which number sentence does the following number line represent?

1 + (-5) = 6
5 + 1 = 6
1 + (-6) = -5
-5 + 6 = 1

According to the given data the specified type of proof. two-column proof are:

A two-column geometric proof is made up of a set of claims and the reasons why we know they are true. The statements are stated in the left column, while the reasons for making them are mentioned in the right column.

Geometric proofs are assertions that demonstrate the truth of a mathematical notion. Proof must comprise numerous phases in order to be proven true. These steps consist of reasons and declarations. Geometric proofs come in a variety of forms, include two-column proofs, paragraph proofs, and flowchart proofs.

Given: RSTUV is a pentagon.

Prove: m ∠ S+m \VS T U+m∠ T U V +m ∠ V+m ∠ V R S=540

1. RSTUV is a pentagon. (Given)

2. m∠ S + m ∠1 + m ∠2 = 180;

m ∠3 + m ∠4 + m∠ 7 = 180;

m ∠6 + m ∠V + m∠ 5 = 180 ( Sum Thm.)

3. m∠ S + m∠ 1 + m∠ 2 + m ∠3 + m ∠4 + m∠ 7 + m∠ 6 + m∠ V + m∠ 5 = 540 (Add. Prop.)

4. m ∠VRS = m ∠1 + m∠ 4 + m ∠5;

m∠ TUV = m∠ 7 + m ∠6;

m ∠STU = m ∠2 + m∠ 3 ( Addition)

5. m ∠S + m ∠STU + m ∠TUV + m∠ V + m∠ VRS = 540 (Subst.)

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Answer:

1. 0.6 (continues)

2. 1.3 (continues)

3. 2

4.  2.7

The area that is not covered by the sprinkler is 33.49 m².

The sprinkler is placed in one corner of the garden.

It has a reach of 8 m.

radius = r = 8 m

It means that it will form a segment of 90°.

So, the area it should cover will be:

Area that should be covered = 1 / 4 π r²

= 1 / 4 π (8)² m²

= 1/ 4 π (64) m²

= 16 ( 3.14 ) m²

= 50.24 m²

Now, it only rotates 30°.

It means that, it covers only 1 / 3 area.

So, the area actually covered = 1 / 3 × 50.24 m²

= 16.75 m²

The area that is not covered = 50.24 m² - 16.75 m²

The area that is not covered = 33.49 m²

Therefore, we get that the area that is not covered by the sprinkler is 33.49 m².

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We can conclude that line QT ≅ WU.

So,

Given: QR ≅ SR ≅ WR ≅ VR

To Prove: QT ≅ WU

Therefore, we can conclude that line QT ≅ WU.

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The coordinates of the other vertices are (2a, 2b) and (2a. 0) after using the mid-point theorem.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

From the data, we can draw a triangle as shown in the attached picture.

Let the coordination of B is at (0, 0)

The coordinate of point A:

A(x, y):

a = (x + 0)/2

x = 2a

y = 2b

A(x, y): (2a, 2b)

The coordinate of point C:

C(X, Y):

2a = (X + 2a)/2

4a = X + 2a

X = 2a

b = (Y + 2b)/2

Y = 0

Thus, the coordinates of the other vertices are (2a, 2b) and (2a. 0) after using the mid-point theorem.

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Step-by-step explanation:

5p − q − p; use p = 3, and q = 4

5*3-4-3

=15-7

=8

An expression that defines this quadratic function is ax² + bx + c = 0.

An expression that defines the quadratic equation in vertex form is equal to y = -16(x - 1)² + 20 and y = -16x² + 32x + 4.

Given the following data:

A quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the graph of any quadratic function is parabolic because it is a u-shaped curve. Also, the standard form of a quadratic function is given by;

ax² + bx + c = 0

Mathematically, the standard equation with the vertex for any parabola is given by:

y = a(x - h)² + k.

where:

Substituting the given parameters into the formula, we have;

y = a(x - h)² + k.

4 = a(0 - 1)² + 20.

4 = a + 20

a = -20 + 4

a = -16.

Therefore, an expression that defines this quadratic function is equal to ax² + bx + c = 0.

For the quadratic equation in vertex form, we have:

y = -16(x - 1)² + 20.

y = -16(x - 1)(x - 1) + 20.

y = -16(x² - x - x + 1) + 20.

y = -16(x² - 2x + 1) + 20.

y = -16x² + 32x - 16 + 20.

y = -16x² + 32x + 4.

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The average rate of change of a function [tex]f(x)[/tex] as [tex]x[/tex] varies from [tex]x=a[/tex] to [tex]x=b[/tex] is given by the so-called difference quotient

[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]

If we plot [tex]f(x)[/tex], this difference quotient would correspond to the slope of the line through two points [tex](a,f(a))[/tex] and [tex](b,f(b))[/tex] and intersecting with the curve [tex]y=f(x)[/tex].

(a) The average rate of change of height from 0 to 6.6 seconds is

[tex]\dfrac{H(6.6) - H(0)}{6.6 - 0}[/tex]

and is measured in m/s.

Consult the table for the values of [tex]H(t)[/tex] - it tells us [tex]H(0)=0[/tex] and [tex]H(6.6)=198[/tex]. So the average rate of change of height in this time is

[tex]\dfrac{198 - 0}{6.6 - 0} \dfrac{\rm m}{\rm s} = \boxed{30\dfrac{\rm m}{\rm s}}[/tex]

(b) Similarly, the average rate of change of height from 8.8 to 13.2 seconds is

[tex]\dfrac{H(13.2) - H(8.8)}{13.2-8.8} \dfrac{\rm m}{\rm s} = \dfrac{0 - 44)}{4.4} \dfrac{\rm m}{\rm s}= \boxed{-10 \dfrac{\rm m}{\rm s}}[/tex]

The distance between pair of parallel lines with the given equation

y=-6 y=1 is 7 units

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The two lines have the coefficient of x, zero. So, the slopes are 0.

Therefore, the lines are horizontal lines passing through y = −6 and y = 1.

The perpendicular distance between the these horizontal lines is

1 - (-6) = 7 units.

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The required value of constant of variation, k does not exist for which x and y vary directly.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion.  Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation  

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Given relation is y = 4x + 1

On comparing it with equation 1, we get, that y does not vary directly with x

Hence, the required value of constant of variation does not exist.

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Distance between parallel lines y=2x-3 and 2x-y=-4 is [tex]\frac{7\sqrt{5} }{5}[/tex] .

Two lines a₁x+b₁y+c₁=0   and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.

Distance between two two parallel lines is given by [tex]\frac{|c1-c2|}{\sqrt{a^{2} +b^{2} } }[/tex].

In the given question

2x-y-3=0   and 2x-y+4=0

Given the coefficient of x and y is same in both the line therefore they are parallel.

given, a(coefficient of x)=2 , b(coefficient of y= -1  , c₁=-3 , c₂=4.

Substituting the values in the distance formula we get

[tex]d=\frac{|-3-4|}{\sqrt{2^{2}+(-1)^{2} } }[/tex]

[tex]=\frac{7}{\sqrt{4+1} } =\frac{7}{\sqrt{5} }[/tex]

on rationalizing we get

[tex]d=\frac{7\sqrt{5} }{5}[/tex]

Therefore , the distance  between parallel lines y=2x-3 and 2x-y=-4 is [tex]\frac{7\sqrt{5} }{5}[/tex].

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In linear equations,   x = 5 is value of x .

What are instances of linear equations?

-7x-3x+2=-8x-8

-7x -3x + 8x = -8 - 2

 -10x + 8x = -10

  -2x = -10

   x = 5

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Answer:

[tex] \sqrt{(x2 - x1) ^{2} } + (y2 - y1) {}^{2} [/tex]

Answer: 24.3

Step-by-step explanation:

A tenth would be the first decimal place.

Since the digit after the digit we need to round is above 5, then we need to round up.

The two turns into a 3.

I would really appreciate if you give brainliest.

318* 0.75= $238.5

12*12=144 doughnuts total

144*1.25= $180

238.5+180= $418.50

the total sales were $418.50

Using translation concepts, the formula for function g(x) is given by the following option:

D. g(x) = 2^(x - 2)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

From the graph of the functions, we have that:

This means that g(x) is a shift right of 2 units of f(x), that is:

g(x) = f(x - 2).

Hence:

g(x) = 2^(x - 2)

The formula for function g(x) is given by the following option:

D. g(x) = 2^(x - 2)

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Answer:

2(v-3) = 5

Step-by-step explanation:

2(v-3) = 5

The length of the slide should be approx. 16 ft long.

Pythagoras Theorem states that sum of square of two sides of triangle  is equal to the square of longest side of the right angle triangle..

From the given figure

we will use ratio to find the vertical distance

given that vertical/horizontal=4/7

[tex]\frac{vertical.distance}{horizontal.distance} =\frac{vertical.distance}{horizontal.distance}[/tex]

[tex]\frac{4}{7} =\frac{v}{14}[/tex]

By cross multiplying we get v=8 feet.

As we can see in the figure  that Vertical distance, Horizontal distance and the Slide forms a Right angled Triangle.

Pythagoras Theorem can be used to find the length of the slide.

Applying Pythagoras Theorem in ΔABC

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

given that AB=14 and BC=8

Substituting in the above equation we get

[tex](14)^{2} +8^{2} =AC^{2} \\\\ 196+64=AC^{2} \\ \\ 260=AC^{2}[/tex]

[tex]AC=\sqrt{260}=16.12[/tex]

approx. 16 feet

Therefore , the length of the slide should be approx. 16 ft long.

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A parabola is defined as a curve where each point is equidistant from:

fixed point (focus) and

fixed line (director).

The properties of a parabola can be defined as given below:

Rays parallel to the axis of symmetry are reflected straight from the surface to the focal point.

Because the vertex of the parabola is at (0,0) and the focus is at (-3,0).

This means that the parabola axis is the negative x-axis.

The parabola equation is x^2 =4ay and a=3.

So, the parabola equation is x^2 =12y.

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The zeros of the given polynomial equation are {-1, -2, -3}.

The given polynomial equation is g(a)=4a³+24a²+44a+24.

The rational root theorem is also known as the rational zero theorems (or) the rational zero tests (or) rational test theorem and is used to determine the rational roots of a polynomial function. The general form of a polynomial function is [tex]f(x) = a_nx^n+a_{n-1}x^{n-1}+.......+a_2x^2+a_1x+a_0[/tex]. Here, the value(s) of x that satisfy the equation f(x) = 0 are known as the roots (or) zeros of the polynomial.

Now, g(a)=4a³+24a²+44a+24

⇒ 4a³+24a²+44a+24=0

⇒ 4(a³+6a²+11a+6)=0

⇒ a³+6a²+11a+6=0

Now, put ....-3, -2, -1, 0, 1, 2, 3,....in a³+6a²+11a+6=0 and simplify and check they are equal to 0.

Put a=-3 and check.

That is, (-3)³+6(-3)²+11(-3)+6=0

⇒-27+54-33+6=0

⇒0=0

So, -3 is the zero of the given equation.

Put a=-2 and check.

That is, (-2)³+6(-2)²+11(-2)+6=0

⇒-8+24-22+6=0

⇒0=0

So, -2 is the zero of the given equation.

Put a=-1 and check.

That is, (-1)³+6(-1)²+11(-1)+6=0

⇒-1+6-11+6=0

⇒0=0

So, -1 is the zero of the given equation.

Therefore, the zeros of the given polynomial equation are {-1, -2, -3}.

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The midpoint is at (11/2, 15/2, 1/2)

In the given statement is

To find the midpoint of the line segment joining the pair of points

A(4,7,9) and B(-3,8,-8)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =(  [tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} ,\frac{z_{1}+z_{2} }{2}[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points A(4,7,9) and B(-3,8,-8)

Solving for the midpoint , we have,

m = ([tex]\frac{4+7}{2} ,\frac{7+8}{2} , \frac{9+(-8) }{2}[/tex])

m = (11/2, 15/2, 1/2)

Therefore, the midpoint is at ( 11/2, 15/2, 1/2)

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The domain are -3, -1, 1 . The range is -2, 0, 2 .

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Answer: -3,-1, and 1.

Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.

456.25 male lion weigh for the zoo to obtain the male lion.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Given:

A male lion grows to weight about 420 lbs with a standard deviation of 35 lbs.

A zoo would like to have a lion that is in the largest 25% of male lions based on weight.

So,

z= (x- [tex]\mu[/tex])/[tex]\sigma[/tex]

Now substituting the value

1.036 = X-420/35

36.25= X- 420

X= 36.25 + 420

X= 456.25

Hence, 456.25 male lion weigh for the zoo to obtain the male lion.

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here for the solution We have here, that jet is equal to 0.52. Their score corresponding to 30 area under standard normal distribution. By using jet table to the right up ahead here, X is equal to zero multiplied by sigma plus mu. Here by substituting the value for the next step, we get 0.52 dataset, multiply by sigma. That is 35 plus mu, That is four 20. By simplifying this, we get the value is 4 83.2, which is approximately equal to 4 38.4. Which is our Answy for the answer is 4:38.4 is the correct choice for the answer. So here is the solution. The answer. Please go through this.

A translation vector describing the receiver's path < -12, 17 >.

The distance vectors that almost all atoms in the grouping are translated through just to form another cluster inside the solid are defined by translation vectors.

Now, as per the stated question;

The horizontal (lateral, x) change is represented by the number 12. This same player runs 12 yards to the left.

The vertical (up/down, y) transition is represented by the number 17. In addition, the player runs 17 yards up the field.

When you put it all together, you get < -12, 17 >.

Therefore, the receiver's route is defined by translation vector < -12, 17 >.

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An example is a counterexample to a general statement if it makes the statement false is given by an example of the opposite of each whole number is not a whole number, it is an integer.

As given,

Given statement:

Opposite of each whole number is a whole number

Consider whole number=2

Opposite of 2 is -2

-2 is not a whole number it is an integer.

Therefore, an example is a counterexample to a general statement if it makes the statement false is given by an example of opposite of each whole number is not a whole number.

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When Pablo bought a sweater on sale for 25% off the original price and another 40% off the discounted price, if the sweater originally cost 48 then the final price of the sweater is $21.6

Given,

The Original cost of the sweater = $48

First,

Pablo bought a sweater on sale for 25% off the original price

Then,

[tex]48-48(\frac{25}{100} )[/tex]= $36

Then another 40% off the discounted price

Final price = [tex]36-36(\frac{40}{100} )[/tex]

=$21.6

Hence, when Pablo bought a sweater on sale for 25% off the original price and another 40% off the discounted price, if the sweater originally cost 48 then the final price of the sweater is $21.6.

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Answer:

Step-by-step explanation:

3t + 4 = 12 + 3t

4 = 12  (subtract 3t from both sides)

0 = 8   (subtract 4 from both sides)

Answer:

Step-by-step explanation:

The solution of the given linera equation in one variable 12=2-k is at k = 10.

According to the given question.

We have a linear equation in one variable 12 = 2 - k.

As we know that, linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Therefore, the solution of the linear equation in one variable 12 = 2 - k is given by

12 = 2 - k

⇒ 12 - 2 = -k         (subtracting 2 from both the sides)

⇒ 10 = -k

⇒ k = 10  

Hence, the solution of the given linera equation in one variable 12=2-k is at k = 10.

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