The last statement of a two column proof is always what you are asked to Prove.
Select the correct response:
True
False

Answer:

The three properties of congruence are reflexivity, symmetry, and transitivity. These properties can be applied to segments, angles, triangles, or any other shape.

The points given represent a function. The rate of change in the function is 5. The correct option is C.

It is the average amount by which the function is modified per unit throughout that time period. The specified points' coordinates should be found. The choice to label them is yours. The difference between the output values should be found. The difference between the input values should be found.

It is calculated using the gradient of the line linking the interval's ends on the graph that represents the function. The average rate of change of the function is given as,

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

Therefore, the correct option is C, 5.

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Answer:

  -1/2

Step-by-step explanation:

You want to know the exact value of sin(-5π/6).

The reference angle is the smallest angle its terminal side makes with the x-axis. The angle -5π/6 is a 3rd-quadrant angle, whose reference angle is ...

  -5π/6 +π = π/6

You know that the signs of the sine and cosine trig functions are negative in the 3rd quadrant. Since you have memorized the short table of trig functions (first attachment), you know the value you're looking for is ...

  sin(-5π/6) = -sin(π/6) = -1/2

__

Additional comment

The second attachment shows the functions that are positive in the different quadrants. The ones not listed are negative.

The third attachment shows the coordinates on the unit circle as (cos, sin). The angle 7π/6 is the same as the angle -5π/6.

The fourth attachment shows you can put your calculator in radian mode and have it tell you the answer.

Answer:

J is a function

K is not a function

Step-by-step explanation:

A function is when every input (x) has only one output (y).

J

The ordered pairs are:

(-4,2) ( -8,2) (4, 1) ( 5,1)  Every x has only 1 y.

K

The ordered pairs are:

(4,-3) (3, -5) (2, -5) (2, -4)

the input (x) 2 has two outputs (-5, and -4)  This is why this is not a function.

The number of solutions of the system of equations 10x - 12 = 10x + 4 is given as follows:

Zero.

The system of equations 10x - 12 = ax + b would have an infinite number of solutions when:

The systems in this problem are defined by linear functions, which have the following format:

y = mx + b.

In which:

The slope and the y-intercept are used to determine the number of solutions of the system, as follows:

The system of equations 10x - 12 = 10x + 4 falls in the second case, while for a system to have an infinity number of solutions, it must fall on the third case.

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The original fraction is 10/19

Let the fraction be [tex]\frac{x}{y}[/tex]

Now , according to question

[tex]\frac{x+2}{y+5}[/tex] =[tex]\frac{1}{2}[/tex]

⇒ 2(x+2)=y+5

⇒2x-y-1=0-------(1)

and [tex]\frac{x-4}{y-1}[/tex]=[tex]\frac{1}{3}[/tex]

⇒3(x-4)=y-1

⇒3x-y-11=0------(2)

subtracting 1 from 2 we get

2x-y-1

3x-y-11

-  +  +

⇒ x=10

putting in (1)

20-y-1=0

y=19

∴ The actual fraction was 10/19

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The height of BC is calculated from the knowledge of similar triangles to be 2.76 m

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

AE and DE, AC and BC.

The solution is worked out using the proportion as follows

AE / DE = AC / BC

5 / 0.92 = (5 + 10) / BC

5 * BC = 0.92 * 15

BC = 2.76 m

hence  BC = 2.76 m

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The value of x is given as follows:

x = 1.5.

The measure of each segment is given as follows:

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For this problem, we have that segment WY is divided into two smaller segments, WX and XY.

This means that the equation to find the value of x is presented as follows:

WY = WX + XY

7x - 3 = 9x - 11 + 4x - 1

13x - 12 = 7x - 3

6x = 9

x = 1.5.

Hence the segment lengths are given as follows:

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The slope of the line made by these given coordinates is 7/6.

In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one double, and both decrease in size when one drops to a tenth of its original value.

Given coordinates of a graph. Since the coordinates are proportional thus, these coordinates represent the graph of the line as shown in the figure below.

From the general formula of the slope of the line (m) =  [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

The slope of the line = (14-7) / (12- 6)

The slope of the line = 7/6

Equation of the line id y = 7/6x + c

Since, the line passes through the point (18, 21)

21 = 7 /6 * 18 + c

c = 0

thus, the equation of the line is 6y = 7x

therefore, the slope of the line made by these given coordinates is 7/6 and this line passes through the origin.

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Answer:

True

Step-by-step explanation:

The equations that have the solution x = 5 are 25/x + 4 = 9 and 32 − 4x = 12

From the question, we have the following parameters that can be used in our computation:

x⁵ + 5 = 6

25/x + 4 = 9

32 − 4x = 12

11 + 6x = 22

3x + 1 = 9

18 − 2x = 9

Solving each equation, we have

Equation 1: x⁵ + 5 = 6

Evaluate the like terms

x⁵  = 1

Take the fifth-root

x = 1

Equation 2: 25/x + 4 = 9

Evaluate the like terms

25/x = 5

So, we have

5x = 25

Divide by 5

x = 5

Equation 3: 32 − 4x = 12

Evaluate the like terms

4x = 20

Divide by 4

x = 5

Equation 4: 11 + 6x = 22

Evaluate the like terms

6x = 11

Divide by 4

x = 11/6

Equation 5: 3x + 1 = 9

Evaluate the like terms

3x = 8

Divide by 3

x = 8/4

Equation 6: 18 − 2x = 9

Evaluate the like terms

2x = 9

Divide by 2

x = 9/2

Hence, the equations are 25/x + 4 = 9 and 32 − 4x = 12

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The measure of the angle ∠IHD is congruent to the measure of the angle ∠FGE.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In triangles ΔIHD and ΔFGE, we have

∠IHD ≅ ∠FGE        (Given)

The measure of the angle ∠IHD is congruent to the measure of the angle ∠FGE.

Congruent means equal. Then The measure of the angle ∠IHD is equal to the measure of the angle ∠FGE.

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The list of types of angles from the smallest angle to the largest angle measurement is listed below:

Acute --> right angle--> Obtuse angle --> Straight angle --> Reflective angle and circle.

The types of angles that are commonly used in mathematics include the following from the least angle to the largest:

Reflective angle and circle.

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The hybrid car needs 17 gallons of gas for 714 ​-mile trip.

The problem is solved using the unit rate.

Where unit rate refers to an item's consumption or price for one of it. This is expressed as a ratio with one as the denominator.

In the problem, we have that 4 gallons travels 168 miles the unit rate is solved as follows

unit rate =  number of gallons / number of miles

unit rate = 4 gallons /  168 miles

unit rate = 1/42 gallons per mile

solving for 714 miles trip

= unit rate * number of miles

= 1/42 * 714

= 17 gallons

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Answer:

17 gallons

Step-by-step explanation:

714 * 4 / 168 = 17 gallons

The ratio of the lengths of  ( AD, IH ) is 2:1

A chord that passes through the center of the circle is known as diameter of he circle. Chords IH and EF are diameters of our given circle.

Point A is the center of this circle.

In the given diagram we have EF is the diameter of the circle.

BC is the chord of the circle and Diameter and chord length will vary.

AD is the radius of the circle and IH is the diameter of the circle.

Diameter of the circle IH is 2 times the radius AD

So,

The Answer is option B

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Answer: He will have to plant 14 rows

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

:)

1) write slope formula:

       rise        y2-y1

m= -------   =-----------

       run         x2-x1

put your problem in the y and x your problem

     1 - 2            -1

m=---------=  -----------=-1

      2 - 1            1

Also you don't even need need to do this entire you can just see what it is decreasing  or increasing by it it is a whole number

The  the area and perimeter of the shapes in terms of pi are 36pi - 72.

You should understand that the perimeter of the object is the distance round the object.

A circle's area is calculated as pi*r², so a semicircle is pi*r² / 2, and a quarter circle is pi*r² / 4.

A triangle's area is 0.5*base*height.

We have a quarter circle of radius 12, of which the area is pi*(12² / 4) = 36pi.

The area of the triangle ABC is 0.5*12*12 = 72,

This means that the shaded area is 36pi - 72.

Rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of AD is actually identical in area to the blank semicircle-shaped space to the left of BC.

So if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. The area of a square is s² = 24² = 676 cm².

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Correct question:

For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer:

5

Step-by-step explanation:

set everything equal to a to solve for a.

a + 1 - 2 = 4

a + 1 = 6

a = 5

so your answee would be 5.

we can check this by plugging back in.

5+1-2=4

The total amount of money Williams will pay if he downloaded 45 song is 36.5 dollars.

The total cost if he download s song is 14 + 0.50s.

William signed up for a streaming music service that costs $14 per month. The service allows William to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $0.50 per song.

Therefore, the amount of money Williams will save to download 45 songs is as follows:

Using equation,

y = 14 + 0.50x

where

Therefore,

y = 14 + 0.50(45)

y = 14 + 22.5

y = 36.5 dollars

If he downloaded s songs,

total cost = 14 + 0.50s

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Answer: An exponential decay function models a situation in which a value decreases over time at a rate that is proportional to its current value. The function has the form:

y = A*e^(-kt)

Where y is the final value, A is the initial value, e is the base of the natural logarithm (approximately 2.718), k is the decay factor, and t is the time.

In this case, the initial value is 42 and the decay factor is 0.7. So the exponential decay function that models the situation is:

y = 42 * e^(-0.7t)

To compare the average rates of change over the given intervals, we need to find the derivative of the function, which represents the instantaneous rate of change of the function at any given point in time.

The derivative of this function is:

dy/dt = -0.742e^(-0.7t)

The negative sign indicates that the value is decreasing over time. The absolute value of the derivative will be the rate of decay.

So, the average rate of change over the given intervals is -0.7*42 which is -29.4

The rate of decay is always -29.4 for this function.

Step-by-step explanation:

Option A is correct.

The given line has a slope of 5 which can be calculated by counting the change in the y-direction with respect to the change in the x-direction from the graph. And the y-intercept is -1

The equation of the line is,

y=5x-1 or

5x-y=1

Checking the point (0,0) into the equation we can see that 0<1, hence, the correct inequality is,

[tex]5x-y\leq 1[/tex]

Hence, the correct inequality is not listed.

-3x +12 -6x +21 = 12 - 9x + 21

Here the Additive property of the Equality was demonastrated.

Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root qualities are the main nine properties of equality. Algebraic equations involving real numbers can be resolved with the aid of the addition, subtraction, multiplication, and division characteristics of equality.

When the same quantity is added to both sides of an equation, the equation still holds true, according to the definition of the addition property of equality. This condition may be formally expressed as follows: for real numbers a, b, and c, if a = b, then a + c = b + c. Equations involving algebra and arithmetic can both leverage this characteristic.

-3x +12 -6x +21 = 12 - 9x + 21

Here the Additive property of the Equality was demonastrated.

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Answer:

5:2

2/5

5 to 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

In this equation, 500 is the coefficient of the variable h, 4,000 is the constant, and E and h are both variables. Therefore, the equation should be written as:

E = 500h + 4000

The equation y = 10/x is a nonlinear equation

From the question, we have the following parameters that can be used in our computation:

y = 10/x

As a general rule, a linear equation can be represented using any of the following forms

y = mx + c

y = mx

y = c

x  = c

Ax + By = c

y - y1 = m(x - x1)

Any form other than the above is a nonlinear equation

The equation y = 10/x does not take any of the forms

Hence, the equation is nonlinear

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Answer: 18, 28, 38, 48, 58

Step-by-step explanation:

Answer:

18, 28, 38, 48, 58

Step-by-step explanation:

I think this is pretty self explanatory.

Answer:

y = -2x

Step-by-step explanation:

Slope = change in y/ change in x
Points: -3, 6 / -2 4
x, y
-3 - -2 = -1
6 - 4 = 2
2/-1 = -2

y = mx
y = -2x

Answer:

6

Step-by-step explanation:

Solution for 7.4x+3-9=6+7.4x equation:

Simplifying

7.4x + 3 + -9 = 6 + 7.4x

Reorder the terms:

3 + -9 + 7.4x = 6 + 7.4x

Combine like terms: 3 + -9 = -6

-6 + 7.4x = 6 + 7.4x

Add '-7.4x' to each side of the equation.

-6 + 7.4x + -7.4x = 6 + 7.4x + -7.4x

Combine like terms: 7.4x + -7.4x = 0.0

-6 + 0.0 = 6 + 7.4x + -7.4x

-6 = 6 + 7.4x + -7.4x

Combine like terms: 7.4x + -7.4x = 0.0

-6 = 6 + 0.0

-6 = 6

Solving

-6 = 6

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.