Solve the system. 23x - 12y = 1 - 43x +y =-3

To determine the fourth vertex of an isosceles trapezoid given three vertices, we use symmetry and properties of isosceles trapezoids, concluding the missing vertex is likely at (-1,3).

To find the fourth vertex of an isosceles trapezoid given three vertices, we need to use the properties of isosceles trapezoids. The properties pertinent to solving this problem include parallel bases and non-parallel sides of equal length. Given vertices at (2,5), (6,5), and (9,3), we know the top base is parallel to the x-axis, as the y-coordinate is the same (5) for the first two points.

For the trapezoid to be isosceles, the fourth vertex must follow the pattern of equal non-parallel sides. Observing the pattern of the given points, and noting that the length of the non-parallel side from (9,3) should equal that of the side starting from (2,5), we conclude the missing point must maintain this equality in distance and form a right angle, mirroring the shape on the opposite side.

Without specific lengths, we apply symmetry principles. The height difference between the known base and the third vertex (3) indicates a 2-unit drop, suggesting the opposite side will mirror this. Thus, the fourth vertex should be 2 units below the other base vertex, at (2,5), making the y-coordinate 3. Given the distances in x are equal (4 units from each end vertex to their respective base vertex), the fourth vertex is at (-1,3).

Answer:

1.971

Step-by-step explanation:

7.211 - 5.24 = 1.971

Answer:

1.971

Step-by-step explanation:

Temporarily add a zero at the end of 5.24, so both numbers have 3 decimal places.  We get"

7.211 - 5.240, or

   7.211

- 5.240

--------------

   1.971

Option C:

[tex]y+6=\frac{3}{5} (x-4)[/tex]

Solution:

Given point (4, –6) and slope, [tex]m=\frac{3}{5}[/tex]

Formula for equation of a straight line when passing through the point [tex](x_1, y_1)[/tex] and slope m is [tex]y-y_1=m(x-x_1)[/tex]

Here, [tex]x_1=4, y_1=-6, m=\frac{3}{5}[/tex]

Substitute these in the above formula, we get

⇒ [tex]y-(-6)=\frac{3}{5} (x-4)[/tex]

⇒ [tex]y+6=\frac{3}{5} (x-4)[/tex]

Hence, [tex]y+6=\frac{3}{5} (x-4)[/tex] is the equation in point-slope form.

Answer:

[tex]-6\cdot6\cdot6=-\underbrace{6\cdot6\cdot6}_{3}=-6^3[/tex]

Step-by-step explanation:

[tex]a^n=\underbrace{a\cdot a\cdot a\cdot a\cdot ...\cdot a}_{n}[/tex]

Answer:

b/4+9

Step-by-step explanation:

Answer:

I dont now cause it depends on what you teacher asks of you

Answer:

2

Step-by-step explanation:

if you take half of something then you divide my 2

Final answer:

The perimeter of a rectangle whose width is half its length is three times the length of the rectangle. This can be calculated using the formula p = 2(l + w), substituting w with l/2, which simplifies to p = 3l.

Explanation:

The student is asking how many times a rectangle's length is its own perimeter if the width of the rectangle is half its length. Using the formula for the perimeter of a rectangle, which is p = 2(l + w), and knowing that the width (w) is half the length (l), we can substitute w with l/2.

Hence, the formula becomes p = 2(l + l/2) = 2(3l/2) = 3l. Therefore, the perimeter is three times the length of the rectangle.

Answer:

267.3 in.

Step-by-step explanation:

Using the Sine Rule:

90 / sin 60 = BC/ sin 50

BC = 90 sin 50 / sin 60 = 79.6 in.

Angle C = 180 - 50 - 60 = 70 degrees.

90 / sin 60 = AB / sin 70

AB =  90 sin 70 / sin 60 = 97.7 in.

So the perimeter = 90+ 79.6 + 97.7

= 267.3 in.

Answer: 267

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 less then the product of 9 and a number is 4

" the product " is the result of multiplication

the product of 9 and a number...9x

2 less......-2

is 4...= 4

9x - 2 = 4 <===

Steps to solve:

2x + 6 < 30

~Subtract 6 to both sides

2x + 6 - 6 < 30 - 6

~Simplify

2x < 24

~Divide 2 to both sides

2x/2 < 24/2

~Simplify

x < 12

Best of Luck!

64x^2-121

Rewrite 64x^2 as 8x^2

Rewrite 121 as 11^2

Now you have 8x^2-11^2

Use the difference of squares formula, a^2- b^2 = (a+ b)( a-b) where a= 8x and b = 11

Answer is:

(8x+11)(8x-11)

Answer:

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b) where a=8x and b=11

.

(8x+11)(8x−11)

Step-by-step explanation:

Average = 0.56 inches

Solution:

Given data: Total rainfall = 16.8 inches

Total number of days for a month = 30

To find the average of the rainfall.

Formula for average:

[tex]\text {Average}=\frac{\text {Sum of the observations}}{\text {Total number of observations}}[/tex]

[tex]\text {Average}=\frac{16.8}{30}[/tex]

            = 0.56 inches

Average = 0.56 inches

Hence, average of daily rainfall is 0.56 inches.

Answer:

I do

Step-by-step explanation:

To solve the inequality, isolate/get w (the variable) by itself in the inequality

w + 6 ≤ -3      Subtract 6 on both sides

w + 6 - 6 ≤ -3 - 6

w ≤ - 9

Answer:

[tex]2\frac{1}{10}[/tex] km

Step-by-step explanation:

We are given;

We are required to find the length of the rectangle;

We need to know how to find the area of a rectangle first;

Area of rectangle = Length × Width

Rearranging the formula;

Length = Area of rectangle ÷ Width

            = 7/10 km² ÷ 1/3 km

   We get;

           [tex]=\frac{7}{10} *\frac{3}{1}[/tex]

           [tex]=\frac{21}{10}[/tex]

           [tex]=2\frac{1}{10} km[/tex] (improper fraction)

Thus, the length of the rectangular park is [tex]2\frac{1}{10}[/tex] km

The length of the parking lot is 21/10 kilometers. This is found by rearranging the formula of the rectangular area to solve for length, substituting the given values and simplifying.

The problem is about finding the length of a rectangle when we know the area and the width. The formula of the area for a rectangle is the product of its length times its width. In this case, the area of the parking lot is 7/10 square kilometers and the width is 1/3 kilometers. The formula becomes: Area = Length * Width .

From this we can solve for length by dividing the area by the width, thus: Length = Area / Width. Substituting the values, we get: Length = (7/10) / (1/3), which simplifies to Length = (7/10) * (3/1) = (21/10) km.

So the length of the parking lot is 21/10 kilometers, or 2.1 kilometers written in decimal form.

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I'll do the first two problems (13 and 14) to get you started.

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Problem 13

I'm going to use square blocks instead of marbles. The same idea applies either way. I'm using blocks because they are easier to draw out.

Draw 9 square blocks that are connected end-to-end forming a long chain. Write O in the first four blocks to represent "orange". Write G in the remaining 5 blocks to represent "green". See figure 1 in the attached image below.

This diagram represents the fact that the orange and green blocks form a ratio of 4:5. There are 4 parts that are orange and 5 parts that are green.

If we have 6 rows of these blocks (see figure 2), then we'll have 6*5 = 30 green blocks overall. This leads to 6*4 = 24 orange blocks. So far we have 30+24 = 54 blocks that are green or orange.

-----

Let x be the total number of blocks

40% of the total x is the number of yellow

40% of x = 0.40*x

60% of x is the remaining number

0.60*x = 54

x = 54/0.60

x = 90

There are 90 blocks total

40% of 90 = 0.40*90 = 36 are yellow

60% of 90 = 0.60*90 = 54 are either green or orange

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Problem 14

Michael has 40 books. Susan has 50% more books than Michael. This means she has 1.5 times as many books

1.5*40 = 60

Susan has 60 books

If Michael buys 8 more books, then he will have 40+8 = 48, which is still less than 60. Susan still has more books.

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Let's compute the percentage difference

A = 48 is the amount of books Michael has

B = 60 is the amount Susan has

C = percent difference

C = 100*(B-A)/A

C = 100*(60-48)/48

C = 25%

Susan has 25% more books compared to Michael

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Answer: 9 is the coefficient and 'y' is the variable.

Step-by-step explanation:

Answer:

x ≈ 31°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{20}[/tex], thus

x = [tex]tan^{-1}[/tex]([tex]\frac{12}{20}[/tex]) ≈ 31° ( to the nearest whole number )

Answer: 10

Step-by-step explanation:(-x)(5y)(-2x)

=(-5xy)(-2x)

=10x^2y

therefore,the coefficient of the equation is 10.

Answer:

2/3

Step-by-step explanation:

1-1/3=3/3-1/3=2/3

Owen earned $ 36 on Saturday afternoon

Solution:

Let "x" be the amount earned by Owen between morning and afternoon

On Saturday morning , Owen earned $ 24

By the end of the afternoon he had earned a total of $ 60

From given information,

Amount earned on saturday morning + Amount earned on saturday afternoon = Total money earned

Therefore,

24 + x = 60

x = 60 - 24

x = 36

Hence Owen earned $ 36 on Saturday afternoon

Answer:

Step-by-step explanation:

Slope m = -2/7

Points are (2,1)

y1 = 1 and x1 = 2

y - y1 = m(x - x1)

y -1 = -2/7(x - 2)

Multiple each term by 7

7y - 7 = -2(x - 2)

7y - 7 = -2x + 4

7y = -2x + 4 + 7

2x + 7y = 11

The expression which is equivalent to 40 divided by 1/4 is 40 × 4 or the value is 160.

Given expression is 40 divided by 1/4.

We have to find the value of the expression and the equivalent expression for this.

This is a division expression.

40 ÷ 1/4

We know that when a fraction is the divisor of a division problem, then the problem can be redefined into multiplication problem by taking the reciprocal.

So 1/4 is taken in to the reciprocal and becomes 4/1 = 4

So the expression is,

40 × 4 = 160

Hence the equivalent expression is 40 × 4.

Learn more about Expressions here:

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Answer:

7÷5

1.4×5

Solution

7÷5=1.4

1.4×5=7

Answer:

25 * 36% = 9

Step-by-step explanation:

25 * .36 = 9

Answer:

910

Step-by-step explanation:

65×14=910

Answer:

9x2-18+18 or 18-18+9x2

Step-by-step explanation:

There are a couple ways to find this answer but these I recommend or this one: 9^2-70+7.

Answer:

B

Step-by-step explanation:

y = mx + b

m = 1

b = 4

y = 1(x) + 4

y = x + 4

To find Robert's minimum age, we need to determine the ages of George and Edward first. Let's assume Edward's age is x. According to the information given, George is twice as old as Edward, so George's age is 2x. Edward's age exceeds Robert's age by 4 years, meaning Robert's age is x - 4. The sum of the three ages is at least 56 years, so we can write the equation x + 2x + (x - 4) >= 56.

To find Robert's minimum age, we need to determine the ages of George and Edward first.

Let's assume Edward's age is x. According to the information given, George is twice as old as Edward, so George's age is 2x.

Edward's age exceeds Robert's age by 4 years, meaning Robert's age is x - 4.

The sum of the three ages is at least 56 years, so we can write the equation x + 2x + (x - 4) >= 56. Simplifying this, we get 4x - 4 >= 56. Adding 4 to both sides, we have 4x >= 60. Dividing by 4, we find that x >= 15.

Therefore, Edward's minimum age is 15 years, and Robert's minimum age is 15 - 4 = 11 years.