What are the 4 properties of solution?

The length of diagonal AC is 54.8 inches when two sides are 29inches and 25 inches long.

To find the length of diagonal AC in the kite-shaped sandbox, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the length of the hypotenuse (the longest side) is equal to the square root of the sum of the squares of the other two sides.

Identify the right triangle. In this case, we can see that the right triangle is formed by diagonal DB and the two sides of length 25 inches, which we'll call side a.

Substitute the known values into the formula, where AC is the hypotenuse and a and DB are the other two sides of the triangle: AC^2 = a^2 + DB^2

Solve for AC by taking the square root of both sides: AC = √(a^2 + DB^2)

Substitute the given values for a and DB: AC = √(25^2 + 49^2) = √(625 + 2401) = √3016 = 54.8

It's important to note that the kite shape can be considered as two congruent right triangles. The sides 25 and 29 are the legs, and the diagonal DB (49 inches) is the hypotenuse of one of the triangles. Since the triangles are congruent, their hypotenuse will have the same length. Therefore, the diagonal AC, which is the hypotenuse of the other triangle, also has a length of 49 inches.

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The time taken by 5 large solar panels and 3 small solar panels to charge a car, found using the unitary method, is 576 minutes.

The unitary approach is a method for problem-solving that involves first determining the value of a single unit, and then determining the necessary value by multiplying the single unit value.

Given

Time taken by 2 large solar panels to charge a car = 240 minutes

Time taken by 2 large solar panels to charge a car

       = Time taken by 6 small solar panels to charge a car = 240 minutes

The unitary method can be used to find the charging times of 1 large and 1 small solar panel.

The time taken by 1 solar panel is greater than time taken by 2 large and 6 small solar panels.

Time taken by 1 small solar panel = 240 * 6 = 1440 minutes

Time taken by 1 large solar panel = 240 * 2 = 480 minutes

Therefore the time taken by 5 large solar panels and 3 small solar panels to charge a car = (480/5)+ (1440/3) =96 + 480= 576 minutes.                    

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No, the square root of 1 is 1, but 1 is not equal to the square root of 1. The square root of a number, represented by the symbol √, is a value that, when multiplied by itself, gives the original number.

For example, the square root of 4 is 2, because 2 x 2 = 4. In the case of 1, the square root is also 1, because 1 x 1 = 1.

In mathematics, the square root of a number is always non-negative, real number. It is positive for positive numbers and zero for zero. So, in short, the square root of 1 is 1, but 1 is not equal to the square root of 1. It is just a value that gives 1 when multiplied with itself.

It's important to note that the square root is not a number but an operator, an action which you perform on a number. The square root of a number is a value that, when multiplied by itself, gives the original number.

In this case, the square root of 1 is 1, which means that 1 multiplied by 1 is 1.

Also, it's worth mentioning that there are two types of square roots: principal square root and non-principal square roots. Principal square root is the positive value of the square root and non-principal square roots are the negative value of the square root.

In this case, the square root of 1 is 1, which is the positive value of the square root.

In conclusion, the square root of 1 is 1, and it is the positive value of the square root, but 1 is not equal to the square root of 1, as the square root is a value that gives the original number when multiplied by itself.

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Answer:

Step-by-step explanation:

[tex]\frac{a^{3}-2a^{2}-15a }{a^{3}+a^{2}-30a} =\frac{a^{2}-2a-15}{a^{2}+a-30}[/tex]

[tex]\frac{a^{2}-2a-15}{a^{2}+a-30}=\frac{(a-5)(a+3)}{(a-5)(a+6)}= \frac{(a+3)}{(a+6)}[/tex]

The system of Equation the tables represent are:

y = 11.5x + 22 and y = –13x + 218

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Manuel:

slope = (33.50- 22)/ (1-0)

slope = 11.5

So, the Equation for Manuel

y- 22= 11.5 (x- 0)

y- 22 = 11.5x

y= 11.5x + 22

Ruben:

slope = (205- 218)/ (1-0)

slope = - 13

So, the Equation for Ruben

y- 218= -13 (x- 0)

y- 218 = -13x

y= -13x + 218

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Answer:

The height is 32

Step-by-step explanation:

The ratio of width to height is

4:3

We know the height is 24  so to go from 3 to 24 is multiplying by 8.

Multiply all terms by 8

4 * 8  : 3 * 8

32: 24

The ratio of the width to height is

32:24

The height is 32

=================================================

Work Shown

width/height = 4/3

w/24 = 4/3

3w = 24*4

3w = 96

w = 96/3

w = 32 cm is the width

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

Another approach.

The ratio of width to height is 4:3, meaning a screen that has width 4 cm and height 3 cm is possible. Instead, we want the "height 3 cm" to be "height 24 cm". This is a jump of "times 8".

Multiply both parts of that ratio by 8 to get...

4:3

8*4:8*3

32:24

A screen that is 32 cm wide and 24 cm tall will give us a ratio 4:3 when simplifying fully.

The order of the numbers is important. We have the width listed first simply because it was listed first in the phrasing "ratio of width to height".

Answer:

128 дней (days)

Step-by-step explanation:

5375/42 = 128 (округляем)

Answer:

128 days

Step-by-step explanation:

To solve this problem, we simply have to divide the total amount of oil in the tank by the amount of oil used each day.

[tex]5375 \textrm{ liters} \times \dfrac{1 \textrm{ day}}{42 \textrm{ liters}} = \dfrac{5375}{42} \textrm{ days} \approx 128 \textrm{ days}[/tex]

So, the tank will be empty after 128 days.

Note that the number of days is approximate; normally when measuring in the real world, whole numbers are used, as decimals in certain contexts (like in this situation) are confusing. So to simplify our answer, we can simply round up to 128 because by the end of the 128th day, the tank will be empty.

The ratio between the weights, giving how much Piglio is heavier than Whiskers, is given as follows:

1.5.

The ratio between two amounts a and b is obtained applying the proportion between these two amounts, that is, dividing a by b, as follows:

Ratio = a/b.

Which gives how many times greater the measure a is than the measure b, if the ratio is greater than 1.

The weight for each cat in this problem is given as follows:

The ratio between the weights of Piglio and Whiskers is given as follows:

Ratio = 4/2.67

Ratio = 1.5.

Meaning that Piglio is 1.5 times heavier than Whiskers.

Whisker's weight is given as follows: 2 and 2/3 kg.

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The random variable X represents the length of each engineering conference, and is measured in days.

The normal distribution should be used for this problem, as the underlying population is normal. The normal distribution is a continuous probability distribution that is characterized by a symmetric bell-shaped curve. It is a useful model for events that follow a normal or Gaussian pattern, such as the lengths of engineering conferences.

c. i. The 95% confidence interval for the population mean length of engineering conferences is (3.38, 4.50) days.

ii. The graph of the 95% confidence interval for the population mean length of engineering conferences is shown below.

iii. The error bound for the 95% confidence interval is 0.77 days. This can be calculated using the formula: Error Bound = 1.96*(standard deviation/√sample size). In this case, the error bound is calculated as: 1.96 * (1.28/√84) = 0.77.

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Answer:

Perimeter = 162 units

Area = 1508 square units

Step-by-step explanation:

Given expressions:

If x = 10, then:

The formula for the perimeter of a rectangle is:

where w is the width and l is the length.

Therefore, the perimeter of the rectangle is:

[tex]\implies \sf P = 2(29 + 52)[/tex]

[tex]\implies \sf P = 2(81)[/tex]

[tex]\implies \sf P = 162\;units[/tex]

The formula for the area of a rectangle is:

where w is the width and l is the length.

Therefore, the area of the rectangle is:

[tex]\implies \sf A=29 \cdot 52[/tex]

[tex]\implies \sf A=1508\;square\;units[/tex]

Answer:

Area of rectangle = 1508

Perimeter of rectangle = 162

Step-by-step explanation:

Now we have to,

→ find the perimeter and area.

→ where x = 10.

Perimeter of rectangle is,

→ P = 2 × (L + W)

→ P = 2 × (5(10) + 2 + 3(10) - 1)

→ P = 2 × (50 + 2 + 30 - 1)

→ P = 2 × 81

→ [ P = 162 ]

Area of rectangle will be,

→ A = L × W

→ A = (5(10) + 2) × (3(10) - 1)

→ A = (50 + 2) × (30 - 1)

→ A = 52 × 29

→ [ A = 1508 ]

Hence, these are the values.

Answer:

Step-by-step explanation:

If two right triangles share an acute angle measure, they are similar by angle-to-angle similarity. Corresponding side length ratios in the triangle are the same. The ratio of the side lengths of a right triangle depends only on the acute angle.

Answer:

Drew is incorrect

Step-by-step explanation:

Let the number be x such that if the product of the number and 4 is 1.08 then

x * 4 = 1.08

Divide both sides by 4

x = 1.08/4

= 0.27

Drew is incorrect because the result (1.08) has 2 decimal places and not one like he concluded. The number of digits before the decimal point for the numbers being multiplied must be 2.

Circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

Thus, circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.

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Circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.

Any building, whether open or closed, with a specific shape and characteristics composed of lines, curves, and points is referred to as a geometric shape. Squares, rectangles, circles, cones, cylinders, spheres, and so on are a few examples of well-known geometric forms. Each of these forms has specific characteristics that set them apart from other shapes.

Figures enclosed by a boundary created by combining a specific number of curves, points, and line segments are referred to as geometric forms. Every shape has a distinctive name like a circle, square, triangle, or rectangle, for example. In everyday life, we are surrounded by a variety of fundamental geometric forms, such as the triangle-shaped pizza slice, rectangle-shaped doors and windows, and many more.

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The area of the figure, which has a triangle and a rectangle with the same height, is 275 cm2.

You may also refer to it as a quadrilateral that is equiangular, meaning that all of its angles are equal. The parallelogram could alternatively have a straight angle. Rectangles with four sides that are all the same size are called squares. Four 90-degree vertices and equal parallel sides make up a quadrilateral with the rectangular shape. A rectangle is also referred to as a parallelogram since its opposing sides are parallel and equal.

given

Area of Figure = Area of Rectangle + Area of Triangle 

= l*b+ 1/2*b*h 

= 10 * 20 * 1/2 * 15 * 10 

= 275cm2

The area of the figure, which has a triangle and a rectangle with the same height, is 275 cm2.

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The area of the triangle GHJ is 48 square units.

The area of a triangle can be found using the formula:

Area = (1/2) * base * height.

In this question, we are given that triangle GHJ has a base of 12 units and a height of 8 units. To find the area of the triangle, we simply substitute these values into the formula and solve.

Area = (1/2) * 12 * 8 = 48 square units

To be more specific, first, we multiply the base and height together to get 12*8 = 96. Then we divide 96 by 2 to get 48. Therefore, the area of triangle GHJ is 48 square units.

It's important to note that the base and height of a triangle must be perpendicular to each other in order for the formula to be accurate. Also, the unit of measurement used for the base and height must be consistent, otherwise, the area calculated will not be correct.

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A triangle GHJ has a base of 12 units and a height of 8 units. What is the area of the triangle GHJ?

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The length of the beach towel is 4.135 feet.

Area of a two dimensional shape is the total region which is bounded by the object's shape

Given that

Hugo needs a total of 22.23 square feet of terry cloth to make a beach towel and a beach bag.

Total area of the terry cloth = 22.23 square feet

The beach bag requires 5.13 square feet of cloth.

Area of cloth for beach bag = 5.13 square feet

Area of the cloth for beach towel = 22.23 - 5.13 = 17.1

Area of the beach towel is 17.1 square feet.

Assuming the towel is square shape,

(Length of the towel)² = 17.1

Length of the towel = √(17.1) = 4.135

Hence the length of the beach towel is 4.135 feet.

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The slope of the green line is -4/3.

The correct option is C.

What is the slope of the line?

The slope of a line is a measure of how steep the line is and the direction it is going. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on the line.

The slope of a line is often represented by the letter "m" and can be calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

It is given that the lines graphed below are parallel.

We know that if two line having slopes m₁ and m₂ are parallel, then

m1 = m2

In other words, the slopes of two parallel lines are the same.

The slope of the red line is -4/3 and it is parallel to the green line. It means the slope of red and green line are the same.

The slope of green line = Slope of the red line

The slope of the green line = -4/3

Hence, The slope of the green line is -4/3.

The correct option is C.

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The slope of the green line is -4/3. The correct option is C.

What is the slope of the line?

The slope of a line is a measure of how steep the line is and the direction it is going. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on the line.

The slope of a line is often represented by the letter "m" and can be calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

It is given that the lines graphed below are parallel.

We know that if two line having slopes m₁ and m₂ are parallel, then

m1 = m2

In other words, the slopes of two parallel lines are the same.

The slope of the red line is -4/3 and it is parallel to the green line. It means the slope of red and green line are the same.

The slope of green line = Slope of the red line

The slope of the green line = -4/3

Hence, The slope of the green line is -4/3.

The correct option is C.

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The value of k in the equation is  3x + e^(x^2-3x/2)

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

y = 2ln(k - 3x) + x^2 - 3x

The x-axis is the set of points where y = 0. To find where the curve crosses the x-axis, we need to solve the equation y = 0 for x.

y = 2ln(k - 3x) + x^2 - 3x

so

0 = 2ln(k - 3x) + x^2 - 3x

We can re-arrange this equation to solve for x:

x^2 - 3x + 2ln(k - 3x) = 0

Now we can use the quadratic formula to find x.

x = (3 +/- sqrt(3^2 - 4(2ln(k - 3x))))/2

Now we know that there is only one root, we can pick the positive value and solve for k using k-3x = e^(x^2-3x/2)

k = 3x + e^(x^2-3x/2)

This is the final solution for k.

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Using simple mathematical operations, we know that Adalyn can purchase 14 cans if she spends no more than $30.

An operation is a function in mathematics that transforms zero or even more input values into a clearly defined output value.

The firm's arity is influenced by the number of operands.

Most people believe that addition, subtraction, multiplication, and division are the four basic operations in mathematics.

So, we know that:

Money =30 + 3 = 33

Price per can 2.25.

Then, she can buy:

33/2.25 = 14.67

Round off to 14 cans.

Therefore, using simple mathematical operations, we know that Adalyn can purchase 14 cans if she spends no more than $30.

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Total discount ticket at the amusement park were 51. If 75% of the sold ticket were discounted tickets and if the amusement park sold 68 tickets in all.

Total number of ticket sold = 68

75% of them were discount tickets, = 75 × 68/100

= 51 tickets

So 51 tickets were discount tickets and (68-51) = 17 tickets were without discount tickets. We can also calculate the without discount ticket by a different method. Remaining 25% tickets were the without discount tickets. So,

= 25 × 68/100

= 17 Tickets

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The part of the field would Roni mow will be 4 3/7 of the field.

To find out what part of the field Roni would mow if he and Allie worked together to mow the field, you would need to calculate their combined rate of mowing.

You can find the combined rate by adding the rates of each person working alone:

Combined rate = (Roni's rate) + (Allie's rate)

Combined rate = (1/30 hour) + (1/75 hour) = (5/150) + (2/150) = (7/150) hour

Then divide the rate of Roni by the combined rate to find the proportion of the field that Roni would mow:

(Roni's rate) / (Combined rate) = (1/30 hour) / (7/150 hour) = (30/7) / 1 = 4.2857142857142856

So Roni would mow about 4.29 or roughly 4.3/7 of the field if he and Allie worked together.

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The length of side of the cube with 181 square inches surface area is 5.5 inches

The information that was provided indicates that the surface area of the cube is 181.5 square inches. A cube's surface area is calculated as the square of the length of each side multiplied by 6. The formula to use in order to get the total surface area of a cube is = 6a²

Where "a" represents the side of the cube.

As a result, 6a² = 181.5 square inches

a² = 181.5/6

a² = 30.25

a² = √30.25

a = 5.5 inches

Therefore, each face of the cube is 5.5 inches on a side.

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y = (x - 4) (x - 4) The factored quadratic function (x - 2) has a vertex with an x-coordinate of 3, and two unique roots.

The study of mathematics covers numbers and their variations, equations and related structures, shapes and their locations, and locations where they can be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)

Vertex form of a quadratic equation: (h,k) is vertex

y = a(x-h)^2 + k

The x of the vertex needs to equal 3

y = a(x-3)^2 + k

y = (x-3)^2 - 1

y = x^2 -6x + 8

y = (x - 4) (x - 4) The factored quadratic function (x - 2) has a vertex with an x-coordinate of 3, and two unique roots.

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The Volume of shape Q is 25,600 cm³.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared.

Let z be the scale factor

x be the surface area of shape Q

and, y be the surface area of shape P

So, z²=x/y

we have,

x = 2880 cm², y= 720 cm²

z² = 2880/720

z² = 4

z = 2

Now, If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

z³ = x/y

We have z= 2 and y = 3200 cm³

So, 2³ = x/3200

x = 8×3200

x = 25,600 cm³

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The velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: V(x)=0.9×4.4√x

Thus if x=100feet or 30.47 m putting this value in the equation we get

V(30.47)=0.9×4.4√30.47

             = 21.86 m/sec

Hence, the velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec

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To find the equation of the line, we can use the two points on the line.

An equation is a mathematical statement that expresses the relationship between two or more variables, or a condition that two or more expressions must satisfy. An equation typically involves an equal sign, with an expression on either side of the sign. The expressions on each side of the equation can contain constants, variables, functions, operations, and other mathematical symbols. Equations are used to solve problems in mathematics, physics, engineering, chemistry, economics, and other scientific and practical fields.

The distance between a point (P) and a line (L) can be found using the following formula:
d = |(ax + by + c)|/√(a^2 + b^2)

where (a, b, c) are the coefficients of the line equation, and (x, y) are the coordinates of the point.

To find the equation of the line, we can use the two points on the line. Let's say these two points are (x1, y1) and (x2, y2). We can calculate the equation of the line using the following formula:

a = (y2 - y1)/(x2 - x1)
b = -1
c = y1 - ax1

Using these equations, we can easily calculate the distance between the point and the line.

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The set of properties for inequalities is as follows:

1. Additive characteristics of inequality

2. Inequality's subtraction property

3. The inequality's multiplication property

4. The unequal division property

5. Converse Property

An inequality is a relationship between two expressions that can be described mathematically and can be represented by any of the following symbols: >, <, ≤, ≥, =, and ≠.

The set of properties for inequalities is as follows:

1. Additive characteristics of inequality: The inequality remains the same even if both sides are given the same value.

2. Inequality's subtraction property: The inequality remains the same even after deducting the same amount from each side of it.

3. The inequality's multiplication property: Take p and q, two positive numbers. When p and q are both multiplied by the same positive value, the inequality stays the same. However, the inequality changes when p and q are both multiplied by the same negative value.

4. The unequal division property: Take p and q, two positive numbers. When p and q are both divided by the same positive number, the inequality is unaffected. However, the inequality is reversed when p and q are split by the same negative value.

5. Converse Property: According to the converse property, all we need to do to reverse the inequality symbol is flip the number.

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