01 L1 - Perimeter Word Problems

Cooper, Sha Niya

11

1 of

A piece of Plexiglas has a width which is 5 centimeters shorter than its length. What represents the area of the Plexiglas, in terms of its length (L)?

The expression for the nth term is aₙ = 37+6n

An arithmetic sequence is a type of sequence in which the difference between the successive and preceding term is constant.

Given that, The 9th term of an arithmetic sequence is -5 and the 15th term is 31

The formula for nth term is given by;

aₙ = a+(n-1)xd

Where, a is the first term

n = number of terms

d = common difference

a₉ = a+(9-1)xd

a+8d = -5.......(i)

And

a₁₅ = a+(15-1)xd

a+14d = 31........(ii)

Solving the equation, we get,

d = 6

Putting, d = 6 in eq(i)

a+8x6 = -5

a = -5+48

a = 43

Now solving for nth term,

aₙ = 43+(n-1)x6

aₙ = 43+6n-6

aₙ  = 37+6n

Hence, the nth term is (37+6n)

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The solution is

a) The x represents the number of sales

b) The y represents the total earnings in dollars

c) The slope of the line m = 50 earnings (in dollars) per sale

d ) The slope represents the total earnings per sales and it is $ 50 per sale

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is given by the equation

Let the number of sales be = x

Let the total earnings be = y

Now , let the two points on the graph be A and B

where the value of A = A ( 3 , 200 )

And , the value of B = B ( 5 , 300 )

Now , the slope of the line between the points A and B is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 300 - 200 ) / ( 5 - 3 )

Slope m = 100 / 2

Slope m = 50

So , the slope of the line is given by m = 50 earnings per sales

And , Slope m = $ 50 per sales

The equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 200 = 50 ( x - 3 )

y - 200 = 50x - 150

Adding 200 on both sides of the equation , we get

y = 50x + 50

Therefore , the equation of line is y = 50x + 50

Hence ,

a) The x represents the number of sales

b) The y represents the total earnings in dollars

c) The slope of the line m = 50 earnings (in dollars) per sale

d ) The slope represents the total earnings per sales and it is $ 50 per sale

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Answer:

To solve the equation X/5 = -2 in one step, we can multiply both sides of the equation by 5 to isolate the variable X. This gives us the equation X = -2 * 5 = -10. Therefore, the value of X that satisfies the equation X/5 = -2 is X = -10.

Step-by-step explanation:

Answer:

x=8/7

Step-by-step explanation:

16+7/x=24

Subtract 16 on each side

7/x=8

multiply 1/7 on each side

x=8/7

Answer:

98.3% or 98% if your doing sig. figs.

Step-by-step explanation:

you take 14.75 (the approximated) and divide it by the actual 15

The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

x+3y=3..........(2)

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

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Using the trigonometry ration, the value of x is 53.6.

In the given question, a park ranger stands a certain distance from an observation tower.

We have to write an equation and then solve for x and choose the right option.

From the diagram we can see that the height of an observation tower is 45 and angle is 40.

To find the value of x we use the trigonometry ratio.

As we know that tangent is the ratio of perpendicular side and adjacent side.

From the given diagram

tan(40)=45/x

Now simplifying

0.8391 = 45/x

Multiply by x on both side, we get

0.8391x = 45

Divide by 0.8391 on both side, we get

x = 53.6 feet

Hence, the value of x is 53.6.

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The equations are x+y=50 and 7x + 12y = 450

x = the number of mirrors = 30

y = the number of pouches = 20

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x be the number of mirrors

Let y be the number of pouches

x+y=50......(1)

Each mirror is $7

cost of x mirrors = 7x

Each pouch is $12.

cost of y pouches = 12y

7x + 12y = 450 .........(2)

(1) => x=50-y ...........(3)

Substitute (3) into (2)

(2) =>  7(50-y)  + 12y = 450

          350 - 7y + 12y = 450

               5y = 450 -   350 = 100

                 y= 100/5 = 20

(1) => x = 50 - 20 = 30

Thus,  x = the number of mirrors = 30

          y = the number of pouches = 20

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Answer:

[tex]\sqrt[3]{3375}=15[/tex]

Step-by-step explanation:

[tex]3375=15^2 \implies \sqrt[3]{3375}=15[/tex]

m =4e-3 is the equation represents the number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions.

Two or more expressions with an Equal sign is called as Equation.

Let the multiple questions be denoted by m.

The essay questions be denoted by e.

The given sentence is the number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions.

In the sentence there is less than which means a value is subtracted and it has times which is meant by product.

m =4e-3 is the required equation of the given sentence.

Hence, m =4e-3 is the equation represents the situation.

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Evaluating each expression with x = -2 and y = 3 gives

3x²y - x = 38

3y - x = 11

x² - y = 7

x + 2xy = 14

4y - 2xy + 2y = 33

2x - y = -7

6 -x =  8

3x - 2y = -12

3x - 2y + xy = -18

The expressions are evaluated by substituting the values of x and y into the equations and solve

solving the expressions

3x²y - x

substituting x = -2 and y = 3

= 3(-2)² * 3 - (-2)  

= 38

3y - x =

substituting x = -2 and y = 3

= 3 * 3 - (-2)

= 11

x² + y

substituting x = -2 and y = 3

= (-2)² + 3

= 7

x + 2xy

substituting x = -2 and y = 3

= -2 + 2 * -2 * 3

= -14

4y - 2xy + 3y

7y - 2xy

substituting x = -2 and y = 3

= 7 * 3 - 2 * -2 * 3

= 21 - (-12)

= 33

2x - y =

substituting  x = -2 and y = 3

= 2 * -2 - 3

= -7

6 - x

substituting  x = -2

= 6 - (-2)

= 8

3x - 2y

substituting  x = -2 and y = 3

= 3 * -2 - 2 * 3

= -6 - 6

= -12

3x - 2y + xy

substituting  x = -2 and y = 3

= 3 * -2 - 2 * 3 + -2 * 3

= -6 - 6 + (-6)

= -18

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According to SAS congruent the △abc congruent △def. Thus using the given information, it can be prove.

What is congruent?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

There are four rules to prove congruency. They are SAS, AA, ASA, and SSS.

Given that ∠c ≅ ∠f

ab ≅ de

bc ≅ ef.

According to SAS rule, if two sides and one angle of a triangle is equal to two sides and one angle of another triangle, they the triangle are congruent.

Here two sides and one angle of △abc  is congruent of two sides and one angle of △def.

Therefore △abc congruent △def.

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Percent to the nearest whole number = 7%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Probability = (Number of possible outcomes)/(Total number of outcomes)

Total number of outcomes = 2 + 15 + 2 + 11 = 30

Number of possible outcomes = 2

Probability = 2/30 = 1/15 = 0.0666

Percent to the nearest whole number =  0.0666 *100 = 7%

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Answer:7

Step-by-step explanation:

The given measurement not forming the right triangle. So the option D is correct.

In the given question, we have to determine if a triangle with the following measurements is a right triangle.

The given measurement is:

a=14, b=16, c=18

We have to explain why or why not the given statement is correct or not.

The given options are:

(a) No. 14+16 does not equal 18

(b) Yes. 14^2+16^2=18^2

(c) Yes. The longest side is c, which is 18.

(d) No. 14^2+16^2 does not equal 18^2

As we know that the given measurement form right triangle we he follows the Pythagorean Theorem.

To prove the right triangle, the square of largest value is equal to the sum of square of other two values. So;

18^2 = 14^2+16^2

324 = 196 + 256

324 = 452(False)

So, the given measurement not forming the right triangle. So the option D is correct.

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Using the corresponding angle theorem, the value of y is 36 degree.

In the given question, b||c.

We have to find the value of y.

Given: b||c

Find: Value of y

Let x be the value of side angle of (2y+34) degree.

So, using the corresponding angle theorem

x = 74 degree

As we know that the sum of straight line is 180 degree.

So 2y+34+x = 180

Now putting the value of x

2y+34+74=180

After simplifying

2y+108=180

Subtract 108 on both side, we get

2y=72

Divide by 2 on both side, we get

y=36

Hence, the value of y is 36 degree.

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Answer: C

Step-by-step explanation:

A function cannot have repeated x value in a set, and c is the only one without repeated x value

The corresponding sides of two triangles are proportionate if they are identical then the length of side ZX exists 10.5 units.

If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. 90 degrees is the sum of the other two angles. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

If two triangles are similar, then their corresponding sides are proportional.

Since [tex]$\triangle A B C \sim \triangle X Y Z$[/tex], therefore

AB/X Y = BC/YZ = CA/ZX

substitute the values in the above equation, we get

2/7 = 4/14 = 3/N

2/7 = 2/7 = 3/N

2/7 = 3/N

On cross multiplication, we get

2 × N = 3 × 7

2N = 21

Divide both sides by 2

N = 21/2

N = 10.5

Therefore, the length of side ZX exists 10.5 units.

The complete question is:

In the figure below, ABC is similar to XYZ . What is the length of ZX ? Enter only the number as an integer or decimal. An image shows two similar right triangles, A B C and X Y Z. Triangle A B C is smaller than triangle X Y Z. In triangle A B C, side A B is 2, side B C is 4, and side C A is 3. In triangle X Y Z, side X Y is 7, side Y Z is 14, and side Z X is labeled N.

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Answer:

ST and RQ

Step-by-step explanation:

The 'arrows'  on the line segments mean they are parallel

The value of x is 11.8. So the option c is correct.

In the given question, we have to find the value of x.

The given options are:

(a) 12.2

(b) 24.5

(c) 11.8

(d) 8.4

To find the value of x we use the trigonometry ratio.

As we know that cosine is the ration of adjacent side and hypotenuse.

From the given diagram

Cos(46) = x/17

Now simplifying

0.695=x/17

Multiply by 17 on both side, we get;

x = 11.8

Hence, the value of x is 11.8. So the option c is correct.

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If f(x) = 7x2 + 5, then 0 is the critical point. As a result, the interval f grows when f is positive.

Although this may appear like a frivolous issue—t = 0 is designated as a key point in each case—it is occasionally crucial to understand why is it that a position is indeed a critical point. In fact, we'll observe a fact which only holds true at crucial sites where the derivative equals zero in a few sections.

f is maximal because we replace x = 0 well at derivatives at the crucial point. After calculating the derivative, equating x to zero, and arriving at 0, we arrive at the critical point, which is at this position.

The interval just on left of the crucial moment is - infinity f 0 on the this interval increasing whilst also f is negative on the right of the critical point 0 >= f +infinity on this interval f is rising whilst also f is positive. This indicates that f is maximum since at the critical point people substitute x = 0 at the variant we have 5 > 0.

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Answer:

To approximate the square root of 46 to the tenths place, we need to find the two-digit number that is closest to the square root of 46. Since the square root of 46 is between 6 and 7, we can estimate that it is about 6.5. We can check this estimate by finding the square of 6.5, which is 42.25. This is close to 46, but it is still a little bit lower than 46, so we can estimate that the square root of 46 is slightly larger than 6.5. Therefore, an approximation of the square root of 46 to the tenths place is 6.6.

Step-by-step explanation:

Answer:

If you receive a 15% discount on a shirt that normally costs £42, the discounted price of the shirt will be £42 - (15/100) * £42 = £35.70. If you pay £50 for the shirt, you will receive £50 - £35.70 = £14.30 in change. Therefore, the correct answer is D- £14.30.

Step-by-step explanation:

The value of side MN is 18.2

What is a Trapezoid?

A quadrilateral is a polygon with four sides.

There are many special types of quadrilateral.

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

Given data ,

Let the side to be calculated be = MN

Now , the two quadrilaterals are GHIJ and KLMN

And , quadrilaterals GHIJ and KLMN are congruent

So ,

The sides are in the ratio

MN / IJ = NK / JG

On simplifying the equation , we get

Substituting the values in the equation , we get

MN / 47 = 12 / 31

Multiply by 47 on both sides of the equation , we get

MN = ( 12 x 47 ) / 31

On simplifying the equation , we get the value of side MN

MN = 564 / 31

MN = 18.19

On rounding to the nearest tenth , we get

MN = 18.2

Therefore , the value of side MN is 18.2

Hence , The value of side MN is 18.2

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Answer:

Triangle PQR maps onto triangle KLM. This is possible because △PQR ≅ △KLM by ASA, and one congruent figure can be mapped onto another using rigid motions.

Step-by-step explanation:

For the first blank, we are given congruence statements for 1 side on each triangle and their two adjacent angles. This means we can use the Angle-Side-Angle theorem to declare △PQR and △KLM congruent.

For the second blank, we know that rigid transformations do not change the figure, they simply move its position on a plane, so this is the correct answer; had the △PQR and △KLM not been congruent, a non-rigid transformation would have to have occured, but this is not the case here.

Answer:

Step-by-step explanation:

Given triangles PQR and KLM with QR ≅ LM, ∠Q ≅ ∠L, and ∠R ≅ ∠M, you want to know the applicable congruence postulate and whether the triangles are mapped to each other by rigid or non-rigid motion.

The segment QR has angle Q at one end and angle R at the other end. That means the side lies between the two angles. Likewise, segment LM lies between angles L and M.

When claiming congruence of these triangles, the appropriate postulate is the one that refers to the geometry with the congruent side between the congruent angles: ASA.

"Rigid" motion is motion that preserves angle and length measures. By contrast, "non-rigid" motion may involve stretching or compression in one or more directions. It may or may not preserve angles or lengths.

Congruence is about showing that angles and lengths are the same from one figure to another. If you want to map congruent figures to each other, you must do so using rigid motion.

__

Additional comment

The rigid motions include ...

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The given quadratic equation 5x^2+6x+4=0 has no real roots or 0 real roots.

A quadratic equation is any algebraic expression that can be expressed in a standard form where x represents an unknown number, a, b, and c represent known values, and where a 0 is true.

So, we have the equation:

5x^2+6x+4=0

Discriminant (D): b² - 4ac

Insert values in the given formula as follows:
b² - 4ac is 6² - 4(5)(4).

= 36 - 80

= - 44 and it is less than zero.

No real roots

Therefore, the given quadratic equation 5x^2+6x+4=0 has no real roots or 0 real roots.

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