A triangle having area of √135 square meter and perimeter 18 meter has a side 4 meter. Find the measurement of the remaining two sides.

a. Shorter side = 10 feet

b. Longer side = 24 feet

c. Hypotenuse = 26 feet

d. The side lengths of the triangle are 10ft, 24ft, and 26ft.

Let the length of the shorter leg be x.

The length of the longer leg of a right triangle is 4ft more than twice the shorter leg. This will be: = 2x + 4

The length of the hypotenuse is 6ft more than twice the shorter leg. This will be: = 2x + 6

Note that the square of the hypothenuse will be equal to the square of the other two sides. This will be:

x² + (2x + 4)² = (2x + 6)²

x² + (2x + 4)(2x + 4) = (2x + 6)(2x + 6)

x² + 4x² + 8x + 8x + 16 = 4x² + 12x + 12x + 36

x² + 4x² + 16x + 16 = 4x² + 24x + 36

5x² + 16x + 16 = 4x² + 24x + 36

Collect like terms

5x² - 4x² + 16x - 24x + 16 - 36 = 0

x² - 8x - 20 = 0

x² - 10x + 2x - 20 = 0

x(x - 10) + 2(x - 10) = 0

Therefore, x - 10 = 0

x =

a. length of the shorter side = 10ft

b. Length of the longer side = 2x + 4 = 2(10) + 4 = 20 + 4 = 24ft

c. length of the hypotenuse = 2x + 6 = 2(10) + 6 = 20 + 6 = 26ft

d. The side lengths of the triangle are 10ft, 24ft, and 26ft.

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The complete question is:

The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. The length of the hypotenuse is 6ft more than twice the length of the shorter leg. Find the side lengths of the triangle.

a. Find the length of the shorter side

b. Find the length of the longer side

c. Find the length of the hypotenuse

d. Find the side lengths of the triangle

There are 7 people in Mr. Wilson's class, as Zach is the second person and Mary is the seventh person.

To calculate the total number of people in the class, we can use the formula 2x = 7, where x is the total number of people. Solving for x, we get x = 7.

To determine the number of people in Mr. Wilson's class, we can use the formula for the number of people in a circle, which is N = 2(n-1), where n is the number of people standing opposite each other in the circle. In this case, n is 2 (Zach and Mary). Therefore, N = 2(2-1) = 2 people. However, since there are 7 people in total in the circle, we can conclude that the number of people in Mr. Wilson's class is 7. To explain further, based on the given information, we can say that Zach is the second person, which means there are 2 people before him in the circle. Therefore, there are 7 people in Mr. Wilson's class. To further explain, we can break down the equation as follows: The person opposite of Zach is the seventh person, or 7th, so we can say that 7 is equal to the number of people in the class multiplied by 2, or 2x. Then, solving for x, we get x = 7. This means that the total number of people in the class is 7.

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The Parent function f(x) = (x) is Horizontal shift: Right 2 units and Vertical shift: Down 6 units.

A family of functions simplest version of an equation is a parent function. A family of functions is a group of functions that exhibit the same traits as or undergo the same transformations as their parent function. There are various degree values that can be used to represent a parent function, including degrees 1, 2 and 3.

The parent function is the simplest form of the type of function given

f(x) = (x)

The transformation being described is from f(x) = (x) to g(x) = 3(x-2) -6

f(x) = (x)--> g(x) = 3(x-2) -6

The horizontal shift depends on the value of h. the horizontal shift is described as:

g(x) = f(x+h) - The graph is shifted to the left h units.

g(x) = f(x-h) - The graph is shifted to the right h units.

Horizontal shift: Right 2 units

The vertical shift depends on the value of k. The vertical shift is described as:

g(x) = f(x)+k – The graph is shifted up k units.

g(x) = f(x)-k – The graph is shifted down k units.

Vertical Shift: Down 6 units

The graph is reflected about the x-axis when

g(x) = -f(x)

Reflection about the x-axis is none

The graph is reflected about the y-axis when

g(x) = f(-x)

Reflection about the y-axis is none

Compare and list the transformations.

Parents function: f(x) = (x)

Horizontal shifts: Right 2 units

Vertical shifts: Down 6 units

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Answer:

see below

Step-by-step explanation:

Independent & dependent variables

An independent variable is the input value, also known as the x-value. A dependent variable is the output value, or the y-value.

The five types of variables are - dependent variables, independent variables, control variables, random variables, and categorical variables.

What are variables?

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

Any thing that has multiple possible values is considered a variable. The 5 different sorts of variables are:

Dependent Variables: A variable whose state quality depends on the estimation of another variable is referred to as a dependent variable.

Independent Variables: Variables with independent values are those whose values are not affected by change.

Control Variables: These variables, known as control variables, are impacted by changes in independent variables in terms of their values.

Random Variables: Mathematical representations of numbers or objects that depend on chance events are known as random variables.

Categorical Variables: Variables that can only take one of a small number of often fixed values are referred to as categorical variables, sometimes known as qualitative variables.

Therefore, there are five major types of variables.

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Answer: The 4 in front of the h.

Step-by-step explanation: A coefficient simply means the number in front of a variable. If its a plain variable like x, the coefficient is basically 1.

the answer is 6h +1x

because we add the 4h and 2 than if there is one x that means is one if there is that will be 2x

i hope that helps you

thanku

(2, 14) is not a solution to the system of equations.

An equation is a mathematical statement consisting of an expression or a system of expressions that states equality or equivalence between two values. Equations are typically used to describe relationships between different variables, such as x + 2 = 4. Equations can also be used to solve for an unknown value, such as x = 4 − 2.

(2, 14): No, this is not a solution to the system of equations.
When we plug in x = 2 and y = 14 into the first equation,
we get -3(2) + 8 = 2,
which does not equal 14.
When we plug in x = 2 and y = 14 into the second equation,
we get 6(2) + 2(14) = 28,
which does not equal 16.
Therefore, (2, 14) is not a solution to the system of equations.

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The probability that the greater of the two numbers obtained is 3 is A) 4/n(n - 1).

It is given that two chips are drawn at random without replacement from a bowl which contains n chips numbered 1 through n and n ≥ 3.

We are asked to find the probability that the greater of the two numbers obtained is 3.

The possible outcomes when two chips are drawn at random and the greater of the two numbers obtained is 3 = (1,3) and (2, 3)

So, there are only 2 outcomes

Total possible outcomes = ⁿC₂ = n(n - 1)/2

So, Probability = 2/(n(n - 1)/2)

                        = 4/n(n - 1)

Hence, the probability of getting 3 as the greatest of the two numbers is 4/n(n - 1)

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The ice cream no of tasters relative frequency. The correct option is B.

Strawberry                4 0.2

Choco Nuts              12 0.6

orange mints               4 0.2

Wagenlucht Ice Cream Company is always trying to create new flavors of ice cream. They are market-testing three kinds to find out which one has the best chance of becoming popular.

They give small samples of each to 20 people at a grocery store. 4 ice cream tasters preferred the Strawberry Cream, 12 preferred Choco- Nuts, and 4 loved the Orange Mint. Construct a Pareto chart to represent these preferences. Choose the vertical scale so that the relative frequencies are represented.

Ice cream no of tasters relative frequency.

Strawberry                4 0.2

Choco Nuts              12 0.6

orange mints               4 0.2

Relative frequency is frequency over the total frequency.

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Answer: What is the question itself you need help with?

Step-by-step explanation:

The graph of the inequalities y ≥ (1/3)x - 2 and y ≤ -4x - 2 is attached

An equation is an expression that shows the relationship between two or more numbers and variables.

The slope intercept form of a line is:

y = mx + b

where m is the slope and b is the y intercept

Inequalities are expressions that show the non equal comparison of two or more numbers and variables

Given the inequalities:

y ≥ (1/3)x - 2

and:

y ≤ -4x - 2

The graph of the inequalities are attached

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The height of the swing path for a performer whose maximum speed is 7 meters per second is 0. 35m

The formula for calculating the maximum speed of the swing is given by the function:

v = 2gh

Given that the parameters are;

From the information given, we have that;

v = 7 meters per second

g = 9. 8 meters per square second

Now, substitute the values into the formula, we get;

7 = 2× 9. 8 × h

Multiply the values, we get'

7 = 19.6 h

Divide both sides by the coefficient of h, we get;

h = 7/19.6

h = 0.35 m

Thus, the value is 0.35 m

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The significance of the z-score will be 1.6226.

According to the question,

The given values are:

Mean,

μ = 2.46

Standard deviation,

σ = 0.53

GPA,

x'= 3.32

Now,

→ The z-score will be:

= (x-μ)/σ

By putting the given values, we get

= [tex]\frac{3.32 - 2.46}{0.53}[/tex]  ( by using subtraction)

= [tex]\frac{0.86}{0.53}[/tex]           (by using division)

= 1.6226

So, the z-score for a GPA of 3.32 is 1.6226.

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The measure of angle D is, 67.4°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In triangle DEF, DE = 21, EF = 24, and DF = 26.

By the formula, we get;

⇒ sin θ = Opposite / Hypotenuse

Substitute all the values, we get;

⇒ sin D = 24/26

⇒ sin D = 0.9430

⇒ ∠D = sin⁻¹ (0.9430)

⇒ ∠D = 67.4°

Thus, The measure of angle D is, 67.4°.

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The news article related to a current, specific U.S. trade barrier issue is given below.

Trade barriers are government-induced restrictions on international trade.The barriers can take many forms, including the following:

Tariffs,Non-tariff barriers to trade, Import licenses, Export licenses,Import quotas, Subsidies, Voluntary Export Restraints, requirements, Embargo, Currency devaluation, Trade restriction.

Trade barriers such as tariffs raise prices and reduce available quantities of goods and services for U.S. businesses and consumers, that lead to lower income, reduced employment, and lower economic output.

An increase in U.S. trade barries may also result in a decline in international trade in the United States.

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This problem can be solved using a system of equations. Let x be the number of nickels and y be the number of dimes. We know that the total number of coins is 23, so we can write the first equation:

x + y = 23

We also know that the total value of the coins is $2.20. Since nickels are worth $0.05 and dimes are worth $0.10, we can write the second equation:

0.05x + 0.1y = 2.2

Now we have a system of two equations with two variables. To solve for x and y, we can use substitution or elimination method.

Substitution method:

We can solve for one variable in one equation, and substitute it into the other equation.

From the first equation: x + y = 23

y = 23 - x

Substitute this into the second equation

0.05x + 0.1(23-x) = 2.2

0.05x + 2.3 - 0.1x = 2.2

-0.05x = -0.1

x = 2

So, Bob has 2 nickels in his pocket. We can substitute this value of x back into the first equation to find the number of dimes:

x + y = 23

2 + y = 23

y = 21

Bob has 21 dimes in his pocket.

Elimination method

We can multiply one equation by a constant so that when we add the two equations, one variable will cancel out.

x + y = 23

0.05x + 0.1y = 2.2

multiply the first equation by 5

5x + 5y = 115

add both equations

5x + 5y = 115

0.05x + 0.1y = 2.2

5x + 0.05x = 115+2.2

5.05x = 117.2

x = 23.2/5.05 = 2

So, Bob has 2 nickels in his pocket. We can substitute this value of x back into the first equation to find the number of dimes:

x + y = 23

2 + y = 23

y = 21

Bob has 21 dimes in his pocket.

Both methods give the same result, which is Bob has 2 nickels and 21 dimes in his pocket.

Answer:

Step-by-step explanation:

x + y = 23

.05x + .10y = 2.20

5x + 10y = 220

-5x -5y = 115

5y = 105

y = 21 dimes

x + 21 = 23

x = 2 nickels

(2 nickels, 21 dimes)

The estimated minimum monthly cost of natural gas for 1 year is represented by the function C(a) = 3 - 42a + 187.

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Answer:

Mean of the sampling distribution: 0.86

Standard deviation of the sampling distribution: 0.0000119

Step-by-step explanation:

The cross product of two vectors [tex]\vec{A} =3\hat{i} +2\hat{j}-4\hat{k}[/tex] and [tex]\vec{B}=2\hat{i}-3\hat{j}-6\hat{k}[/tex] is -24[tex]\hat{i}[/tex] + 10[tex]\hat{j}[/tex] - 13[tex]\hat{k}[/tex].

The two vectors are [tex]\vec{A} =3\hat{i} +2\hat{j}-4\hat{k}[/tex] and [tex]\vec{B}=2\hat{i}-3\hat{j}-6\hat{k}[/tex].

We may utilise properties to get the cross product of two vectors. Finding the cross product of two vectors depends heavily on features like the anti-commutative property and the zero vector property.

The area of a rectangle with sides A and B is represented by the cross product of two vectors, which is equal to the product of their magnitudes.

From the vector [tex]\vec{A} =3\hat{i} +2\hat{j}-4\hat{k}[/tex], a(1) = 3, a(2) = 2, a(3) = -4.

From the vector [tex]\vec{B}=2\hat{i}-3\hat{j}-6\hat{k}[/tex], b(1) = 2, b(2) = -3, b(3) = -6.

We determine the cross product using the matrix.

[tex]\vec{A}\times\vec{B}=\begin{vmatrix}\hat{i} &\hat{j} &\hat{k} \\ a(1) &a(2) &a(3) \\ b(1) & b(2) & b(3)\end{vmatrix}[/tex]

Now solving the matrix

[tex]\vec{A}\times\vec{B}=\hat{i}\begin{vmatrix}a(2) &a(3) \\ b(2) & b(3)\end{vmatrix}-\hat{j}\begin{vmatrix}a(1) &a(3) \\ b(1) & b(3)\end{vmatrix}+\hat{k}\begin{vmatrix}a(1) &a(2) \\ b(1) & b(2)\end{vmatrix}[/tex]

[tex]\vec{A}\times\vec{B}[/tex] = [tex]\hat{i}[/tex](a(2)b(3)-a(3)b(2)) - [tex]\hat{j}[/tex](a(1)b(3)-a(3)b(1)) + [tex]\hat{k}[/tex](a(1)b(2)-a(2)b(1))

Now putting the values

[tex]\vec{A}\times\vec{B}[/tex] = [tex]\hat{i}[/tex](2·(-6) - (-4)·(-3)) - [tex]\hat{j}[/tex](3·(-6) - (-4)·2) + [tex]\hat{k}[/tex](3·(-3)-2·2)

[tex]\vec{A}\times\vec{B}[/tex] = [tex]\hat{i}[/tex](-12 - 12) - [tex]\hat{j}[/tex](-18 + 8) + [tex]\hat{k}[/tex](-9 - 4)

Now simplify

[tex]\vec{A}\times\vec{B}[/tex] = -24[tex]\hat{i}[/tex] + 10[tex]\hat{j}[/tex] - 13[tex]\hat{k}[/tex]

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The complete question is:

Find the cross product of two vectors [tex]\vec{A} =3\hat{i} +2\hat{j}-4\hat{k}[/tex] and [tex]\vec{B}=2\hat{i}-3\hat{j}-6\hat{k}[/tex].

If a negative charge is spread uniformly over the surface of the balloon, it will contract.

A spherical balloon that is initially uncharged will expand if the positive charge is spread uniformly over its surface. This is because the positive charge creates an electrostatic force that pushes the surface of the balloon away from the center, causing it to expand.

On the other hand, if a negative charge is spread uniformly over the surface of the balloon, it will contract. This is because the negative charge creates an electrostatic force that pulls the surface of the balloon towards the center, causing it to contract.

In both cases, the magnitude of the force depends on the amount of charge added to the surface and the distance between the charged particles. However, the direction of the force is determined by the sign of the charge, with a positive charge causing the balloon to expand and a negative charge causing the balloon to contract.

Therefore, If a negative charge is spread uniformly over the surface of the balloon, it will contract.

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Total integers between 30 and 50, inclusive, and 21 - 5 = 16 integers that are not possible total scores.

For a score of 30, the number of correct answers would be 6 (30 / 5), and for a score of 50, the number of correct answers would be 10.

Thus, the possible number of correct answers is between 6 and 10, inclusive. So, the possible total scores are [30, 35, 40, 45, 50].

Therefore, there are 50 - 30 + 1 = 21 total integers between 30 and 50, inclusive, and 21 - 5 = 16 integers that are not possible total scores.

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The value of a car purchased for 16400 dollars will depreciate at 12.5% per year.

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hence the value of the given limit is =4.

In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in the theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals. The upper limit and lower limit for definite integrals are correctly defined. whereas unbounded expressions of indeterminate integrals

We have f(x) = 4x+5

and we have to evaluate the limit-

[tex]\lim_{h \to0 }\frac{f(2+h)-f(2)}{h} \\[/tex]

Now, f(2+h)=4(2+h)+5

                 = 8+4h+5

                 =4h+13

f(2+h)=4h+13

and,

f(2)= 2*4+5=13

now the limit is-

[tex]\lim_{h \to 0} \frac{4h+13-13}{h}\\\\ \lim_{h \to 0} \frac{4h}{h}=4.[/tex]

hence the value of the given limit is =4.

the complete question is -

Fill in  the blanks.

evaluate  [tex]\lim_{h \to0 }\frac{f(2+h)-f(2)}{h} \\[/tex] ,where f(x)=4x 5 . if the limit does not exist enter DNE.   --------

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The amount of money spent by Jose on the purchase of Hotdogs is, $6.325

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

At the baseball game,

José bought 2 hotdogs at a cost of 2.75 each,

He also gave the vendor a 15% tip,

Amount spent = ?

15% of total cost of  hotdogs = 2x2.75x15/100

                                               =  0.825

Amount spent =  Price of 2 hotdogs + Tip

                        =  5.5  + 0.825

                        =   6.325

Thus, the total amount spent $6.325

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Acute triangle is the answer

An acute triangle has three acute angles (less than 90 degrees)

An obtuse angle has one obtuse angle (greater than 90 degrees)

A right triangle would have a perfect 90 degree angle

An equiangular triangle would have all equal angles.

Hope this helps!

We can say that a's reduced row echelon form will have no zero rows.

Systems of linear equations can be solved using a type of matrix called reduced row echelon form.

If Ax = b has a unique solution for every b, then A must have full row rank, meaning that its reduced row echelon form will have no zero rows. This means that the reduced row echelon form of A will have a leading 1 in every non-zero row and will be in the form of an identity matrix. Therefore, the reduced row echelon form of A is the invertible matrix and A has a unique solution for every b.

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Answer:

Area = 4ab - 2(ab-b^2) - ab - ab

simplified version: 2ab -2(ab-b^2)

Step-by-step explanation:

- instead of finding the area of shaded region, we can take a different appraoch. We can subtract the non-shaded region from the overall rectangle because white triangles are easier to measure.

area of rectangle is = length * base

= 2b * 2a

=4ab

1. Area of Left white triangle = 1/2 (base)(height)

=1/2 (2a-2b)(2b)

=1/2 (4ab-4b^2)

=1/2 4(ab-b^2)

=2(ab-b^2)

2. Area of bottom right triangle= 1/2 (base)(height)

=1/2 (2a)(b)

=ab

3. Area of Top Right triangle: 1/2 (base)(height)

=1/2 (2b-b)(2a)

=1/2 (b)(2a)

=ab

Area of grey triangle = area of rectangle - area of triangle 1 - area of triangle 2 - area of triangle 3

Area = 4ab - 2(ab-b^2) - ab - ab

Area = 4ab -2(ab-b^2) - 2ab

Area = 4ab - 2ab -2(ab-b^2)

Area = 2ab -2(ab-b^2)

The area left for children for playing 114464 sq. m

As per the given data inside a park:

The length of the park is 400 m

The breadth of the park is 300 m

The formula for the area of the park = Length × Breadth

= (400 × 300) sq. m

= 120000 sq. m

The width of the walking track inside the park is 4 m

The length of the park without the walking track

= 400 − (4 + 4) m

= 400 − 8 m

= 392 m

The breadth of the park without the walking track

= 300 − (4 + 2) m

= 300 − 8 m

=292 m

Area of the park without the walking track:

= 392 × 292

= 114464 sq. m

Therefore the area left for children for playing other than the walking track is 114464 sq. m.

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No, Joe is not correct.

The percentile score is a measure of relative standing, indicating the percentage of scores that fall below a certain score. So, if Joe scored in the 30th percentile, it means that 30% of the scores on the test are below his score, and 70% of the scores are above his score.

This does not mean that he scored better than 70% of the people who took the test; it only means that his score is better than 30% of the scores.

The 30th percentile means that Joe scored higher than 30% of the people who took the test and lower than 70% of the people who took the test. So, Joe cannot claim that he scored better than 70% of the people who took the test.

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The cost of renting a tank is: 235.5 * 3 = $706.5

What is the volume of a cylinder?

The amount of space inside a cylinder is its volume. You can find it by dividing the base area by the height. V = πr²h is the formula for the volume of a cylinder with base radius "r" and height "h."

Here, we have

Given: A company rents water tanks shaped like cylinders. Each tank has a diameter of 10 feet and a height of 3 feet The cost is 3$.

We have to find the volume of one tank and multiply it by the cost of renting the tank per cubic foot.

The volume of a cylinder is:

V = πr²h

where r = radius

h = height

Each tank has a diameter of 10 feet (radius = 5 feet) and a height of 3 feet.

The volume of the tank is therefore:

V =  π(5)²(3)

V = 235.5ft

The cost of renting is $3 per cubic foot.

Hence, the cost of renting a tank is:

235.5 * 3 = $706.5

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The rate of change of the area is 30π when the circumference is 10π.

The formula for the circumference of a circle is given by:

C= 2πr

where r is the radius and π is approximately 3.14.

If the circumference is 10π, then r = 5.

Let A be the area of the circle. The formula for the area of a circle is given by A = πr².

Taking the derivative of the area with respect to time, we get:

dA/dt = (2πr) dr/dt.

Substituting the expression for r and dr/dt, where r = 5 and dr/dt = 3, we get:

dA/dt = 2π(5)(3) = 30π.

Therefore, the rate of change of the area is 30π when the circumference is 10π.

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