Patty and Carol cach go for walks around a lake a few times per week. Last week, Patty walked7 miles more
"than Carol.
a. If e represents the number of miles Carol walked, write an equation that represents the total number of
miles T the two girls walked. (You may only use the variables c and T in your equation.)
b. If Carol walked 9 miles during the week, how many miles did Patty walk?
c. If Carol walked 11 miles during the week, how many miles did the two girls walk together?


Porfavor me urge :,3

Answer:

3x + 3

Step-by-step explanation:

4x + 3 - x can be expressed as:

x + x + x + x + 3 - x

If we combine like terms:

x + x + x + x - x + 3
x + x + x + 3
3x + 3

Answer:

x/(1-x)

Step-by-step explanation:

We start by induction. The first 2 terms are x/(1-x^2) and x^2/(1-x^4), respectively. When we add them together using special factorizations, we get: (x^3+x^2+x)/(1-x^4). We quickly realize that the numerator is a geometric series. Applying the following formula, we can simplify our expression to (x^4-x)/(1-x^4)(x-1). Now, we introduce our 3rd term, and add that to our sum. That gets us: (x^7+x^6+...+x)/(1-x^8). This is another Geometric series, and we apply the exact same formula, for this new fraction: (x^8-x)/(1-x^8)(x-1). We realize this is a pattern, and we can utilize this pattern for the sum of the first n terms.
We look at the exponents. For the first 3 terms, the Degree is 8, for the first 2 terms, the Degree is 4. We take note that this looks like x^2^n.

Using that our general formula IS: (attached to this text) (x^2^n-x)/(1-x^2^n)(x-1). Now, when 0<x<1 and n approaches infinity, what do we get?
all terms x^2^n are so small, it's basically redundant, and can be crossed off. This leaves us with -x/(x-1), which can be simplified to x/(1-x).

Applying the same-side-interior angles theorem, the values are:

x = 95°

z = 35

An examples of angles that are referred to as same-side-interior angles are x° and 85°.

According to the same-side-interior angles theorem, the sum of x and 85 will give 180 degrees if lines h and o are parallel to each other.

Since h║o, therefore:

x + 85 = 180

x + 85 - 85 = 180 - 85

x = 95°

(6z - 115)° and x° are vertical angles, therefore:

6z - 115 = x

Plug in the value of x

6z - 115 = 95

6z - 115 + 115 = 95 + 115

6z = 210

6z/6 = 210/6

z = 35

Thus, applying the same-side-interior angles theorem, the values are:

x = 95°

z = 35

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1. The missing side of triangle is 10 CM

2. The missing side of triangle is 13 mi

3. The missing side of triangle is 3[tex]\sqrt{2}[/tex] mi

4. The missing side of triangle is [tex]\sqrt{219}[/tex] yd

The Pythagoras theorem equation is expressed as, , [tex]c^{2}[/tex]=[tex]a^{2}[/tex]+[tex]b^{2}[/tex], where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

We have different right triangles and their measurements.

we have to find the missing side of triangle.

The Pythagoras theorem equation is expressed as, [tex]c^{2}[/tex]=[tex]a^{2}[/tex]+[tex]b^{2}[/tex]

1. For diagram 1,

Let the length c=x,

a=6

b=8

then according to the Pythagoras theorem.

⇒[tex]x^{2}[/tex]=[tex]6^{2}[/tex]+[tex]8^{2}[/tex] ⇒  [tex]x^{2}[/tex]= 36+64=100

⇒x=10

therefore missing side of triangle is 10 CM

2. For diagram 2,

Let the length c=x,

a=5

b=12

then according to the Pythagoras theorem.

⇒[tex]x^{2}[/tex]=[tex]5^{2}[/tex]+[tex]12^{2}[/tex] ⇒  [tex]x^{2}[/tex]= 25+144=169

⇒x=13

therefore missing side of triangle is 13 mi

3. For diagram 3,

Let the length c=x,

a=3

b=3

then according to the Pythagoras theorem.

⇒[tex]x^{2}[/tex]=[tex]3^{2}[/tex]+[tex]3^{2}[/tex] ⇒  [tex]x^{2}[/tex]= 9+9=18

⇒x=3[tex]\sqrt{2}[/tex]

therefore missing side of triangle is 3[tex]\sqrt{2}[/tex] mi

4. For diagram 4,

Let the length a=x,

c=16,

b=[tex]\sqrt{37}[/tex]

then according to the Pythagoras theorem.

⇒[tex]16^{2}[/tex]=[tex]x^{2}[/tex]+[tex](\sqrt{37} )^{2}[/tex] ⇒  [tex]x^{2}[/tex]= 256-37=219

⇒x=[tex]\sqrt{219}[/tex]

therefore missing side of triangle is [tex]\sqrt{219}[/tex] yd

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Based on the amount the investment would pay at the end of next year, and the market interest rate, C. ​Yes, because the investment will yield $95,040 more than putting the money in a bank.

The investment of $220,000 at the market rate of 8% would earned:

= 220,000 x 8%
= $17,600

The amount that the investment would make instead is:

= 332,640 - 220,000

= $112,640

The difference is:

= 112,640 - 17,600

= $95,040

In conclusion, the investment should be made.

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The transformation that occurred to get from the figure ABCD to EFGH, including the necessary terminologies is as follows:

Step 1: Reflection

The reflection using the y axis as the line of reflection at point C After the reflection the points changed A = E,  D = H, C = G, and B = F

Step 2: Rotation

The rotation occurred with point A now E as the center of rotation.  The angle of rotation is 90 degrees anticlockwise direction.

Step 3 Translation

The quadrilateral is now moved 4 units to the left to arrive at the new position.

Transformation is a term used in mathematics to describe some technical movements that objects makes. This objects are usually plotted to ensure that every movement can be calculated.

Some terms in transformation are reflection, rotation, translation and so on. Reflection produces mirror image of the object, Rotation is achieved using a specified angle and the direction is specified with either clockwise or anticlockwise then Translation is more of a straight forward movement.

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Answer:

I have 5 apples and give u 2 how much I have

Answer:

(-4;2)

Step-by-step explanation:

The graph show us line on the -4 and 2 and I think the answer us (-4;2)

The area of the rectangular arena can be represented as A = (8y2 - 18y) square feet.

Here, we are given the dimensions of a rectangular arena, which are as follows-

Length = 4y - 9 feet

width = 2y feet

The area of a rectangle is given by the formula-

Area of a rectangle = length x breadth

Thus, in this case, area (A) can be calculated as follows

A = (4y - 9) * 2y

Now, we simplify the equation-

A = (4y)(2y) - 9(2y)

A = 8 - 18y

Thus, the area of the rectangular arena can be represented by the following equation- A = (8 - 18y) square feet.

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Answer:

Step-by-step explanation:

Find the degree, leading term, and leading coefficient.

Polynomial Degree:

2

Leading Term:

5x²

Leading Coefficient:

5

Let x be the shortest side

Let x+1 be the second side

Let x+2 be the third side

Let x+3 be the fourth and longest side

[tex]perimeter = s_{1} + s_{2} + s_{3} + s_{4} \\ 86 = x + (x + 1) + (x + 2) + (x + 3) \\ 86 = x + x + 1 + x + 2 + x + 3 \\ 86 = 4x + 6 \\ 4x = 80 \\ x = 20[/tex]

Shortest side is 20 cm

Longest side is x+3 so 20+3=23

The probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher is 0.0192.

It should be noted that from the information, after the special training was complete the 25 workers produced 28.2 units every hour with stand deviation of 2.9.

Therefore, the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher will be:

= 1 - P[(Z (28.2 - 27)/29/✓25)]

= 1 - P(Z < 2.07)

It should be noted that this will be looked on the distribution table.

= 1 - 0.9808

= 0.0192

Therefore, the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher is 0.0192.

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Answer:270 calories in 3 servings; 450 calories in

5 servings.

270 ÷3   90     450 ÷ 5     90

 3    ÷3    1        5    ÷ 5        1

The unit rates are the

same so they are equal.

hope it helps! :)

Answer:

www

Step-by-step explanation:

www

The midpoint of the segment where the segment has the  endpoints (-8,-7) and (-7,-8)  is (-15/2, -15/2)

On the segment, we have the following endpoints

(-8,-7) and (-7,-8)

The midpoint of the segment is calculated using

Midpoint = 1/2 * (x1 + x2, y1 + y2)

Where

(x1, y1) = (-8,-7)

(x2, y2) = (-7,-8)

Substitute the known values in the above equation

So, we have

Midpoint = 1/2 * (-8 + -7, -7 - 8)

Evaluate the difference in the above equation

So, we have

Midpoint = 1/2 * (-15, -15)

Evaluate the product in the above equation

So, we have

Midpoint =  (-15/2, -15/2)

Hence, the midpoint of the segment where the segment has the  endpoints (-8,-7) and (-7,-8)  is (-15/2, -15/2)

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Using ratio, we concluded that there are total 144 people at the basketball game.

Ratios contrast two figures by typically dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.

Let x be the number of people at the basketball game.

4x = number of males

5x = number of females

Total females = 80

⇒ 5x = 80

⇒ x = 16

4x = 4 × 16

⇒ 64

∴ Total males  = 64

Total people present = number of males + number of females

⇒ 64 + 80

⇒ 144

∴Total people at basketball game are 144

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Answer:

x = √(5) - 8

x = -√(5) - 8

Step-by-step explanation:

Let's solve the problem,

→ (x+8)² - 43 = -38

→ x² + 64 - 43 = -38

→ x² + 21 = -38

→ x² = -38 - 21

→ x = √(-59)

→ [ x = √(5) - 8 ]

(or) [ x = -√(5) - 8 ]

Hence, it is the value of x.

The answer of the above question is [0,30]

An absolute value inequality is one with an absolute value sign and a variable inside.

An important point to remember: | x |= {x if x ≥ 0 }

| x |= {x if x< 0}

taking the expression  |-2z+30| ≤ 30

Write the equivalent compound inequality.

-30≤ -2z+30 ≤ 30

= -30-30 ≤ -2z ≤ 30-30

= -60≤ -2z ≤ 0

= -60/2 ≤ -z  ≤ 0

= -30 ≤ -z  ≤ 0

Solve the compound inequality.

= 0 ≥ z ≥ 30 (reversing of signs)

Hence, the solution using interval notation  [0,30].The check is left to you.

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Answer:

468

486

648

684

846

864

Step-by-step explanation:

[tex] {(x + 3)}^{2} + {(y + 7)}^{2} = {16}^{2} \\ {(x + 3)}^{2} + {(y + 7)}^{2} = 256[/tex]

The estimated number of students at the M College who agree climate change is a serious issue is  1759

The percentage of total students is 59.42%

The method used can be biased.

The students surveyed are the sample while the students in the M College are the population. A population is the party of interest in an experiment. A population consists of all the members of the group. A sample is a smaller group of the population.

The limitation of using a sample to estimate for the population is that the sample might be a biased estimate of the population. If the sample is biased, the result of the experiment would be inaccurate.

Estimated number of students at M College = (sample that agree that climate change is a serious problem / total number of people surveyed) x number of students

(205 / 345) x 2960 = 1759

Percentage = (1759 / 2960) x 100 = 59.42%

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Answer:

365 x 4 = 1460

Step-by-step explanation:

The area model shows that 365 multiplied by 4 is equal to 18.

First, we draw a rectangle to represent the number 365. We divide it into three parts vertically to represent the digits 3, 6, and 5.

  3       6       5

Next, we draw a rectangle to represent the number 4. We position it to the right of the rectangle for 365.

  3       6       5

                  4

To find the area, we calculate the individual areas of each section and then add them up.

The area of the rectangle representing 3 is 3 times the height, which is 1.

 3       6       5

 |         |         |

 |         |         |

 |         |         |

The area of the rectangle representing 3 is 3.

The area of the rectangle representing 6 is 6 times the height, which is 1.

  3       6       5

 | |       |         |

 | |       |         |

 | |       |         |

The area of the rectangle representing 6 is 6.

The area of the rectangle representing 5 is 5 times the height, which is 1.

  3       6       5

 | | |     |         |

 | | |     |         |

 | | |     |         |

The area of the rectangle representing 5 is 5.

The area of the rectangle representing 4 is 4 times the height, which is 1.

  3       6       5

 | | |     | |     |

 | | |     | |     |

 | | |     | |     |

So, the area of the rectangle representing 4 is 4.

Now, the total area, we add up the areas of the individual sections:

= 3 + 6 + 5 + 4

= 18

Therefore, the area model shows that 365 multiplied by 4 is equal to 18.

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Answer:

m=√14,−√14

Decimal Form:

m=3.74165738, -3.74165738

Step-by-step explanation:

The given expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation is 4.2 × 10^5.

According to the question.

We have an expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10².

Since, we have to write the above expression as a number in scientific notation.

As we know that, scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Thererefore, the expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation

(7 x 10³)(5.4 x 10⁴)/ 9 x 10²

= (7 × (10^7) × 54)/ 9 × (10^2) × 10

= 7 × 6 × 10^(7 - 3)

= 42 × 10^4

= 4.2 × 10^5

Hence, the given expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation is 4.2 × 10^5.

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The best prediction of the population in the year 2013 is 3541 based on the fact that the population decreases by 1.4% every year

What is the number of years between 2008 and 2013?

The number of years between 2008 when the population figure was at 3,800 and 2013 is 5 years, hence when determining the population for the year 2013 we need to bear in mind that the population has decreased by 1.4% over a period of 5 years

FV=PV*(1-r)^N

FV= best prediction of the population in the year 2013

PV=population in 2008=3800

r=decreasing rate of the population=1.4%

N=number of years that have passed between 2008 and 2013

FV=3800*(1-1.4%)^5

FV=3541

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Answer: 27

Step-by-step explanation:

3^2 = 3 x 3= 9  

9 x 3 = 27

Answer:

Step-by-step explanation:-12+7=-5