What is the area of the base of this right triangular prism?

if the sides of an isosceles triangle are 29,29 and 20m long then the area of the triangle is, 613.52 m²

Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two angles that are equal in size and opposed to its equal sides.

Given that,

The sides of an isosceles triangle are 29,29 and 20m long

The area of the triangle = ?

To find the area of the isosceles triangle, we can use the formula:

A  = (b x h)/2

b = 20m

h = ?

h² =  (b/2)² + c²

h =   √[(b/2)² + c²]

  =  √[ (10)² + 29²]

  =  30.676

A  = (20 x 30.676)/2

    = 613.52 m²

Therefore, the area of the isosceles triangle is approximately 613.52 m².

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Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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The constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream

The proportional relationship between the number of scoops of ice cream and the amount of milk can be expressed as:

1 scoop of ice cream = 1/2 cup of milk

we evaluate for k the constant of proportion as follows:

1 = k × 1/2

k = 2 {cross multiplication}

if we represent a scoop of ice cream with y and a cup of milk with x, then we can write the equation that represent the relation as:

y = 2x.

In the graph of y = 2x, for every value of x on the x–axis, there are 2 units of x for y on the y–axis, that is when x = 1, y = 2 or x = 3 then y = 6.

For 18 scoops of ice cream, we will evaluate for the amount of cup of milk as follows:

18 = 2x

x = 18/2 {divide through by 2}

x = 9.

In conclusion, he constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream

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Approximately 4% of people are carriers of the cystic fibrosis allele in the United States, according to the Hardy-Weinberg equilibrium.

In the Hardy-Weinberg equilibrium, the frequency of alleles in a population is given by the equation p^2 + 2pq + q^2 = 1, where p and q are the frequencies of the two alleles. For a recessive disease like cystic fibrosis, q^2 represents the frequency of affected individuals, which is 1/2,500 or 0.0004.

Solving for q, we get:

q^2 = 0.0004

q = sqrt(0.0004) = 0.02

Since q represents the frequency of the recessive allele, the frequency of the dominant allele (p) is 1 - q = 0.98.

The frequency of carriers (heterozygous individuals) can be calculated as 2pq, which is approximately:

2pq = 2 * 0.98 * 0.02 = 0.0392

Multiplying by 100 to express the frequency as a percentage and rounding to the nearest whole number, we get:

Carrier frequency ≈ 4%

Therefore, according to the Hardy-Weinberg equilibrium, 4% of people in the US are carriers of the cystic fibrosis allele.

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The statements that must be true are

A. KL = 15

B. JL bisects overline IK

D. JL is the perpendicular bisector of overline IK .

2. JL = 15 units

3. angle IJK = 90

angle JKI = 45

angle kW = 45

The value of x is solved by the information given in the problem

IL = LK

3x = 2x + 5

solving for x

3x - 2x = 5

x = 5

angle IJL = 0.5 angle JIK,

< JIL = < KJL base angles of isosceles triangle

< JIL +  < LJI  + 90 = 180

< LKJ + < KJL + 90 = 180

equating both

< JIL +  < LJI  + 90 = < LKJ + < KJL + 90

< JIL +  < LJI  = < LKJ + < KJL

and  < JIL = < KJL

hence  < LJI  = < LKJ

we can therefore say that

< JIL = < LJI = < LJK = < JKL = 45 degrees

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The width of Cade's picture is 7.09cm. The perimeter of Cade's picture is 101.58 inchs.

What is a rectangular object?

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with four equally long sides.

Given that Jens's picture is 36 centimeters long and 24 centimeters wide.

The area of a rectangular object is the product of length and width.

The area of Jens's picture is 36 × 24 cm² = 864 cm².

1 inches = 2.54 cm

The length of Cade's picture is 48 inches = 48× 24 cm = 121.92 cm

Assume that the width of Cade's picture is x.

The area of Cade's picture is 121.92x cm².

Given that the area of Cade's picture is the same as that of Jens's picture.

According to the question,

121.92x = 864

Divide both sides by 121.92:

x = 7.086

x = 7.09

The perimeter of a rectangular object is 2(l + w)

The perimeter of Cade's picture is 2(121.92 + 7.09) = 258.02 cm

Now convert it cm to inches:

=  258.02/2.54 inch

= 101.58 inchs

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The two rectangles are not similar because the scale factor is not the same.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.

Given dimension of the rectangle is 2 cm and 4 cm. The dimension of the second rectangle is 6 cm and 4 cm.

The scale factor for the two sides should be,

6 / 2 = 3

4 / 4 = 1

Since the scale factor is not constant so the rectangles are not similar.

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The value of 130 mm is 5.118 inches and both are unit of measurement of length.

To convert 130mm to inches, simply divide 130 by 25.4 which is the conversion factor , which is the number of mm in an inch.

This will give you 5.118 inches. Alternatively, you can use an online converter or look up a conversion chart to find the exact conversion. 130mm is a common size for wheel bolt patterns, and the conversion to inches is 4 x 5.118, or 4 x 4 7/8.

This is important to know when purchasing wheels, as they must have the correct fitment for the vehicle they are being installed on.

Additionally, many measurements in the automotive industry are given in metric measurements, so it is important to be familiar with the conversion between metric and imperial units.

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Answer:

Surface Area is the space occupied by a two-dimensional flat surface is called the area.

Total surface area is the area including the base(s) and curved part(s).

Calculating Surface Area:

To find the surface area of a shape, we need to find the measurement (in this case, centimeters) of each face/side and add them together.

Volume:

The amount of space an object/3D shape occupies. (Ex: A circle does not have volume, a sphere, however, does.)

Calculating Volume:

Volume = the length times the width times the height. (Volume = length x width x height)

The derivative of of f(x) = 10 is 0

The derivative of a function is the measure of the rate of change of the function. They are fundamental to the solution of problems in calculus and differential equations.

Here the function is not changing as 10 is a constant. So, if f(x) = c where c is a constant then f'(x) = 0 as the derivative of a constant is always zero.

Mathematically:

           d(f(x))/dx = [tex]\lim_{h \to 0}[/tex] (f(x+h) - f(x))/h

There  is no x to substitute for x + h so no difference is noticed:

             [tex]\lim_{h \to 0}[/tex] (f(x+h) - f(x))/h =   [tex]\lim_{h \to 0}[/tex] (10 - 10)/h = 0

Hence, the derivative of f(x) = 10 is 0

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Based on this rate of defect, a total of 256 calculators to be defective in all 64 crates are expected to be defective

Mathematically, a proportion is calculated by dividing the number of individuals in a population who have the characteristic of interest by the total number of individuals in the population. For example, if we are interested in the proportion of people in a city who are left-handed, we would count the number of left-handed people in the city and divide it by the total population of the city.

Proportions are commonly used in statistics to describe the prevalence of certain characteristics or outcomes in a population, and they can be used to make comparisons between different populations or subgroups within a population. Proportions are typically expressed as fractions, decimals, or percentages, and they can range from 0 (indicating that none of the population has the characteristic of interest) to 1 (indicating that all of the population has the characteristic of interest).

We can start by finding the proportion of defective calculators in the sample of tested calculators. If 2 out of 12 tested calculators were found to be defective, then the proportion of defective calculators in the sample is:

2/12 = 1/6

This means that, on average, we would expect 1 out of every 6 calculators in the population to be defective.

To find the total number of expected defective calculators in all 64 crates, we need to multiply this proportion by the total number of calculators in the population:

(1/6) * (64 crates) * (144 calculators per crate) = 1536/6 = 256

Therefore, we can expect a total of 256 calculators to be defective in all 64 crates.

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Answer:

Step-by-step explanation:

The least common multiple (LCM) of two numbers is the smallest number that is divisible by both of the numbers. The greatest common factor (GCF) of two numbers is the largest number that divides both of the numbers evenly.

For the numbers 12 and 18, we can find the LCM and GCF as follows:

Prime factorize the numbers:

12 = 2^2 * 3

18 = 2 * 3^2

Find the LCM by taking the highest exponent for each prime factor:

LCM(12, 18) = 2^2 * 3^2 = 36

Find the GCF by taking the lowest exponent for each prime factor:

GCF(12, 18) = 2 * 3 = 6

So, the LCM of 12 and 18 is 36 and the GCF is 6.

Answer: the first question answer is 16.03 ft

the answer for number two is here too hand the way to get this answer

answer: Elijah is  standing from the base of the monument 159.14 feet

Step-by-step explanation:

see the attached figure to better understand the problem

In the right triangle ABC

----> by TOA (opposite side divided by the adjacent side)

substitute the given values

solve for AC

therefore

Elijah is  standing from the base of the monument 159.14 feet

Answer: Elijah is standing from the base of the monument - 1

And the answer for number 3 is 850.9 feet

(0, 6) and (1, 2) is the solutions to the given system of equation. Option A is correct.

Given the following system of equation

y = x^2 - 5x + 6

y = -4x + 6

Equating both equations, we will have:

x^2 - 5x + 6 = -4x + 6

Collect the like terms

x^2 - 5x + 6+4x - 6 = 0

x^2 - x = 0

x^2 = x

x = 0, 1

If x = 0

y = -4(0) + 6

y = 6

One of the solution is (0, 6)

If x = 1

y = -4(1) + 6

y = 2

The other solution will be (1, 2)

The solution to the given system of equation will be (0, 6) and (1, 2).

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Answer: 0.75j or 3/4j

Step-by-step explanation:

If we divide (1/3) liter of water into four equal cups each cup will (1/12) liter.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A bottle contains 1/3 liter of water.

Now, If we divide this (1/3) liters of water into 4 equal cups, Each cup will have (1/3)÷4 liters,

= (1/3)×(1/4) liters.

= (1/12) liters.

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The domain of f(g(x)) = (-infinity, -4) U [-4, 4) U (4, infinity).

To find the domain of f(g(x)), we first need to find the domain of g(x) and then the domain of f(x).

The domain of g(x) is the set of all real numbers x such that x + 4 >= 0. So, g(x) is defined for all x >= -4.

To find the domain of f(x), we need to exclude the values of x for which f(x) is not defined. In this case, f(x) is not defined for x = 4. Hence, the domain of f(x) is all real numbers except 4, i.e., (-infinity, 4) U (4, infinity).

Therefore, the domain of f(g(x)) is the set of all real numbers x such that g(x) is defined and g(x) belongs to the domain of f(x). This means that f(g(x)) is defined for all x >= -4, except x = 4.

So, the domain of f(g(x)) = (-infinity, -4) U [-4, 4) U (4, infinity).

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Answer:

1/3

Step-by-step explanation:

constant proportionality = x/y

x1/y1 , x2/y2 , x3/y3 , ....

5/15 , 10/30 , 6/18 , 9/27 , 2/6

= 1/3 , 1/3 , 1/3 , 1/3 , 1/3

since in all the cases x/y = 1/3 ,

Therefore, the contant proportionality in the given table is 1/3

Hope it's helpful..

Answer:

Step-by-step explanation:

Instance variables are created when an object is created with the use of the keyword 'new' and destroyed when the object is destroyed. Static variables are created when the program starts and destroyed when the program stops

The solutions of  y > 3x - 4 are (-5,-3), (-3,4), (0,0) and (0, -4)

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given equation of the graph is y>3x-4.

We have to check each of the ordered pair is a solution or not.

(-5, -3)

Plug in the values ion inequality

-3>3(-5)-4

-3>-15-4

-3>-19

(-5, -3) is the solution of  y>3x-4.

(-3, 4)

4>-9-4

4>-13, So (-3, 4) is the solution of  y>3x-4.

(-4, 0)

0>-12-4

0>-16, So (-4, 0) is the solution of  y>3x-4.

(0, 0)

0>-4 So (0, 0) is the solution of  y>3x-4.

(1, -7)

-7>-3-4 So (1, -7) is not the solution of  y>3x-4.

(1, 1)

1>3-4

1>-1, so (1, 1) is not the solution of  y>3x-4.

(2, 2)

2>6-4

2>2, so (2, 2) is not the solution of  y>3x-4.

(4, 2)

2>12-4, so (4, 2) is not the solution of  y>3x-4.

Hence, (-5,-3), (-3,4) , (0,0) and (0, -4) are the solutions of  y > 3x - 4.

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Answer: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192

Step-by-step explanation:

To find all the factors of a number, multiply all the prime factors of the number in all possible solutions.

Answer:

B=240-2w

Step-by-step explanation:

.

The orientation of the figure may be unchanged, while in other cases it may be altered. For example, in a rotation transformation, the orientation of the vertices will change but the orientation of the figure as a whole will remain unchanged.

The orientation of the vertices in transformation refers to the position and arrangement of the vertices of a figure after a transformation has been applied. A transformation is a change in position or size of a figure, such as a translation, rotation, reflection.

While the orientation of the figure in transformation refers to the overall shape and arrangement of the figure after a transformation has been applied. This can be thought of as the orientation of the entire figure, including the position of its vertices, edges, and any other features.

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Answer:

19/3 (6 1/3)

Step-by-step explanation:

The change in electric potential energy of an alpha particle is:

1.3V/cm

"Information available from the question"

In a region where there is a uniform electric field, the potential, v1, is 1. 3 v at position y1=26 cm.

At position y2=28 cm , the potential, v2, is 3. 9 v.

Now, According to the question:

Calculation of magnitude:

Since  V1 is 1.3 V at position y1=26 cm. At position y2=28 cm, the potential, V2, is 3.9 V

So, We know that

[tex]E =\frac{V_2-V_1}{Y_2-Y_1}[/tex]

[tex]E=\frac{3.9-1.3}{28-26}[/tex]

[tex]E=\frac{2.6}{2}[/tex]

E = 1.3V/cm

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You can make 8 headbands with all the fabric, which is 12 feet of blue fabric and 4 feet of yellow fabric.

To find out how many headbands you can make with all the fabric, you need to convert the fabric measurements to the same unit and then divide by the amount needed for one headband.

First, convert the 12 feet of blue fabric to yards:
12 feet ÷ 3 = 4 yards

Next, convert the 4 feet of yellow fabric to yards:
4 feet ÷ 3 = 1.333 yards

Now, add the two amounts of fabric together:
4 yards + 1.333 yards = 5.333 yards

Finally, divide the total amount of fabric by the amount needed for one headband:
5.333 yards ÷ 2/3 yard = 8 headbands

Therefore, you can make 8 headbands with all the fabric.

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Algebra was made to solve mathematical problems that involve unknown quantities.

Two or more expressions with an Equal sign is called as Equation.

Algebra was developed to solve mathematical problems that involve unknown quantities.

It provides a way to represent and manipulate mathematical equations using symbols and rules, making it easier to solve complex problems and answer questions about relationships between variables.

The earliest known algebraic text is the "Al-jabr wa'l muqabalah" by the Persian mathematician Al-Khwarizmi, which was written in the 9th century.

Hence, Algebra was made to solve mathematical problems that involve unknown quantities.

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The proportion of Alice's porridge is milk is 1/3.

A proportion is an equation that sets two ratios at the same value.

A ratio is a numerical relationship showing how often one value includes or is included inside another. It is used to compare two numbers.

Given:

Alice makes porridge from milk and oats.

The ratio of milk to oats is 1:2.

Let x and 2x be the amount of milk and the number of oats in the porridge respectively.

The proportion of Alice's porridge is milk,

= x/3x

= 1/3

Hence, 1/3rd of the amount of milk is in the porridge.

And 2/3rd of the number of oats is in the porridge.

Therefore, the required proportion is 1/3.

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Answer:

A. f(x) = 0.8 (5)ˣ

Step-by-step explanation:

This is the only one that fits the x and f(x) values

x             0.8 (5)ˣ

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

1              0.8 x 5¹ = 0.8 x 5 = 4

2             0.8 x 5² = 0.8 x 25 = 20

3             0.8 x 5³ = 0.8 x 125 = 100

4             0.8 x 5⁴= 0.8 x 625 = 500

The others will not eve yield proper results for x = 1, you can try them out

Multiply the denominators and numerators together. GCD(12, 5) = 1, keeping the result fraction to the lowest denominator feasible. To put it another way, six times two fifths equals twelve fifths.

For instance, the fraction bar is the line that separates the digits 4 and 5, and 45 is a fraction. Thus, the numerator is the amount above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or number of pieces out of the total, is represented by a numerator.

The top number in a fraction is referred to as the numerator, while the bottom value is referred to as the denominator. 4/5, for instance, is a fraction. In this case, the numerator is 4 and the denominator is 5.

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