Triangle MRN is created when an equilateral triangle is folded in half.

Triangle N R M is shown. Angle N R M is a right angle. An altitude is drawn from point R to point S on side M N to form a right angle. The length of N S is 6, the length of S M is 2, the length of R M is x, the length of N R is y, and the length of R S is z.

What is the value of y?

2 StartRoot 3 EndRoot units
4 units
4 StartRoot 3 EndRoot units
8 units

Answer:

angle 2 is equal to angle 1 ... vertically opposite angles equal

therefore angle 2 and angle 3 are supplementary...co-interior angles supplementary

therefore m is parallel to n

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

Hello,

2x² - 9x - 35 = 0

a = 2 ; b = -9 ; c = -35

∆ = b² - 4ac = (-9)² - 4 × 2 × (-35) = 361 > 0

x1 = (-b - √∆)/2a = (9 - 19)/4 = -10/4 = -5/2

x2 = (-b + √∆)/2a = (9 + 19)/4 = 28/4 = 7

S = {-5/2 ; 7}

Answer:

So x = -5/2, 7.

Step-by-step explanation:

2x^2 - 9x - 35 = 0

Let's see if we can factor this.

We need 2 numbers whose product is  2* -35 ( that is -70) and whose sum is -9.

They are -14 and 5, so we write:

2x^2 - 14x + 5x - 35 = 0

Now we factor by grouping:

2x(x - 7) + 5(x - 7) = 0

(2x + 5)(x - 7) = 0

So x = -5/2, 7.

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 distance between car B's original point and the point where car A and car  B pass each other is 20 miles, given the speed of car A is twice the speed of car B, and they are 60 miles apart initially.

We assume the speed of car B to be x miles/hour.

Given car A going at twice the speed of car B, the speed of car A = 2x miles/hour.

When moving toward each other, the relative speed of the cars is the sum of their speeds.

Therefore, the relative speed = x + 2x miles/hour = 3x miles/hour.

The total distance between the cars is given as 60 miles.

Therefore, the time taken by car A and car B to reach the same point = 60/3x hours = 20/x hours.

Therefore, the distance from car B's original point and the point where car A and car B pass each other = Speed of car B*Time = x*(20/x) miles = 20 miles.

Therefore, the distance between car B's original point and the point where car A and car  B pass each other is 20 miles, given the speed of car A is twice the speed of car B, and they are 60 miles apart initially.

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Answer:

See below.

Step-by-step explanation:

1) Simplify √20 to 2√5.

√5 × 2√5

2) Simplify.

2√5×5

3) Simplify 5 × 5 to 25.

2√25

4) Since 5 × 5 = 25,  the square root of 25 is 5.

2 × 5

5) Simplify.

10

When evaluated, this expression equals a positive whole number, therefore showing it is a integer.

Answer: 1: 34 units    2: 24.5

Step-by-step explanation:

For figure 1, just split the area into squares and triangles and find the area of each. If you split figure 1 into 1 square and 3 triangles you get...

4x4= 16

(4x3)/2= 6

(4x4)/2= 8

(4x2)/2= 3

16+6+8+3 = 34

You do the same for figure 2, but use 4 triangles and 1 tiny square

1x1= 1

(4x3)/2= 6

(3x3)/2= 4.5

(4x4)/2= 8

(5x5)/2= 5

1+6+4.5+8+5= 24.5

You shouldn't need to worry about negative numbers because you are looking at the area

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 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:

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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Answer: the correct answer is choice A

Step-by-step explanation:

This is because the inequality symbols are pointed the correct way. The symbols are also showing the correct answers with the greater than or equal to sign is on the correct point value. You find the place for the equal to or greater/less than symbol by the open or closed circle point. An open circle means the number is not included in the answer while a closed circle is included in the answer.

Solving the quadratic function, the sales are of 9 million in the years of 2000 and 2012.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The number of sales(in millions of dollars), in t years after 2000, is modeled by the following function:

[tex]S(t) = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]

The sales are of 9 million when S(t) = 9, hence:

[tex]S(t) = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]

[tex]9 = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]

[tex]72t^2 + 90t + 900 = 20t^2 + 800t + 300[/tex]

[tex]52t^2 - 710t + 600 = 0[/tex]

Which is a quadratic equation with coefficients a = 52, b = -710, c = 600, hence:

[tex]\Delta = (-710)^2 - 4(52)(600) = 379300[/tex]

[tex]x_1 = \frac{710 + \sqrt{379300}}{104} = 12.7[/tex]

[tex]x_2 = \frac{710 - \sqrt{379300}}{104} = 0.91[/tex]

t is measured in years after 2000, the sales are of 9 million in the years of 2000 and 2012.

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Answer:

The answer is C. 270° < ∅ < 360°

Step-by-step explanation:

Given information:

sine < 0 and tans > 0.

Quadrant where sine < 0 is either III or IV.

Quadrant where tans > 0 is either I or III.

It is Quadrant III that has both sines < 0 and tans > 0.

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:

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! :)

Two angles which are next to each other is referred to as adjacent angle in this case.

These are angles which have a common vertex and side and do not overlap with one another.

This angle lie next to each other when plotted hence the reason why they share a common vertex.

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The value of x + y is 12

The equation is given as:

x^3 - y^3 = 218

Make x^3 the subject

x^3 = 218 + y^3

The next cubic expression greater than 218 is 343.

So, we assume

x^3 = 343

This gives

x = 7

Substitute x^3 = 343 in x^3 = 218 + y^3

343 = 218 + y^3

Evaluate the like terms

y^3 = 125

This gives

y = 5

So, we have:

x + y = 7 + 5

Evaluate

x + y = 12

Hence, the value of x + y is 12

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Answer:

C

Step-by-step explanation:

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Answer:

Choice C

Step-by-step explanation:

2654^0 and 5^0

Which is greater?

There's a law of exponents for solving this type of question.

The law states that,

Same case here.

And,

Hence, they are same.

2654⁰ = 5⁰

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:

When you bisect something, you cut it into two equally sized pieces. (from Latin: "bi" = two, "sect" = cut)

Bisecting an interval creates two smaller intervals each with half the length of the original interval. Some examples:

• bisecting [0, 2] gives the intervals [0, 1] and [1, 2]

• bisecting [-1, 1] gives the intervals [-1, 0] and [0, 1]

• bisecting an arbitrary interval [tex][a,b][/tex] gives the intervals [tex]\left[a,\frac{a+b}2\right][/tex] and [tex]\left[\frac{a+b}2,b\right][/tex]

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 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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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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Step-by-step explanation:

4^2

5^4

3^1×7^4

2^2 ×9^4

Answer:

In 1942 , the U.S. Mint produced 154,500,000 nickels. The scientific notation of 154,500,000 is obtained as [tex]$1.545 \times 10^{8}$[/tex].

Step-by-step explanation:

Step 1 of 2

Obtain the scientific notation.

Here the original number, 154,500,000 is greater than 1 so we will have a positive power of 10 .

Move the decimal point to get 1.545, a number between 1 and 10 . Then we get,

1.54500000

The count of the number of decimal places the point was moved is 8 .

Write as a product with a positive power of 10 .

[tex]$1.545 \times 10^{8}$[/tex]

Step 2 of 2

Check the answer.

Rewrite and simplify to check our answer.

[tex]$$\begin{gathered}1.545 \times 10^{8}=1.545 \times 100000000 \\=154500000\end{gathered}$$[/tex]

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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Using the law of cosines on the given triangle, we see that; cosθ = 0.22

The law of cosines is expressed as;

c² = a² + b² - 2ab cos C

Now, in this case the angle is θ and employing this law of cosines gives us;

10.2² = 5.7² + 9.8² - 2(5.7 * 9.8)*cosθ

104.04 = 32.49 + 96.04 - 111.72 * cosθ

104.04 = 128.53 - 111.72 * cosθ

(128.53 - 104.04)/111.72 =  cosθ

cosθ = 0.22

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A quantity with an initial value of 130 decays exponentially at a rate such that the quantity cuts in half every 9 weeks. 103.18 is the value of the quantity after 21 days.

A process known as exponential decay is when a quantity diminishes over time at a pace that reduces proportionately as the amount shrinks.

The term "exponential decay" refers to a population's or group's rate of decline when it is proportionate to the size of the population. The overall value falls in exponential decay, yet the percentage that departs stays constant over time.

Let, y = 130. aˣ

here, x = number of days

Given that,

A quantity with an initial value of 130 decays exponentially.

the quantity cuts in half every 9 weeks

the value of the quantity after 21 days = ?

So, 130 × [tex]a^{(7\times9) }[/tex] = 130 × (1/2)

or, a⁶³ = 1/2

or, a [tex](1/2)^{(1/63)}[/tex]

Thus, y = 130 × [tex](1/2)^{(x/63)}[/tex]

when x = 21

thus, y = 130 ×[tex](1/2)^{(21/63)}[/tex]

y = 130 × [tex](1/2)^{(1/3)}[/tex]

y ≈ 103.18

Hence, 103.18 is the value of the quantity after 21 days.

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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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