Find the measure of each numbered angle. (Lesson 4-2)

m ∠ 4

A triangle's exterior angle is always greater than its two remote interior angles. The exterior angle ∠1 is greater than ∠3, ∠5, ∠7, and ∠8.

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

Since, angle 1 is an exterior angle of Δ ABE,

m∠1 > m∠3 and m∠4

Since, angle 1 is an exterior angle of Δ ABD,

m∠1 > m∠5

Since, angle 1 is an exterior angle of Δ ABC,

m∠1 > m∠7 and m∠8

Therefore, ∠1 is greater than ∠3, ∠5, ∠7, and ∠8.

The complete question is:

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.

a. Measures less than m ∠ 1 .

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The solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12

In this question, we have been given an equation.

11/3x - 1/3 = -4/x²

We need to solve given equation.

⇒ 11/3x - 1/3 = -4/x²

⇒ (33 - 3x)/9x = -4/x²

⇒(33 - 3x)/9 = -4/x

⇒ x(33 - 3x) = -36

⇒ -3x² + 33x + 36 = 0

⇒ x² - 11x - 12 = 0

⇒ x² - 12x + x - 12 = 0

⇒ x(x - 12) + 1(x - 12) = 0

⇒ (x - 12)(x + 1) = 0

⇒ x - 12 = 0           or       x + 1 = 0

⇒ x = 12           or          x = -1

Now we need to check above solutions.

Substitute x = 12 in given equation.

⇒ 11/3(12) - 1/3 = -4/(12)²

⇒ 1/3 (11/12 - 1) = 1/3(-4/48)

⇒ -1/12 = -1/12

⇒ LHS = RHS

Now substitute x = -1 in given equation.

⇒ 11/3(-1) - 1/3 = -4/(-1)²

⇒ -12/3 = -4/1

⇒ -4 = -4

⇒ LHS = RHS

Therefore, the solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12

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Answer:

[tex]y - 2 = -\frac34(x - 4)[/tex]

Step-by-step explanation:

Hello!

The equation in #17 is written in Slope-Intercept Form: [tex]y=mx+b[/tex]

Point Slope form is the equation given slope and a point: [tex]y - y_1 = m(x - x_1)[/tex]

The point given to us is (4,-2), which we can use as x1 and y1.

The slope is given in the slope-intercept form equation: -3/4

Plug in the values to find the equation:

The equation is [tex]y - 2 = -\frac34(x - 4)[/tex].

The sum of finite arithmetic series  8+9+10+. . . . . . +15 is 92

Suppose we are given an arithmetic series:

      a(1) + a(2) + ... + a(n)

Then the sum is:

      S(n) = n/2 (a(1) + a(n))

Where: a(1) = first term

a(n) = nth term

The given series is:

      8+9+10+. . . . . . +15

We need to find n such that a(n) = 15.

Recall that in an arithmetic sequence:

      a(n) = a(1) + (n -1) . d

where d = difference between 2 consecutive terms.

Substituting a(1) = 8, and  d = 9 - 8 =1 into the formula:

a(n) = 8 + (n -1) . 1

15 = 7 + n

n = 8

Substitute n = 8 into the sum formula:

S(n) = n/2 (a(1) + a(n))

S(8) = 8/2 . (8 + 15)

        = 4 . 23 = 92  

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Answer:

g(x) = |4x+3|

Step-by-step explanation:

g(x) = f(x) - 2

=|4x+3|

Answer: (8w) - 6 = 7

Step-by-step explanation:

         To write an equation, we will look at the phrase given.

Six less than ➜ - 6

the product of ➜ multiplication

is equal to 7 ➜ = 7

Six less than the product of 8 and a number is equal to 7.

(8w) - 6 = 7

A variable is any property, number, or quantity that can be measured or counted. Variables can also be referenced as data items.

Inference: Inference uses selected samples from a population to estimate the properties of unknown people.

A record (or record) is a collection of data. For tabular data, a record corresponds to one or more database tables, each table column represents a specific variable, and each row corresponds to a particular record in that data set.

Therefore:

All the data collected in particular is referred to as Data Set.

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The location point of S if RS is 7 will be 4

When two vectors are added using the vector addition postulate, it is known as the vector sum.

Suppose that R and S are points on the number line. If RS=7 and R lies at -3, then;

RS = S - R

Given the following

RS = 7

R = -3

Substitute

7 = S  - (-3)

7 = S + 3

S = 7 - 3

S = 4

Hence the location point of S if RS is 7 will be 4

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Answer: 100 times

Explanation: 6 times 100 would be 600 so 600 would be 100 times bigger than 6.

The statement "The distance between a line and a plane can be found" is sometimes true.

Given,

The statement "The distance between a line and a plane can be found".

The distance between the point and the plane can be found by the taking a point on the line and finding the perpendicular distance from line to the plane.

But we can't apply this method in every case. We can only apply when either the line is parallel to the plane or the line intersects the plane.

Hence, the statement "The distance between a line and a plane can be found" is sometimes true.

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Answer:

$138.45

Step-by-step explanation:

The original price was 100% of the original price since 100% is the whole thing.

The price was discounted by 9%.

100% - 9% = 91%

That means the discounted price is 91% of the original price.

Let x = original price.

91% of x = $125.99

0.91x = 125.99

x = 125.99/0.91

x = 138.45

Answer: $138.45

(x + 100, y - 75) is the function notation used to characterise the translation to a bottom of the hill.

The Pythagorean theorem states that the sum of a squares on a legs of a right triangle equals the square on hypotenuse (this same side opposite this same right angle)—or, in recognizable algebraic notation, a² + b² = c².

Now, as per the given question;

From the shown diagram,

AC  = b

Ab  = c

We must find the coordinates of a point B. If C(x,y), then the coordinates of points A and B are:

A(x, y−b) and B(x+c, y−b)

We need to figure out b and c. To find c, we should use sine function.

sinC = perpendicular/hypotenuses

sinC = c/BC

​Thus, c = BC sinC

c = 125sin53°

  =125⋅0.79863551

c ≈100

To find b, we are using the Pythagorean Theorem.

BC² = AC² + AB²

125² = b² + 100²

b² = 125² - 100²

b = √5625

b = 75

The coordinates of a point B are as follows:

B(x+c, y−b)

B(x+100, y−75).

Therefore, the translation to the bottom of the hill defined by the function notation is B(x+100, y−75).

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Answer:|x| means “distance between a number and zero

Step-by-step explanation:

Also known as absolute value

ex l5l=5 & l5l=-5

The equation that represents the linear relationship between the x- values and y-values in the table is y = 6x - 5 .

What is a linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The equation y = 6x - 5  can represent the linear relationship between the x- values and y-values because it satisfies all the given values for x and y.

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The number of meters away that dolphins cab hear sounds underwater will be 0.0024 m

From the information, Dolphins can hear sounds underwater that are 24 kilometers away.

The number of meters away that dolphins can hear sounds underwater will be:

= 24 / 1000

= 0.0024 m

Therefore, the correct option is D.

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Answer:

Greater than

Step-by-step explanation:

2x2+7x+2

----------

The co-ordinates of point B is (4, -5).

Let the endpoints of a line segment be [tex]x_{1}[/tex], [tex]y_{1}[/tex], and [tex]x_{2}[/tex], [tex]y_{2}[/tex]. The midpoint is equal to half of the sum of the two points' x-coordinates and half of the sum of the two points' y-coordinates.

Point at A ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) = (8,1)

Point at B ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) = (x,y)

The mid point AB is M (2,-2)

Using the mid point formula:
( [tex]\frac{x_{1} +x_{2} }{2}[/tex], [tex]\frac{y_{1} +y_{2} }{2}[/tex] ) = ( x,y )

[tex]\frac{8 +x_{2} }{2}[/tex] = 2

8 + [tex]x_{2}[/tex] = 4

[tex]x_{2}[/tex] = - 4

And

[tex]\frac{1 + y_{2} }{2}[/tex] = -2

1 + [tex]y_{2}[/tex] = -4
[tex]y_{2}[/tex] = - 5

So, the co-ordinate of point B is (4, -5).

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The sentence describes the error is that A) Both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

It should be noted that the expression given is illustrated as 32x and 16.

In this case, it should be noted that the common factor between the expression is 8.

Therefore, the sentence describes the error is that both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

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Answer: Therefore, the sentence describes the error in that both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.

Step-by-step explanation:

hi

let take two points :  

( 0; -1)  and  (4 ;  2)

here is  a = 0 ; f(a) = -1

            b = 4   ; f(b) = 2

Slope is  :   f(a) -f(b)   / a-b

let's apply :   -1 - 2  / 0-4   =    -3/-4   =  3/4

Slope is   3/4

if you want to check result, you can calculate the coordonate of an other point and see if it match.

here I read that      there is a point on the line for  -4 ; -4  

here  I can read that  Y axis  value for   X = 0  is  -1  

as a line is defined  by :   mx+p  

with m =  slope  and p  value for  x = 0

so  : p = - 1

with   m =  3/4  ;   x = -4  and   p = -1  

I can test my line equation   and see if it match the result  :

3/4 ( -4)  - 1 =   -12/4 - 1 =   -3 -1 = -4  

Result match what I see on the graph, so previous result is correct.  

:  Slope is  3/4

ps :  if line grows, the slope can only be  positive. if line decrease, slope is negative, if line is constant, then slope is  still and equal 0

The simplest version is one that utilizes fundamental algebraic and mathematical ideas, such as exponents.  The simplified equation of (7/2c) - (2/c²) is (7c - 4)/(2c²).

Let the expression be (7/2c) - (2/c²)

Taking LCM of the denominator

⇒ (7/2c²) - (4/2c²)

simplifying the above equation, we get

⇒ (7c - 4)/(2c²)

Simplifying a mathematical expression means putting it in the most basic form. Typically, the simplest version is one that utilizes fundamental algebraic and mathematical ideas, such as exponents. The phrase is intended to be made simpler by eliminating any repetition or duplication.

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Answer: y = -4x + 3

Step-by-step explanation:

Line touches at point 3 on the y axis

Goes up 4 and left by 1

Answer:

4.24-(8*2)/4)=

4.24- 4= 0.24

If Edgar is a high school senior who has great grades and just received a notification that he was awarded a few scholarships in the amounts of $4,500, $7,500, and $750 while his expected tuition with books and fees is $25,000, then the amount of money Edgar will need to pay for the rest of his education bill is equal to $12,250.

The amount of money Edgar will need to pay can be determined by the subtraction of the total tuition with books and fees from the total amount of scholarships awarded to Edgar.

The total amount of scholarships awarded to Edgar can be determined by the sum of all of the scholarships.

Total amount of scholarships = 4500 + 7500 + 750

Total amount of scholarships = $12,750

Now the amount that Edgar will need to pay for the rest of his education bill can be determined by subtraction.

Amount to be paid by Edgar =  Tuition with books and fees - Total amount of scholarships

Amount to be paid by Edgar  = 25,000 - 12750

Amount to be paid by Edgar = $12,250

Hence, the amount of money Edgar will need to pay for the rest of his education bill is calculated to be $12,250.

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According to the given statement The preceding population was =  62,500.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is a one-hundred part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Percent originated from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century. Later, it was abbreviated to % with a period. The period was eventually eliminated, and the two components amalgamated to form the contemporary one-word form %.

The current population of a city = 80000

A city's population has grown by 28% since the last census.

measured.

We have to calculate the previous population before increasing 28%.

Let the previous population be p

p +(28% × p) = 80000

p + 0.28p = 80000

1.28p = 80000

p = 80000/1.28

p = 62,500

The preceding population was =  62,500.

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Answer:

7.5

Step-by-step explanation:simply divide 30 and 4 and the answer is 7.5

Ricardo will be left with $23.92 after 3 hours of Jet ski riding

Ricardo is on vacation so he went jet skiing

The Jet ski has a rental flat rate of $25

They also charge $17.75 per hour

Ricardo had $102.17

The amount spent in 3 hours is

17.75(3) + 25

= 53.25 + 25

= 78.25

The amount left is

= 102.17 - 78.25

= 23.92

Hence Ricardo has $23.92 left after the Jet ski ride

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Vertically Stretching and Compressing

It multiplies a function by a positive constant that yields a position whose graph is vertically stretched or compressed relative to the original function's graph. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done and you will get vertical compression.

Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values ​​are affected.

Solution

Y=x

Multiplying the right side by ½

Y= (1/2) *X

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The correct statements are:

Check all that applies:

A The integer −21 represents the sale of 21 books.

True

B After Monday's sales, 26 copies are available.

False

Saturday = 45 - 21

= 24 books available

Monday = 25 - 14

= 11 books available

Total books available = 24 + 11

= 35 copies available

C The integer 25 represents the new shipment.

True

D After Monday's sales, 35 copies are available.

True

E The integer 14 represents the sale of 14 books.

False

Therefore, option A, C and D are the correct statements.

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Answer:

Step-by-step explanation:

1. We know it travels 346 meters in a second, we now need to multiply 346 by 20. This equals 6920

2. Sound travels 5971 meters per second. We need to multiply this by 12 to find the distance it travels in 12 seconds. 71652 meters

3. We know sound travels 5971 meters per second in stone and 5000 meters per second from the chart. We need to find the difference between these and multiply that by 17 to find the distance covered in 17 seconds.

5971-5000=971

971*17=16507

Sound travels 16507 more meters in 17 seconds through stone than it would travel in aluminum

Answer:

DF=12√2

FG=12√2

DG=24

Step-by-step explanation:

Ratio of special Right Triangle (45:45:90): x:x:x√2

Triangle DEF: x:x:x√2

x=12

12: 12: 12√2

So, DF= 12√2

Opposite (if q, then p) Base angle theorem. So, FD≅FG.

FD=12√2

FG=12√2

Ratio of 45:45:90 Triangle: x:x::x√2

x in triangle FDG= 12√2

12√2:12√2:12√2(√2)

12√2*√2=24

=12√2: 12√2: 24

DG=24