ABC is an equilateral triangle whose vertex A has the co-ordinates (0, √3). Find the co- ordinates of B and C. ​

Usando un sistema de ecuaciones, se encuentra que Juan tiene 12 años e su madre tiene 39 años.

Un sistema de ecuaciones es cuando dos o más variables están relacionadas y las ecuaciones se construyen para encontrar los valores de cada variable.

En este problema, las variables son:

La edad de juan es un año menos que la tercera parte de la edad de la madre, por eso:

[tex]x = \frac{y}{3} - 1[/tex]

Dentro de 5 años, la edad de la madre sera 10 años mas que el doble de juan, por eso:

[tex]y + 5 = 2(x + 5) + 10[/tex]

[tex]y + 5 = 2x + 20[/tex]

Como [tex]x = \frac{y}{3} - 1[/tex]:

[tex]y + 5 = \frac{2y}{3} + 18[/tex]

3y + 15 = 2y + 54

y = 39

[tex]x = \frac{y}{3} - 1 = \frac{39}{3} - 1 = 13 - 1 = 12[/tex]

Juan tiene 12 años e su madre tiene 39 años.

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The value should be placed in the second column for the range 11 - 15 will be 4. Then the correct option is C.

The data is given below.

3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.

Arrange the data in ascending order, then we have

2, 3, 3, 6, 12, 12, 13, 15, 17, 17, 18, 19, 20, 21, 25.

Then the frequency table will be

Range         Number of values

 1 - 5                      3

6 - 10                     1

11 - 15                    4

16 - 20                   5

21 - 25                   2

The value should be placed in the second column for the range 11 - 15 will be 4.

Then the correct option is C.

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Answer:

5 × 5

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length ) , then

A = 5² = 5 × 5 = 25 in²

Using proportions, it is found that she will pay $8.28 in total after the discount.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Before tax, the total price is given by:

P = 3.59 + 4.25 + 3.99 = $11.83.

She gets a 30% discount, hence the proportion she pays is 70% of this amount, hence:

P = 0.7 x 11.83 = $8.28.

She will pay $8.28 in total after the discount.

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The graph of the function can be seen in the image at the end.

I assume that the function we have here is:

[tex]y = x^3 + \sqrt{x + 2}[/tex]

This is a kinda cubic function. Notice that because we have a square root, then we have a restricted domain.

The argument of the square root can't be smaller than zero, then the minimum value of x is:

x + 2 = 0

x = -2

Then the domain is:

x ≥ -2

With that in mind, the graph of the function is the one below.

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Answer:

SSS Postulate

Step-by-step explanation:

AB=CD (Given)

AC=BD (Given)

BC=BC (Given)

So SSS Postulate

Side Side Side postulate

Both triangles are congruent by ''SSS Postulates.''

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

AB = DC, AC = DB

And, To prove that, ΔABC ≅ ΔDCB

Since, We have;

AB = DC,

AC = DB

And, BC = BC (common sides)

Hence, Both triangles are congruent by ''SSS Postulates.''

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The value of the angle ∠IMJ using  angles of Intersecting Chords Theorem is; 62.5°

From the given image, we see that;

mIJ = 40°

mLK = 85°

Now from angles of Intersecting Chords Theorem, we know that If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle. Thus;

∠IMJ = ¹/₂(mIJ + mLK)

∠IMJ = ¹/₂(40+ 85)

∠IMJ = 62.5°

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Area of Eliza's bedroom = 192 sq. inch

Scaling is a method used in measurement when large data has to be shown in a small area.

It is given that

The drawing shows a room that is 4“ x 3“

The scale used is 1 inch: 4 inch

So the actual dimensions will be 16'' x 12"

The area of a rectangle is Length * Breadth

Area of her bedroom = 16 * 12

Area of her bedroom = 192 sq. inch

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A triangle is a three-edged polygon with three vertices. The length of LM is 3√3 cms.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The triangle formed by MN, MO, and NO is an equilateral triangle, with the length of each side of the triangle equal to the radius of the triangle. Therefore, the length of MN will be,

MN = r

Now, the length of arc MN can be written as,

2 × π × r × (60° /360°) = π

r = 360 / (60 × 2)

r = 3 cms

Further, the radius of the circle can be written as,

LO = ON = OM = MN = Radius = 3 cms

Since, the triangle formed in a semicircle is a right-angle triangle, therefore, using the Pythagorean theorem we can write,

LM² + MN² = LN²

LM² + MN² = (LO + ON)²

LM² + r² = (r+r)²

LM² + r² = 4r²

LM² = 3r²

LM² = 3(3²)

LM = √27 cms

LM = 3√3 cms

Hence, the length of LM is 3√3 cms.

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The total money Dana spent in all is $24.75

Ratio are written as fractions of two integers. For instance a/b.

Amount spent for grandmother = $13.75

Amount spent on grand father = 4/5 * 13.75

Amount spent on grand father = $11

Take the sum

Total money spent = $13.75 + $11

Total money spent = $24.75

Hence the total money Dana spent in all is $24.75

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The number of CDs the students at your high school bought in 2008 is 100

The graph of the question is added as an attachment

From the graph, we have the following highlights:

2008 is 4 years from 2004.

So, the prediction is;

Year 2008 = 200 - 4 * 25

Evaluate

Year 2008 = 100

Hence, the number of CDs the students at your high school bought in 2008 is 100

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Answer + Step-by-step explanation:

your question is about equation 4 :

[tex]b_{1}=14-b_{2}[/tex]

Then

[tex]\left( b_{1}\right)^{2} =\left( 14-b_{2}\right)^{2} \ \text{(this is a special product )}[/tex]

Then

[tex]\left( b_{1}\right)^{2} =14^{2}-2\times 14 \times b_{2}+ (b_2)^2[/tex]

Then

[tex]\left( b_{1}\right)^{2} =196-28 b_{2}+ (b_2)^2[/tex]

The answer choice which could be the length of side BC is; BC < 12.

It follows from the task content that the possible length of the side BC is to be determined.

Since, the sides given AB and BC both have length sum equal to 12. It follows from the triangle inequalities that the length of the third side must be less than the sum of lengths of the other two sides.

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Answer:

Step-by-step explanation:

Declaration

Let Heather's number of messages = x

Let Eric's number of messages = x + 9

Let Chang's number of messages = 3(x +9)

Equation

x + x + 9 + 3(x + 9) = 116    

Solution

x + x + 9 + 3(x + 9) = 116                             Remove the brackets

x + x + 9 + 3x + 27 = 116                             Combine like terms

x + x + 3x + 9 + 27 = 116

5x + 36 = 116                                               Subtract 36 from both sides

5x + 36 - 36 = 116 - 36                                Combine

5x = 80                                                       Divide both sides by 5

5x/5 = 80/5

x = 16

Answer

Heather = 16

Eric = 16 + 9 = 25

Chang = 3*25 = 75

Answer:

8 people in the original group.

Step-by-step explanation:

Let x be the number of people who were originally present for the dinner that cost $160.  Their average cost per person would be:

$160/x

If 2 more people join, there are x+2 people.  Ignoring the awkward situation that they apparently did not order any additional food, they agree to share the cost of the dinner.  The average cost is now:

$160/(x+2)

We are told that this new average is now $4 less per person.

$160/(x+2) = ($160/x)  - $4

$160 = (($160/x)  - $4)(x+2)

x = 8 people

The distance of plane from the starting point is 69.46 km.

Given that the plane first flies 35 km in the direction N30W and then 60 km in the direction N60E.

We have to find the distance of plane from starting point.

We have to use pythagoras theorem in this which says that the square of hypotenuse is equal to sum of squares of the base and perpendicular.

[tex]H^{2} =P^{2} +B^{2}[/tex]

From the figure we can say that P=35 km .and B=60 km

In this we have to find the value of H when P=35 and B=60

[tex]H^{2} =35^{2} +60^{2}[/tex]

[tex]H^{2}[/tex]=1225+3600

[tex]H^{2}[/tex]=6946

H=69.46

Hence the distance of plane from starting point is 69.46 km.

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Answer:

1/0.7

Step-by-step explanation:

The expression x-y equals to 0.7 so we have to substitute 0.7 in the place of x-y....

----> 1/0.7

Dividing would make this equal to a long division answer (1.42857142857) so let's just leave it as a fraction!

I hope this helps! :)

f(x) does have an inverse function since it does pass the horizontal line test

The statement  that is true is option A that  is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

The law of the side- splitter connote that when f the line is parallel to a side of the triangle and if that said line do intersects the other 2 sides, tt is said to divides those  given sides proportionally.

So the converse means that when the sides are proportional so therefore, the side TU is said to be parallel to the side RS.

Thus;

[tex]\frac{QT}{TR}[/tex] = [tex]\frac{32}{36} = \frac{8}{9}\\\\ \\[/tex]

[tex]\\\frac{QU}{US} =\frac{40}{45} = \frac{8}{9}\\[/tex]

Therefore,  the ratios are equal and as such TU is parallel to RS

Hence, The statement  that is true is option A that  is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

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Answer: OPTION A

Step-by-step explanation:

Answer:

y = -15x + 50

Step-by-step explanation:

the pattern in the x side is +1 and the pattern on the y side is -15 so it is 15/1 which = m in y = mx + b

then you multiple -15 times whatever x and add 50 to get y like

y = -15 x 2 + 50 = 20

A fraction is a way to describe a part of a whole. The correct option is B.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The fraction that is equivalent to 2/6 is,

3/9, because 2/6 = 1/3, and 1/3= 3/9. Therefore, 2/6 = 3/9

Hence, the correct option is B.

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Answer:

Graph #1

Step-by-step explanation:

In this distance v time graph, a negative slope means moving toward Mr. Wilson, a positive slope means moving away from Mr. Wilson, and a flat section means staying at a particular location without moving.

The error in Amie's evaluation as described in the task content is; Amie should have multiplied 54 by Two-thirds.

Since it follows that the she needs the volume of the sphere in which case the radius of the sphere is half the height.

Hence we have;

V(sphere) = (4/3) πr² × h/2

V = (2/3) × πr²h

Where πr²h = Volume of the cylinder = 54cm

Hence, Amie should have multiplied 54 by Two-thirds.

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Answer:

X will be less than -5 :)

Step-by-step explanation:

We first need to put like terms together so lets do that now :)

5x + 1 < 4x - 4 

5x < 4x - 5

x < -5

Have an amazing day!!

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Answer:

x < -5

Step-by-step explanation:

The goal of this problem is for the x to be in the form of x < or > {Number}.

So let's isolate x!

5x + 1 < 4x - 4

Let's remove the x and its factor from the right side by subtraction.

5x + 1 < 4x - 4

-4x        -4x

______________

1x + 1 < -4

Now X is on one side, however, whenever a coefficient is 1, it can be excluded from the formula.

x + 1 < -4

So let's subtract 1 from the left, so x is isolated.

x + 1 < -4

    -1    -1

_______

x < -5

There we go!

We can check the direction of the inequality sign by putting in a number that fulfills the inequality.

For example, if X has to be less than -5, we can use -6.

5(-6) + 1 < 4(-6) -4

-30 + 1 < -24 - 4

-29 < -28

This is true, so the problem is complete!

Answer:

Step-by-step explanation So if you take that times 21 25 times two gives you X equals 250. So the answer is 2 50. And I use these equivalent fractions and then solve the proportion to come up with 2 50. Instead of doing a little aero trick you could have cross multiplied 200 times 1 25 and 100 times X.ion:

The missing step in solving the inequality is x > -9

From the question, we are to determine the missing step in solving the given inequality

1. The distributive property: 4x – 12 + 4 < 10 + 6x

2. Combine like terms: 4x – 8 < 10 + 6x

3. The addition property of inequality: 4x < 18 + 6x

4. The subtraction property of inequality: –2x < 18

5. The division property of inequality: ________

Applying the division property of inequality

-2x/-2 < 18/-2

x > -9

Hence, the missing step in solving the inequality is x > -9

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Answer:

the answer to this question is 1.

Answer:

2 1/2 divided by 5/2 = 1

Step-by-step explanation:

The number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members is 240 ways. Computed using permutations.

The permutation is the way of choosing a set of objects from a larger set of objects in a specific sequence.

If we are choosing r number of objects, from n number of objects in a specific sequence, then we follow permutation, and it is given as:

nPr = n!{(n - r)!}.

In the question, we are asked to find the number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members.

Since the position is to be chosen in a specific order, we will follow permutation.

The number of positions to be chosen (r) = 2.

The number of members (n) = 16.

Thus, the number of ways is given as:

nPr = n!{(n - r)!},

or, 16P2 = 16!{(16 - 2)!},

or, 16P2 = 16!/14! = 15*16 = 240.

Thus, the number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members is 240 ways. Computed using permutations.

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The location of the largest element in the matrix is a₂₁, which is 54. The location of the largest element in the matrix is a₂₁, which is 54.

Matrix is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.

The following details about the matrix can be written,

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