Match the following reasons with the statements to complete the following proof.

A rise of 8 and a run of 6. Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space.

On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).

The distance between AB will be

AB² = (-5 + 5)² + (-2 + 4)²

AB² = 4²

AB = 4

The distance between BC will be

BC² = (-2 + 5)² + (-2 + 2)²

BC² = 3²

 BC = 3

Then the rise and run will be

rise / run = 4 / 3

Then this can be written as

rise / run = 8 / 6

Then the correct option is B.

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Answer:

Here's a little trick I learned in 8th grade. The first numbers don't matter all that matters are the 2nd numbers, and if you have 2 of the same kind of numbers then it's not a function so your answer would be B.

The distance of the yacht from the ship is 35 km

See attachment for the diagram that represents the given parameters.

The distance of the yacht from the ship is then calculated using the following law of cosine.

YS^2 = ST^2 + YT^2 - 2 * ST * YT * cos(T)

This gives

YS^2 = 24^2 + 12^2 - 2 * 24 * 12 * cos(155)

Evaluate the exponents and the products

YS^2 = 576 + 144 + 522

Evaluate the sum

YS^2 = 1242

Take the square root of both sides

YS = 35

Hence, the distance of the yacht from the ship is 35 km

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Answer:

Circumference of a circle = 2 pie r

237 = 2 * pie * r

237 / 2 * Pie

118.5/ pie = r

118.5 = Pie*r

Area of circle = Pie *r²

= Pie r * r

= 118.5 * 118.5/ Pie

= 118.5 * 118.5 / pie

= 14042.25/ pie

taking value of pie = 3.14

= 4472.05 sq. cm

Answer:

A. 4 root 3

Step-by-step explanation:

Answer:

[tex]144 cm^{2}[/tex]

Step-by-step explanation:

Step 1: Find the true length of each side

We know that the perimeter is 56cm and the ratio of AD:AB:DC:BC is 5:12:6:5. It is safe to assume that this ratio is the simplified version, which means that if we multiply each of these numbers by a scale factor of [tex]x[/tex], then we get the true length of each side, so we would get [tex]5x, 12x, 6x, 5x[/tex] for the sides. We also know that when we add these numbers, we get the perimeter, which is 56. So, we can create the equation [tex]5x + 12x + 6x + 5x = 56[/tex]. Then, solve the equation for x, which would be 2, and go back and multiply each number with 2 to get the following:

AD = 5*2 = 10cm, AB = 12*2 = 24cm, DC = 6*2 = 12cm, BC = 5*2 = 10cm  

Step 2: Calculate the Height

Now we know the lengths of each side, lets take a look at the formula for the area of a trapezium: [tex]\frac{base_{1} + base_2}{2}*height[/tex]. So, the next step would be to calculate the height. We can draw the height by drawing a line straight down from the vertex D and another straight down from the vertex C. These lines are both the height, and will be the exact same length. We can calculate that the height is 8 because AB is 24 cm, but the length from the height at vertex D to the height at vertex C is 12 cm, so that means that the base of each triangle is 12/2 = 6 cm. Then we can use Pythagorean theorem to figure out that the height is 8cm.

Step 3: Calculate the Area

Lastly, we can calculate the area. The formula is [tex]\frac{base_{1} + base_2}{2}*height[/tex]. In this case, the numbers would be [tex]\frac{12 + 24}{2} * 8 = 144cm^{2}[/tex]

I know this is a lot, so let me know if you have any questions!

Answer:

D

Step-by-step explanation:

(f • g)(x)

= f(x) × g(x)

= (x + 4)(3x² - 7)

each term in the second factor is multiplied by each term in the first factor , that is

x(3x² - 7) + 4(3x² - 7) ← distribute both parenthesis

= 3x³ - 7x + 12x² - 28

= 3x³ + 12x² - 7x - 28 ← in standard form

Each given factor written as a polynomial in descending order is;  (7x + 6y)(49x² - 42xy + 36y²)

We are given the polynomial;

343x³ + 216y³

343x³ + 216y³ is a sum of cubes and factors in general as;

a³ + b³ = (a + b)(a² - ab + b²)

Thus;

343x³ + 216y³ = (7x)³ + (6y)³

= (7x + 6y)((7x)² - 7x(6y) + (6y)² )

= (7x + 6y)(49x² - 42xy + 36y²)

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Answer:

I don't see a correct answer.  See below.

Step-by-step explanation:

Thanks for clarifying the question.  But if 27√3 is the correct expression, I don't see an answer option that fits.  

√3 = 1.732

27*(1.732) = 46.77

But all the answer options are whole numbers.  The presence of√3 makes it difficult to find an expression that would result in a whole number.  Expressions such as:

27/√9 = 9, or

√27/√3 = 3

would be more consistent with producing a whole number result.

I hope this helps.

Answer:

A. 1

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x.

x-intercept(s): (-5,0)

Considering (-5,0) is the only intersection on the x-axis, 1 is your answer.

If you want a visual of this, I recommend you use the Desmos graphing calculator to input your equation. It will show you what the curved line looks like.

Answer:

B. Matter

Explanation:

When rocks break down and become smaller ex: mountains eventually becoming sand, the matter does not disappear or get destroyed, it becomes smaller particles, but the matter is always preserved.

Hope It Helps!!!

Answer:

matter

Step-by-step explanation:

The conservation of matter states that

Here big matters gets down into smaller pieces

but they are not destroyed

The result follows from the fundamental theorem of calculus. Since [tex]f''(x)[/tex] is the derivative of [tex]f'(x)[/tex], we have

[tex]\displaystyle \int_0^c f''(x) \, dx = \boxed{f'(c) - f'(0)}[/tex]

(E)

Answer:

B.  7/2 miles per 1 hour

Step-by-step explanation:

The unit rate in this case ,means ,

the number of miles  for every 1 hour

Since Taylor walks 7 miles in 2 hours

Then

He walks 7/2 miles in 1 hour

Thus

The unit rate that Taylor walks at is :

7/2 miles per 1 hour

Answer:I think observational

Step-by-step explanation:They want to study it so they trying it on people who are willing so they are looking closely to what happens.

Answer:

see the attachment photo!

The value of a₄₁ mean the expression in 4th row and 1st column will be 2. Then the correct option is B.

The complete question is attached below.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.

The matrix is given below.

[tex]\begin{bmatrix} 1&3&8&5&\\ 5&4&6&2\\6&7&1&8\\2&9&3&7&\\\end{bmatrix}[/tex]

Then the value of a₄₁ mean the expression in 4th row and 1st column will be 2.

Then the correct option is B.

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Based on the four expressions written above (image attached) one can say that She is right about the remaining four expressions as they all can shown or expressed as binomials.

Binomial distribution is known to be a kind of probability distribution whos models or show the probability of getting one of two outcomes in any  said number of points or parameters.

Note that:

5abc -2a² + 6abc

Add like terms

= 11abc - 2a²

5x³∙ 2x² -10x⁴ +3x⁵+ 3x∙(-2) x⁴

Simply

=5 . 2x³⁺² - -10x⁴ +3x⁵+ 3x∙ 2x⁴

=10x³⁺²  -10x⁴ +3x⁵+ 3∙ 2xx⁴

= 7x⁵ + 10x⁴

(t+2)²-4t

Simply

= (t² + 2t.2 + 2²) - 4t

=  (t² + 2t.2 + 4) - 4t

= t² + 4

The same applies for the rest. Therefore, one can say that Based on the four expressions written above (image attached) one can say that She is right about the remaining four expressions as they all can shown or expressed as binomials.

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The probability that the items drawn are two pencils and one highlighter is 0.25

To do this, we make use of the following representations:

Since there are three boxes, the number of possible outcomes is:

Outcomes = 2³

Outcomes = 8

See attachment for the tree diagram.

From the tree diagram, we have:

So, the probability is:

P = 2/8

Evaluate

P = 0.25

Hence, the probability that the items drawn are two pencils and one highlighter is 0.25

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When the coefficient of x is positive, the graph of a line rises and moves to the right. Option C is correct.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

The complete question is

"The graph of a line goes up and to the right when:

a) the coefficient of x is 0

b) the coefficient of x is negative

c) the coefficient of x is positive

d) there is no coefficient of x"

When the coefficient of x is positive, we know that the graph of a line will move upward and to the right.

Since we are aware that a line's upward and rightward movement indicates that the line is advancing, we will obtain a positive slope for the line, and we are also aware that the slope-intercept of a line is provided as:

y= mx+c

If m is a positive number, then positive is the coefficient of x.

The graph of a line goes up and to the right when the coefficient of x is positive.

Hence option C is correct.

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Answer:

56.52 inches

Step-by-step explanation:

pi is the ratio of the circumference to the diameter so you can simply multiply the diameter by pi to get the circumference which is 3.14 * 18 = 56.52

Answer: -50

Step-by-step explanation:

5 - 6 / 5p = 125 degrees

1/2p = ?

First, subtract 5 from both sides, that way, the 5 on the left side will cancel out.

-6/5p = 125-5 degrees

-6/5p = 120 degrees

now, multiply 5p on both sides.

-6 = 120 * 5p degrees

-6 = 600p degrees

divide 600 on both sides

-6/600 = p degrees

-0.01 = p degrees

p = -0.01

1/2p = 1 / -0.02 = -50

Hope I helped!

Answer:

x = -2, y = 3

Step-by-step explanation:

2x + 3y = 5

5x - 2y = -16

In order to find the value of a variable, we must eliminate the other variable by multiplying the equations to get the same coefficient.

We can multiply the first equation by 5 and the second one by 2 to get the same coefficient for x, the equations then become:

10x + 15y = 25

10x - 4y = -32

Now we can subtract:

19y = 57

y = 3

Since we know the value of y, we can substitute it into one of the original equations:

2x + 3(3) = 5

2x + 9 = 5

2x = -4

x = -2

Answer:

15

Step-by-step explanation:

3x/4+1=19/4+1x/2

3x/4-x/2=19/4-1

x/4=15/4

collect like terms

x=15

The points which are solutions to the linear inequality are; (-3, -2), (-1, -2) and (1, -2)

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

-2 < 0.5(-3) + 2

-2 < 0.5 (satisfied)

1 < 0.5(-2) + 2

1 < 1  (Not satisfied)

-2 < 0.5(-1) + 2

-2 < 1.5 (Satisfied)

2 < 0.5(-1) + 2

2 < 1.5 (Not satisfied)

-2 < 0.5(1) + 2

-2 < 1.5 (Satisfied)

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Answer:

23

Step-by-step explanation:

If Kelsey spent 32 hours in the first week. We subtract 32 from 55. 55-32=23. That means she worked 23 hours in the second week.

Answer:

Step-by-step explanation:

y = x² + 7x - 5 ............ (1)

2x - y = - 9 ................ (2)

(1) ------> (2)

2x - ( x² + 7x - 5 ) = - 9

- x² - 5x + 14 = 0 ........ (3)

- 1 × (3)

x² + 5x - 14 = 0

( x + 7 )( x - 2 ) = 0

[tex]x_{1}[/tex] = - 7 and [tex]x_{2}[/tex] = 2

2( - 7) - [tex]y_{1}[/tex] = - 9 ⇒ [tex]y_{1}[/tex] = - 5

2(2) - [tex]y_{2}[/tex] = - 9 ⇒ [tex]y_{2}[/tex] = 13

The solutions of system are

( - 7, - 5 ) and ( 2, 13 )

Answer:

x =  17.32 units

Step-by-step explanation:

In a right triangle tan (angle) = opposite leg / adjacent leg...

  for this triangle   tan 27° = 34 / x

      then x = 34 tan 27° = 17.32 units

Answer:

Step-by-step explanation:

-16p+37=49-21p what is the answer?

-16p + 37 = 49 - 21p

-16p + 21p = 49 - 37

5p = 12p =

p = 12/5