What is the slope of the line in the graph?

The following are the statement justifications and explanatory reasons ;

(a) AD + DB = AB; Is justified by segment addition postulate

Reason

Segment addition postulate states that let A and B represent two points,

Then a third D can be on the line joining A and B, if and only if the

relationship between the points is according to the equation, AD + DB = AB

only

(b) m∠1 + m∠2 = m∠CDB; Is justified by angle addition postulate

Reason

Angle addition postulate states that given that a point B lies between an angle m∠AOC, then we have;

m∠AOC = m∠AOB + m∠BOC

(c) ∠2 ≅ ∠6; Is justified by vertically opposite angles theorem

Reason

Vertical angles formed by the crossing of two lines are always equal

(d) If D is the midpoint of [tex]\overline{AB}[/tex], then AD = [tex]\dfrac{1}{2}[/tex]×AB; Definition of midpoint

Reason

The midpoint of a line is the point that is of equal distance from both ends of the of the line. It is the point halfway between the endpoints

(e) If [tex]\underset{DF}{\rightarrow}[/tex] bisects ∠CDB then ∠1 ≅ ∠2; Definition of angle bisector

Reason

An angle bisector is a ray or line that divides an angle into two angles that are congruent

(f) m∠ADF + m∠FDB = 180°; Linear pair postulate

Reason

The linear pair postulate states that where we have two angles that form a linear pear (their addition forms a straight line), then the two angles are supplementary  (their sum is 180°)

(g) ∠ADF and ∠4 are supplements, then m∠ADF + m∠4 = 180°; Definition of supplementary angle

Reason

Supplementary angle are defined as angles that when added together, have a sum of 180°

(h) If ∠4 is complementary to ∠5, and ∠6 is complementary to ∠5, then ∠4 ≅ ∠6; Transitive property

Reason

Transitive property states that given three real numbers, a, b, and c, if a = b and c = b, then a = c

Learn more about angle properties postulates, and theorems here;

https://brainly.com/question/14437065

Answer:

[tex]h = \frac{2A}{b + c}[/tex]

Step-by-step explanation:

Given

[tex]A = \frac{1}{2}(b + c)h[/tex]

Required

Solve for h

We have:

[tex]A = \frac{1}{2}(b + c)h[/tex]

Multiply sides by 2

[tex]2A = (b + c)h[/tex]

Make h the subject

[tex]h = \frac{2A}{b + c}[/tex]

Step-by-step explanation:

Part A: Linear Equation.

We can find the slope

[tex] \frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10[/tex]

So our equation is

[tex]y = - 10x + 15[/tex]

Part B: Exponential Equation

We know that

[tex]15 = a \times b {}^{0} [/tex]

B to the zero power is 1 so

[tex]15 = a[/tex]

This means a =15. Now let find b.

[tex]5 = 15 \times b {}^{1} [/tex]

[tex] \frac{1}{3} = b[/tex]

So the equation is

[tex]y = 15( \frac{1}{3} ) {}^{x} [/tex]

Answer:

(-3)

Step-by-step explanation:

follow me if you want

We want to compute the probability P(A or B) because we could either solve it following path A, path B, or doing both paths.

P(A) = 1/3

P(B) = 2/5

P(A and B) = P(A)*P(B)  assuming A,B are independent

P(A and B) = (1/3)*(2/5)

P(A and B) = 2/15

--------

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 1/3 + 2/5 - 2/15

P(A or B) = 5/15 + 6/15 - 2/15

P(A or B) = (5 + 6 - 2)/15

P(A or B) = 9/15

We could reduce this to 3/5, but it appears your teacher has chosen not to.

Answer:

d

Step-by-step explanation:

trust me gang

Answer:

the degree is the value of the highest exponent... 4x^3 the exponent is a three

answer "D"

Step-by-step explanation:

see the attachment hope this helps you

Answer:

45 times 89

Step-by-step explanation:

The instuments are irrelevant and are only there to distract you.

Answer:

45 times 89 equals 4005

Step-by-step explanation:

Answer:

Area of rectangle = 150 cm

Step-by-step explanation:

Given the following data;

To find the area of the rectangle;

First of all, we would determine the dimensions (length and width) of the rectangle;

For length;

Length, L = 2x

For width;

Width, W = 3x

Mathematically, the perimeter of a rectangle is given by the formula;

P = 2(L + W)

50 = 2(2x + 3x)

50 = 2(5x)

50 = 10x

x = 50/10

x = 5

Length, L = 2x = 2 * 5 = 10 cm

Width, W = 3x = 3 * 5 = 15 cm

Now, we would find the area of the rectangle;

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = length * width

Area of rectangle = 10 * 15

Area of rectangle = 150 cm

LOL

Answer:

D. The over 30s have a larger range and interquartile range than the under 30s

Step-by-step explanation:

In a data set, the range is the difference between the maximum and minimum. So, the range for under 30s is 20, while the range for over 30s is 24. Additionally, the interquartile range is the difference between Q3 and Q1. For a boxplot, Q3 is the line where the box ends and Q1 is the line where the box begins. Therefore, the IQR for the under 30s is 8, and the IQR for over 30s is 11. So, D must be correct.

Answer:

x + y = 320

8x + 5y = 1900

Step-by-step explanation:

The equation x + y = 320 represents how 320 tickets were sold in total, from combining the adult and child tickets sold.

Since adult tickets are $8 each, the money from adult ticket sales can be represented by 8x.

The money from child ticket sales can be represented by 5y.

The equation 8x + 5y = 1900 represents how $1900 worth of tickets were sold.

So, the system of equations for the situation is:

x + y = 320

8x + 5y = 1900

Answer:

y = 220

x = 100

Step-by-step explanation:

x + y = 320

8x + 5y = 1900

x = 320 - y

8(320 - y) + 5y = 1900

2560 - 8y + 5y = 1900

2560 -3y = 1900

-2560        -2560

-------------------------

   -3y = -660

   -----    -------

    -3        -3

      y = 220

x + 220 = 320

    -220   -220

----------------------

        x = 100

Answer:

Fill up the .3 container and then pour it into the .5

fill up the .3 again and fill up the .5 ... if all is poured in the .5 will overflow over the top.

stop when the .5 is totally full... only .3 will fit... the liquid left in  the .3 will be .1

Step-by-step explanation:

Answer:

? ≈ 37°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex] , then

? = [tex]cos^{-1}[/tex] ([tex]\frac{4}{5}[/tex] ) ≈ 37° ( to the nearest degree )

Answer:

the angle GHJ would be 76 because the central angle is always double the measurement of the inscribed angle

Answer:

A

Step-by-step explanation:

cause it will be more faster just because it is in a solid phase or it is solid

The time taken to hit the ground is 6.25 sec.(Option B)

How to calculate time?

It is given that penny follows the trajectory:

[tex]y = -4.9x^2 + 32x + 425[/tex]

Differentiating it we get:

[tex]\dfrac{dy}{dx} =-9.8x+32[/tex]

At y=425, it is obvious that x=0

So dy/dx at x=0 is 32.

Now the vertical component of the velocity is 32sinФ (where Ф is the angle at which penny is thrown).

Ф[tex]=\tan^{-1}(32)[/tex]

Vertical component=[tex]32*\sin(\tan^{-1}(32))[/tex]=31.98 ft/sec

Now applying the equation of motion: acceleration=-32ft/sec^(2)

u=31.98ft/sec   s=-425   t=?

[tex]s=ut+\frac{1}{2} at^{2}[/tex]

[tex]-425=31.98t-16t^2[/tex]

[tex]16t^2-31.98t-425=0[/tex]

Solving the quadratic equation we get:

t=6.249 sec≅6.25 sec

Therefore, the time taken is 6.25 sec.

To know more about equation of motion refer:https://brainly.com/question/24966506

#SPJ2

Actually its false

In algebra 4x and 4x² are two different terms and are not like terms.

Must click thanks and mark brainliest

Answer:

So the sqrt(46) is between 6 and 7

Step-by-step explanation:

sqrt(46)

5*5 = 25

6*6=36

7*7=49

So the sqrt(46) is between 6 and 7

Answer:

70.20%

Step-by-step explanation:

Since you seem to be in a rush, let's go for a concise answer.

Let's add 146 and 344 to get 490, and do 344 / 490. This gives us the decimal proportion of ice cream cones that was sold. 344 / 490 = 0.70204.

Excellent. To get the percentage, let's multiply 0.70204 by 100 to get 70.204%. Rounding this to the nearest hundredth gives us 70.20%.

Hope this helps!

Note: This question seems to be badly worded, your 42.44% is correct if it's percentage of ice cream bowls in ice cream cones. I'm assuming that it's the percentage of all ice cream. :)

Answer:

D

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 94 and d = a₂ - a₁ = - 112 -  (- 94) = - 112 + 94 = - 18 , then

S₁₀ = [tex]\frac{10}{2}[/tex] [ (2 × - 94) + (9 × - 18) ]

     = 5(- 188 - 162)

     = 5 × - 350

     = - 1750

18 people is 25% less people so will take 25% longer

25% of 15 is 3.75

3.75+ 15 = 18.75 days ?

Answer:

A. -5

Step-by-step explanation:

First of all this is a line that shows a negative slope.

Secondly, the formula for slope is rise/ run.

5 is your rise and 1 is your run, therefore: -5/1

And this can be reduced to :  -5

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\frac{1}{6}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Box Probability}}\\\\\rightarrow \frac{\text{# of boxed flawed}}{\text{# of boxes checked}} \\\\\rightarrow \frac{3}{18}\\\\\rightarrow \frac{3/3}{18/3}\\\\\rightarrow\boxed{\frac{1}{6}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: 180 gallons

Step-by-step explanation:

If you take 8 times 6 you get 48, now take 132 plus 48 and you get 180.(hope this helped):)

Answer:

152

Step-by-step explanation:

Substitute the given value for x.

[tex]8(3(6)+1)\\8(18+1)\\8(19)\\152[/tex]

Answer:

152

Step-by-step explanation:

8(3x+1)

Let x = 6

8(3*6+1)

Multiply inside the parentheses

8(18+1)

Add inside the parentheses

8(19)

Multiply

152

⇒x (x+2) + x + 2

⇒x² + 2x + x + 2

⇒x² + 3x + 2

☛ By Splitting the middle term method

⇒x² + 3x + 2

⇒x² + 2x + x + 2

⇒ x(x+2)+1(x+2)

⇒ (x+1) (x+2)

Answer:

12

Step-by-step explanation:

F(x)=x^2−2x+4

Let x = |-4| = 4

F(|-4|)=4^2−2(4)+4

     = 16 -8+4

    = 8+4

     = 12