(i) Write an equation to represent the relationship between the two unknows x and y.​

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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\(\\ \rm\longmapsto (x-5)^2+3(x-5)-4\)

\(\\ \rm\longmapsto x^2-10x+5^2+3x-15-4\)

\(\\ \rm\longmapsto x^2-7x+25-19\)

\(\\ \rm\longmapsto x^2-7x+6\)

The given function is:

Split 25 into two using factors of 144 (-16 and -9):

Factorize each pair of expressions:

Factorize further using the difference of two squares:

Hence, the factored form of the function is:

EXPLANATION.

The whole numbers are the same natural numbers that start from zero to infinity, they are positive and negative, for example in the number line we can see them from zero to positive infinity, and from zero to negative infinity.

Whole numbers express a complete unit, this means that they do not have an integer part and a decimal part.

Now according to what has already been mentioned, we can see in the exercise that the integers are 9 and 1.00000, which we must enclose in a circle.

\(Answer: \large\boxed{Cos(\theta_{1} )=\frac{84}{85}}\)

Step-by-step explanation:

Thinking about a triangle in Quadrant IV, we can imagine sin as opposite/hypotenuse. Therefore, the hypotenuse is 85 and the opposite angle is -13. To find the adjacent angle, we use the pythagorean theorum,

\(a^2+b^2=c^2\)

\(-13^2+b^2=85^2\)

\(169+b^2=7225\)

\(b^2=7056\)

\(b=\sqrt{7056}\)

\(b=\pm84\)

Taking only the positive number, the adjacent angle is 84

Now that we have all 3 sides, we can find the cosine.

Cosine is adjacent/hypotenuse

Therefore,

\(Cos(\theta_{1} )=\frac{84}{85}\)

See the attached picture:

Answer:

Step-by-step explanation:

Answer:

On the map, the endpoint of the string of buoys are located at (6,18) and (18,34). The midpoint of the string is located at (12,26). Each anchor is located at the midpoint of one of the two halves of the string of  buoys. We can illustrate this using a sketch like this

The first anchor, A1, is located at the midpoint of (6,18) and (12,26):

(6+12/2, 18+26/2)= (9,22)

The second anchor, A2, is located at the midpoint of (12,26) and (18,34) :

(12+18/2, 26/34/2) = ( 15,30)

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

This is impossible. x+1 is not x+2

Variables are always the same: x=x

Answer:

No their isn't

Step-by-step explanation:

156 short sleeve shirts were sold in Emily's clothing store during the given period.

To determine the number of short sleeve shirts sold in Emily's clothing store, we need to calculate 3/10 of the total number of shirts sold, since the ratio of short sleeve to long sleeve shirts is 3:7.

We know that the total number of shirts sold is 520. To find 3/10 of 520, we multiply 520 by 3/10:

3/10 * 520 = (3/10) * 520 = (3 * 520) / 10 = 1560 / 10 = 156

Therefore, 156 short sleeve shirts were sold in Emily's clothing store in August.

Alternatively, we can solve this problem using proportions. If we set up the proportion:

(3/10) = x/520,

where x represents the number of short sleeve shirts sold, we can cross-multiply to find:

10x = 3 * 520,

10x = 1560,

x = 156.

Hence, 156 short sleeve shirts were sold in Emily's clothing store during the given period.

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The statement which is not true about the given function is lim f(x) = [0, -∞).

Given, the function f (x) = (x - 1) e^(-2x)

The graph of the function f(x) = (x - 1) e^(-2x) is shown below:

Domain of the given function is all real numbers, which is true. As we see from the graph, the curve is decreasing, which means it approaches negative infinity as x approaches infinity.Limit, lim f(x) = [0, -∞) is not true.

There is no vertical asymptote, which is true.As we see from the graph, the curve passes through the points (0, -1) and (1, 0), which is true.From the above explanation, we can say that option B is not true.

We have given a function f(x) = (x - 1) e^(-2x). We need to find the statement which is not true about this function.The domain of the given function is all real numbers. We can say that the domain of the function is all real numbers because the function contains exponential terms and polynomial terms, both can have any real value, which is true.

The limit of the function as x approaches infinity is negative infinity, which is true.The function does not have any vertical asymptote, which is also true.The function passes through the points (0, -1) and (1, 0), which is true.We have to find the statement that is not true, which is lim f(x) = [0, -∞), this statement is not true because we can see from the graph of the function that the limit of the function as x approaches infinity is negative infinity.

So, this statement is not true.

Hence, the statement which is not true about the given function is lim f(x) = [0, -∞).

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the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

To find the set difference C - A, we need to remove all elements from A that are also present in C. Let's examine the sets:

C = {0, 6, 12, 18}

A = {2, 4, 6, 8, 10, 12}

We compare each element of A with the elements of C. If an element from A is found in C, we exclude it from the result. After the comparison, we find that the elements 2, 4, 8, 10 are not present in C.

Thus, the set difference C - A is {0, 18}, as these are the elements that remain in C after removing the common elements with A.

Therefore, the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

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Answer:

Top: 33°

Bottom: 70°

Step-by-step explanation:

For the top one, we are trying to find an unknown angle ∠WUV.

we have a 90° angle ∠TUV, where ∠TUW is 57°.

90 - 57 = 33

so, ∠WUV = 33°.

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

For the second one, we are trying to find the size of ∠ACB (5x+20). The problem establishes it is on a straight Line ∠BCD, with ∠ACD (10x+10) adding together with ∠ACB to equal 180, so let's start there.

We know Both of those statements above add up to equal 180°, so let's add them together to = 180.

(5x+20) + (10x + 10) = 180

15x + 30 = 180

Now we need to solve for X. First, isolate the variable by subtracting 30 from both sides.

15x = 150.

Next, just divide both sides by the coefficient (15).

x = 10.

Now just plug it in to the equation for the measurement of our angle.

5(10) + 20

50 + 20

70

So, the size of ∠ACB = 70°.

Answer:

-0.8 - 0.5b - 1.4c

Step-by-step explanation:

Take the b and the c away

Then times the 0.2 by all the numbers but don't add them

Once your done you and the b and c back to you equation

If the test scores are normally distributed then the exam score corresponding to a standard score of -0.95 is 83.15  .

In the question ,

it is given that ,

the mean of the normally distributed score is (μ) = 86 ;

the standard deviation of the normally distributed is(σ)  = 3 ;

we have to find the exam score(z score) corresponding to the standard score of -0.95 .

we know that z-score for the population mean (μ) and standard deviation(σ) is

Z = (x - μ)/σ

rewriting ,

we get ,

x = μ + Zσ

given that standard score (z) is = -0.95 .

the exam score corresponding to z = -0.95 can be calculated using the formula ,

x = μ + Zσ

Substituting Z = -0.95 , μ = 86 and σ = 3 ;

we get ,

x = 86 + (-0.95)×3

x = 86 - 2.85

x = 83.15

Therefore , the exam score corresponding to the standard score of "-0.95" is 83.15  .

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Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

Using inequalities we know that x=68 and x=66 respectively.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

So, solve the inequalities as follows:

x+3>70

x>70-3

x>67

Then, it will be x = 68.

Then,

x+3<70

x<70-3

x<67

Then, it will be s = 66.

Therefore, using inequalities we know that x=68 and x=66 respectively.

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The air pressure at the peak of Mount Marcy is approximately 164.17 pascals.

Air pressure, also known as atmospheric pressure, is the force exerted by the weight of the Earth's atmosphere on any given surface. It is the weight of the column of air that extends from the Earth's surface up to the top of the atmosphere.

The Pascal (symbol: Pa) is the SI (International System of Units) unit of pressure, named after the French mathematician and physicist Blaise Pascal. One pascal is defined as the pressure exerted by the force of one Newton on an area of one square meter. In other words, 1 Pa = 1 N/m².

We are given the formula that relates the altitude (a) and the atmospheric air pressure (P):

a = 15,500 (5 - log₁0 P)

We are also given that the altitude at the peak of Mount Marcy is 1629 meters. We can use this information to find the atmospheric air pressure at the peak of Mount Marcy by plugging in a = 1629 and solving for P:

1629 = 15,500 (5 - log₁0 P)

Dividing both sides by 15,500, we get:

(5 - log₁0 P) = 1629 / 15,500

Subtracting 5 from both sides, we get:

-log₁0 P = (1629 / 15,500) - 5

Simplifying the right-hand side, we get:

-log₁0 P = -1.5454

Taking the inverse logarithm (base 10) of both sides, we get:

P = 10⁻¹.⁵⁴⁵⁴

Using a calculator, we can evaluate this expression to get:

P ≈ 164.17 pascals

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The slope-intercept form of the equation -15y=18x+7 will be y= -1.2x-0.46.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line. If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that, the equation is -15y=18x+7. We have to write the equation in the slope-intercept form.

The slope-intercept form of the equation is,

y=mx+c

Where, m is the slope and c is the intercept,

-15y=18x+7

y=(-18/15)+(-7/15)

y= -1.2x-0.46

Thus, the slope-intercept form of the equation -15y=18x+7 will be y= -1.2x-0.46.

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Solution

Step 1

Write the area of a circle formula

Step 2:

Substitute the value of r = 7 ft

Answer:

1128 Yard²

Step-by-step explanation:

From the question,

The surface area of a triangular prism is

A = bh+H(a+b+c)...................... Equation 1

Where a = First side of the triangular face, b = base of the triangular face, c = the other side of the triangular face, H = heigth of the prism, h = height of the triangular face

Given: a = 15 yard, b = 18 yards, c = 15 yards, h = 12 yards, H = 19 yards.

Substitute these values into equation 1

A = (18×12)+ 19(15+15+18)

A = 216+19(48)

A = 216+912

A = 1128 Yard²

Hence the surface area of the triangular prism is 1128 yard²

Answer:

Range

Step-by-step explanation:

To obtain the difference between two extreme values (peak or highest and the bottom or lowest) value of a distribution, the statistical measure which best captures this differ ce is the RANGE. As the range is specifically used for determining the variation between the highest and lowest value of dataset.

The range is defined Mathematically as ;

Range = Maximum value - Minimum value

Hence. To obtain the difference between the maximum and least number of votes, the range is the best measure to use.

Answer:

The gas bill increases by $50

Step-by-step explanation:

We know that the increase in gas bills is directly proportional to the temperature setting. Let's take the increase in gas bills as g and increase in temperature setting as t. Thus, this can be written as:

g ∝ t

In every proportionality, there is a constant k, so it will be:

g = kt

It is mentioned that when the temperature setting increases by 4, the gas bill increases by $20, so in terms of the constant, we can write it as:

20 = k 4

We don't know the value of the constant, so we have to first find it out.

k = 20 ÷ 4

k = 5

Thus,

g = 5t

Now that we know the value of the constant, we can find by how much the gas bill will increase if the temperature setting increases by 10.

g = 5 × 10

g = 50

∴ the gas bill increases by $50 when the temperature setting increases by 10 degrees Fahrenheit.

In mathematics, the use of "es" and "son" can refer to different concepts.

"Es" is typically used when talking about powers or exponents. An exponent is a number that indicates how many times a base number is multiplied by itself. The base number is written before the exponent, and the exponent is written as a small number to the right and above the base number.

For example, in the expression "2^3" (read as "two to the power of three"), the base number is 2 and the exponent is 3. This means that 2 is multiplied by itself 3 times, or 2 x 2 x 2 = 8.

On the other hand, "son" is used to indicate a mathematical operation known as "summation." In mathematics, summation is the addition of a sequence of numbers.

The summation notation is represented by the Greek letter capital sigma “Σ” (sigma) and an index, which is the variable that is being summed, followed by the limits of the sum and the mathematical expression. For example, the summation notation Σ(n=1)^3 (n+1) is read as “the sum of (n+1) as n goes from 1 to 3”. That will be (1+1) + (2+1) + (3+1)=6

In summary, when doing math, it is proper to use "es" when talking about powers or exponents, and "son" when talking about summation or adding a sequence of numbers.

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The solution of the equations is x = 7 and y =- 10. The value of x and y will satisfy the given equations.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Given equations are  

2x + y = 4 ......(i)

3x + 2y = 1 ....(ii)

There are various methods to solve of equations.

To solve the equations, use the elimination method:

Multiply equation (i) by 2 and then subtract it from (ii):

3x + 2y = 1

4x + 2y = 8

(-)  (-)       (-)

_________

-x           = -7

x = 7

Putting x = 7  in equation (i):

2×7 + y = 4

14 + y = 4

y = 4 - 14

y = -10

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Answer:

y = 5(3)+3

= 15 +3

= 18

y = 18

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The relation between the radius and the diameter of a circle is given by:

r = d/2

where r is the radius and d the diameter.

Hence, radius is half of a diameter

Linear pairs are two adjacent angles that form a straight line, with their sum equal to 180 degrees.

To determine which of the given angle pairs are linear pairs, we'll check if they meet these criteria.

a. ∠SRT and ∠TRV: These angles are adjacent and form a straight line. They are a linear pair.
b. ∠SRT and ∠TRU: These angles do not form a straight line, so they are not a linear pair.
c. ∠VRW and ∠WRS: These angles are adjacent and form a straight line. They are a linear pair.
d. ∠VRU and ∠URS: These angles do not form a straight line, so they are not a linear pair.
e. ∠URW and ∠WRS: These angles do not form a straight line, so they are not a linear pair.

Thus, the linear pairs are: ∠SRT and ∠TRV, and ∠VRW and ∠WRS.

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