For a project in her Geometry class, Mila uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.45 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.2 meters to the other side of the mirror, until she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

The graph of the inequality (x + y >1),  will be:

{(x^2+(y-1)^2-0.05)((x-1)^2+y^2-0.05)(x+y-1)=0 [-10, 10, -5, 5]} and we can shade right-side of the line.

As per the question statement, we are supposed to graph the inequality

x + y >1. So, first we solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For x = 0, y = 1 or (0,1)

For y = 0, x = 1 or (1,0)

So now we can graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

The boundary line would be solid because the inequality contains "or equal to" clause.

Graph: {(x^2+(y-1)^2-0.05)((x-1)^2+y^2-0.05)(x+y-1)=0 [-10, 10, -5, 5]}

We can shade right-side of the line.

Because the inequality operator lacks a "or equal to" phrase, the boundary line will be altered to a dashed line.

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a=2cm. b=50cm. x=?

x=b:a. x=50:2. x=25

Given:

The length of yarn needed, l=23 1/4 feet.

The length of a yarn bundle, L=11 1/2 feet.

The number of bundles of yarn needed can be calculated as,

Therefore, 3 bundles is needed by Jenna to make the scarf.

The part of leftover yarn is,

Hence, 45/46 part of a bundle of yarn will be left.

Now, the length of leftover yarn is,

Therefore, 111/4 feet of yarn will be left.

Answer: es

Step-by-step explanation: I know Spanish

Answer:  3 1/4 Is the correct answer.

The Domain and the range of the function are given as

x ≥ 0, y ≥ 3000

This is the complete set of values that is used to represent the independent variable in the function. The independent variable that we have here is represented by x and it is 0.

This is the set of the possible values that the dependent variable in the function is to have. The dependent variable is given by y.

The range of x would have to start from 0 for the range of all values of x. Hence x ≥ 0, while y is seen to be in  the form of y ≥ 3000 because this is the value of trout that was stocked.

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The driving time in hours for the remaining of Guenther's trip would be = 9.5 hours.

The Speed of a moving object is defined as the change in distance divided by change in time.

The first distance covered by Guenther = 260 miles.

The time it took to cover the first distance= 5 hours.

The remaining distance = 494 miles

The time it will take to cover the remaining distance = X hours

But if , 260 miles = 5 hours

494 miles = X hours

Make X the subject of formula;

X hours= 494 × 5 / 260

X hours = 2,470 / 260

X hours = 9.5 hours.

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 x = 41/6 is value of x in transversal lines.

What are transversal lines?

 ( 12x + 1)° = 2

 2 = 83°

 ( 12x + 1)° = 83°

  12x° + 1° = 83°

12x = 83 - 1

12x = 82

 x = 82/12

 x = 41/6

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The number has been assigned to be number line and attached as a picture

A number line refers to a picture representing array of numbers arranged to suit the calculation intended to represent.

The picture shows a number line from -6 to 6

The division in the number line is showing two lines representing 1/3 and 2/3 before the next number.

This means that the point before point 6 counting from point 5 is 5 1/3, 5 2/3 then point 6

For the negative direction we have

-5, -5 1/3, -5 2/3, -6

The required answer to the questions attached

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Answer:

The answer is 35:19

Step-by-step explanation:

First what is a ratio?

A relationship between two quantities, normally expressed as the quotient of one divided by the other. For example, if a box contains six red marbles and four blue marbles, the ratio of red marbles to blue marbles is 6 to 4, also written 6:4. A ratio can also be expressed as a decimal or percentage.

So as a result

= There are 35 mangoes and 19 strawberries

And since we are comparing mangoes to strawberries

The answer would be

= 35:19

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Answer:  The equation is written as:   " 7x  +  28  =   8  −  3x " .
  The value for x , when the equation is solved, is:  " -2 ."

Step-by-step explanation:

Let the "unknown number" be represented by the variable, x ;

7 (times) the [sum of: (x + 4)] ; (is the same as):  8 [decreased by]:

  3(times)x ;  
Rewrite:    " 7(x + 4) = 8 − 3x ".   This is the written expression.

____
Now, if we wish to "solve for x" ;
Let's examine the 'left-hand side' of the equation:
     7(x + 4)  ;

Note the 'distributive property' of multiplication:
  a(b + c) = ab + ac ;

____
 So:  7(x + 4) = 7*x + 7*4 =  7x + 28 ;

Now, let's write the entire equation:
  7x + 28 = 8 − 3x  ;
Let's add 3x , and subtract 8 ;  from Each Side of the equation:

 7x + 28 + 3x − 8 = 8  + 3x − 8 ;

→ 7x + 3x + 28 − 8 = 8 − 3x + 3x;

 to get:
 10x + 20  = 0 ;

Now:  Subtract 20 from Each Side of the equation:
  10x + 20 − 20 = 0 − 20 ;

to get:
   10x = -20 ;  Now, divide both sides of the equation by 10 ;

to isolate x on one side of the equation; & to solve for x :

    10x/10 = -20/10 ;
to get:  " x = - 2 " .
____
Alternate method:
 10x + 20 = 0 ;

Divide the Entire Equation by 10 ;

(10x + 20) / 10 = 0____ ;

 to get:  (10x/10) + (20/10) = 0 ;

  →  x + 2 = 0  ;

Now subtract 2 from each side of the equation;

 to isolate x on one side of the equation; & to solve for x :

     x + 2 − 2 = 0 − 2 ;

to get:  " x  =  -2 " .

____

Answer:
 The equation is written as:
 " 7x + 28 =  8 − 3x " .
The value for x, when the equation is solved, is  "-2".
____
Hope this is helpful to you!  Best wishes!
____

you need first see something all the numbers in the polynomial can be divided by 3 then we can rewrite the polynomial as

3(x^3+4x^2+x-6)

the polynomial x^3+4x^2+x-6 is easier to solve and find the roots

the roots are

x = -3

x = -2

x = 1

and finally

we can rewrite the polynomial as

3(x+3)(x+2)(x-1)

so we can say that the right answer is D. 3(x-1)(x+3)(x + 2)

The expansion of ( 2x - y⁵)² using algebraic identity, as a polynomial is  4x² - 4xy⁵+ y¹⁰

Algebraic identities are the identities which aids in solving products or powers of algebraic expressions. Most common identities are :

(a+ b)² = a² + 2ab + b²

(a- b)² = a² - 2ab + b²

a² -b² = (a+ b) (a- b), where a and b can be variable or constants or algebraic expressions.

For expanding (2x - y⁵)²

Use identity (a-b)² = a²-2ab+b², let a = 2x and b = y⁵

Then, ( 2x - y⁵)² = (2x)² - 2(2x)( y⁵) + (y⁵)²

⇒  ( 2x - y⁵)²  = 4x² - 4xy⁵+ y¹⁰

Therefore, the standard form of  ( 2x - y⁵)² as a polynomial is  4x² - 4xy⁵+ y¹⁰

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Answer:

look at the step by step

Step-by-step explanation:

I think -12 x-12 and something with the other number I think you have to mulitply it all

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

The question provides that ΔABC and ΔDEF are similar. By the definition of similar triangles, we have that:

Since congruent angles are equal, we have:

From the provided diagram, we have the measures of the following angles:

Comparing the congruent angles, we have that:

The sum of angles in a triangle is 180°. If we add up the angles of ΔDEF, we can get the value of z:

Given the value of z, we can get the measure of [tex]\begin{gathered} m\angle E=10z-5 \\ m\angle E=10(5)-5=50-5=45\degree \end{gathered}[/tex]By comparing the congruent angles, we have that:

ANSWER:

Angle B = 45 degrees.

The value of z is 5.

A. -234

B. -62

C. [tex]-72+151=79[/tex]

D. [tex]612+144=756[/tex]

Answer:

The third step would be to construct a hypothesis.

Step-by-step explanation:

The amount of money that June has is $40 and Maria has $400. The total amount is $440.

From the information, John has $400 June has 1/10 of that and June has 0.1 of Maria’s money.

Therefore the amount that June has will be:

= 0.1 × John's money

= 0.1 × 400

= 40

June has 0.1 of Maria’s money. Let Maria's money be x. Therefore, 0.1 × x = 40

0.1x = 40

Divide

x = 40 / 0.1

x = 400

Maria's money = 400

Therefore, the total amount that they have will be:

= Amount that John has + Maria's amount

= 400 + 40.

= $440

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Answer:

y = 2x

Step-by-step explanation:

I am basing this off of your straight line that you drew.

Slope is found by using [tex]\frac{rise}{run}[/tex] . This means that you change in your y-axis divided by change in your x axis.

This can also be modeled by Δy/Δx

I used point (0,0) and the peak of the slope (100,200)

Your line starts at 0 and rises 200 and runs to the right 100.

Thus, you can write:

y = [tex]\frac{200}{100}[/tex] x

This simplifies to y = 2x

Answer:

x = 16 degrees

Step-by-step explanation:

Since this is an isosceles triangle, both sides are the same. We then come up with the equation:

5x - 7 = 8x - 55

Next, we subtract 5x on both sides

5x - 7 = 8x - 55

-5x        -5x

____________

-7 = 3x - 55

Afterward, we add 55 on both sides:  

-7 = 3x - 55

+55      +55

___________

48 = 3x

Lastly, you divide 48 by 3 to get the answer 16!!

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Answer:

positive

Step-by-step explanation:

this is because it is going up if it is going down it’ll be negative and if it was zero it would be flat

There are 4/5 of the fraction 5/8 in the fraction 1/2

The mathematical statement is given as

"how much of the 5/8 is in the 1/2"

The above means that

Dividend = 1/2

Divisor = 5/8

The number of fractions is then calculated as

Count = Dividend/Divisor

Substitute the known values in the above equation

So, we have the following equation

Count = (1/2)/(5/8)

Evaluate

Count = 4/5

Hence, the number of 5/8 in 1/2 is 4/5

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The number of Quarter coins that she has is 8 and the number of Dimes is 16.

It is given in the question that the woman has twice as many Dimes as the quarters in her purse.

We know that the value of Dimes is 0.10$ and the value of Quarters is

0.25 $

Let the number of Quarter coins is y and the number of Dimes coin be u.

According to the question above,

u = 2y  equation (i)

The total value z = 0.25y + 0.10u

Putting here the value of u from equation (i) we have,

z = 0.25y + 0.10(2y)

⇒ z = 0.25y + 0.20y

⇒ z = 0.45y equation (ii)

Now it has been mentioned that if the Dimes were Quarters and the Quarters were the Dimes, she would have $ 1.20 greater than she has now.

So we have,

z + 1.2 = 0.25u + 0.10y

Putting the value of u from above eqation (i),

z + 1.2 = 0.25(2y) + 0.10y

⇒ z + 1.2 = 0.50y + 0.10 y

⇒ z + 1.2 = 0.60y

Putting the value of z from equation (ii)

⇒ 0.45y + 1.2 = 0.60y

⇒ 0.45y - 0.60y = - 1.2

⇒ -0.15y = - 1.2

⇒ y = [tex]\frac{-1.2}{-0.15}[/tex]

⇒ y = 8

Therefore u = 2y

⇒ u = 2 x 8 = 16

Hence the number of Quarter coins is 8 and the number of Dimes is 16

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16 dimes, 8 quarters

I checked RSM it's correct

Answer:

x = 25 when y = 8

Step-by-step explanation:

If y is inversely proportional to square root of x we write it as
[tex]y \propto \dfrac{1}{\sqrt{x}}[/tex]

This is also equivalent to
[tex]y = k \dfrac{1}{\sqrt{x}} \;\;\;\;\ \text{ [1]}[/tex]

where k is a constant known as the constant of proportionality

Given y = 10 when x = 16 we can find k by substituting for y and x in [1]

[tex]\rightarrow 10 = k\dfrac{1}{\sqrt{16}}\\\\\rightarrow 10 = k \dfrac{1}{4}\\\\\drightarrow 40 = k \:\:\:\: \text{by multiplying both sides by 4}\\\\\text{which can be written as }\\\\k = 40\\[/tex]

So constant of proportionality k = 40

To find x when y = 8, substitute y and k in [1] to get
[tex]y = k \dfrac{1}{\sqrt{x}}\\\text{Multiply both sides by \sqrt{x} and divide by y at the same time to get}\\\\\sqrt{x} = \dfrac{k}{y}[/tex]

Dividing both sides by y and multiplying by √x gives us
[tex]\sqrt{x} = \dfrac{k}{y}\\\\\text{Substituting k = 40, y = 8}:\\\\\sqrt{x} = \dfrac{40}{8}\\\\\sqrt{x}= 5\\\\\text{Squaring both sides: }\\\\(\sqrt{x})^2 = 5^2\\\\x = 25 \;\;\;\text{since $(\sqrt{x})^2$ = x}[/tex]

The answer is

x = 20

Formulate y=k/x based on the following criteria.

Replace: 10= k/16

Change the sides so that k/16 = 10.

Subtract the coefficient of the variable from both sides of the equation: k = 10×16

Determine the quotient or product: k = 160

Replace with y = 160/x.

Replace with: 8 = 160/x

The denominator cannot be zero if the fraction is defined: as x ≠ 0

As the domain, append the inequality: 8= 160/x, x≠0

Divide the common denominator by both sides of the equation: 8x = 160x/x, x≠0

8x=160x/x, where x ≠ 0. Reduce the fraction.

By the variable's coefficient, multiply both sides of the equation (x=160÷8, x ≠ 0).

Calculate the quotients or product: x = 20,x ≠ 0

Find the junction at x=20.

Answer : x = 20

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The relationship between x and y is y = 0.25x + 1.

Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form. One of the formulas used to get a line's equation is the slope-intercept formula. Y = mx + b is the slope-intercept formula for a line with slope m and y-intercept b. Any point on the line is (x, y) in this case.

Given,

A basket with 4 apples weighs 2 pounds.

Slope intercept form:

y = mx + b

Equation:

2 = 4m +b ..(1)

A basket with 12 apples weighs 4 pounds

4 = 12m + b ... (2)

Solving,

2 = 4m + b

4 = 12m + b

4 = 8m

Divide the second equation by 8:

2 = 4m + b

m = 0.25

b = 1

The relationship between x and y is y = 0.25x + 1.

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The graph of g(x) is the graph of f(x) translated 7 units right

According to the question; g(x)=f(x−7).

Given f(x) then f(x + a) represents a horizontal translation of f(x).

Thus, f(x - 7) represents a shift right of 7 units.

What is Graph ?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

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Answer: The graph of g(x) is the graph of ​f(x)​ translated 7 units right.

Step-by-step explanation:

The ratio of the lengths of PR and QS is 1:1.

Given that, PQ is parallel to RS . PR and are perpendicular to PQ and RS.

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.

The slope of parallel lines is equal to each other.

If PQ is parallel to RS.

PR is perpendicular to PQ and RS.

QS is also perpendicular to PQ and RS.

The figure that will be formed using the two parallel lines, and the two perpendicular is a square.

When two lines are parallel to each other and the end points of the parallel lines are used to draw perpendiculars, then the line segments PQ and RS will be congruent.

By the property of Congruence, the ratio of the lengths PR and QS is equal to 1:1.

Therefore, the ratio of the lengths of PR and QS is 1:1.

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"Your question is incomplete, probably the complete question/missing part is:"

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

PQ is parallel to RS . PR and are perpendicular to PQ and RS .

The ratio of the lengths of PR and QS is __:__ .

Answer:

x = 45

y = 20

Step-by-step explanation:

Since the two horizontal lines are parallel

angles with measures of 6y and 3y are supplementary angles and add up to 180°

So 6y + 3y = 180
9y = 190

y = 20

Similary 2x and 90 are supplementary angles

2x + 90 = 180

2x = 90°

x = 45

Answer:

x=45 y=20

Step-by-step explanation:

you can tell x is 45 because is is a right angle and those are 90 degrees.

9y+180=360   360 because that is the sum of all the angles added up in a quadrilateral.

9y=180

y=20