Solve the system {-x+y=-3
3x+3y=9 check your solution by graphing

The dimensions of the original mat are 27 inches by 21 inches.

A closed figure bounded by four sides in which opposite sides are equal is known as rectangle.

The area of rectangle is calculated by the given formula,

A = length x breadth

Length and width  of the rectangle can be found from the following expression after solving for x. The expression is given by :

outside area - inside area = 184 square inches

{(2·x - 3)·(x + 8)} - {(2·x - 7)·(x + 4)} = 184  (On substitute length and width expressions. Each area is the product of length and width.)

⇒{( 2·x² + 16·x - 3x - 24)} - {(2·x² +  8x  -7x -28) }= 184

⇒(2·x² + 13x - 24) - ( 2·x² + x -28) = 184

⇒ 12·x + 4 = 184 .................(On simplifying the expression)

⇒ 12·x = 180

⇒ x = 15

Then the original length of the mat is given by substituting value of x in outside length expression :

2·x - 3 = 2·15 - 3 = 30 - 3 = 27 inches

and the original width of the mat is given by :

x + 6 = 15 + 6 = 21 inches

Hence, the overall dimensions of the original mat are 27 inches by 21 inches.

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Answer:

here are a total of 14 + 15 + 9 + 11 = 49 donuts.

The probability of selecting a maple donut is the number of maple donuts divided by the total number of donuts:

P(maple donut) = 14/49

So the probability of selecting a maple donut is 14/49, which can also be written as a fraction in simplest form: 2/7.

The conversion factor between kilometers per hour and miles per hour is 1.609344. Therefore, to convert from kmh to mph, we need to divide the speed in kmh by this conversion factor. 80kmh is equivalent to approximately 49.71 mph.

To find the speed in mph, we can use the following formula:

mph = kmh / 1.609344

Plugging in the given speed of 80kmh, we get:

mph = 80kmh / 1.609344

mph = 49.70969538

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If A, B, and C are nxn invertible matrices, the equation   C^-1(A+X)B^-1=I(n) has a solution which is X=CB-A. Since invertible matrices are those whose inverse matrix exists.

For A to be the matrix  here A⁻¹ is the inverse of it, so AA⁻¹=I, here I is the identity matrix ,since the matrix equation given to us is: C⁻¹(A+X)B⁻¹=In, now multiplying B on the right side and  C on the left side we get :CC⁻¹(A+X)B⁻¹B=CIₙB

=>Iₙ(A+X)Iₙ=CIₙB

=>A+X=CB, according to the property  of the identity matrix.Now adding -A on both sides we get,

=>A+X+(-A)=CB+(-A)

=>X=CB-A, so here the solution for the given matrix equation is: X=CB-A

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Answer:11/28

Step-by-step explanation:

we should find Lowest common denominator which is 4*7=28

1/4+1/7=4+7/4*7

Answer: 11/28.

Step-by-step explanation: Add 1/4 to 1/7.

1/4 + 1/7 = 11/28

The inequality that can be used to determine how many hours Matilda will need to babysit to buy the dress is 40 + 9x >= 112 , here the x needs to be greater than or equal to 8 i.e. x >=8.

Given, Matilda needs at least $112 to buy a new dress.

Money she has =$40

Money she earns for each hour of babysitting = $9

Let, x be the number of hours she will work to earn the minimum amount.

Therefore, the inequality that can be used to determine how many hours Matilda will need to babysit to buy the dress = 40 + 9x >= 112

                                                                               x >=8 hour

So, The inequality that can be used to determine how many hours Matilda will need to babysit to buy the dress is 40 + 9x >= 112 . She needs to work for at least 8 hours to earn the minimum required amount.

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The statement which is true is more males were surveyed than females, the correct option is A.

Suppose two dimensions are there, viz X and Y. Some values of X are there as X_1, X_2, ... , X_n and some values of Y are there as Y_1, Y_2, ... , Y_n

List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  X_i  and Y_j  (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

We are given that;

            Males  Females  Total

Soccer      |  31   |    50   |  81

Basketball  |  21   |    50   |  71

Total       |  52   |   100   | 152

Now,

A. More males were surveyed than females.

True. From the table, we can see that 52 males were surveyed, while only 100 females were surveyed.

B. More females like soccer.

False. From the table, we can see that 31 males and 50 females like soccer, so a total of 81 people like soccer. This is the same as the number of females surveyed, so we cannot say that more females like soccer.

C. An equal number of people like soccer and basketball.

False. From the table, we can see that 81 people like soccer, while 71 people like basketball.

D. Twice as many females than males like basketball.

False. From the table, we can see that 21 males and 50 females like basketball. Twice the number of females who like basketball is 100, which is the total number of females surveyed, but this is not twice the number of males who like basketball.

Therefore, by the two-way table the answer will be more males were surveyed than females.  

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The height of the antenna which is the distance from point A to point B is 4.5657 m.

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

Given:

We have to find two height h and H.

So, for distance H

H/ 27= tan 41

H= 27 x 0.8693

H = 23.4711 m

Now, for distance h

h/ 27 = tan 35

h= 27 x 0.7002

h= 18.9054

So, the height of the Antenna

= 23.4711- 18.9054

= 4.5657 m

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Answer: 8521.8 ÷ 8 = 1065.225

Step-by-step explanation: This is extremely simple all you require is a calculator with which you can plug in the variables

The cost of each pineapple juice bottle at Store A is $0.90 more than at Store B.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

The rate of the pineapple juice bottle at store A is given as,

Rate = $7.32 / 3

Rate = $2.44 per bottle

From the graph, the two points are (10, $15.40) and (20, $30.80). Then the rate is given as,

Rate = ($30.80 - $15.40) / (20 - 10)

Rate = $1.54

The difference between the rates is given as,

⇒ $2.44 - $1.54

⇒ $0.90

The cost of each pineapple juice bottle at Store A is $0.90 more than at Store B.

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The complete question is attached below.

Kelly has to pay a tax of $22,562.50 which is approximately around of 20% her taxable income.

The term "taxable income" describes the basis on which an income tax system levies tax. In other words, the amount of income that was taxed by the government.

In most cases, it covers some or all sources of income and is then diminished by costs and other deductions. Every gross income received and utilized to determine your tax liability is referred to as taxable income.

It can be stated simply as your adjusted gross income less any deductions. This covers all pay, gratuities, salaries, and bonuses received from employers. Investments and ill-gotten gains are also mentioned.

The given taxable income is over $43,650. So use the information on line 3 to determine the tax.

Tax =$5,975+25% of the amount over 43,650

=5,975+0.25(110,000 - 43,650)

=5.975+16587.50

=22,562.50

Kelly has to pay a tax of $22,562.50 which is approximately around of 20% her taxable income.

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The perimeter of the given triangle in mixed fraction form is 4 1/2 ft.

A triangle is a closed, 2-dimensional shape with three straight sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. There are many types of triangles, including equilateral triangles (all sides and angles are equal), isosceles triangles (two sides and two angles are equal), scalene triangles (no sides or angles are equal), right triangles (one angle is a right angle, or 90), and obtuse triangles (one angle is greater than 90). Triangles are used in many areas of mathematics, science, and engineering.

Here,

The perimeter of the triangle:

=2 1/8+5/6+1 3/4

First, we need to convert all the mixed numbers into improper fractions:

2 1/8 = 17/8

5/6 = 10/16 = 15/24

1 3/4 = 7/4

Now we can add the three fractions:

17/8 + 15/24 + 7/4

To add these fractions, we need to find a common denominator. The smallest number that all three denominators divide into is 24. So we can rewrite the fractions with 24 as the denominator:

17/8 = 51/24

15/24 (already in the correct form)

7/4 = 42/24

Now we can add the numerators:

51/24 + 15/24 + 42/24 = 108/24

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 12:

108/24 = (9 × 12)/(2 × 2 × 2 × 3) = 9/2

=4 1/2 ft

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106$ money will be in the account after one year if the initial amount is $100.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

we have

Money in particular savings accounts increases by about 6% after a year.

we know that

The simple interest formula is equal to

A = P(1 +rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is the Number of Time Periods

Part 1) How much money will be in the account after one year if the initial amount is $100

in this problem we have

P = 100

r =6%

t = 1 year

substitute in the formula above

A = 100(1 +0.06)

A = 106$

Part 2) How much money will be in the account after one year if the initial amount is $50

in this problem we have

P = 100

r =6%

t = 1 year

substitute in the formula above

A = 50(1 +0.06)

A = 53$

Part 3) How much money will be in the account after one year if the initial amount is $200

in this problem we have

P = 100

r =6%

t = 1 year

substitute in the formula above

A = 200(1 +0.06)

A = 212$

Part 4) How much money will be in the account after one year if the initial amount is $125

in this problem we have

P = 100

r =6%

t = 1 year

substitute in the formula above

A = 125(1 +0.06)

A = 132.5$

Part 5) How much money will be in the account after one year if the initial amount is $x

in this problem we have

P = 100

r =6%

t = x year

substitute in the formula above

A = 100(1 + 0.06x)

A = 6x +100

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Answer: D, 1.01

1.01 is in between 0.62 and 1.05

Answer: D-1.01

Step-by-step explanation:

The probability that the country is in the south Asia region is 7/87

The probability is a mathematical concept that tells us how likely an event is to occur.

The probability that a country is in South Asia given that it has high business startup costs is represented as P(A|B). This is calculated as follows:

P(A|B) = P(A and B) / P(B)

Where P(B) is the probability that a country has high business startup costs and can be calculated as:

P(B) = B / Total number of countries

And P(A and B) is the probability that a country is in South Asia and has high business startup costs, which can be calculated as:

P(A and B) = A / Total number of countries

So, substituting the values, total high startup cost is 87 and and, South Asia start up cost is 7, Then, the probability that the country is in the south Asia region is

=> 7/87

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Answer: 0 or No answer

Step-by-step explanation:

2t-2t is 0 so there is no t and 5-5 is 0 so theres no number.

The nearest whole number after rounding is, 14

Rounding a number to the nearest tenth means finding the nearest multiple of 0.1.

To do this, you need to look at the digit in the hundredths place (the second digit after the decimal point) of the number you want to round.

If that digit is 5 or greater, you round the number up by adding 0.1 to the nearest whole number.

If that digit is 4 or less, you round the number down by leaving the nearest whole number unchanged.

For example, rounding 3.456 to the nearest tenth gives 3.5, while rounding 3.444 to the nearest tenth gives 3.4.

Given that,

The decimal number  13.5,

after using rules of rounding,

it can be rounded as 14

Hence, the nearest whole number is 14

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The rate of change of the function represented in the table is 12 For the given x- and y-values, the function is f(x)=12x+34

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=26-2/5-3

=24/2

=12

Rate of change is 12.

Now let us find y intercept

26=12(5)+b

26=60+b

26-60=b

b=34

So the function is y=12x+34

Hence, the rate of change of the function represented in the table is 12 For the given x- and y-values, the function is f(x)=12x+34

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Question

A function is represented by the table. x y

3 -2

5 -26

7 -50

The rate of change of the function represented in the table is_____

. For the given x- and y-values, the function is____

Answer:

Step-by-step explanation:

Prim's algorithm is a greedy algorithm used to find the minimum spanning tree (MST) of a connected, undirected graph. It works by growing the tree one vertex at a time, always adding the vertex with the lowest weight edge that connects it to the growing tree. The algorithm starts with an arbitrary vertex, adds it to the tree, and then repeats the following steps until all vertices are in the tree:

Find the vertex that is not in the tree but has the minimum weight edge connecting it to the tree.

Add the vertex to the tree and mark it as visited.

Update the minimum weight edges connecting the vertices that are not yet in the tree to the growing tree.

This process continues until all vertices are in the tree, and the final result is the minimum spanning tree. The visualization of Prim's algorithm for minimum spanning tree can be represented graphically by showing the growth of the tree one vertex at a time, and highlighting the edges that are added to the tree in each step. The animation can be used to show how the algorithm is making decisions based on the weights of the edges and how it is gradually building the minimum spanning tree.

Answer:

length = 21 in , width = 14 in

Step-by-step explanation:

the ratio of length : width = 3 : 2 = 3x : 2x ( x is a multiplier )

the area (A) of a rectangle is calculated as

A = length × width

given A = 194 , then

3x × 2x = 194

6x² = 194 ( divide both sides by 6 )

x² = 49 ( take square root of both sides )

x = [tex]\sqrt{49}[/tex] = 7

then

length = 3x = 3 × 7 = 21 in

width = 2x = 2 × 7 = 14 in

Answer:

$1350.

Step-by-step explanation:

If Justin files a claim for $2100, he will pay the first $750 toward the claim, and his insurance company will pay the remaining costs.

So, Justin will pay $750.

And, the insurance company will pay $2100 - $750 = $1350.

The Zucchini will be longer than 11 feet on the ninth day.

Since 12 inches is equal to 1 foot, then 11 feet will be equal to 132 inches. Below, we are going to describe the rate of the plant's growth from day 1.

Day 1 = 6 inches

Day 2 = 6 + 9 inches = 15 inches

Day 3 = 15 + 9 + 3 = 27 inches

Day 4 = 27 + 12 + 3 = 42

Day 5 = 42 +15 + 3 = 60

Day 6 = 60 + 18 + 3 = 81

Day 7 = 81 + 21 + 3 = 105

Day 8 = 105 + 24 + 3 = 132

Day 9 = 132 + 27 + 3 = 162

We are told that on the second day, the tree grew up to 15 inches and subsequently, it grew by the same amount as the day before plus another three inches.

Going by that calculation, on the third day, the tree will grow by 9 inches plus three more inches and this continues. Finally, on the ninth day, the tree would have grown up to 162 inches which is greater than 132 inches or 11 feet.

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Using the law of tangents, the angle of the person’s eyes to the top of the building is approximately 36.87 degrees.

Angle  isc figure that can be described as the amount of rotation between two straight line not planes and angles is measured in degree with the full circle being 360°.

This can be calculated by setting up the following equation:

tan(angle) = 80 ft / (200 ft - 4 ft)

Solving for the angle, we get:

angle = tan-1(80 ft / 196 ft)

angle = tan-1(0.408163265)

angle = 36.87 degrees (to the nearest hundredth of a degree).

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Van 't Hoff's law, also known as the law of osmotic pressure, states that the magnitude of the osmotic pressure is directly proportional to the concentration of solute particles in a solution at a given temperature.

Van 't Hoff's law is an important concept in chemistry and thermodynamics. It explains the relationship between osmotic pressure and the concentration of solute particles in a solution. According to the law, the osmotic pressure of a solution is directly proportional to the number of solute particles in the solution, regardless of the type of solute. This means that if the concentration of solute particles in a solution increases, the osmotic pressure also increases, and vice versa. This law has numerous applications, particularly in the field of biology, where it is used to explain the movement of water and nutrients in and out of cells. For example, when a plant cell is placed in a hypertonic solution, water moves out of the cell, causing it to shrink. On the other hand, when a plant cell is placed in a hypotonic solution, water moves into the cell, causing it to expand. Understanding Van 't Hoff's law is therefore critical in many fields of science, particularly in biology, chemistry, and chemical engineering.

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Step-by-step explanation:

FCP fundamental counting principle :

in total there are

3×3×2 = 18

different combinations

listing method means listing all different triplets of such outfit combinations.

white shirt = ws

red blouse = rb

floral shirt = fs

short = sh

jeans = j

jogger pants = jp

shoes = s

sandals = sa

{

(ws, sh, s),

(ws, sh, sa),

(ws, j, s),

(ws, j, sa),

(ws, jp, s),

(ws, jp, sa),

(rb, sh, s),

(rb, sh, sa),

(rb, j, s),

(rb, j, sa),

(rb, jp, s),

(rb, jp, sa),

(fs, sh, s),

(fs, sh, sa),

(fs, j, s),

(fs, j, sa),

(fs, jp, s),

(fs, jp, sa)

}

tree diagram (I cannot draw here) :

OOTD

/ | \

ws rb fs

/ | \ / | \ / | \

sh j jp sh j jp sh j jp

/ | / | / | / | / \ / | / | / | / |

s sa s sa s sa s sa s sa s sa s sa s sa s sa

as you can see, we get a expected 18 different triplets in our listed set, and we get 18 different end leaves in and therefore 3-level paths through our tree.

Answer:

10 = 3(z + 1) + 1

To start off we simplify boths sides of the equation,

10=3(z+1)+1

10=(3)(z)+(3)(1)+1

10=3z+3+1

Combining like terms*

10=3z+4

Now you flip the equation:

3z+4=10

Now Subtract 4 from both sides.

3z+4−4=10−4

3z=6

Divide by 3**

Andd you gettt

z=2

Step-by-step explanation:

Hope this helps :)

The cost of each battery would be Battery 1 = $195, Battery 2 = $80 and Battery 3 = $65.

Battery 1 (most expensive).= 3(X)

Battery 2 ( third battery) = 15+ X

Battery 3 (least expensive) = X

The total cost of the whole battery = $340

That is;

$340 = 3x + 15+ X + X

340 = 5x + 15

5x = 340 - 15

5x = 325

X = 325/5

X = $65

Therefore the cost of each battery;

Battery 1 = 3× 65 = $195

Battery 2 = 15 + 65 = $80

Battery 3 = $65

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