An instrument maker creates a triangle in the shape of an isosceles triangle by bending a metal rod. The rod is 13 inches long, and the bottom of the triangle is longer than the two sides. What is the length of the longest side?.

The distance between two places cab be found using distance formula if you know the coordinates of the places.

The distance formula is a mathematical equation that can be used to find the distance between two points in a two-dimensional or three-dimensional space. The formula is as follows:

Distance = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

Where x₁, y₁, and z₁ are the coordinates of the first point and x₂, y₂, and z₂ are the coordinates of the second point. The formula is based on the Pythagorean theorem, which states that the square of the distance between two points is equal to the sum of the squares of the differences in their coordinates.

For example, if you have the coordinates of two places on a map, you can use the distance formula to calculate the distance between them. Let's say the coordinates of place A are (x₁, y₁) = (4, 5) and the coordinates of place B are (x₂, y₂) = (9, 12). The distance between place A and place B would be:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

= √((9 - 4)² + (12 - 5)²)

= √(5² + 7²)

= √(25 + 49)

= √(74)

= 8.6

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The equation of the function shown in the provided graph is y = 1

                                                                                                         (x+3)²  

The parent function is f(x) =  1

                                              x²

Graph can be defined as a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things

How horizontal shifting of the graph takes place

If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+k) where k>0

Since the graph is shifted towards the negative x-axis by 3 units

So, the parent function f(x) will become f(x+3)

 f(x)=  1

         x²

f (x+3)= 1    

           (x+3)²

So, the equation of the function will be y = 1    

                                                                       (x+3)²  

Therefore, The equation of the function shown in the provided graph is  

y = 1

    (x+3)²                                          

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Answer:

the requisite answer for this question is 10 meter.

Step-by-step explanation:

the analysis for this question's answer is as follows:

since, he has a 50 meter long role of cable, correct to the nearest meter,with him and also he uses 10 meter of that role each time during his job to the nearest meter.

therefore, if he does four jobs then the maximum amount of cable that could be left with him would be;

he took (40-m) to finish the entire work,

this simplifies, 50-(10×4) which is equal to 50-40 which in turn is equal to 10

hence, the solution to the afore-mentioned problem is 10 meters.

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Gallons of gas used 40 gallons.

The given equation, m = pace / 40g, represents the distance in miles (m) that a car can travel using a certain number of gallons (g) of gas. The variable "pace" represents the miles per gallon (mpg) of the car. To find the number of gallons used, we need to solve for g in the equation.

Here are the key steps:

Finally, we can solve for g and we get the answer that the car used 40 gallons of gas.

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The surface area of the rectangular prism, as a function of x, is given by:

A = 2*( (x - 2)*(x + 4) + (x + 4)*(2x + 1) + (x - 2)*(2x + 1))

For a prism whose dimensions are X, Y, and Z, the surface area is:

A = 2*(X*Y + X*Z + Z*Y)

In this case we know that the dimensions of the rectangular prism are:

X = x - 2

Y  =x + 4

Z = 2x + 1

Replacing that on the surface area equation we will get:

A = 2*( (x - 2)*(x + 4) + (x + 4)*(2x + 1) + (x - 2)*(2x + 1))

That equation gives the surface area as a function of x.

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The probability that the spinner lands on an odd number and then a shaded number is given as follows:

5/12.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

The probabilities of each event in this problem is given as follows:

Hence the probability that the spinner lands on an odd number and then a shaded number is calculated as follows:

p = 1/2 x 5/6 = 5/12.

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Yes, AB ≅ DE, EF ≅ DE, then AB ≅ EF. The property of congruence illustrated in the question is the transitive property.

The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.

In the statement "If AB ≅ DE, EF ≅ DE, then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.

The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.

--The given question is incorrect; the correct question is

"Is AB ≅ DE, EF ≅ DE then AB ≅ EF? explain"--

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Triangle ABC and triangle DEF are not congruent.

What does a math congruent mean?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

The measure of angle A and angle D are both 40 degrees, but the measure of angle B and angle F are not equal. The measure of angle B is 20 degrees, while the measure of angle F is 120 degrees.

In a triangle, the sum of all three angles is 180 degrees. So in triangle ABC, the measure of angle C is 180-40-20 = 120 degrees.

In triangle DEF, the measure of angle E is 180-40-120 = 20 degrees.

Therefore, angle B and angle E are not congruent, so the triangles are not congruent.

In order for two triangles to be congruent, they must have corresponding sides and angles of the same measure. Since the measure of angle B and angle E are not equal, then triangle ABC and triangle DEF are not congruent.

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The sum law of limits is the total of their limits equals the limit of the sum of functions. It is also referred to as the addition rule of limits and is known as the sum rule of limitations.

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

The limit of the sum of two functions is equal to the total of the limits of two functions, according to the sum law for limits.

[tex]\lim_{x \to \} a (f(x)+g(x))[/tex]

= L + M

Objective of Sum of limits are:

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A binomial is an algebraic expression containing two different terms connected by addition or subtraction.

An algebraic expression containing only two terms is called a binomial expression. This is called a binomial polynomial. Also called the sum or difference of two or more monomials. This is the simplest form of polynomial. Binomials are classified into algebraic expressions based on the number of terms they contain, along with monomials, trinomials, quaternions, etc. In other words, two different monomials of different degrees connected by a plus or minus sign form a binomial. For example, consider two monomials 2x and 5x¹⁰. Adding these monomials gives the binomial given by 2x + 5x¹⁰.

2) For example, 2xy + 7y is binomial because it has two terms.

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Answer:

-7[tex]x^{2}[/tex] - 35x - 42

Step-by-step explanation:

-7(x+3)(x+2)

(-7x - 21) ( x + 2)

-7[tex]x^{2}[/tex] - 14x - 21x - 42

-7[tex]x^{2}[/tex] - 35x - 42

Answer:

Step-by-step explanation:

y=-7(x+3)(x+2)

y=(-7x - 21) ( x + 2)

y=-7 - 14x - 21x - 42

y=-7 - 35x - 42

Angles 1 and 5 are called corresponding angles.

Corresponding angles refer to angles that occur on the same side of the transversal line. Corresponding angles are equal in size and can both be obtuse or acute. In other words, corresponding angles are any pair of angles which occur on the same side of the parallel lines which are cut by another line. As shown in the given figure, a transversal line intersects two parallel lines which produces eight angles. It contains four pairs of corresponding angles, i.e., 1 and 5, 2 and 6, 3 and 7, and 4, and 8. Corresponding angles are congruent angles. All angles possess the same position in reference to the parallel lines and the transversal are corresponding pairs.

Note: The question is incomplete. The complete question probably is: In the given figure, what are angles 1 and 5 called?

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The equivalent expressions are

(3x² + 21x + 18) / (x² - 7x - 8)
3 (x + 6) (x + 1) / (x + 1) (x - 8)

Options A and E are the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(3x² + 21x + 18) . x² - 7x - [tex]8)^{-1}[/tex]

This can be written as,

(3x² + 21x + 18) / (x² - 7x - 8) ______(A)

Now,

Solve for (3x² + 21x + 18).

(3x² + 21x + 18)

3 (x² + 7x + 6)

3 (x² + (6 + 1)x + 6)

3 (x² + 6x + x + 6)

3 (x (x + 6) + 1 (x + 6))

3 (x + 6) (x + 1)

Solve for (x² - 7x - 8).

x² - (8 - 1)x - 8

x² - 8x + x - 8

x (x - 8) + 1 (x - 8)

(x + 1) (x - 8)

Now,

(3x² + 21x + 18) / (x² - 7x - 8)

= 3 (x + 6) (x + 1) / (x + 1) (x - 8) _____(B)

Thus,

From (A) and (B),

(3x² + 21x + 18) / (x² - 7x - 8)  and 3 (x + 6) (x + 1) / (x + 1) (x - 8) are the equivalent expressions.

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The mathematical expressions in order of their values from least to greatest will be

(8.32 x 10⁴)/(7.56 x 10¹¹) · (9.67 x 10¹)/(5.79 x 10⁻⁸)

(7.25 x 10⁵)/(7.95 x 10⁻²) · (9.36 x 10⁻⁷)/(4.13 x 10⁻³)

(4.27 x 10⁸)·(9.2 x 10⁻⁵)

(6.96 x 10⁵)·(8.43x 10⁻²)

(1.89 x 10⁴)/(2.74 x 10⁻²) · (5.92 x 10³)/(4.67 x 10²)

The following mathematical expressions are written in their scientific notation, a way of expressing numbers that are too large or too small to be conveniently written in decimal form. In scientific notation, a number is represented as a coefficient (a number between 1 and 10) multiplied by a power of 10.

To multiply scientific notation/expressions, you need to:

1. Multiply the numerical coefficients.

2. Add the exponents of the bases (usually "10").

The opposite goes to division, where the numerical coefficients are divided and the exponents are subtracted.

(4.27 x 10⁸)·(9.2 x 10⁻⁵)

39.284 x 10³

3.9284 x 10⁴

(6.96 x 10⁵)·(8.43x 10⁻²)

58.6728 x 10³

5.86728 x 10⁴

(7.25 x 10⁵)/(7.95 x 10⁻²) · (9.36 x 10⁻⁷)/(4.13 x 10⁻³)

(9.12 x 10⁶) · (2.27 x 10⁻⁴)

2.061 x 10³

(8.32 x 10⁴)/(7.56 x 10¹¹) · (9.67 x 10¹)/(5.79 x 10⁻⁸)

(1.10 x 10⁻⁷) · (1.67 x 10⁹)

1.84 x 10²

(1.89 x 10⁴)/(2.74 x 10⁻²) · (5.92 x 10³)/(4.67 x 10²)

(6.90 x 10⁵) · (1.27 x 10¹)

8.86 x 10⁶

Rearranging these values from least to greatest, we have

1.84 x 10², 2.061 x 10³, 3.9284 x 10⁴, 5.86728 x 10⁴, 8.86 x 10⁶

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Answer:

Yes, an acute angle is an angle that measures less than 90 degrees.

Step-by-step explanation:

To solve nth problems we use the formula stated as  aₙ = a + (n – 1)d.

A series in which the differences between each pair of following terms are the same is known as an arithmetic progression (AP). A formula for the nth term of the AP could be derived from this kind of progression. Because it follows a pattern where each number is acquired by adding 4 to the preceding term, the sequence 2, 6, 10, 14,... is an example of an arithmetic progression (AP). In this series, the nth term equals 4n-2. By changing the nth term to n=1,2,3,..., the sequence's terms can be obtained. i.e.,

First term when n = 1 is 4n-2 = 4. (1)

-2 = 4-2=2

second term = 4n-2 = 4 when n = 2 (2)

-2 = 8-2=6

The third term is 4n-2 = 4 for n = 3. (3)

-2 = 12-2=10

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The first waiter with $60 tips share $15 dollar to the second waiter and the second waiter with $80 share $20 to the first waiter.

As per data given is two different earned from tips, there will be two different amount of share from each. For a waiter that earned $60 from tip, the share will be:

First waiter share = tips earned x 1/4

First waiter share = $60 x 1/4

First waiter share = $60 x 0.25

First waiter share = $15

The share of the second waiter that earned $80 from tip will be:

Second waiter share = tips earned x 1/4

Second waiter share = $80 x 1/4

Second waiter share = $80 x 0.25

Second waiter share = $20

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y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex]  is the rational function  that has a horizontal asymptote of y = 0.

When the denominator of a polynomial has a degree of at least 1, it is said to be a rational function. Or to put it another way, the denominator must contain a variable.

When p(x) and q(x) are polynomials and q(x) ≠ 0, the general form of a rational function is p(x)/q(x).

Asymptotes are lines that the function graph approaches but never crosses. Both the x and y axes are asymptotes in the parent function f(x)=1x. The parent function's graph will approach the asymptotes steadily but never actually touch them.

If the degree of the denominator > degree of the numerator, there is a horizontal asymptote at y = 0.

Here, only y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex] has the degree of the denominator > degree of the numerator.  

Thus, y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex]  is the rational function  that has a horizontal asymptote of y = 0.

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The main difference between a true solution and a colloidal solution is the particle size of the dispersed substance. In a true solution, the particles are so small that they cannot be seen with the human eye, while in a colloidal solution, the particles are intermediate in size and are visible under microscope.

A true solution is a homogeneous mixture of two or more substances where one substance is completely dissolved in the other. The particles of the dissolved substance, called solute, are so small that they cannot be seen with the human eye and are evenly distributed throughout the solution. A true solution is transparent, and the particles of the dissolved substance do not scatter light, thus not visible under a microscope. Examples of true solutions are sugar dissolved in water, and salt dissolved in water.

On the other hand, a colloidal solution is a type of mixture where one substance is dispersed throughout another substance in small particles that are not large enough to settle out but are large enough to scatter light. The particles of the dispersed substance, called the dispersed phase, are intermediate in size between those of a true solution and a suspension. The particles are visible under microscope, but not to the human eye, and the mixture is usually cloudy or opaque. Examples of colloidal solutions are milk, fog, and blood.

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The total amount of tips that the waiters collected that night is $1,622.60.

To find the total amount of tips, you can multiply the mean tip by the number of waiters.

In this case, the mean tip is $115.90 and there are 14 waiters, so:

$115.90 x 14 = $1,622.60

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Principal, P = $ 300,000

Rate, R =  20%

Time, T = 30 years

The down payment would be 300,000 x 20% = $60,000.

The principal for the home loan after the down payment would be 300,000 - 60,000 = $240,000.

The total amount owed to the bank including principal and interest would be 240,000 + 232200 = $462200.

To calculate the monthly payment for a 30 year mortgage, you would use the formula:

(principal + interest) / (number of months in 30 years)

which would be ($462200) / (360 months) = $1283.33

To calculate the total monthly cost including another 300 per month for taxes and 150 per month for insurance, you would add the mortgage payment to the additional costs:

1283.33 + 300 + 150 = $1733.33.

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Equivalent 4/5 is equals to 20/25 in fractions.

In mathematics, equivalent fractions are those with the same denominator but different numerators. For instance, since they both equal 1, 2/4 and 3/6 are comparable fractions. An element of the whole is a fraction. To represent identical components of the total, equivalent fractions are utilized.

The numerator and denominator of each fraction can be multiplied by the same integer to determine the equivalent fraction. Equivalent fractions are those that, despite visible differences, signify the same value. For instance, if you take a piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.

= 4/5 ( multiply by 5/5)

= 4/5 * 5/5

= 20/25

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Correct Question:

What is 4/5 as an equivalent fraction?.

Answer:5 pieces

Step-by-step explanation:

4/0.8=5

I have left 6 mangoes after I got 5 extra from father and mother ate 2

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating how many mangoes I have after I got 5 from my father:

No. mangoes 1 = Have + got

No. mangoes 1 = 3 mangoes + 5 mangoes

No. mangoes 1 = 8 mangoes

Calculating how many mangoes I have after my mother ate 2 mangoes:

Final No. mangoes = No. mangoes 1  - eat

Final No. mangoes = 8 mangoes - 2 mangoes

Final No. mangoes = 6 mangoes

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When you are skiing on a mountain with an altitude 12 meters and angle of depression is 21 degrees then you will ski down for a distance of 31.57 meters.

Solution:

Here we have ,

Height i.e altitude of mountain (h) = 12 meters

Angle of depression (∅) =21°

And let the distance coverd be (b)

Using theorm of trigonometery,

tan∅ = [tex]\frac{height}{base}[/tex]

       = [tex]\frac{12}{b}[/tex]

Therefore,

tan(21°) = [tex]\frac{12}{b}[/tex]

b = [tex]\frac{12}{tan(21)}[/tex]

b = [tex]\frac{12}{0.38}[/tex]

b = 31.57 meters

Hence ,

You will ski down 31.57 meters.

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The ratio of e:f from 2 different squares are 1.2:1.

From the case, we have 2 squares that:

Square E side = e

Square F side = f

Area of E = (1 + 44%) Area of F

Using the area of square formula, we know that:

Area of square = side x side

Area of square = side²

Area of E = e x e

Area of E = e²

Area of F = f x f

Area of F = f²

We will compare the area of both squares:

Area of E = (1 + 44%)Area of F

e² = (1 + 44%) f²

e² = 1.44 f²

√e² = √(1.44 f²)

e = 1.2 f

Hence the ratio of e : f would be:

e : f = 1.2f : f

e : f = 1.2 : 1

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The mirror image of (4,5) is (4,-5) or (-4,5)

The term mirror image in math is defined as a reflected duplication that appears identical but in reverse.

Here we need to find the mirror image of (4,5).

As we all know that the rule used here is written as the image of (x, y) in the y-axis is (–x, y).

Then according rule here the given that the mirror image of (4,5) along x axis is written as (4,-5).

Then as per the point lies in fourth quadrant.

Then the another form of the mirror image of ( 4,5) along y axis is written as (-4,5) and then the point lies in second quadrant.

Complete Question:

What is the mirror image of the coordinate (4,5)?

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The new mean of the data-set, with the observation 2 removed, is given as follows:

12.67 attempts.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

Removing the observation 2, the data-set is given as follows:

11, 11, 11, 12, 13, 13, 14, 14, 15.

The sum of all these observations is given as follows:

3 x 11 + 12 + 2 x 13 + 2 x 14 + 15 = 114.

There are nine observations, hence the mean of these observations is given as follows:

114/9 = 12.67.

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Answer:

136 acres

Solution:

My way of doing this is by putting it in a fraction.

So,

0.2/100 × 68000/1 = x

Do the math and x = 136