If the mortgage interest rates increase, this would be an example of changing your external environment.

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;

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Explanation:

We can prove this by contradiction.

Let's say

and

A+B = C

We'll show that a contradiction happens based on this.

If A is rational, then A = p/q where p,q are two integers. The q cannot be zero.

If C is rational, then C = r/s for some other integers. We can't have s be zero.

Note the following

A+B = C

B = C - A

B = r/s - p/q

B = qr/qs - ps/qs

B = (qr - ps)/qs

B = (some integer)/(some other integer)

This shows B is rational. But this is where the contradiction happens: We stated earlier that B was irrational. A number cannot be both rational and irrational at the same time. The very definition "irrational" literally means "not rational".

In short, I've shown that if A+B = C such that A,C are rational, then B must be rational as well.

The template is

rational + rational = rational

Therefore, we've shown that if A is rational and B is irrational, then C cannot possibly be rational. C is irrational.

Another template is

rational + irrational = irrational

Answer:

[tex]344 {cm}^{2} [/tex]

Step-by-step explanation:

[tex]area \: of \: the \: square \\ = 40cm \times 40cm \\ = 1600 {cm}^{3} \\ [/tex]

[tex]area \: of \: the \: circle \\ = \pi {r}^{2} \\ = 3.14 \times {(20)}^{2} \\ = 3.14 \times 400 \\ = 1256 {cm}^{2} \\ [/tex]

[tex]area \: of \: shaded \: region \\ = 1600 {cm}^{2} - 1256 {cm}^{2} \\ = 344 {cm}^{2} \\ [/tex]

Answer:

I'm pretty sure it is 3 hours.

Step-by-step explanation:

Well, when you add 9 plus 6, you get 15. Then you divie 45 by 15, which gives you three. Hope this helps. Good luck :D

Answer:

7x=11

Step-by-step explanation:

do it

Answer:

The probability of choosing a girl is 1/2.

The probability of choosing an A student who is a BOY is 5/28.

1/2 = 14/28, and 14/28 + 5/28 = 19/28. This can be simplified to 0.68

Thus, the answer is B. 0.68

Let me know if this helps!

The required probability of choosing a girl or an A student is 0.82. Option A   is correct.

Given that,
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade.
A student is chosen at random from the class. What is the probability of choosing a girl or an A student is to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Total sample space = 28
Number of girls = 14
Number of boys = 14
Number of girls A grade student  = 9

probability of a girl = 14/28 = 0.5
probability of A grader girl  = 9 / 28 = 0.32
Now the probability of choosing a girl or an A grader girl student,
= 0.32 + 0.5
= 0.82

Thus, the required probability of choosing a girl or an A student is 0.82. Option A  is correct.

Learn more about probability here:

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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:

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:

x = 360°

Answered by GAUTHMATH

Bill before tax = $32

Tax = 10/100×32

= $3.2

Tip = 15/100×32

= $4.8

Total cost = 32 + 3.2 + 4.8

= $40

Answered by Gauthmath must click thanks and mark brainliest

Answer:

Step-by-step explanation:

Let the number be x

14 ÷ x = [tex]\frac{14}{x}[/tex]

Answer:

14 / x

Step-by-step explanation:

quotient = /

14 = 14

a number = the variable, let's call it x

Brainliest please!

Answer:

n>-4

Step-by-step explanation:

8+n>4

n>4-8

n>-4

Answer:

-4

Step-by-step explanation

Subtract 8 from 4 to get -4.

N = -4

God Bless.

Answer:

The difference will be increasing too

Step-by-step explanation:

If f(x) and g(x) is increasing in nature then

f(b) < f(a) and g(b) < g(a) for any a and b in the interval.

Subtracting these 2 equations, we get

f(b) - g(b) < f(a) - g(a) for any a and b in the interval.

Which means f-g is increasing in the interval (a, b) but as a and b were random real numbers we took, f(x) - g(x) will be increasing for an interval

9514 1404 393

Answer:

  D (compute the mean)

Step-by-step explanation:

A box plot is a visual representation of the 5-number summary of a set of data. It is plotted against a number line.

The 5-number summary of the data set is most easily determined from an ordered set of the data, so ordering the data is usually the first step. Since the 5-number summary is plotted against a number line, the next steps are finding the 5-number summary, and creating a suitable number line.

__

The business of adding the data and dividing by the number of data items is a description of computing the mean of the data. That value is not part of the 5-number summary, and is not needed in the creation of the box plot.

Answer:

x = 17

Step-by-step explanation:

x ^2 = 8^2+ 15^2

√x^2 =√64+225

x=17

Answer:

17cm.

Step-by-step explaination:

The given triangle is a right angled triangle.

Using Pythagorean Theorem,

a² + b² = c²

Putting the given values in the equation;

(15)² + (8)² = c²

225 + 64 = c²

289 = c²

17² = c² (square root of 289 = 17)

17 = c

c = 17

Therefore, the missing side of the triangle is equal to 17 cm.

Answer:

x=15.75 y=59

Step-by-step explanation:

In total there is 360 degrees. We know y is 59 so we will replace it with that.

59+59=118. 360-118=242. 242/2=121. 29+29=58. So we can subtract that to equal 63. Now 63=4x. We can divide so 2x=31.5. x=15.75.

Therefore, 15.75=x and 59=y

I hope this helped ^^.

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:

For the equation (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, the value of k = 5/6.

Since the equation is (2k + 1)x² + 2x = 10x - 6, we collect subtract 10x from both sides and add 6 to both sides.

So, we have (2k + 1)x² + 2x - 10x + 6 = 10x - 6 - 10x + 6

(2k + 1)x² - 8x + 6 = 0

For the equation, (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, this new equation (2k + 1)x² - 8x + 6 = 0 must also have two real and equal roots.

For the equation to have two real and equal roots, its discriminant, D = 0.

D = b² - 4ac where b = -8, a = 2k + 1 and c = 6.

So, D =  b² - 4ac

D =  (-8)² - 4 × (2k + 1) × 6 = 0

64 - 24(2k + 1) = 0

Dividing through by 8, we have

8 - 3(2k + 1) = 0

Expanding the bracket, we have

8 - 6k - 3 = 0

Collecting like terms, we have

-6k + 5 = 0

Subtracting 5 from both sides, we have

-6k = -5

Dividing through by -6, we have

k = -5/-6

k = 5/6

So, for the equation (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, the value of k = 5/6.

Learn more about quadratic equations here:

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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

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:

c.8,625grams of flour

4a. X=12

Y=30

Z=60

Step-by-step explanation:

For c. , You have to convert the mixed numbers to fractions.

2¾ cups of flour= 2×4=8

8+3=11

Answer: 11/4 (11 over 4)

You multiply the 2 (whole number) by the 4 (bottom number) and then you get *8*

You then take the 8 (which was your answer) and add 3. This will give you 11

You take the 4 and use it as your denominator (bottom number) for the 11. So no need to find a denominator, because you just use the 4

For the fruit cake, she uses *1½* cups of flour more than carrot cake

Calculation:

1½ converted to an improper fraction= 1×2=2

2+1=3

Answer: 3/2 (3 over 2)

"Customer orders *3* carrot cakes and *4* fruit cakes

How many cups of flour are required to bake for the cakes ordered by the customer?"

11/4÷3= 8,25grams

3/2÷4= 0,375grams

8,25+0,375=8,625grams in total

*Feel free to correct me as I might be wrong!*

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

9514 1404 393

Answer:

  169 ft

Step-by-step explanation:

The law of cosines can be used to find the distance from the outfielder to the pitcher. It tells you for triangle ABC, the length of side c can be found from ...

  c² = a² +b² -2ab·cos(C)

Here, we hve a=60.5, b=214, and C=36°. Then the desired distance is ...

  c = √(60.5² +214² -2·60.5·214·cos(36°)) ≈ √28507.56 ≈ 168.84

The outfielder throws the ball about 169 feet.

Answer:

Step-by-step explanation:

Angle opposite to 6 is complementary of α:

Similarly, angle opposite to side 4 of the triangle in the right side is:

Sum of the interior angles of the triangle on the bottom:

From the smaller triangles we get:

Use the identity below and find the value of tan γ:

Hey there!

8 0/1

8 * 1 + 0/1

= 8 + 0/1

= 8/1

Therefore your answer is most likely: 8/1

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

A) (√3-√2)/(√3+√2)

Step-by-step explanation:

i think so

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):)