Which of the following statement is NOT true?
a. Congruent triangles are triangles with corresponding congruent sides.
b. Two triangles with corresponding congruent angles are congruent.
c. Triangles with corresponding congruent sides and an included angle are congruent.
d. Triangles with corresponding congruent angles and an included side are congruentâ

To solve this problem, we can use the Pythagorean theorem to find the height of the balloon. In particular, we can consider the right triangle formed by the stake, the top of the balloon, and the part of the string that is attached to the stake.

[asy]

unitsize(2 cm);

pair A, B, C, D, E;

A = (0,0);

B = (0,15);

C = extension(A,B,A+(1,0),B+(1,0));

D = extension(A,C,A+(0,1),C+(0,1));

E = extension(B,D,B+(0,-1),D+(0,-1));

draw(A--B--C--cycle);

draw(A--D--E--cycle);

draw(rightanglemark(A,D,C,2));

label("$A$", A, S);

label("$B$", B, N);

label("$C$", C, E);

label("$D$", D, E);

label("$E$", E, W);

[/asy]

Let $a$ be the distance from the stake to the top of the balloon, $b$ be the height of the balloon, and $c$ be the length of the string. We know that $a = 15$ feet and $c = 15$ feet, so we can use the Pythagorean theorem to find $b$:

$a^2 + b^2 = c^2$

$15^2 + b^2 = 15^2$

$225 + b^2 = 225$

$b^2 = 0$

$b = \sqrt{0} = 0$ feet

Therefore, the height of the balloon is 0 feet. This is because the balloon has been pulled up by the wind so that its top is directly above the stake, and therefore its height is 0 feet.

Answer:

Step-by-step explanation:

There are just two triangles stuck together , here.  Don't let that throw you off your game :DD  

solve for a

then b

for a it's  180 = 2*36 +a   ( b/c of the red marks , again)

180 = 72 +a

180-72 =a

108 = a

Now solve for b

180 = 2b + 42  (red marks tell us this formula works,  again)

180-42 = 2b

138 =2b

138/2 =b

69 = b

Do you see , now,  how I get those formulas???

Answer:

1. $80 dollars for the month she used 3 GB over her data limit.

2. 10x + 50.

Explanation:

1. Autumn used 3 GB data more than her plan offered. $10 dollars a gigabyte of data times 3 gigabytes equals 30, plus 50 dollars for the base smartphone plan (which, off topic, sucks) equals 80 dollars for the month.

2. 10x + 50 means 10 dollars per X gigabytes, plus the base 50 dollars a month Autumn has to pay.

Consequently, the room has a 7 meter width. The room's length is

[tex]= 7 * 3 meters = 21 meters[/tex]

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Given that the length of the rectangular space is three times its breadth

The chamber has a 56-meter perimeter.

Assume that the room's width is x.

As a result, the room is three times as long.

The room's perimeter is now equal to 2(3x + x).

[tex]Here, 2(3x + x) = 56\\ 2 * 4x = 56\\ 8x = 56\\ x = 7.[/tex]

Consequently, the room has a 7 meter width.

The room's length is

[tex]= 7 * 3 meters\\= 21 meters[/tex]

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Answer:

I am not sure which form you want.

Points slope: y -2  = 3(x -4)

Slope intercept:  y = 3x -10

Step-by-step explanation:

Point slope form for the line

y- y = m(x -x)  

slope of 3 and the point (4,2)  Use 4 for x and 2 for y

y -2  = 3(x -4)

Slope intercept form of a line

y = mx + b

2 = 3(4) + b

2 = 12 + b  Subtract 12 from both sides

2 - 12 = 12 - 12 + b

-10 = b

y = mx + b

y = 3x -10

The expression be 1/4(c³+ d²) then the value exists 9.

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (from left to right).

The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations.

Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are in the following order: PEMDAS (from left to right).

Let the given expression be 1/4(c³+ d²)

The value of c = -4 and d = 10

substitute the values in the above equation, we get

Follow the PEMDAS order of operations

Calculate within parentheses  ((-4)³ + (10)²) = 36

1/4((-4)³ + (10)²)

simplifying the above equation, we get

= 1/4 × 36

= 9

Therefore, the correct answer is option B. 9.

The complete question is:

What is the value of this expression when c = -4 and d = 10?

1/4(c³+ d²)

A. 2

B. 9

C. 21

D. 41

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Answer:

5

Step-by-step explanation:

There are 6 total skeins, and 1.2 is needed to make one

So you would divide 6 by 1.2

6 / 1.2 = 5

And to confirm it is 5, you can now multiply 5 by 1.2

5 x 1.2 equals 6

Answer:

It costs $0.49 for each avocado and $0.36 for each tomato.

Step-by-step explanation:

This is a system of equations problem.

Let x represent the avocados and y represent tomatoes:

4x + 5y = 3.76  <--- scenario 1

6x + 3y = 4.02 <---- scenario 2

If we graph these out on a graphing calculator, the lines will intersept at point (0.49,0.36)

The x coordinate represents how much it costs for each avacado and the y coordinate represents how much it costs for each tomato

The answer in the solution set that makes 4f − 10 = 3f − 18 true is (a) -8

From the question, we have the following parameters that can be used in our computation:

4f − 10 = 3f − 18

And we have the solution set to be

S: {−18, −8, 3, 8}

Subtract 3f from both sides of the equation

So, we have the following representation

f - 10 = - 18

Add 10 to both sides of the equation

This gives

f = -8

Hence, the solution is (a) -8

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The average number of children in a family under the age of 1818 is 0.76, which is the predicted value of this distribution.

The product of each potential result and its associated probability yields the anticipated value of a probability distribution. The probable outcomes in this scenario are 0, 1, 2, 3, & 4 minors, with the associated probability shown in the table.

We may add the products of each result and its probability to determine the estimated return of this distribution:

Expected value = (0)(0.58) + (1)(0.18) + (2)(0.16) + (3)(0.06) + (4)(0.02)

= 0 + 0.18 + 0.32 + 0.18 + 0.08

= 0.76

Therefore, 0.76 children below the age of 18 per household are the anticipated value of this distribution.

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The factor is  [tex](t^4+rs^5)(t^8-rs^5t^4+r^2s^{10})[/tex].

Option (D) is correct.

What is factorization?

Factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors.

Given:

[tex]t^{12}-r^{3}s^{15}[/tex]

For factorizing the above expression is

now, using the formula

(a³ - b³) = ( a+ b)( a² -ab + b²)

Then,

[tex]=(t^4)^{3}-(rs^{5})^{3}\\=(t^4+rs^5)((t^4)^2-(t^4\timesrs^5)+(rs^5)^2)\\=(t^4+rs^5)(t^8-rs^5t^4+r^2s^{10})[/tex]

Hence, the correct factorization is [tex](t^4+rs^5)(t^8-rs^5t^4+r^2s^{10})[/tex].

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Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

x - 3 = 5

(x -3) +3 = 5+3

x - 3 + 3 = 8

so,

x = 8

When n is large the distribution of the sample means will approach a normal distribution.

The central limit theorem (CLT) is a statistical theory that predicts that given a large enough sample size from a population with a certain level of variation, the mean of all the samples from that population will be close to the population mean.

To put it another way, the central limit theorem predicts with absolute certainty the form of the distribution of means when we take repeated samples from a certain population. In particular, the distribution of means derived from repeated sampling will tend toward normality as sample sizes increase.

In other words, when n is large, the distribution of the sample means will resemble a normal distribution if we continually pick independent, random samples of size n from any population.

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Since, The equation of the height with the time is provided and the balloon is thrown upwards against gravity from 5 feet, The answer is 0.255 sec.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration.

initial height = 5

final height =20

height to travel =20-5 =15

[tex]15 = 16t^{2}+35t+5\\16t^{2}+35t-10 =0[/tex]

solving we get, t = 0.255 or -2.44

since, -2.44 is not possible,

t = 0.255 seconds.

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In order to plot the region enclosed by the given graphs we have to find the intersection points of all the 3 graphs taking 2 at a time

so finding intersection point of the y=4/x and y=16x

4/x=16x

=> [tex]x^{2}[/tex] = 1/4

=> x = 1/2 as x>0

and y=16x

=> y =8

now finding intersection point of y=4/x and y=1/16x

=> 4/x =x/16

=> [tex]x^{2}[/tex] = 64

=> x = 8 as x>0

and y= 4/x

=> y=1/2

now finding intersection point of y=16x and y=1/16x

the intersection point of both line is x=0

so y=16x

=> y=0

so we will get the intersection point of all the lines now after plotting all the points below we will get the graph as attached below.

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Answer:

A. 113 degree

Step-by-step explanation:

These are Alternate Interior Angles, which means the 113-degree angles and the? are equal. So, the answer is A

1) The relation in the right is not a function.

2) domain

D: {-60, 20, 70}

range

R: {-6, 3, 2, 5}

3) Angelo is correct.

A function is a relation that maps elements from one set called the domain into another set called the range, such each element from the domain is mapped into only one of the elements of the range.

Thus, if an element of the domain is being mapped into two or more elements of the range, then the relation is not a function.

1) If you look at the relationship in the right, you can see that the input -60 is being mapped into two different outputs, this, it is not a function.

2) The domain is the set in the left:

D: {-60, 20, 70}

And the range is the set in the right side:

R: {-6, 3, 2, 5}

3) Angelo is correct, functions are relations,  but not all relations are functions, only the relations that meet the condition written above.

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Answer:

first option

Step-by-step explanation:

inequalities of the type | x | > a have solutions of the form

x < - a or x > a

given

| 7 + m | - 4 > 8 ( add 4 to both sides )

| 7 + m | > 12

then

7 + m < - 12 (subtract 7 from both sides )

m < - 19

OR

7 + m > 12 ( subtract 7 from both sides )

m > 5

solution is m > 5 or m < - 19

Answer:

Below in bold.

Step-by-step explanation:

The definition of direct variation is  y = kx where k is a constant.

So, if y/x is a constant for the data, we have direct variation.

So, checking the rows in the given table:

y/x = 11/8

y/x = 22/16 = 11/8

y/x = 33/24 = 11/8

- we see that this is direct variation.

So, k = 11/8 and

The equation is

y = (11/8) x

or

y = 11x/8

or

y = 1.375x  in decimal form.

Answer:

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

Direct variation equation:

Use the pairs of coordinates and find the value of k, then compare:

The value of k is same with all ordered pairs and the equation is:

Answer: A

Step-by-step explanation:

Answer: If Lin sells b boxes of cookies, she will earn 3.75b dollars. Therefore, the inequality that will be true whenever Lin makes her goal is:

3.75b > 30

This inequality can be read as "the total amount of money Lin earns selling cookies is greater than $30."

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-1 - 3)/(3 - 0) = -4/3

y - 3 = -4/3(x - 0)

y - 3 = -4/3x + 0

y = -4/3x + 3

The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Calculate the slope of each line,

LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,

Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3

Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.

Thus, the solution of the pair of lines has been shown above.

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Answer: 10 cm

Step-by-step explanation:

Given, length=8cm

breadth=6 cm

Pythagoras theorem states that sum of square of base and square of perpendicular height is equal to square of hypotnyse.

Thus, we can write:

Considering, base=length=8cm

Perpendicular=breadth=6cm

Therefore, length of diagonal =√(length∧2+breadth∧2)

                                                 =√(8∧2+6∧2) cm

                                                = 10 cm

Therefore the length of diagonal = 10cm.

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In order to estimate the mean height of all bears in the Smokies within 4 inches of the actual height with a 99% confidence level, you would need a sample size of 25 bears.

You must calculate the sample size using the formula below in order to estimate the mean bear height in the Smokies within 4 inches of the actual height at a 99% confidence level:

n = [tex](\frac{2 X SD}{E})^2[/tex]

Where,

n = sample size

SD = standard deviation of the population (which you have estimated to be 10 inches)

E = margin of error (which you want to be 4 inches)

Putting these values into the formula, we get:

n = [tex](\frac{2 X 10}{4})^2[/tex]

= 25

In order to estimate the mean height of all bears in the Smokies within 4 inches of the actual height with a 99% confidence level, you would need a sample size of 25 bears.

It's important to note that this is only a rough estimate, and the exact sample size may change depending on the population's real characteristics and the level of precision you require. To enhance the accuracy of your estimate, it's also critical to select a sample that is typical of the total population.

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The line l and line m are parallel.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

Given that, transversal t cuts line l and line m.

∠2≅∠7

Transversal t cuts line l and line m (Given)

∠2≅∠7 (Given)

∠2≅∠3 (Vertical angles theorem)

∠3≅∠7 (Converse of corresponding angles postulates)

l║m proved

Hence, the line l and line m are parallel.

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Answer: y=-3x-5

Step-by-step explanation:

(0,-5)   (-1,-2)

[tex]\displaystyle\\\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}[/tex]

x₁=0     x₂=-1     y₁=-5    y₂=-2

[tex]\displaystyle\\\frac{x-0}{-1-0}=\frac{y-(-5)}{-2-(-5)} \\\\\frac{x}{-1} =\frac{y+5}{-2+5} \\\\-x=\frac{y+5}{3}[/tex]

Multiply both parts of the equation by 3:

[tex]-3x=y+5\\\\-3x-5=y+5-5\\\\-3x-5=y[/tex]

[tex]Thus,\ y=-3x-5[/tex]

The probability that the top card is an Ace of Spades and the bottom card is a Queen of Hearts is extremely low, as there are 52 cards in a standard deck of cards and only two of those cards are an Ace of Spades and a Queen of Hearts.

Therefore, the probability of the top card being an Ace of Spades and the bottom card being a Queen of Hearts is 1/2652 or approximately 0.000038%.The probability of getting an Ace of Spades as the top card and a Queen of Hearts as the bottom card is 1/52 x 1/52 = 1/2652. This can be expressed as a percentage by multiplying the fraction by 100 which gives us 0.000038%. The probability that the top card is an Ace of Spades and the bottom card is a Queen of Hearts is extremely low, as there are 52 cards in a standard deck of cards and only two of those cards are an Ace of Spades and a Queen of Hearts.

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Considering a circle whose equation is (x + 6)² + (y + 8)²  = 9. The radius of the circle is 3 units

Information given in the question

Circle F is represented by the equation (x + 6)² + (y + 8)²  = 9

Equation of a circle is given as

(x - h)² (y - k)² = r²

The equation of the circle is written in standard form is sown above comparing the equation with the given question gives

rewriting the equation

(x + 6)² + (y + 8)²  = 9

(x + 6)² + (y + 8)²  = 3²

comparing shows that r = 3

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Answer:

9

Step-by-step explanation: