Solve the following equations for ×. Check for extraneous solutions.

Answer:

see explanation

Step-by-step explanation:

A

for the triangles to be similar by the AA postulate then 2 angles in both triangles must be congruent.

In this case we are only given 1 pair of congruent angles.

Thus not able to say similar by AA postulate, therefore Sharon is incorrect in her assumption.

B

the sides are of different lengths but the ratios of corresponding sides are equal, that is

[tex]\frac{JK}{GH}[/tex] = [tex]\frac{8}{4}[/tex] = 2 and [tex]\frac{JL}{GI}[/tex] = [tex]\frac{10}{5}[/tex] = 2

If the ratios of 2 pairs of corresponding sides of 2 triangles are equal and the included angles are congruent , then the triangles are similar, so

Δ GHI and Δ JKL are similar by the SAS postulate

C

the ratios of corresponding sides are equal , then

[tex]\frac{KL}{HI}[/tex] = [tex]\frac{JL}{GI}[/tex]

[tex]\frac{KL}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )

KL = 14

The longest side of a triangle is always opposite to the largest angle because  the endpoints of the lines on either side are going to be further apart if the angle is wider .

What is Triangle  ?

The triangle can defined as a three-sided polygon that consists of three edges and three vertices.

Let the angle opens up to its opposite side.

So , the larger the angle, the wider will be it's opening. which means that the endpoints of lines on either side of the angle are going to be further apart if angle is wider.

If the endpoints are further apart, then the line connecting them, which makes up the side opposite will be going to be more longer.

So , the longest side will always be opposite to the largest angle

Similarly , the smallest angle will result in shortest side opposite side for the same reasons.

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Answer:

The median of the data is 1

Answer:

1.  $76,000

2. $58,000 + $2,000 * t

Step-by-step explanation:

2. Now, you might be questioning why we are going with the second question first, but this will be useful as it sets up our equation to make the first question easier. So, we will start with Luke's base salary of $58,000. Then, we will add $2,000 for every year he works at the company. If he works for t years and gains $2,000 on his salary per year, our equation will look like this:

$58,000 + $2,000 * t

That is the equation.

1. Now, using our previous equation, $58,000 + $2,000 * t, we will substitute 9 in for t. We get:

$58,000 + $2,000 * 9

Then, we simplify, giving us:

$58,000 + $18,000 = $76,000

Answer:

Obtuse and isosceles

Step-by-step explanation:

obtuse because an angle is more than 90* and isosceles because two sides are equal.

Hope this helps!

An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:

                           W = S / R

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:

W = S / R

where W is the number of wreaths, S is the total length of ribbon on the spool, and R is the length of ribbon used per wreath.

Plugging in the given values, we get:

W = 20 / 2.5

Solving for W, we get:

W = 8

So Nicole could decorate 8 wreaths using one spool of ribbon.

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The value would be [tex]34^{-1} \pmod{47}=30[/tex]

What is the modulus in mathematics?

In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.

Given that 13^-1 ≡ 29 (mod 47), we can use this information to find the inverse of 34 mod 47. The inverse of a number modulo m is a number x such that the product of the number and its inverse is congruent to 1 mod m.

In the case of the given equation, [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex] is saying that 29*13 = 377 is congruent to 1 mod 47.

We can use this congruence to find the inverse of 34 mod 47. The inverse of 34 mod 47 is the number x such that 34*x = 1 mod 47. So we can write this congruence as [tex]$34x \equiv 1 \pmod{47}$[/tex]

We can use the given congruence of 13^-1 ≡ 29 (mod 47) to find the inverse of 34 mod 47.

Since [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex], we can multiply both sides of the congruence by 34 as:

[tex]$13^{-1} * 34 \equiv 29 * 34 \pmod{47}$[/tex]

Now we can substitute the right side of the equation:

[tex]$13^{-1} * 34 \equiv (13*29) \pmod{47}$[/tex]

And now we can substitute the left side of the equation:

[tex]$34^{-1} \equiv (13*29) \pmod{47}$[/tex]

And since [tex]$13*29 = 377$[/tex] this is congruent to 30 (mod 47) the inverse of 34 mod 47 is 30.

Therefore, the value would be [tex]34^{-1} \pmod{47}=30[/tex]

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The value would be 13.

What is the modulus in mathematics?

In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.

We can use the property of modular inverse that

[tex]$(ab)^{-1} \equiv b^{-1}a^{-1} \pmod{m}$[/tex]

So, [tex]$(13*34)^{-1} \equiv 34^{-1} \cdot 13^{-1} \pmod{47}$[/tex]

[tex]$13^{-1} \equiv 29 \pmod{47}$\\$(13*34)^{-1} \equiv 34^{-1} \cdot 29 \pmod{47}$So, $34^{-1} \equiv (13*34)^{-1} \cdot 13 \pmod{47}$$34^{-1} \equiv 1 \cdot 13 \pmod{47}$$34^{-1} \equiv 13 \pmod{47}$[/tex]

Hence, The value would be 13.

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The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.

Two triangles' area: 18×24÷6x3 = 432cm^2

The widest rectangle's area: 30×7 = 210cm^2

The rectangle facing the left's area: 18×7= 126cm^2

The rectangle facing the ground's area: 24×7= 168cm^2

Total Surface Area: 432+210+126+168 = 936cm^2

=936cm^2

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So Dylan needs 1.375 liters of water more for his experiment.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

To find out how much more water Dylan needs, we can subtract the amount of water he currently has from the amount of water he needs for the experiment.

2.5 - 1.125 = 1.375 liters

So Dylan needs 1.375 liters of water more.

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The value 'k' for which '4x^2 + 8xy + ky^2 = 9' is the second degree equation of a pair of straight lines is 4.

Therefore the answer is 4.

A general second-degree equation of a pair of straight lines is given by:

ax² + 2hxy + by² + 2gx + 2fy + c = 0

Where a, b, c, d, e, and f are constants, x and y are variables.

For the equation to represent a pair of straight lines, the following conditions must be met :

abc + 2fgh - af² - bg² - ch² = 0

In the equation 4x^2 + 8xy + ky^2 = 9, a = 4, h = 4, b = k, g = f = 0 and c = -9.

That is 4×k×(-9) + 2×0×0×4 - 4×0² - k×0² + 9×4² = 0

4×k×9 = 9×4²

k = 4

--The question is incomplete, complete question is given below--

"For what value of k is 4x^2 + 8xy + ky^2 = 9 the equation of a pair of straight lines?"

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As you can see, 5y is an external angle of triangle ABC

we know that 5y=180-x

since angle B is 40, and angle A=x and C=x, we have

x%2Bx%2B40=180

2x=180-40

x=140%2F2

x=70

so, angle A=70 and C=70

then

5y=180-70

5y=110

y=110%2F5

y=22

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The number of mole O₂ is 2. Since the subscript of oxygen denotes the number of moles.

What is a diatomic element?

Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).

One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.

The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.

The subscript part of a chemical compound represents the number of moe of the chemical compound. The subscipt of O₂ is 2. Thus the number of mole is 2.

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On solving the provided question, we can say that the sum of the two expressions will be -4n + 6

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.

Expression, Number/Variable, and Mathematical Operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

let the two expression be

-4nand 6 and the sum will be -4n + 6

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Answer:

4(3p - 7)

Step-by-step explanation:

First find the factors of 12 and 28:

12: 1, 2, 3, 4, 6, 12

28: 1, 2, 4, 7, 28

Notice any common factors: 1, 2, 4

Now, out of these factors, 4 is the GCF since it is the greatest common factor, so divide 12 and 28 by 4:

12/4 = 3.  28/4 = 7.

Hence, 12p-28 = 4(3p - 7)

Answer:

  y +8 = -1/9(x -9)

Step-by-step explanation:

You want the point-slope form of the equation of the line through point (9, -8) with slope -1/9.

The equation of the line through point (h, k) with slope m is ...

  y -k = m(x -h)

You have (h, k) = (9, -8), and m = -1/9. Using these values, the equation is ...

  y +8 = -1/9(x -9)

Answer:0.23

Step-by-step explanation:

Answer  

x=-1/2,=29/4

explanation

The exact value is required. In this case, they don't have enough for 1 3/4 cups of flour.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, the person had 2/3 cup of flour in a bin and 7/8 flour was still in the bag. In this case, it should be noted that they also wanted to know of they had enough for 1 3/4 cups of flour.

This will be calculated thus:

= 2/3 + 7 / 8

= 16/24 + 21/24

= 37 / 24.

= 1 13 / 24

This is not enough for 1 3/4 cups of flour.

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Answer:

77.4 inches

6 feet 4 inches

Step-by-step explanation:

what persent of 14 is 10.83 is 77.35

what persent of 84 is 77.3571428571 is 92.08

what is 92.08% of 84 is 77.34

77.34 inches to feet is 6 feet and 4 inches

The circle equations for circles with diameters of 12 units that lie on the y-axis are:

We want to find the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis, now, remember that the general equation for a circle of radius R and a center (a, b) is:

(x - a)^2 + (y - b)^2 = R^2

If we want a circle that lies on the y-axis, then a = 0, and if the diameter is 12 units, then the radius is R = 6 units.

Then the equation is something like:

x^2 + (y - b)^2 = 6^2 = 36

The two circle equations with this form are:

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Answer: Let x be the number of $13 books that Auggie bought and y be the number of $24 books. Then we can represent the given information in the following system of linear equations:

x + y = 8 (the total number of books Auggie bought is 8)

13x + 24y = 159 (the total amount of money Auggie spent is $159)

This system of linear equations represents the given situation. We can use this system to find out how many books Auggie bought of each price by solving the system of equations.

The equation (1) represents the number of books that Auggie bought is 8, and equation (2) represents the amount of money he spent $159. This system of equations is a valid representation of the given situation because the values of x and y that satisfy the system of equations will be the number of $13 books and the number of $24 books that Auggie bought.

Step-by-step explanation:

No solution is when a system of equations has no solution. This means that the equations are inconsistent, and there is no set of values that can make the equations true.

For example, if the system of equations is 2x + 3y = 4 and 2x + 3y = 5, then there is no solution. This is because no matter what values are chosen for x and y, the equations cannot both be true. This means that the system of equations is inconsistent, and there is no solution.

To symbolically represent no solution, you can use the following notation:

2x + 3y = 4, 2x + 3y = 5   No solution

This notation is used to indicate that the equations are inconsistent and that there is no solution.

Complete question: What is the solution to the equation 2x + 3y = 4 and 2x + 3y = 5?

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Store Z charges $8 per movie.

An expression is the mathematical statement that is formed by numerical and variable terms along with operators. It represents the method of a mathematical operation in a symbolic form.

given, store A charges $8 per movie.

for each order shipping fee = $10

if store A is ordered x movie at a time than the total cost for one order

represented by the expression, $8 x + $10.

As per question, store Z cost always the same as store A for one order.

so, cost for one order in case of store Z = $8x + $10

if x denotes the number of movies that is ordered at a time, then the Z store charges $ 8 per movie.

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Inverse of function is written by using notation f⁻¹

The function that can be reversed into another function is termed as inverse function. It is also called anti function. There are different types of inverse function such as inverse trigonometric function, inverse rational function, inverse log function and so on.

We can determine an inverse function by interchanging the elements that present in the given expressions.

Inverse of the function f is denoted by notation f⁻¹

let, we have given a function, f(x) = 8x + 9

now, we need to find the inverse of the above function.

in the first step we write the function using y and set equal to x

                      x = 8y +9

in the next step, we arrange to make the y subject,

                 x - 9 = 8y

               8y = x - 9

                y = (x - 9)/ 8

 use the notation f⁻¹ = (x - 9)/ 8

this is the inverse of function f.

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[tex]\dfrac{15}{4} \div\dfrac{5}{8}[/tex]

In order to divide two fractions, you will need to use the KCF method.

Keep

Change

Flip

This means that we will keep the first fraction, change the division to multiplication, and flip the second fraction(reciprocal).

[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]

Multiply:

[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]

[tex]\dfrac{15\times8}{4\times5}[/tex]

[tex]=\dfrac{120}{20}[/tex]

Simplify:

[tex]120\div20[/tex]

[tex]=\fbox{6}[/tex]

Answer: 6

Step-by-step explanation:

1. 15/4 divided by 5/8 = 120/20

15/4 / 5/8 = 15/4 times 8/5 = 15 time 8 over 4 time 5 = 120/20

2. 120/6 = 6

Answer:

Step-by-step explanation:

1 ft= 12 inches

So 5ft = 60 Inches

4= 0.3

Thus, Its 60.3

The minimal number of employees who did not get their preferred shift that week was 20.

Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.

But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.

We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.

But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.

Thus, 20  is the minimum number of staff members who failed to receive her preference of shift that week.

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Equation = P(1+r)^x, where P is the initial amount invested, r is the fixed interest rate, and x is the number of years.

It is important to note that the equation provided is the formula for compound interest. P is the initial principal, r is the annual interest rate, and x is the number of years the money is invested. The equation gives the total amount of money in the account after x years.

It should be also noted that the interest rate is given as a decimal and not a percentage.

For example, if the interest rate is 5%, then r = 0.05.

In order to use this equation, the value of P, r and x should be known

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