find the measure of CDE,BC,AB, and CAB.

The dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.

The area of Rectangle is length times of width.

Area of rectangular pool = 6x² − 11x + 3

To factor the trinomial, we need to find two binomials that multiply together to give the trinomial 6x² − 11x + 3.

We use product-sum method of factoring to find the two binomials.

We need to find two numbers that multiply to 6 (the coefficient of the x² term) and add to -11 (the coefficient of the x term).

6x² − 11x + 3

6x² −2x-9x + 3

(2x − 1)(3x − 3)

Hence, the dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.

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Answer:

We can use the triangle inequality theorem to determine the possible lengths of the third side of the triangle. According to the theorem, the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

So, for a triangle with sides of length 16 and 17, the length of the third side must satisfy the following inequality:

17 - 16 < third side < 17 + 16

1 < third side < 33

Therefore, the length of the third side must be described by the expression:

1 < third side < 33

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

the square root basically means ___ multiplied by ___ equals the number in the square root, in this case being 9. the +/- symbol means that -3 multiplied by -3 equals positive 9 and positive 3 multiplied by positive 3 equals positive 9

90 degrees Fahrenheit is equal to approximately 32.2 degrees Celsius using conversion formula method.

To convert Fahrenheit to Celsius, the following formula can be used:

Celsius = (Fahrenheit - 32) x 5/9

Plugging in 90 degrees Fahrenheit, we get:

Celsius = (90 - 32) x 5/9

Celsius = 58 x 5/9

Celsius = 290/9

Celsius ≈ 32.2

Therefore, 90 degrees Fahrenheit is approximately 32.2 degrees Celsius.

Fahrenheit is a temperature measurement system developed by the German physicist Daniel Gabriel Fahrenheit in 1724.

The Celsius scale is widely used throughout the world for measuring temperature, and it is the standard unit of temperature used in most scientific research and international trade. In addition to measuring air temperature, Celsius is used to measure temperature in a variety of fields, including chemistry, biology, and engineering.

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0.08$/fl. Ounce

The first step in finding the unit price of a can of pineapple juice in dollars per fluid ounce is to determine the volume of juice contained in the can. If a can holds 4 cups of juice, then we need to convert that volume to fluid ounces. One cup is equal to 8 fluid ounces, so 4 cups is equal to 32 fluid ounces.

Next, we need to determine the price of the juice in dollars per fluid ounce. We are told that the can costs 2.56 dollars, so we need to divide that cost by the number of fluid ounces in the can to find the unit price.

So, the unit price of the juice in dollars per fluid ounce is:

2.56 / 32 = 0.08 dollars per fluid ounce

So, for each fluid ounce of pineapple juice, the cost is 0.08 dollars. This is the unit price of the juice in dollars per fluid ounce. It is important to note that this unit price is only valid for this specific can of juice and may not be the same for other sizes or brands of pineapple juice.

In conclusion, the unit price of a can of pineapple juice containing 4 cups or 32 fluid ounces, and costing 2.56 dollars, is 0.08 dollars per fluid ounce.

Answer:

Step-by-step explanation:

Put ' - 3' whre 'x' is and compute the answer

f(-3) = 3 (-3) - 7

      = -9 - 7 = - 16

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

Mixture word problems require you to combine two or more separate items, and then calculate some quantity of the resulting mixture (such as a percentage, price, or number of liters, for example). There will always be some type of "rate," like miles per hour or price per pound. Mixtures are substances that contain two or more distinct substance categories. To separate them, utilize physical tools. Examples include air, different gases, a mixture of sugar and water, a solution of salt and water, and so on.

here, we have,

Given,

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution.

Equation:

X + y = 119

y = 119 - x

0.40x + 0.12y = 119 of 0.32

0.40x + 0.12y = 38.08

Using y = 119 -x

0.40x + 0.12(119 - x) = 38.08

0.40x + 14.28 - 0.12x = 3808  Eq(2)

0.28x = 23.8

x = 85

and,

y = 119 - 85

y = 119 - 85

y = 34

Equating values in equation (2),

=0.40(85) + 0.12(34)

=34 + 4.08

=38.08

A pharmacist wants to mix a 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

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In linear equation, $869,776  will her total payment for the home be .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.

The number is $6.74.

That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.

2. Amount borrowed

You will make a 22% down payment:

Thus the amount borrowed is $426,000 - $93,720 = $332,280

3. Monthly payment

Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:

4. Total monthly payments:

Multiply the number of payments by the monthly payment.

Number of payments = 20 years × 12 payments /year = 240 payments.

5. Total payment for the home.

The total payment for the home will be the down payment plus the amount paid to the bank:

$322,280 + $537,496 = $869,776

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Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.

To find the answer, we need to use the formula for permutations:

Permutations = n! / (n-r)!

Where:

- n is the total number of items

- r is the number of items to be arranged

- ! means factorial (e.g. 5! = 5 x 4 x 3 x 2 x 1)

In this case:

- n = 10 (the total number of plants)

- r = 3 (the number of plants to be arranged on the window ledge)

Plugging these values into the formula, we get:

Permutations = 10! / (10-3)! = 10! / 7! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (7 x 6 x 5 x 4 x 3 x 2 x 1) = (10 x 9 x 8) / 1 = 720

Therefore, Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.

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Answer:

Step-by-step explanation:

75%

The value of the length, x is 5√3

From the question, we have the following parameters that can be used in our computation:

Rise = 11

Length = x

Hypotenuse = 14

The value of the length , x is calculated as

x^2 = Hypotenuse^2 - Rise^2

Substitute the known values in the above equation, so, we have the following representation

x^2 = 14^2 - 11^2

So, we have

x^2 = 75

Take the square root of bpth sides and evaluate

x = 5√3

Hence, the value of x is 5√3

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The percentage of decrease is 20%

First, if we have an initial value A, and we increase it by x (a percentage in decimal form) then the new value will be:

A' = A*(1 + x)

Whle a decrease is written as:

A' = A*(1 - x)

In this case we have an increase of the 25%, it is written as:

A' = A*(1 + 0.25)

A' = A*1.25

IF we pass the factor to the other side, will get:

(1/1.25)*A' =  A

(0.8)*A' = A

Now we want to write the coefficient on the left in the form (1 - x)

We will get:

0.8 = 1 - 0.2

0.2 is the percentage (in decimal form) decreased  from A' to get A. Then the answer is 20%.

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The coordinates of A' in triangle A'B'C' which was produced after reflection with condition y =x is equal to option d. ( 1, 2).

Graph is attached.

Triangle A'B'C' is produced after reflection of the triangle ABC over the line y = x.

From the graph we have ,

Coordinates of A is ( 2 , 1)

Coordinates of B is (-1, 4)

Coordinates of C is ( 0, -2)

Condition of reflection of triangle ABC over the line y = x.

x-coordinates replace by y and y replace by x.

Coordinates of triangle A'B'C' are

Coordinates of A' is ( 1, 2)

Coordinates of B' is (4, -1 )

Coordinates of C' is ( -2, 0 )

Therefore, if the coordinates of point A in triangle ABC are (2, 1), the coordinates of point A' in triangle A'B'C' would be option d. (1, 2).

The above question is not complete , the complete question is:

Triangle ABC is reflected over the line y = x to produce triangle A'B'C'. What will be the coordinates of A'? Graph is attached.

a.  (2,−1)            b.  (−2,−1)                 c.  (2,1)                d.  (1,2)

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Answer: i think it is 538.4

Step-by-step explanation:

Answer:

Step-by-step explanation:

i don't know

In a case whereby two planes, which are 2235 miles apart, fly toward each other. Their speeds differ by 45 mph. If they pass each other in 3 hours, the speed of slower is 350mph and faster is 395mph.

The concept here is simplification.

Let represent the speed of the slower plane using the( x),

Let us represent the speed of the faster to be ( x + 45)

The distance traveled  that can be associated to the slower plane ( 3x).

then the distance that can be attributed toi that of the faster plane = 3(x + 45).

given that the  total distance=(2235 miles).

[3x + 3(x + 45) ]= 2235

3x + 3x + 135= 2235

[6x ]= 2235-135

6x = 2100

x=350

hence,  the speed of the slower plane is 350

the speed of the faster= x + 45 = 350+45= 395

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The speed of first plane is 350 miles/hour and the speed of second plane is 395 miles/hour .

Given, Distance between the planes = 2235 miles

Let, the speed of the first plane be 'x' miles/hour.

Let, the speed of the second plane be 'x+45' miles/hour.

Since, they are flying towards each other, their speed will get added.

The collective speed of both the planes = (2x + 45) m/h.

A/Q, they pass each other in 3 hours, i.e. they collectively covers the distance of 2235 miles in 3 hours.

We know Distance = Speed × Time

Given, Distance = 2235 miles , Time = 3 hours , Speed = (2x + 45) m/h

                      2235 = 3  × (2x + 45)

                       745 = 2x + 45

                        x = 350 miles/hour.

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From the sum of the interior angles, it is possible to find x=70°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square, all angles are 90° and all sides present the same value.

The sum of the interior angles of a quadrilateral is equal to 360°.

The question gives a trapezoid and its respective angles. Thus,

x+85+150+55= 360

x+140+150=360

x+290=360

x=360-290

x=70°

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Answer:

b) 70°

Step-by-step explanation:

We know that,

→ The sum of all interior angles in a quadrilateral is 360°.

Now we have to,

→ Find the required value of x.

Forming the equation,

→ 85° + 150° + 55° + x = 360°

Then the value of x will be,

→ 85° + 150° + 55° + x = 360°

→ 290° + x = 360°

→ x = 360° - 290°

→ [ x = 70° ]

Hence, the value of x is 70°.

Answer:

Area = 452 cm²

Step-by-step explanation:

[tex] = \frac{\pi }{4} {d}^{2} [/tex]

[tex] = \frac{\pi}{4} {(24)}^{2} = 452.39 \: cm²[/tex]

The solution to the simultaneous equation given is (3, 4)

Given the system of equation below

2x+y=10

3x-y=5

From equation 2, the value of y is expressed as:

y = 3x - 5

Substitute the result into equation to have:

2x + 3x - 5 = 10

5x - 5 = 10

5x = 15

x = 3

Since y = 3x - 5

y = 3(3) - 5

y = 4

Hence the solution to the system of equation is (3, 4)

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Answer:

The mass of 3.5 moles of Ca (Sodium)  is 140 g to two significant figures.

The principal for Account A is $150, and we do not have enough information to find the principal for Account B. Account A earned the most interest the first month because it has a higher monthly interest rate.

The principal for Account A can be found using the formula for simple interest:

I = Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Rearranging the formula to solve for P, we get P = I / (rt).

For Account A, the interest is $9.45, the interest rate is 3.6%, or 0.036, and the time is 21 months, or 1.75 years.

Plugging these values into the formula, we get:

P = $9.45 / (0.036 × 1.75) = $150

So the principal for Account A is $150.

For Account B, we do not have enough information to find the principal. We know the interest rate, but we do not know the interest or the time.

To determine which account earned the most interest the first month, we can compare the monthly interest rates.

The monthly interest rate for Account A is 3.6% / 12 = 0.3%, and the monthly interest rate for Account B is 2.4% / 12 = 0.2%.

Since the monthly interest rate for Account A is higher, it earned the most interest the first month.

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Answer:

7/10

Step-by-step explanation:

Here ya go!

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

[tex]y=b_1x+b_0[/tex]

There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.

Given a collection of pairs (x,y) of numbers, there is a line [tex]y=b_1x+b_0[/tex] that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.

[tex]b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)[/tex]

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

[tex]y=b_1x+b_0[/tex]

specifying the least squares regression line is called the least squares regression equation.

Example,

Find the least squares regression line for the five-point data set

x = 2  2  6  8  10  

y=  0  1   2  3  3.

compute the table,

x   y     x2         xy

2  0     4           0

2  1      4            2

6   2   36       12

8   3   64        24

10  3   100    30

28  9   208    68   (sum)

[tex]S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125[/tex]

The regression line is y=0.34375x-0.125

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Answer:

1. S = 20w + 100

2. M = -400w + 3,500

Step-by-step explanation:

1. Since Mateo is starting with a balance of $100, we can set this as our constant term (the 'b' in y = mx + b). Every week, he earns $20, so we can set this as the coefficient on the variable w (which represents how many weeks have passed).

2. Emily is spending money in this situation, so the coefficient on w is negative, as the amount of money she has left is getting smaller. The exact amount that she spends each week is $400, so the negative of that is going to be the coefficient of w in the equation. We can set the constant term in this equation to $3500, as Emily starts with that much money when no weeks have passed (when w = 0).

The value of x is  15√2

The value of the side y is 30

The sum of angles in a rectangle is 360 degrees

To determine the value of the variable, x

Let's use the trigonometric identity, cosine

cos = adjacent/hypotenuse

substitute the values

cos 45 = 15/x

Find the value

1/√2 = 15/x

cross multiply

x = 15√2

For y, we have;

sin 45 = y/15√2

1/√2 = y/15√2

Make y subject

y= 15√2 /√2

y = 60/2

y = 30

Hence, the values are 30 and 15√2

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the matches are

-2(2x+5) ≤ -7(x+4)         x<=-6

4x-3x-1                          x<=-1

5(x-3)9(x+1)                   x>=-6

3(x-4)+5 2x-9                x>=-2

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

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The correct matching of the inequalities can be shown from the calculations below

Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.

Using the principle of inequalities we have;

1) -2(2x + 5) ≤ - 7(x + 4)

-4x -10 ≤ -7x -28

-4x +7x ≤ -28 + 10

3x ≤ -18

x ≤ -6

2) 4x - 6/2 ≥ 3x - 1

4x - 6 ≥ 6x - 2

4x - 6x ≥ -2 + 6

-2x ≥ 4

x  ≤ -2

3) 5(x - 3) ≤ 9(x + 1)

5x - 15  ≤ 9x + 9

5x - 9x  ≤ 9 + 15

-4x  ≤ 24

x ≥ -6

4) 3(x - 4) + 5 ≥ 2x - 9

3x - 12 + 5≥ 2x - 9

3x - 2x ≥ -9 + 12 -5

x ≥ -2

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Answer:

180 - 119.4 = 60.6

So the answer is 60.6

Answer:

60.6°

Step-by-step explanation:

Supplementary angles equal 180 degrees. So we can show this with the following equation:

119.4 + x = 180

where x is the measure of the other supplementary angle.

If we subtract 119.4 from both sides, we get the the value of x, which is 60.6.

The solution is, B = 245, is a Reflex Angle., when it is given that A=65.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

We know that, a ray is a line that continues on forever inn one direction with a point at it's start.

here, we have,

A = 65°

now,  B is a Reflex Angle ,

so, we know that Reflex Angle means the angle with value >180 to <270.

now, we get,

B = 180 + 65

  = 245

Hence, The solution is, B = 245, is a Reflex Angle.

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Answer:no

Step-by-step explanation:

if it was then it supposed to be like 4*20=5*15 which is not right equation