mike is a good athlete.Mike's father is a good athlete.Mike's sister is a good athlete.Therefore,Mike's son will be a good athlete. (Inductive or Deductive?)

Alternate interior angles are congruent if the two parallel lines are intersected by the transversal.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The parallel lines in the diagram has two red arrows on it.

The transversal line is the one that cut the other two parallel lines.

The angles formed are 9x + 5 and 10x - 5.

Therefore, if the two parallel lines are intersected by the transversal then alternate interior  angles are congruent.

Hence,

9x + 5 = 10x - 5

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Answer:

6.25

Step-by-step explanation:

a quarter=1/4 which is 0.25; 0.25 for each person is 0.25(25)=6.25

The weight of a person in Venus who weighs 210 pounds on Earth is 185.5 pounds.

It is given in the question that weight of a person on Venus varies directly with his or her weight on Earth. Also, a person weighing 120 pounds on Earth weighs 106 pounds on Venus.

We have to find the weight of the person in Venus who weighs 210 pounds on Earth.

Let weight on Earth be e and,

weight on Venus be v.

From the data given in the question, we can write,

e ∝ v

e = kv

Where k is the constant of proportionality

120 = k*106

k = 120/106 = 60/53

Hence, we can write,

210 = (60/53)*v

(210*53)/60 = v

v = 185.5 pounds

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Answer:

1 5/7

Step-by-step explanation:

12/7 x 5/5 = 60/35 or 1 5/7

Answer: Slope 0.5298 ± 0.2372

Y-intercept 1.429 ± 1.198

X-intercept -2.697

Step-by-step explanation: I hope that helped

Answer:

Tile a rectangle with unit squares. It is 8 unit squares long and 7 unit squares wide. Each unit square represents one square inch.

Step-by-step explanation:

The time taken to create a 2-foot by 4-foot pattern drive is 38.4 minutes.

A unit rate means a rate for one of something.

It is written as a ratio with a denominator of one.

We have,

A rectangle tile area = 3-inch by 5-inch

Area = 15 inches

Time taken to position 15 inches tile = 6 minutes.

We can write as,

15 inches = 6 minutes _____(1)

We have a 2-foot by 4-foot pattern drive.

Area = 8 feet

We know that,

1 foot = 12 inches

Multiply both sides by 8.

8 feet = 8 x 12 inches

8 feet = 96 inches _______(2)

Now,

From (1) and (2) we get,

15 inches = 6 minutes

Multiply 96/15 on both sides we get,

96/15 x 15 inches = 96/15 x 6 minutes

96 inches = 38.4 minutes

Thus the time taken to create a 2-foot by 4-foot pattern drive is 38.4 minutes.

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Answer:

4.25c + 3.5p = 36.50

c + 6 = p

c = candies and p = pretzels

Step-by-step explanation:

So for the first equation, the prices will be the coefficients of each variable, since for each candy/pretzel it will be that price. We also know that both of these prices together equal 36.50, so that will be on the other side of the equal sign. So the equation representing this info is 4.25c + 3.5p = 36.50

And for the second equation I saw that Mason bought 6 more pretzels than candies. So no matter what number the candies is, the pretzels should always be 6 more than the candies. So the equation representing this information is c + 6 = p

Lastly I just defined the variables that I used to right the system. That is all! Hope this helps you this should be correct :)

Time is considered to be the dimension on which any system evolves.

9.2 seconds will take for him to strike the ground.

Time can be thought of as the dimension in which the evolution of every system occurs.

It can be calculated using the following units: seconds, minutes, hours, days, weeks, months, and years.

Given,

h = 45m

g = -9.8m/s

Solution:

Vi = 0

h = Vi t + 1/2gt^2

Since Vi is 0

2h = gt^2

t^2 = 2h/g

t = [tex]\sqrt{2h/g}[/tex]

[tex]t =\sqrt{2 * -45/-9.8}[/tex]

t = 9.183s

9.2 seconds will take for him to strike the ground.

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Answer:

add a picture

Step-by-step explanation:

Answer:

D.   [tex]x^4-x^3+x^2-x+1-\frac{6}{5x+5}[/tex]

Step-by-step explanation:

Volume of a rectangular box = Base Area x Height

V = Ah

Here we are give V and h and asked to compute A

From the equation for V, dividing both sides by h gives
V/h = A

A = V/h

V = 5x⁵ - 1
h = 5x + 5

[tex]V = \dfrac{5x^5-1}{5x + 5}[/tex]

The simplified result is [tex]x^4-x^3+x^2-x+1-\frac{6}{5x+5}[/tex]

I solved this using synthetic division and can provide the steps if you want

Answer:

50

Step-by-step explanation:

          i^2 = -1

First simplify the radicals. Then use FOIL method

[tex]\sf (3 + \sqrt{-16})(6-\sqrt{-64}) = (3 +\sqrt{i^2*4^2})(6-\sqrt{i^2*8^2})[/tex]

                                     = ( 3 + 4i)(6 -8i)

                                     = 3*6 - 3*8i + 4i*6 - 4i*8i

                                     = 18 - 24i + 24i - 32i^2

                                      = 18 - 24i + 24i - 32*(-1)

                                       = 18 - 24i +24i + 32

                                       = 18 + 32 - 24i + 24i

Combine like terms,

                                       = 50

Answer:

each point needs to be transformed using (-y,x) for the new coordinate

The equation of the line in the point-slope form is y + 3 = 1/2(x - 5)

From the question, we are to determine the equation of the given line in point-slope form

First, we will determine the slope of the line

Using the points (1, -5) and (3, -4)

From the formula,

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (-4 - -5) / (3 - 1)

Slope = ( -4 + 5) / 2

Slope = 1/2

Now,

For the point-slope form of the line

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

Where m is the slope

The given point is (5, -3)

Thus,

The point-slope form of the line is  

y - -3 = 1/2(x - 5)

y + 3 = 1/2(x - 5)

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Answer: No Solution

Step-by-step explanation:

||3x - 1| + 5| <1  ⇒

[tex]\left \{ {{|3x - 1| + 5 < 1} \atop {|3x - 1| + 5 > -1 }} \right.[/tex]    ⇒

[tex]\left \{ {{|3x - 1| < -4} \atop {|3x - 1| > -6} \right.[/tex]        ⇒

The first equation does not make sense because absolute value and as it is a system of equations, the whole system does not have a solution.

Answer:

Property of Equality

Step-by-step explanation:

B=D and D=B so they are the same value so its a property of equality

The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.

Let variable x =represent the number of associates, assigned to the case

Let variable y represent number of partners assigned to the case.

The system of equations re:

800 x + 1800 y = 17600

y = x + 2

Plug equation 2 in equation 1, we get,

800 x + 1800(x+ 2) = 17600

2600 x + 3600 = 17,600

Collect like terms

2400 x = 14,000

Divide both side by 2400x

x = 14,000 / 2400

x = 5.8

x = 6 (Approximately)

So,

y = x + 2

y = 5.8 +3

y = 7.8

y = 8 (Approximately)

Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.

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The the coordinates of endpoint J on line segment JL with a midpoint of (-2, 6) is ( -3,15 ).

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2

Given the data in the question;

Midpoint K(-2, 6)

Point L(-1, -3).

Point J

To determine the coordinate of point J, plug the given points into the midpoint formula above and simplify.

First, we get the x-coordinate of point J

x = (x₁+x₂)/2

2x = x₁ + x₂

2( -2 ) = x₁ + ( -1 )

-4 = x₁ - 1

x₁ = -4 + 1

x₁ = -3

Next, we get the y-coordinate of point J

y = (y₁+y₂)/2

2y = y₁ + y₂

2(6) = y₁ + (-3)

12 = y₁ - 3

y₁ = 12 + 3

y₁ = 15

Therefore, the coordinates (x₁,y₁) of the endpoint point J is ( -3,15).

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Answer:

INVALID or 16

Step-by-step explanation:

The answer would be invalid due to the double addition signs.

However, if you meant to put a 2 in between those signs, it would be:

4+2+2+2+2+2+2

6+2+2+2+2+2

8+2+2+2+2

10+2+2+2

12+2+2

14+2

16

Answer:

Step-by-step explanation:

14

Answer:

[tex] = 8^{2} \\ = 8 \times 8 \\ = 64[/tex]

ATTACHED IS THE SOLUTION

Incomplete question.No requirement of question

Answer:

Exact form: x= -1 ± √2

Decimal Form: x= 0.41421356..., -2.41421356...

Step-by-step explanation:

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros) replace  with 0 and solve for x.

Step-by-step explanation:

this is very roughly converted from the original question, I bet. no punctuation marks and, and ...

what I understood of the important information is :

there are 23 boxes of books with 12 books in each.

there are 4 teachers dividing the books evenly among themselves for their cells (classes ?) of students.

so, we need to divide the books by 4 to distribute them evenly into 4 parts.

23×12/4 = 23×3 = 69

each teacher got 69 books.

[tex] - 2x + 2 = 180 \\ - 2x = 180 - 2 \\ - 2x = 178 \\ \frac{ - 2x}{ - 2} = \frac{178}{ - 2} \\ x = - 89[/tex]

ATTACHED IS THE SOLUTION of X

Answer:The mean is commonly referred to as average, but it is not the only kind of average. The mean is often used in research, academics and in sports.

Step-by-step explanation:

There are diffrerent ways to use the word

The average in general is the same as the term average in mathematics.

Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

The meaning of average, in general, is quite similar to average in maths.

Suppose If we say the average income of a population is five thousand.

This implies that some portion of the population earns more than five thousand and some portion of the population earns below five thousand.

We can also say that the average rate growth of height of a person per year is 5cm this also means that some years the growth is more than 5cm and some years it is less than 5 cm.

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The equation of the polynomial is P(x) = (x - 4)(x - 6)(x + 3)²

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zeros 4 and 6 is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x - (-3))² * (x - 4) * (x - 6)

This gives

P(x) = (x - 4)(x - 6)(x + 3)²

Hence, the equation is P(x) = (x - 4)(x - 6)(x + 3)²

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In case whereby the factors of 45= 3x3x5  and 75=3x3x5 given the factors, that both 45 and 75 share are 3, 5 , which are two factors

The factors of the two given numbers 45 and 75 can be seen as those whole numbers that when it is been used to divide the numbers 45 and 75 will have no remainders.

For instance , if we divide 45 by 3 then we will have 15 which do no have any remainder, same with when we divide 45 by 5 , it will have no remainder, same thing can be done to 75, we can divide it by 3 as wel as 5 without getting any remainder.

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Answer:

x = 15

z = 64

Step-by-step explanation:

Lets make an equation -

(14x - 94) + z = 8x - 4 +z

Both sides are parallel to each other, and therefore the sum is also 180.

Then we solve it -

14x - 8x - 94 + z = -4 + z

Bring the z on the other side to eliminate it.

6x - 94 = - 4

Add 94 on both sides

6x = 90

Divide 6 on both sides and you get x = 15

Substitute x into 8x -4 + z = 180

8*15 - 4 + z = 180

120 - 4 + z = 180

116 + z = 180

Subtract 116 on both sides.

z = 64.

HOPE THIS HELPS!!

CAN U PLSSS HELP ME! I have been stuck on this problem for hours! Pls try to see if u can solve it. This is the problem -

Sean and Emily love making origami. Sean can make a paper crane in 6 minutes, and

Emily can make a paper crane in 8 minutes. One day, they decided to make some paper

cranes together. They started making cranes at the same time, and after a while, they

have 112 total paper cranes. How many of those paper cranes did Sean make?

THANKS A LOT!!

Answer:

Step-by-step explanation:

1. To find the value of x, you'll need to set 14x-94 equal to 8x-4. We do this since the two angels are congruent, and congruent angles are equal to each other:

[tex]14x-94=8x-4[/tex]

You'll then solve for x by isolating the x value.

[tex]14x-8x=94-4[/tex]

[tex]6x=90[/tex]

[tex]x=\frac{90}{6}[/tex]

[tex]x=15[/tex]

2. To find z I would plug in the x value to one of the equations, such as 8x-4, in order to find the measure of that angle:

[tex]8(15)-4\\=116[/tex]

We now know that 14x-94 and 8x-4 are equal to 116. To find z you'll add the angle opposite to it, the blank angle since they are congruent. Now you'll add all the angles together and set the equation equal to 360:

[tex]z+z+116+116=360\\2z+232=360\\2z=(360-232)\\2z=128\\\frac{2z}{2} =\frac{128}{2} \\z=64[/tex]

Your final answers are x=15 and z=64, hope this helps!

We typically write linear equations in slope-intercept form:

[tex]y=mx+b[/tex]

We're given:

1) Determine the slope (m)

To find the slope, we can use the slope equation:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points through which the line passes

⇒ Plug in the given points:

[tex]m=\dfrac{-1-(-4)}{0-(-13)}\\\\m=\dfrac{-1+4}{0+13}\\\\m=\dfrac{3}{13}[/tex]

Therefore, the slope of the line is [tex]\dfrac{3}{13}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\dfrac{3}{13}x+b[/tex]

1) Determine the y-intercept (b)

In this case, the y-intercept is already given to us.

The y-intercept is the value of y when x=0. Given that the line passes through (0,-1), we know that this is -1.

Plug this into [tex]y=\dfrac{3}{13}x+b[/tex]:

[tex]y=\dfrac{3}{13}x+(-1)\\\\y=\dfrac{3}{13}x-1[/tex]

[tex]y=\dfrac{3}{13}x-1[/tex]

Answer: 4AB

Step-by-step explanation:

[tex](A+B)^2-(A-B)^2=\\((A+B)+(A-B))((A+B)-(A-B))=\\(A+B+A-B)(A+B-A+B)=\\(2A)(2B)=\\4AB[/tex]

Answer:

assuming the percents are out of 100 the order is

14.8 then 15% then 154/5 then 1450%

if thats not the case let me know and i'll correct it

Step-by-step explanation:

15% of 100 = 15

154/5 = 30.8

1450% of 100 = 1450