Write the specified type of proof. two-column proof
Given: ®C
Prove: ΔKML ΔJMH

the maximum time that he can have in his last race is 23 seconds.

We know that the average can not be greater than 22.8 seconds, then if x represents the time of the last race, the maximum value that x can take is given by the equation:

(23.1 + 23.2 + 22.8 + 21.9 + x)/5 = 22.8

(That is the equation for the mean of the 5 times)

Solving that for x we will get:

(23.1 + 23.2 + 22.8 + 21.9 + x) = 5*22.8

91 + x = 114

x = 114 - 91 = 23

So the maximum time that he can have in his last race is 23 seconds.

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The width of walkway is 3 feet.

What is rectangle ?

A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other. The diagonals of a rectangle bisects each other into equal segments.

We have been given that the garden and the walkway around its perimeter have an area of 378 square feet.

Let us suppose the width of the walkway is x feet.

the length of garden and the walkway will be = 15+2x

and, the breadth of garden and the walkway will be = 12+2x

Now, area of the garden and the walkway around its perimeter is given by :

A = (15+2x)(12+2x)

A = 4x^2 + 54x + 180

Now, the area is given is given as 378 square feet. Hence, we have

4x^2 + 54x + 180 = 378

4x^2 + 54x -198 = 0

Using quadratic formula to find the roots of above equation we get :

x = 3, -33/2

Taking positive value of x that is 3 as area cannot be negative.

Therefore, the width of walkway is 3 feet.

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The distance between Amy's initial and final position is 1 mile and she is facing South direction

It is given that,

Amy first moves towards East direction in reference to her initial position  for 2 miles

The distance covered by Amy in East direction = 2 miles

Then,

Amy moves towards South direction in reference to her initial position(facing East side) for 3 miles

The distance covered by Amy in South direction = 3 miles

We need to find,

The distance between Amy's initial and final position which will be given by the displacement between both points

Let's say that the positive direction is East and the negative direction is south.

The distance covered by Amy in East direction = + 2 miles

The distance covered by Amy in South direction = - 3 miles

Then , +2 +(-3) = -1

Hence, the distance between Amy's initial and final position is 1 mile and she is facing South direction

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Answer:

10 24 32 are the answers

Step-by-step explanation:

My mom is a teacher lol

Answer:

skewed right, mean > median

Step-by-step explanation:

just did it

Answer:

skewed right, mean>median

Step-by-step explanation:

edge 2023

assuming 2x= 3x-42,

x=42

2x= 84

and 3x-42= 84

The slope-intercept form is y = mx + b.

If the value of m = -6 and b = 9 then 6x + y = 9 be the standard form.

Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.

Let the value of m = -6(slope)

b = 9 (y -intercept)

The slope-intercept form is given by,

y = mx + b

y = -6x + 9

Therefore,  y = -6x + 9  is the slope-intercept form

Standard form is given by, Ax + By = C

Since, slope-intercept form is y = -6x + 9

⇒ 6x + y = 9

Therefore, 6x + y = 9 is the standard form.

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Answer:

x=3: 2(3) = 6.

Step-by-step explanation:

According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.

The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.

Consider the algebraic relationships that exist for triangle medians.

The centroid of a triangle is 2/3 the distance from one vertex to the midpoint of the opposite side, according to the Centroid Theorem.

Given: [tex]$\triangle XYZ[/tex] with medians [tex]$\overline{X R}[/tex], [tex]\overline{Y S}$[/tex], and [tex]$\overline{Z Q}$[/tex].

By using Centroid Theorem, we get

1. XP = 2/3 XR

2. XR = XP + PR( Segment Addition Postulate)

3. XP = 2/3(XR+PR) (Substitution Property)

4. XP = 2/3 XP + 2/3 PR (Distributive Property)

5. 1/3 XP = 2/3 PR(Subtraction Property)

6. XP = 2PR (Multiplication Property)

7. XP/PR = 2 (Division Property)

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Answer:

k and 16

Step-by-step explanation:

I will cry

Nan

nnan

Nan

i) cost of oil change = $29.99

ii) Balance on December 1 = $252.009

iii) Difference between the two balance = $85.79

According to the question we have been that

           Total balance on November 1 = $337.88

i) We need to find how much did the oil change cost.

  For that we will first calculate how much balance was left after depositing after pay check.

Balance after spending in groceries= $337.88 - $ 42.59 = $295.29

Balance after depositing from savings account = $295.29 + $125.00 = $420.29

Balance after spending in electric bill = $420.29 - $35.67 = $384.62

Balance after depositing from paycheck = $415.00 + $384.62 = $799.62

Therefore, Cost of oil changing = $799.62 - $769.63 = $29.99

ii) For the balance on December 1 after rent had paid, we will first calculate the balance after spending for birthday present.

Balance after spending for birthday present = $769.63 - $17.54 = $752.09

Therefore the balance on December 1 = $752.09 - $500.00 = $252.09

iii) Difference in the two balance is

                                    = balance on November 1 - Balance on December 1

                                    = $337.88 - $252.09

                                    = $85.79

Hence the difference in the two balances is $85.79

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Answer:

No Because 1/1 : 3/4 = 4/3 and 1/3 : 4/1 = 1/12

Answer:

6

Step-by-step explanation:

To find the GCF by factoring, list out all of the factors of each number and select the largest that both have in common.

The equation that represents the cost C for membership for m months is:99.90+24.95m

The cost of a 2-year membership is $698.70

What makes up the total cost for membership for m months?

The fact that each member has to pay an enrollment fee and purchase key card for $79.95  and $19.95 respectively, means that the total fixed charge which is sum of both amounts is computed as shown below:

fixed charge=$79.95+$19.95

fixed charge=$99.90

variable cost per month=$24.95

total variable cost of m months=24.95m

C=99.90+24.95m

m=24(24 months=2 years)

cost of a 2-year membership=99.90+(24.95*24)

cost of a 2-year membership=$698.70

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Answer:

y=2x-7

Step-by-step explanation:

[tex]2x-y=6 \\ \\ -2x+y=-6 \\ \\ y=2x-6[/tex]

Parallel lines have the same slope, so we want the line with a slope of 2 through (3, -1).

This line is y=2x-7.

Answer:The marble that is farthest from the target is the pink marble.

Step-by-step explanation:

Using proportions, it is found that:

a. There are 2736 calories in the fudge recipe.

b. There are 42.75 calories in a 1-inch by 1-inch piece of fudge.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, the recipe is composed by:

Hence the number of calories in the recipe is given by:

6 x 99 + 0.5 x 12 + 4 x 389 + 4 x 145 = 2736.

There are 2736 calories in the fudge recipe.

For item b, the areas are given as follows:

Hence the piece of fugde is 1/64 of the recipe, thus:

1/64 x 2736 = 42.75 calories.

There are 42.75 calories in a 1-inch by 1-inch piece of fudge.

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Answer:

2 or 1/3

Step-by-step explanation:

by getting the product and sum,then the roots

Percentages greater than 100% can be expressed as x% where x is any real number

As a general rule, percentages are represented by %

Take for instance

x% is pronounced x percentage

Where x is any real number

Whether x is greater than 100 or not, the format of the expression remains the same

i.e. 150 percent is written as 150% and 25 percent is written as 25%

Hence, percentages greater than 100% can be expressed as x% where x is any real number

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The size of the segment in the scale drawing using a drawing scale factor of 5 meters to one box is 30 meters.

A scale factor is a value with which the dimensions of an original two dimensional geometric figure or a three dimensional solid can be multiplied to obtain an image.

Scale factors are used in maps and drawings to represent a large geographic area, or a life sized object on paper, such that the relative sizes of the sides of the original figure are maintained

Solution;

Using the height of the arc in the drawing as the reference, we have;

50 m is equivalent to 10 boxes

Therefore;

The length of one box = (50 m)/10 = 5 m

The scale of the drawing is therefore;

The length of the given segment = 6 box length

The length, L, of the segment is too therefore;

L = 6 box × 5 m/box = 30 m

The length of the segment is L = 30 meters

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The area of triangle ΔABC with ∠C = 90°, ∠B = 75° an AB = 12 cm will be 18.16 square centimeters.

We have a right - angled triangle ΔABC.

We have to find the area of ΔABC.

Pythagoras theorem states - In a right - angled triangle ΔABC, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically -

h² = b² + p²

According to the question -

(Refer to the image attached)

∠C = 90°

∠B = 75°

AB = 12 cm

Now -

sin 75° = AC/AB

AC = AB sin(75°) = 12 sin(75°) = 12 x 0.97 = 11.64 cm

and

tan 75° = AC/BC

BC = AC/tan(75°) = 11.64/3.73 = 3.12 cm

Therefore, the area of triangle ΔABC -

A = 1/2 (AC x BC) = 0.5 x 3.12 x 11.64 = 18.16 cm²

Hence, the area of triangle ΔABC will be 18.16 cm².

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The slope of the line containing (7,-3) and (-8,-3) is  Zero(0).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = -3 , [tex]x_{2}[/tex] = -8 , and [tex]x_{1}[/tex] = 7 .

On substituting the values of variables in equation1, we will get

m = ( (-3)-(-3) ) / ( (-8)-(7) ) = (0/(-15)) = 0.

As the slope of a line is Zero(0), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (7,-3) and (-8,-3) is  Zero(0).

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Answer:

Here,

MP=MN+NP=17+3y

or, 5y+9=17+3y

Now do equation and find the value of y.

Answer:

MP = 29

mp = mn + np

17 + 3y = 5y + 9

2y = 8

y= 4, NP = 3(4) = 12

so, MP = mn + np.... 12 + 17

MP = 29

Step-by-step explanation:

The attached image should be what you're looking for.

Answer:

In bold below.

Step-by-step explanation:

There are 12*12 = 144 square inches in a square foot.

So, there are 144 in^2 per 1 ft^2

So, we have:

               144 in^2

32 ft^2     -----------   =      4608 in^2.

                   1 ft^2

For yards it is 1 yd^2 per 9 ft^2 :-

                  1 yd^2

32 ft^2 =   ------------ =   3.56 yd^2.

                    9 ft^2

Answer:

Step-by-step explanation:

4.5 in

Divide the area of the triangle by the height.

The common difference d is 2.2 and the first term a1 is -9.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the two terms of arithmetic sequence,

a4 = -2.4 and a6 = 2.

now, find the common difference d.

a(n) = a1 + (n - 1)d

Let take a(n) = a6 and a1 = a4.

a6 = a4 + (6 - 4)d

a6 = a4 + 2d

now substitute the values of a6 and a4

2 = -2.4 + 2d

2 + 2.4 = 2d

d = 4.4/2

d = 2.2

so, the common difference d is 2.2.

then, find the term a1.

take the formula

a(n) = a1 + (n - 1)d

now, substitute a(n) = a4 and d = 2.2.

-2.4 = a1 + (4-1)d

-2.4 = a1 + 3d

-2.4 = a1 + 3(2.2)

-2.4 = a1 + 6.6

a1 = -6.6-2.4

a1 = -9.

so, the first term a1 is -9.

Hence, the common difference d is 2.2 and the first term a1 is -9.

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The given equation is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.

Here we have the linear equation:

x - 2 = -2 + x

And we want to see how many solutions it has, so let's solve it.

IF we add 2 in both sides we will get:

x - 2 + 2 = -2 + x + 2

x + (-2 + 2) = x + (-2 + 2)

x = x

Now, that is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.

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Using arithmetic sequence concepts, the matching terms are given as follows:

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

Hence, in this problem, the terms are classified as follows:

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