Would anybody be able to help me out with this one question please?

15 points up for grabs!

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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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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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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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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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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.

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]

Step-by-step explanation:

5p − q − p; use p = 3, and q = 4

5*3-4-3

=15-7

=8

Answer:

$240

Step-by-step explanation:

30% of 800 is 240

.30*800

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 coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE are given by: (3,4).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

The rule for a 90º clockwise rotation is given by:

(x,y) -> (y, -x).

From the figure given for the problem, the coordinates of G are given as follows:

G(-4,3).

Applying the rule, we have that:

(-4,3) -> (3, 4), as y = 3, -x = -(-4) = 4.

Hence the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE are given by: (3,4).

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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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Answer:

Step-by-step explanation:

3t + 4 = 12 + 3t

4 = 12  (subtract 3t from both sides)

0 = 8   (subtract 4 from both sides)

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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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.

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Each assertion is supported by a property. The transitive feature of equality justifies this.

If x, y, and z are the three quantities, and then if x is connected to y by some rule and y is related to z through the same rule, we are able to say x is related to z by the same rule.

m∠1+m ∠2=90

m ∠2=m ∠3

m∠ 1+m∠ 3=90 .

The property that justifies each statement is This is justified by the transitive property of equality.

because :

Transitive Property of Equality  show  If a = b and b = c, then a = c.

so in the given statement the  m∠1+m ∠2=90 and ∠2=m ∠3 so m∠ 1+m∠ 3=90.

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Answer:

f(2) = sqrt(4 - 2 ^ 2)

f(2) = sqrt(4 - 4)

f(2) = sqrt(0)

f(2) = 0

Answer: 0

Step-by-step explanation:

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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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Yes, the product of an integer and a natural number will always be an integer.

         A natural number refers to a whole number that does not have any kind of fraction or decimal. Some examples of natural numbers are 1, 2, 3, 4, and so on. Zero is not a natural number.

        Integers refer to all numbers that can be positive and negative. It should not have a fractional part or a decimal part in the number. Integers can be depicted by the positive or the negative sign. Zero is an integer.

       Whenever we are multiplying a natural number with an integer, we are ultimately getting the result as a positive number, negative number, or zero. Thus, it will become an integer.

       Example 1: We can take the natural number 10 and the integer -5. Its product will be -50. Thus, it is an integer.

       Example 2: We can take the natural number 16 and the integer 0. Its product will be 0. Thus, it is an integer.

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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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Answer:

Step-by-step explanation:

This is equivalent to 8.75 feet

====================================================

Explanation:

3 & 1/2 inches = 3.5 inches since 1/2 = 0.5

30 boards of this width total to 30*3.5 = 105 inches

This is equivalent to 105/12 = 8.75 feet. I'll leave the answer in inches since the original unit is inches. I would ask your teacher for further clarification.

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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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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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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The number of significant digits the product should have = 2

The given numbers are:

[tex]4.5160 \times 10^{-3}\\ 2.09 \times 10^7\\ 5.8 \times 10^3[/tex]

We first multiply them.

[tex]4.5160 \times 10^{-3}\times 2.09 \times 10^7\times 5.8 \times 10^3 = 54.743\times10^7[/tex]

In measurement problems, we usually write it as [tex]5.474\times10^7[/tex]

Significant digits are the numbers which decide the precision and accuracy in measurement problems.

The fewest number of significant digits in each factor of multiplication is considered as the significant digits of the product.

So number of significant digits in [tex]4.5160\times10^{-3}[/tex] = 5

Number significant digits in [tex]2.09\times10^7[/tex] = 3

Number of significant digits in [tex]5.8\times10^3[/tex] = 2

So the product should be rounded into 2 significant digits.

So the product,  [tex]5.474\times10^7[/tex]= [tex]5.5\times10^7[/tex] with 2 significant figures.

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a) 4, associative property

      - This is the associative property of multiplication. When everything is multiplied, you can rearrange the parentheses.

b) 8, commutative property

      - This is the commutative property. It means that when multiplying two numbers together, the order doesn't matter.

c) 0, zero property

      - This is the zero property of multiplication. This states that anything times 0 is equal to 0. In this case, 0 times 3 is 0.

d) 8, identity property

      - This is the identity property of multiplication. This means that any number times 1 is itself. In this case, 9 times 1 is 8.

Please note how a property is worded may differ per class.

Answer:

[tex]2x + 9 = y \\ - 4x - 3 = y \\ so \: both \: equation \: is \: equal \\ 2x + 9 = - 4x - 3 \\ 2x + 4x = - 3 - 9 \\ 6x = - 12 \\ x = \frac{ - 12}{6} \\ x = - 2[/tex]

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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Answer:

2(v-3) = 5

Step-by-step explanation:

2(v-3) = 5

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.