An artist is going to cut four similar righttriangles from a rectangular piece of paperlike the one shown to the right. What is thedistance from B and D to the diagonal AC?Write an equation and solve, showing ALLthe work.

We have the next function

First we need to make h(x)=y

Then we make x=y and y=x

Then we isolate the y

Therefore the inverse function is

Given that;

Line a and b are two straight lines cut by two transversal lines l and m.

The tranversal line l shows that;

But also;

Thus,

Then, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

Thus, line l is parallel to m

The perimeter of the rectangle is 6.89

Perimeter of the rectangle:

The perimeter (P) of a rectangle is the total length of all the sides of the rectangle.

The formula for the perimeter of the rectangle is

P = 2(l + w)

The letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle.

Given,

Here we have the graph with the following points:

(-3/2, -1 7/9), (7/2, -1 7/9), (7/2, 3 2/9), and (-3/2 3 2/9)

Now we need to find the perimeter of the rectangle.

To calculate the perimeter, first we have to find the length and width of the rectangle.

To calculate the length, we have to use the values of x axis,

That is,

=> -3/2 + 7/2

=> (-3+7)/2

=> 4/2

=> 2

Therefore, the length of the rectangle is 2.

Now, we have to find the width of the rectangle using the y axis coordinates,

=> -1 7/9 + 3 2/9

Convert the mixed fraction into normal form, then we get,

=> -16/9 + 29/9

=> (-16 + 29)/9

=> 13/9

Therefore, the width of the rectangle is 13/9

Now, we have to use this to calculate the perimeter of the triangle,

P = 2 (2 + 13/9)

P = 2 ((18+13)/9)

P = 2 (31/9)

P = 62/9

P = 6.89

Therefore, the perimeter of the rectangle is 6.89.

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     The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

  For instance, the equation -2x²-8x = 10 consists of the two equations  is rewritten in the form of 2(x-p)²+ q = 0. , which are separated by the 'equal' sign.

Answer :q = -2

-2x²-8x = 10 (divide both sides by -2)

x² + 4x = -5 (Apply completing the square method)

x² + 4x + (4/2)²= -5 + (4/2)²

x² + 4x + 2²= -5 + 2²    (reduce left hand side using a²+2ab+b² =  (a+b)² )

(x+2)² = -5 +4

(x+2)² = -1

(x+2)² + 1 = 0   (multiply both sides by -2)

(-2)(x+2)² + 1 (-2) = 0

-2[x - (-2)]² + (-2) = 0  ---> compare this with -2(x-p)² + q = 0

We can see that p = 2 and q = -2

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By solving matrices  we get,

[tex]A+B= \left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] , C-B=\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right] \\\\\\\\A+B+C = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]

A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity. As an illustration, consider a matrix with two rows and three columns.

Adding matrices, subtracting matrices, and multiplying matrices are the three algebraic operations that make up the majority of matrix operations. Array of numbers or expressions arranged in rows and columns is called a matrix. The field of mathematics has several useful uses for matrices.

Here the matrices A, B and C are given in the question, so we use matrix addition and matrix subraction operations to solve the question.  

When solving by using the matrices solving method we get

[tex]A+B=\left[\begin{array}{ccc}5&7\\-1&6\\3&-9\end{array}\right] +\left[\begin{array}{ccc}8&3\\5&1\\4&4\end{array}\right]= \left[\begin{array}{ccc}5+8&7+3\\-1+5&6+1\\3+4&-9+4\end{array}\right]=\left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] \\[/tex]

[tex]C-B = \left[\begin{array}{ccc}0-8&4-3\\-2-5&5-1\\7-4&-1-4\end{array}\right] =\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right][/tex]

[tex]A+B+C= \left[\begin{array}{ccc}5+8+0&7+3+4\\-1+5+-2&6+1+5\\3+4+7&-9+4+-1\end{array}\right] = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]

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Answer:

4.10 + 2.50x = 36.60

x = 13 miles

Step-by-step explanation:

I hope this helped

have a good day ^^

Answer:

7/6 feet

Step-by-step explanation:

The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.

3 + 1/2 = ?

3/1 + 1/2 = ?

6/2 + 1/2 = ?

(6 + 1)/2 = ?

= 7/2

3 + 1/2 = 7/2

In other words, the board is 7/2 feet long.

Now we have to divide by 3 since Andrea is cutting the board in three pieces.

So:

(7/2)/3       or        (7/2) ÷ 3       or        [tex]\frac{\frac{7}{2}}{3}[/tex]        or     (7/2) × (1/3)

= 7/(2×3)

= 7/6

So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.

The width of the cooling tower at the base of the structure is (D) 40 meters.

Now, calculate the cooling tower's width:

Equation: x2/400 given (y-90)

Calculating the width:

Therefore, the width of the cooling tower at the base of the structure is (D) 40 meters.

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When q = -17, the value of the equation, q - 7 would be: d. -24.

If we are given an equation to evaluate for a given value of a variable, we are to substitute the value of the variable into the equation and solve or simplify.

For example, if an equation is given as 3x + 4, and we are told that the x = 3, to determine the value of the equation, 3x + 4, substitute x = 3 into the equation as:

3(3) + 4

= 9 + 4

= 13

Here, we can now conclude that the value of the equation is 13.

Given the equation, q - 7, to find the value of the equation when q = -17, substitute the value of q into q - 7.

Therefore:

q - 7 = -17 - 7

= -24.

The value of the equation is: d. -24.

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The value of q - 7, when q = - 17 is - 24.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, q = - 17.

∴ q - 7.

To solve our expression we'll substitute the numerical value of q in the given expression.

= (-17) - 7.

= - 17 - 7.

= - 24.

We can also take negative sign common in the second step and distribute them later.

- 17 - 7.

= - (17 + 7).

= - (24).

= -24.

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The most appropriate choice for matrices will be given by-

Required Equation

[tex]y = 2x^2 - 3x + 1[/tex]

What are matrices?

If the numbers are arranged in the form of rows and columns, then the arrangement is called matrix.

Here,

The equation is [tex]y =Ax^2 + Bx + C[/tex]

The function contains the points (0, 1), (-2, 15), (3,10).

On putting these coordinates in the equation,

C = 1

[tex]15 = A(-2)^2 + B(-2) + 1\\4A - 2B = 15-1\\2(2A - B ) =14\\2A - B = \frac{14}{2}\\2A -B = 7[/tex]................ (1)

[tex]10 = A(3)^2 + B(3) + 1\\9A + 3B = 10-1\\3(3A + B ) =9\\3A + B =\frac{9}{3}\\3A + B = 3[/tex].................... (2)

Here matrix method will be used

Let

[tex]P = \begin{bmatrix} 2 & -1\\ 3 & 1 \end{bmatrix}[/tex], [tex]Q = \begin{bmatrix} x \\ y\end{bmatrix}[/tex], [tex]R = \begin{bmatrix} 7\\3 \end{bmatrix}[/tex]

PQ = R

[tex]Q = P^{-1}R[/tex]

Adjoint P =

[tex]\begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}^T\\\\\begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix}[/tex]

Det P = [tex]\begin{vmatrix} 2 & -1\\3&1\end{vmatrix}[/tex]

          = [tex]2\times 1 - 3 \times (-1)\\5[/tex]

[tex]P^{-1} = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}[/tex]

[tex]Q = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}\begin{bmatrix}7\\3\end{bmatrix}[/tex]

[tex]Q = \frac{1}{5}\begin{bmatrix} 10\\-15\end{bmatrix}\\Q= \begin{bmatrix} 2\\-3\end{bmatrix}[/tex]

A = 2, B = -3

Required Equation

[tex]y = 2x^2 - 3x + 1[/tex]

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Complete Question

Use matrices to write the equation of the function in the form [tex]y = Ax^2 + Bx + C[/tex]that contains the points (0, 1), (-2, 15), (3,10).

The approximate air distance from La Sarre to Lebel-sur-Quevillon is 167.71 km.

To determine the air distance from La Sarre to Lebel-sur-Quevillon, analyze the path she has traveled.

When she drove east and drove another north, the total path she ave traveled is similar to the sides of a right triangle, where the distance from the start and end point is the hypotenuse. (see photo attached)

Using Pythagorean theorem, solve the distance from La Sarre to Lebel-sur-Quevillon.

c² = a² + b²

where a = 150 km and b = 75 km

distance² = 150² + 75²

distance² = 22500 + 5625

distance² = 28125

distance = 167.71 km

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The equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].

What is inequality?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Consider the given expression, [tex]\frac{(2g^5)^3}{(4h^2)^3}[/tex]

Using the rule, [tex](a^m)^n = a^m^n[/tex]

So, [tex]\frac{(2g^5)^3}{(4h^2)^3} = \frac{8g^1^5}{64h^6}[/tex]

After simplifying  we get,  [tex]\frac{g^1^5}{8h^6}[/tex]

Therefore, the equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].

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Answer: 1

Step-by-step explanation:

[tex]\lim_{x \to -6} f(x) \neq -1[/tex] because the left and right hand limits are not the same.

[tex]\lim_{x \to -1} f(x) \neq -1[/tex] because the left and right hand limits are not the same.

However, somewhere between 1 and 2, the limit does equal -1 because the left and right hand limits are the same.

The percentage of young adults who send fewer than 218 text messages is 99.87%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 218

μ = mean = 128

σ = standard deviation = 30

z-score = (218 - 128) / 30

z-score = 90 / 30

z-score = 3

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 3

probability = 0.9987

To get the percentage, multiply the probability by 100.

percentage = probability x 100

percentage = 0.9987 x 100

percentage = 99.87%

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two lines are perpendicular when their slope is inverted and have the opposite sign

the general form of the equation line is-3,1

where m is the slope

rewrite

so, the slope 3/8

the slope of the other line is

to write the new equation of the line we use the slope and replace the point (-3,1)

now, replace b and the slope to create the line

We have the following expression

This can't be a vertex, since, in geometry, a vertex is a point where two or more elements meet.

A domain is not either, since, in mathematics, the domain of a function is the set of the existence of itself, that is, the values for which the function is defined.

The Standard Form of a Quadratic Equation looks something like this:

Where a, b, and c are known values and a cannot be 0.

In conclusion, the answer is that is a Quadratic

Area of circle A is 113.04 in²

Area of circle B is 200.96  in²

Area of circle C is 452.16  in²

Area of circle B is 254.34  in²

The number of times that the area of Circle D greater than Circle A is 2.25

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

Area of circle A = 3.14 x 6² = 113.04 in²

Area of circle B = 3.14 x (6 + 2)² = 200.96  in²

Area of circle C = 3.14 x (8 + 4)² = 452.16  in²

Area of circle B = 3.14 x (12 - 3)² = 254.34  in²

Number of time that is the area of Circle D greater than Circle A = 254.34  in² / 113.04 in² = 2.25

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Answer:

x>-2

Step-by-step explanation:

3 times five is fifteen, which is larger than 12, so all x needs to be is be bigger negative 2.

Explanation:

Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.

Examples:

In other words,

(whole number)*(whole number) = whole number

This is why we consider the set closed under multiplication.

Answer:

1) y = 3x + 5

2) y = -12x + 2

3) y = 5/4 - 5

4) y = -6x + 3

Step-by-step explanation:

Total capacity the tower holds 1.034 x 10^5  gallons of water

One tower holds 8.4 x 10^3 gallons of water

Other tower holds 9.5 x 10^4 gallons of water

The combined water capacity of the two towers in scientific notation is,

Total capacity the tower holds = 9.5 x 10^4 + 8.4 x 10^3

    = 9.5 x 10^4 + 0.84 x 10^4

    = 10.34 x 10^4

    = 1.034 x 10^5

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A set of data is given. It is required to find the first, second, and third quartile.

The given data is:

Recall that the lower quartile Q₁, or the first quartile, is the median of the lower half of the data in a set.

The lower half is:

Find the median of the lower half to get the first quartile, Q₁:

Hence, Q₁=9.

Recall that the second quartile Q₂ is the same as the median of the data.

The median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.

Notice that the middle number is 15.

Hence, second quartile Q₂=15.

The upper quartile Q₃, or the third quartile, is the median of the upper half of the data in a set.

The upper half of the data is:

Calculate the median to find the third quartile, Q₃:

It follows that Q₃=17

The complete table is shown below:

The Probability that the system does not fail for 2 days is 0. 053

Given ,

Mean (u) = 37 hours .

Step  1 : Calculate the rate parameter, λ.

λ = 1/ mean

λ = 1/ 37 = 0.02703

Step 2 : Find the probability that the system does not

fall for two days, P ( x[tex]\leq[/tex]2 )  

P ( x[tex]\leq[/tex]2 ) .= 1 - e power (lamda(x))

       = 1 - e - 2(lamda)

        = 1 - e power  -2(0. 02703 )

By solving,

P ( x[tex]\leq[/tex]2 ) = 0.05263

P ( x[tex]\leq[/tex]2 ) = 0. 053 [ upto three decimals]

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We need to know how to read a graph inorder to solve the problem. At the end of 6 weeks, Lorena will have more money, she will have $8 more than Benita.

We know that Lorena started with $40 and she added $8 every week. We need to find out the final amount she has at the end of 6 weeks. For Benita, we can see from the graph that she started with $50, since the graph starts from $50, and if we observe the amount after every week we can see that she adds $5 every week to the savings. We can directly say from the graph that the final amount Benita has after 6 weeks is $80.

amount Lorena has after 6 weeks = 40+ (6x8)=40+48=$88

Therefore we can see that Lorena will have more money after 6 weeks and she has $8 more than Benita.

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Solve for b

-73 = b/7- 81

b= 56

-511=b-567

b-567=-511

b=-511+567

b=56

Solution 2

Add 81 to both sides.

-73+81= b/7

simplify -73+81 to 8

8=b/7

8*7=b

simplify 8*7 to 56

56=b

switch sides b= 56

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If the equation be -73 = b/7- 81 then the value of b is 56.

Solve for b

-73 = b/7- 81

b= 56

-511=b-567

b-567=-511

Hence,

b=-511+567

b=56

Solution 2

Add 81 to both sides.

-73+81= b/7

simplify -73+81 to 8

8=b/7

8*7=b

simplify 8*7 to 56

56=b

switch sides b= 56

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Answer:

Step-by-step explanation:

Given data:

The given amount of equipment purchased by the Sandra is A=$1,200.

The question asks us to solve the following system of equations by elimination:

Solution

Answer

The solution to the system of equation is:

x = -8

y = 9