What property is being used here?
4x-3

x=2

4(2)-3

Given the line shown in the figure passes through the points (-3, -4) and (1, 2)

We will write the equation of the line.

First, we will find the slope of the line using the following formula:

Substitute with the given points:

The equation of the line in point-slope form will be as follows:

Convert tot he slope-intercept form, so, the equation will be:

Now, we will check the options to see the correct equations.

So, the answer will be, we will select the options:

A. y+4 = 1.5 (x+3)

B. y = 1.5x + 0.5

C. y - 2 = 1.5 (x - 1)

We consider a vector with:

• initial point (x₁, y₁) = (4, 3),

• final point (x₂, y₂) = (-4, -1).

The magnitude of the vector is given by:

The angle of the vector is given by:

We have obtained a positive value of the angle θ'. But we see that our vector points in the negative direction. To take into account this, we must sum 180° to this result:

||v|| = 8.944, θ = 206.565°

The quadratic function in standard form is g(x)= x²-10x+0

Quadratic functions are polynomial functions of the second degree, meaning they contain at least one squared term.

Quadratic functions are another name called quadratics. The quadratic function has the following general form: f(x)=ax² + bx + c.

An quadratic function is given as g(x)= x²-10x

In the standard form of the quadratic equation, there should be three terms, terms with power two, one and a constant.

In the given equation, there is a constant term missing.

So, we add a zero to the end because it brings no change to the function quantitatively.

So, the standard form of the given quadratic function will be g(x)= x²-10x+0

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Remember that a difference of squares can be written as the product of two conjugate binomials:

In the given expression, notice that m^4 and n^4 can be written as (m^2)^2 and (n^2)^2:

Once written as a difference of squares, we can factor the expression:

Therefore:

f(x-1) + 2 translates f(x) 1 unit to the right and 2 units up. Then, the graph of the new function is:

Answer:

Step-by-step explanation:

k = 0.2

f(x) = x^2

To translate the function 2 units down (along the y axis) subtract 2

F(x) = x^2 -2

To translate the function 3 units to the right (along the x-axis) subtract 3 units inside the parentheses.

f(x) = (x-3)^2 - 2

a. Distance travelled

Given that he rides at a constant speed and after riding for 5 hours, he had travelled 46.5 miles. Per review, the distance travelled is dependent on time hence distance or miles covered is the dependent variable

For the given ques, the graph is mention in the question.

As, domain are the all set of values lying on the x-axis.

Thus,

A. Domain {-1 to infinity} (In integer or fraction form.)

B. Domain [-1, ∞), (interval notation; half closed half open)

Range of the relation of function are-

A. Range {- infinity to infinity} (In integer or fraction form.)

B. Range (- ∞, ∞), (interval notation open interval both sides)

Thus, the value of domain and range of the function are found.

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The number of quarts of blood in a person who weighs 120 pounds is  3.4

The expression can be written as

W= kV

W represents the weight in pounds

V= number of quarts

k= 140/4

= 35

The number of quarts of blood in a person that weighs 120 pounds can be calculated as follows

= 120/35

= 3.4

Hence 3.4 quarts of blood is gotten from a person who weighs 120 pounds. This was done by dividing 120 by 35

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Given

The final answer is 17 bunnies

When two planes  which are 2505 miles apart and fly toward each other. if their speeds differ by 85mph and If they pass each other in 3 hours, then the speed of first plane is 372.5 mph and the speed of second plane is 462.5 mph

Their speeds differ by 85mph

Consider the speed of first plane = x mph

The speed of second plane = 90+x mph

The relative speed = sum of both speed

= x + x+90

= 2x+90 mph

The distance between the planes = 2505 miles

Time taken to pass each other = 3 hours

Therefore in 3 hours

3(2x+90) = 2505

6x+270 = 2505

6x = 2505-270

6x = 2235

x = 2235/6

x = 372.5 mph

The speed of second plane = 90+x

= 90+372.5

= 462.5 mph

Hence, when two planes  which are 2505 miles apart and fly toward each other. if their speeds differ by 85mph and If they pass each other in 3 hours, then the speed of first plane is 372.5 mph and the speed of second plane is 462.5 mph.

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The greatest common factor is the greatest number that divides both numbers.

The given numbers are 574 and 532.

First, let's decompose each number into their prime factors.

574 | 2

287 | 7

41 | 41

1

574 = 2*7*41

532 | 2

266 | 2

133 | 7

19 | 19

1

532 = 2*2*7*19

As you can observe, the common factors are 2 and 7, so the greatest common factor is 14 since that's the product between 2 and 7.

Answer:

3, 8

Step-by-step explanation:

Let's make the first integer x and the second integer y.

Now, you take the information given and convert it into a system of equations:

xy = 24

x = 5y - 7

y = 24 / x

Now, we substitute:

(5y - 7) · y = 24

Distribute y

5y² - 7y = 24

Rearrange it into a quadratic equation:

ax² + bx + c = 0

5y² - y - 24 = 0

Use the quadratic formula (shown in image) and plug in the values:

x = (- (7) ± [tex]\sqrt{(-7^})^{2} -4(5)(-24)}[/tex] ) / 2(5)

[tex]\sqrt{(-7)^{2} -4(5)(-24)}[/tex] = [tex]\sqrt{49 - (-480)} = \sqrt{529} = 23[/tex]

Remember that ± means there are two y values

[tex]x = \frac{7+23}{10} = \frac{30}{10} = 3[/tex]

and

[tex]x = \frac{7-23}{10} = \frac{-16}{10} = -1.6[/tex]

Since y must be an integer, we know that y = 3

Now, plug in y:

5(3) - y = 24

15 - y = 24

- y = -24

y = 8

Let's check to see if we are right:

5y - 7 = 5(3) - 7 = 15 - 7 = 8

It works!

In order to graph the functiom we need to identify the parent function and the vertical and horizontal shifts that might be done to the function.

In this case we see that the parent function is a cubic function since the greater degree is 3

this means that f(x) is a transformation of g(x)

then

the horizontal shifts since there is sum inside the parentheses the shift will be 1 unit to the left.

the vertical shift will be 1 unit up since there is a sum outside the parentheses.

and finally since there is a - it means that the function is reflected over the x-axis

the parent function will be the red line and the function #15 is the blue line.

In order to find points we can tabulate the values for given xs' and construct the graph.

Start by making a table like this:

now since the function is given we can replace x with the values and find y

then after tabulating values should look like this

Now looking at the graph on the blue function we can see that the function is decreasing until reaching x=-1, however after that the function will continue to decrease but at a different rate, which means that over the interval

the function will be decreasing

The three transformations—rotations, reflections, and translations—can be combined to produce congruent shapes. The truth is that any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.

Explain transformations.

A point, line, or geometric figure has four different transformations that can be applied to alter its appearance. While the term "Image" refers to the position and final shape of the object, "Pre-Image" refers to the object's shape before transformation.

Given Information

The size and shape of the figures are preserved during stiff transformations, as we already know (reflections, translations, and rotations). Always in harmony with one another is the pre-image.

These transformational skills are all possessed by Matt:

Reflection

The reason a reflection maintains its original form Comparable locations between the pre-image and the picture remain apart from the line of reflection.

Rotations as a Transformation of Congruence

When a figure rotates, it twists. Despite being the same size and shape, the figurine appears to have toppled over. A clock is an excellent example of how the globe rotates in reality. Every hour or every day, the connecting arms of a clock revolve around its axis. The degree of a rotation determines what kind of rotation it is; popular rotations include 90, 180, and 270 degrees. Before spinning around completely and going back to where it started, the figure rotates 360 degrees. the clockwise or counterclockwise direction in which a rotation is made. This data can be used to determine the degree, amount, a revolution's speed and direction.

Congruence translational transformation

When an object or shape is transferred from one location to another without altering its size, shape, or orientation, we refer to the transfer as a movement. A translation, often known as a slide, involves moving every point on an object or shape uniformly and in one direction.

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In order to find any pair of points that have a midpoint of (4, -10), we can choose any two values p and q. Then, one of the endpoints will be (4+p, -10+q) and the other endpoint will be (4-p, -10-q).

For example, let's choose p = q = 2, so we have:

Therefore the ordered pairs (6, -8) and (2, -12) have a midpoint of (4, -10).

We are asked to find the value of b that makes quadrilateral RSTU a parallelogram.​

We know from the properties of a parallelogram that the opposite angles are always equal.

Let us equate the angles and solve the equation for b.

Similarly,

Answer:

5 cups of flour.

Step-by-step explanation:

I know the wording of the problem may be confusing at first, but if you look at it a little bit, it's just multiplication and division.

To start,

12 biscuits require 2 cups of flour,

meaning that 6 biscuits (half of the original) only require 1 cup.

(12/2 = 6)

Next,

We need to find how much flour is in 30 biscuits.

We know that 1 cup is in 6 biscuits, and if you were to find how much was in 30 biscuits, you would just need to divide 30 by 6.

(30/6 = 5)

5 cups of flour would be your answer.

To put it mathematically,

(12/2 = 6), (30/6 = 5)

The total cost of leasing the truck for 3 years is $8644.

An equation is an expression that can be used to show the relationship between numbers and variables.

Let y represent the total cost of leasing the truck for x months.

y = 154x + 3100

In 3 years, number of months (x) = 3 * 12 months = 36 months

Total cost in 3 years is:

y = 3100 + 154(36) = 8644

Total cost is $8644

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Let:

y=2x+18 (1)

4x+5y=20 (2)

replace (1) into (2)

4x+5(2x+18)=20

Using distributive property:

4x+10x+90=20

Add like terms:

(4x+10x)+90=20

14x+90=20

subtract 90 from both sides:

14x+90-90=20-90

14x=-70

Divide both sides by 14:

14x/14=-70/14

x=-5

Finally, replace the value of x into (1)

y=2(-5)+18

y=-10+18

y=8

Let:

2x+2y=6 (1)

3x-5y=25 (2)

From (1) let's solve for x:

subtract 2y from both sides:

2x+2y-2y=6-2y

2x=6-2y

Divide both sides by 2:

x=(6-2y)/2

x=3-y (3)

Replace (3) into (2)

3(3-y)-5y=25

Using distributive property:

9-3y-5y=25

Add like terms:

9+(-3y-5y)=25

9-8y=25

subtract 9 from both sides:

9-8y-9=25-9

-8y=16

Divide both sides by -8:

(-8y)/(-8)=(16)/(-8)

y=-2

Finally, replace the value of y into (3)

x=3-(-2)

x=3+2

x=5

Answer:

Serbia

Step-by-step explanation:

Austria-Hungary declares war on Serbia, effectively beggining the first world war

1) Since the sine is the ratio between the opposite leg and the hypotenuse.

And the hypotenuse is always opposite to the right angle

Then we can write

2) The sine of ∠ U can be written as the following ratio

sine (∠U) = 24/25

sine(∠U)= 0.96

SOLUTION:

Case: Unit rates

Given: Brian split 4/5 pounds of candy among 5 people

Method:

The unit rate in pounds per person

Final answer:

The rate in pounds per person is:

4/25 pounds

A.The number of the possible access codes:

B. The probability of randomly select the correct access code on the first try:

C. The probability of not selecting the correct access code on the first try :

Ally has a square backyard with an area of 169 square feet.

Given a square of side length, s

Therefore:

Therefore, the length of one side of the backyard is 13 feet.

Answer:

See below.

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Transitive Property of Equality

If a=b and c=b, then a=c.

Proof that ∠1=∠2

[tex]\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2}\\ \angle 3 = \angle 4 & \textsf{Vertical Angle Theorem}\\\\AB \parallel CD & \textsf{Given}\\\\\angle 3 = \angle 2 & \textsf{Alternate Interior Angles Theorem}\\\\\angle 2 = \angle 4 & \textsf{Transitive Property of Equality}\\\\\angle 1 = \angle 4 & \textsf{Given}\\\\\angle 1 = \angle 2 & \textsf{Transitive Property of Equality}\\\\\end{array}[/tex]

cosecant = hypotenuse / opposite side

Angle = 7pi/4

I suggest to convert radians into angles

180° ------------------------- pi rad

x ------------------------ 7pi/4

x = 315°

Use the calculator to find this value

Cosecant 315° = -1.41

This is the answer