometers to miles

1 kilometer = 0.621371 miles

27 kilometers * 0.621371 miles = [tex]\fbox{16.777 miles}[/tex]

The probability of getting an even number or a 1 is 11/20

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given that there are 20 cards numbers 1,2... 20.

A card is randomly drawn.

We have to find the probability of drawing either 1 or even card.

P(drawing even card) = no of even cards/total cards = 10/20= 0.5

P(drawing one) = no of 1's/total cards = 1/20 = 0.05

P(drawing both one and even card) = 0 (since impossible)

Hence P(drawing even or one) =0.5+0.05-0

=0.55

= 11/20

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The two values of x that are roots of the polynomial are:

x = -5 + i√11/2

x = -5 - i√11/2

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

x² + 5x + 9 = 0

It is in the form of ax² + bx + c

a = 1

b = 5
c = 9

Using the determinant.

x = -b ± √(b² - 4ac) / 2a

x = -5 ± √(25 - 36) / 2

x = -5 ± √-11 / 2

x = -5 ± i√11/2

Where i = √-1

Thus,

The roots of the polynomial are:

x = -5 + i√11/2 and x = -5 - i√11/2

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