prove that triangles abc and def are congruent ​

Your question was incomplete. Please refer below to find the table in the image.

We need to know about powers and indices to solve the problem. The value of nonzero number raised to the power of 0 is 1.

When a number is raised to a certain power, it can be simplified as the number is multiplied to itself the number of times as the power. For example if we write [tex]2^{3}[/tex] we mean 2x2x2 which is 8. Similarly in this question we have to find the various powers of 9, the answer to [tex]9^{4}[/tex] is given, we need to find for the powers 3,2,1, and finally 0.

[tex]9^{3}[/tex]=9x9x9=729

[tex]9^{2}[/tex]=9x9=81

[tex]9^{1}[/tex]=9

[tex]9^{0}[/tex]=1

When any nonzero number is raised to the power of zero the result is one.

Therefore we found out using the concept of powers and indices that the value of a nonzero number raised to the power of 0 is 1.

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Answer:

$-49

Step-by-step explanation:

If he has $42 in his savings account and he takes $7 a week for 13 weeks, we have to multiply 7x13 to find out how much money he takes out of the account.

7x13=91, 91 is more then how much he has in his account so he will be in debt?
42-91=-49

The quotient of √x ³ / √5 x ² is √ ( x / 5 )

To find : the product of √x ³ / √5 x ²

By checking the power of roots for each term

The terms which are given are √x ³ and √5 x ²

Since both the numbers have the same root power they can be combined under the same square root for further operation

Dividing the terms

=> √ ( x ³ / 5 x ² )

=> √ ( x / 5 )

Therefore, we get the quotient of √x ³ / √5 x ² as √ ( x / 5 ).

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The situation is a function; the independent variable is the number of lines and the dependent variables is the total cost

The domain is 0 <= x <= 4 and the range is 0 <= y <= 120

The statement is given as

A cell phone plan costs $30 for each line

Let the number of lines be x and the total cost be y

So, we have

y = cost per line * x

This gives

y = 30x

The above equation represents a linear function

This means that the situation is a function; the independent variable is the number of lines and the dependent variables is the total cost

From the question, we have

You can have a maximum of four lines on a plan.

This means that the possible values of x are

x = 0, 1, ... 4

When these values are substituted in y = 30x, we have

y = 30 * 0 = 0

y = 30 * 4 = 120

Hence, the domain is 0 <= x <= 4 and the range is 0 <= y <= 120

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√6 is greater than √2+1.

Suppose that √6 is greater than √2+1. Then we check if our assumption is correct.

So √6 > √2+1

Squaring both sides and using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex],

⇒ 6 > 3 + 2√2

Subtracting 3 from both sides,

⇒ 3 > 2√2

Again squaring on both sides,

⇒ 9 > 8

This is true. So our assumption is right.

Therefore,  √6 > √2+1

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Answer:

[tex]4\frac{1}{2} [/tex]

Step-by-step explanation:

To make the division easier, we will convert them to improper fraction first.

[tex]12 \frac{3}{8} \div 2 \frac{3}{4} \\ = \frac{99}{8} \div \frac{11}{4} [/tex]

Now we will change the sign to multiply and swap the numerator and denominator of the divisor fraction.

[tex] \frac{99}{8} \div \frac{11}{4} \\ = \frac{99}{8} \times \frac{4}{11} \\ = \frac{396}{88} \\ = \frac{9}{2} = 4 \frac{1}{2} [/tex]

The multiplication equations are :

a. 10 ÷ 5 =  2 × 5 = 10 and  5 × 2 = 10

b. 4.5 ÷ 3 = 3 × 1.5 = 4.5 and1.5 × 3 = 4.5

A complete multiplication equation will have the numbers that are being multiplied together on one side of the equal sign, and what they are equal to on the other side of the equal sign.

a. 10 ÷ 5 = ?

First we will solve the given equation

so, 10 ÷ 5 = 2

In simple way we can write the multiplication equation of above equation in two ways :

First we can write it as 2 × 5 = 10

And second is as         5 × 2 = 10

These two don't have different conclusion but they have just different written pattern.

Same as we will do the other equations.

b. 4.5 ÷ 3 = ?

Let's solve the equation first

4.5 ÷ 3 = 1.5

Multiplication equation :

3 × 1.5 = 4.5

1.5 × 3 = 4.5

c. 1/2 + 4 = ?

Solution of the above equation is :

1/2 + 4 = 9/2 = 4.5

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Answer:

Step-by-step explanation:

I’m pretty sure x= 10

Answer:

x=6

Step-by-step explanation:

The rationalization of the  denominator is  4√3 / 6 .

We have given a fraction √8/√6 .          ...(1)

The denominator of the fraction is √6.

Multiplying and dividing by √6 in equation (1), we get

√8/√6 = √8 × √6 /√6 × √6

           = √48 /6

          = 4√3 / 6

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Jordin after working for 23 hours and 15 minutes would be paid $302. 25

From the information given, we have that;

Let's convert the minutes to hour

60 minutes is equivalent to 1 hour

Then 15 minutes is equivalent = x hour

cross multiply

x = 15/ 60

x= 0. 25 hour

He worked = 23 + 0. 25 = 23.25 hours

Then,

$13. 00 = 1 hour

$x = 23. 25

cross multiply

x = 13 × 23. 25

x = $302. 25

Thus, Jordin after working for 23 hours and 15 minutes would be paid $302. 25

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Answer:

63/2

Step-by-step explanation:

Multiply the fraction.

[tex]\frac{9}{4}\cdot \:14\\=\frac{9}{4}\cdot \frac{14}{1}\\=\frac{9\cdot \:14}{4\cdot \:1}\\=\frac{9\cdot \:14}{4}\\=\frac{9\cdot \:2\cdot \:7}{4}\\=\frac{9\cdot \:2\cdot \:7}{2\cdot \:2}\\=\frac{9\cdot \:7}{2}\\=\frac{63}{2}[/tex]

Answer:

63/2

Step-by-step explanation:

[tex]\frac{9}{4}[/tex] [tex](\frac{14}{1})[/tex]  You can write 14 as a fraction by putting it over 1.

Now, multiple across

[tex]\frac{126}{4}[/tex]

Now divide the top and the bottom by 2

[tex]\frac{63}{2}[/tex]

a. The type of sequence we have here is a Geometric Progression.

b. The common ratio of the sequence is 7/10.

c. iPhone 10 will cost $83 in 2025.

Given sequence is:  

$1000, $700, $490, $343, $240

a. To determine the type of sequence we find the common ratio between terms:

   700/1000 = 7/10

   490/700 = 7/10

All terms differ by a common ratio hence it is a geometric progression.

b. From above,          

 1000 × 7/10 = 700

 700 × 7/10 = 490

 490 × 7/10 = 343

 343 × 7/10 = 240

Hence, the common ratio of G.P is 7/10.

c. The next terms in the given G.P is:

240 × 7/10 = 168

So, iPhone 10 will cost $168 in 2023.

168 × 7/10 = 118

So, iPhone 10 will cost $118 in 2024.

118 × 7/10 = 83

So, iPhone 10 will cost $83 in 2025.

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After factorizing the expression we get: (2x ₋ 1) (2x ₋ 3) as factors of the expression.

Given the expression is 4x² ₋ 8x ₊ 3 = 0

factorize the expression.

The word "factor" is used to describe a number as the result of any two other numbers. Any mathematical object, including numbers, polynomials, and algebraic expressions, can have factors by using the factorization method. Finding the factors of a given algebraic expression is referred to as factorization of an algebraic expression.

4x² ₋ 8x ₊ 3 = 0

4x² ₋ 2x ₋ 6x ₊ 3 = 0

2x(2x ₋ 1) ₋ 3(2x ₋ 1) = 0

(2x ₋ 1) (2x ₋ 3)

Hence we get the factors of the expression as (2x ₋ 1) (2x ₋ 3)

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Solution :

base 10

A number base (or base for short) of a numeral system tells us about the unique or different symbols and notations it uses to represent a value. For example, the number base 2 tells us that there are only two unique notations 0 and 1. The most common number base is decimal, also known as base 10.

Step1:

Converting 1120 to base 10.

1*103=1000

1*102=100

2*101=20

0*100=0

Adding all to get Ans=1120 based 10

Step2

Converting 1120 based 10 to 5

The equation calculation formula for 1120 based 10 numbers to 5 is like this below.

5|1120

5|224|0

5|44|4

5|8|4

5|1|3

5|1|1

Ans:13440 based 5

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Answer:

2.5

Step-by-step explanation:

15/6 (3p + 3s) = 2.5
18/7 (4p + 3s) = 2.5

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A is uniquely associated with an object f(a) in B. A function is therefore a many-to-one (or sometimes one-to-one) relation. The set A of values at which a function is defined is called its domain, while the set f(A) subset B of values that the function can produce is called its range. Here, the set B is called the codomain off.

A function from a set X to a set Y is an assignment of an element of Y to each element of X. The set X is called the domain of the function and the set Y is called the codomain of the function.

A function, its domain, and its co-domain are declared by the notation f: X→Y, and the value of a function f at an element x of X, denoted by f(x), is called the image of x under f, or the value of f applied to the argument x.

Functions are also called maps or mappings, though some authors make some distinction between "maps" and "functions"

f(x) = x - 2

X=0

f(0) = 0-2

f(0) = -2 ...(1)

f(1) = 1-2

f(1) = - 1 .....(2)

f(2) = x-2

f(2)= 2-2

f(2)= 0....(3)

Answer = Straight line figure

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The statement that is true about the graphed function f(x) is that D. F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).

The intersection of the x-axis, the horizontal line, and the y-axis, the vertical line, creates a coordinate plane, which is a two-dimensional plane. The origin is the point at which these parallel lines cross one another.

In this case, the statement that is true about the graphed function f(x) is that F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).

The appropriate graph is attached.

In conclusion, the correct option is D.

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Answer:

(-2, -2)

Step-by-step explanation:

The point U, when rotated 270 degrees, will end up at the point (-2, -2) on the graph.

Answer:

7(n+8)

Step-by-step explanation:

It says 7 times the SUM of a number, n, and 8. According to the order of operations or PEMDAS, you would find the sum first, which would be in parenthesis, and then multiply by the 7.

Hope this helps! :)

Answer: 72 degrees

Step-by-step explanation:

ok, so the interior angles of a pentagon are 108 degrees, and the line that the two angles are on is equal to 180 degrees, so 180-108 is 72 degrees

Answer: x = pm - n

Step-by-step explantake every value on the right to the left ( this also changes the action for that specific value)

Answer: p x m-n = x

Step-by-step explanation: First, minus n on both sides. This will give you m-n =x/p. Then, multiply P on both sides. This will give you p x m-n =x

Answer:

line segment

Step-by-step explanation:

I'm no Einstein, but that looks like a line segement

ngl

The equation of the graph that is obtained by translating the parent function is as follows:

g(x) = |x + 2| + 1

The parent function is given as

f(x)= |x|

The following is a translation of the parent function f(x), which may be derived from the graph as follows:

2 units left translation

1 unit up translation

The translation of the sequence mentioned above is expressed as

(x, y) = (x + 2, y + 1)

So, we have

g(x) = |x + 2| + 1

Therefore, the equation of the graph that has been translated is g(x) = |x + 2| + 1

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sa paanong paraan nagiging instrumento

Answer:

Steps below

Step-by-step explanation:

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Answer:

x = -4

Step-by-step explanation:

x - 16 = -20

16 is being subtracted from x. To get x alone, you need to add 16 to x - 16.

We must do the same to both sides of an equation, so we add 16 to both sides of the equation.

x - 16 + 16 = -20 + 16

x = -4

Answer:

Step-by-step explanation:

11. Areas as Sum: 7d+28

   Areas as Product: 7(d+4)

12. Areas as Sum: [tex]y^{2}[/tex]+3y

    Areas as Product: y (y+3)

Answer:

Step-by-step explanation:

Using the distributive property, you would multiply 7(d+4) for the question after the example. The side length is your root, and you are multiplying the numbers after it by that root.

Answer: Solution is where the x intercepts on the graph

Step-by-step explanation:

The thing that intuition says about the degree measures of these angles is that ABC and DEF are supplementary angles.

It should be noted that the given measures are ABC = 70° and DEF = 110°

it should be noted that supplementary angles are the angles that have the addition as 180°.

In this case,

ABC + DEF

= 70° + 110°

= 180°

Therefore, the thing that intuition says about the degree measures of these angles is that ABC and DEF are supplementary angles.

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The inverse function is given by f⁻¹(x)=∛x+2 and the inverse is a function.

The opposite function is referred to as the inverse of a function. To map the dependent variable y based on the independent variable x, we should ideally utilize a function. The relationship that determines the value of x based on a certain value of y is known as an inverse function.

The domain of a function shifts to the range for an inverse function, and vice versa.

For a function that is mathematically denoted by the formula y=g(x), where g(x) is a polynomial of x. We use y to solve the equation for x.

Given function is in the form  f(x)=(x-2)³

It can be written as

y=(x-2)³

Then we take the cube root on either sides of the equation.

∛y=x-2

or, x=∛y+2

So the inverse function is:

f⁻¹(x)=∛x+2

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36 students will be in each buses for the trip.

The total number of empty seat in the buses is 32

The school ordered 16 buses that each have 40 seats for a school trip.

There are 32 teachers and 576 students.

Each bus must have 2 teachers and the rest students.

The students were distributed evenly amongst the buses.

Therefore,

number of student in each buses = total number of student / number of buses

number of student in each buses =  576 / 16

number of student in each buses = 36

Therefore, 36 students will be in each buses for the trip.

Each buses has 40 seats.

Recall, 2 teachers are even distributed in each buses.

Therefore

number of empty seat in total = 16 × (40 - 36 - 2)

number of empty seat in total = 16 × 2

number of empty seat in total = 32

Therefore, the total number of empty seats in the buses is 32.

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