In the given figure, △ADE ∼ △ABC. Which triangle similarity theorem justifies
this similarity? Show proof toyour answer.

a. Using the figure below, name the three similar triangles.

b. Write the proportions that exist among corresponding parts of similar

Answer:

Just put

a)

b)

c)

in the first column.

Next, substitute the values in the respective places.

For example, next to the a) and -3, put the value of y = x² + 1

In this case, 9 + 1 or 10

So, put 10 in the top left of the white spaces.

Hope you know what to do now.

Thanks

Answer:

Step-by-step explanation:

The expression becomes x-6 > 9 from the given condition The sum of a number and negative six greater than 9.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given,

To find the sum of a number and negative six , greater than 9 .

let the given number be x .

so,

the expression becomes ,

x - 6 > 9

LHS = x-6

as in the question its given the sum of number and negative of six

So whereas in RHS = 9

As it is given greater than 9 .

Hence, the expression becomes x-6 > 9 from the given condition.

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The value of x from the triangle is x = 30

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ABC

Now , the length of the side b = x

The length of the side a = x + 2

The measure of sin A = 4/5

The measure of sin B = 3/4

So , to find the value of x , we use the law of sines

a / sin A = b / sin B

Substituting the values in the equation , we get

( x + 2 ) / ( 4/5 ) = x / ( 3/4 )

On simplifying the equation , we get

5 ( x + 2 ) / 4 = 4x / 3

Multiply by 3 on both sides of the equation , we get

15 ( x + 2 ) / 4 = 4x

Multiply by 4 on both sides of the equation , we get

15 ( x + 2 ) = 16x

15x + 30 = 16x

Subtracting 15x on both sides of the equation , we get

x = 30

Therefore , the value of x is 30

Hence , the value of x is 30

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Answer:

There are several ways to write a proof, depending on the level of rigor and formality required. Some common methods include:

1- Direct proof: A direct proof is a logical argument that begins with the premises and uses logical deduction to arrive at the conclusion.

2- Proof by contradiction: A proof by contradiction starts by assuming the opposite of what needs to be proven and then showing that this leads to a contradiction.

3- Proof by contrapositive: A proof by contrapositive is a proof that starts by assuming the negation of the desired conclusion and then showing that this leads to the negation of the premises.

4- Proof by induction: A proof by induction is a proof that starts by showing that a statement is true for the first few natural numbers, and then showing that if it is true for a particular natural number, it must also be true for the next natural number.

5- Proof by construction: A proof by construction is a proof that shows the existence of a mathematical object by giving an explicit construction of it.

6- Proof by exhaustion: A proof by exhaustion is a proof that considers all possible cases and shows that in each case the statement is true.

7- Proof by casework: A proof by casework is a proof that is split into several cases, each of which is considered separately.

8- Proof by diagram: A proof by diagram is a proof that uses a visual representation to show that a statement is true.

These are some of the common ways of writing proof, and there could be other ways as well. It is important to use the most appropriate method for the problem at hand, and to clearly explain and justify each step of the proof.

Answer: x = 3

Step-by-step explanation: Plug g(x) in to get 11 = 3x+2. Do algebra and you get x = 3

The 3rd-degree polynomial has at least one or three real roots.

Yes, a third degree polynomial can have all real roots. This is because a third degree polynomial has at least one real root, as it is the lowest degree polynomial that can have an imaginary root. The other two roots can be real or imaginary, depending on the coefficients of the polynomial. If the discriminant of the polynomial is greater than or equal to zero, the polynomial will have all real roots. In a cubic polynomial, only one or three real roots are present. Polynomials having odd degrees have at least one real root. A cubic equation's graph must at least once cross the x-axis, giving you at least one real root. Only a quadratic polynomial has two real roots. Quadratic polynomials are those having a degree of two. Polynomials can be represented on the graph, on that basis we can determine whether the roots are real or not.

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Answer:

Francesca

Step-by-step explanation:

Based on the information provided and the discount, Nick will pay a total of $36 for the sweater.

The discount is defined by equation 0.75 x d (regular price) = final price. This means that to find the final price Nick will pay for any product it is required to multiply the regular price by 0.75.

This also means, Nick will pay 75% of the real price, and therefore the store is offering a 35% discount (100 - 75 = 35). This principle can be applied to find the price of the sweater.

Based on the previous information, let's calculate how much is the sweater:

$40 x 0.75 = $36

Based on this, Nick will pay $36 for the sweater.

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On solving the provided question, we can say that the linear equation, will be  10.50x + 12.50y = 4 => x = 23.1 => y = 3.21

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

a large pizza costs =  $10.50 with no toppings other than cheese

Jason wants 4 toppings on his pizza for a cost of =  $12.10

the linear equation, will be

10.50x + 12.50y = 4

x = 23.1

y == 3.21

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We add [tex]-3x^3 + 5x^2 +1[/tex] in the polynomial [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex]. So the option 4 is correct.

In the given question we have to find which polynomial should be added to [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex].

A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.

Let we add the polynomial P to get the polynomial [tex]3x^2 +4[/tex].

[tex]3x^3 - 2x^2 + 3[/tex] + P = [tex]3x^2 +4[/tex]

Subtract the equation [tex]3x^3 - 2x^2 + 3[/tex] on both side, we get

P = [tex]3x^2 +4[/tex] - ([tex]3x^3 - 2x^2 + 3[/tex])

P = [tex]3x^2 +4-3x^3 + 2x^2 - 3[/tex]

Now simplifying the expression

P = [tex]-3x^3 + 5x^2 +1[/tex]

So we add [tex]-3x^3 + 5x^2 +1[/tex] in the polynomial [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex]. So the option 4 is correct.

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Using the formula of probability without replacement, the probability of selecting a heart first is 13 / 52 and a diamond second is 13 / 51

Probability without replacement refers to the likelihood of a specific event occurring when items are removed from a set or collection as they are selected. It differs from probability with replacement, where the items are replaced after each selection and the set remains unchanged.

To calculate probability without replacement, we use the formula:

P(Event) = Number of favorable outcomes / Number of possible outcomes

Where the number of possible outcomes is the total number of items in the set, and the number of favorable outcomes is the number of items that satisfy the conditions of the event.

In the first event;

P(heart) = 13 / 52

In the second event, the first card is not replaced and so, the number of possible outcomes is reduced by 1

p(diamond) = 13 / 51

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Answer:

x = 1/2

y = 7/2

Step-by-step explanation:

Mate, you almost solved the question there by yourself.

You were at the last step.

-6x + 3 = 0

Add 6x on both sides,

-6x + 3 + 6x = 6x

3 = 6x

Divide 6 on both sides,

3/6 = 6/6 x

1/2 = x

So, y = 7x

y = 7/2

Answer:

Step-by-step explanation:

30-12/3=d

d=drinks he bought

$30-$12=$18

$18/$3=6

he got 6 drinks

Your adjusted gross income (AGI) consists of the total amount of income and earnings you made for the tax year minus certain adjustments to income. The dollar amount on line 10 is calculated by subtracting the standard deduction and personal exemptions from the taxable income.

Line 10 on the 1040EZ form is labeled "Taxable income" and is used to calculate the amount of taxes owed to the IRS. Line 11, labeled "Tax," is used to enter the amount of taxes already paid, either through withholding or estimated payments.

If $4184 is on line 11 and the taxpayer will neither receive a refund nor owe the IRS, that means that the amount of taxes already paid, $4184, is equal to the amount of taxes owed, which is calculated on line 10.

Therefore, the dollar amount on line 10 would also be $4184. This indicates that the taxpayer's taxable income and their taxes already paid are equal, resulting in no additional taxes owed or refund due.

It's worth noting that the dollar amounts on line 10 and line 11 are not directly related, the dollar amount on line 10 is calculated by subtracting the standard deduction and personal exemptions from the taxable income.

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The required inequality describes the problem is  x ≤ 12.

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers.

The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus.

We have,

Edna's phone is fully charged, it can operate for up to 18 hours before running out of battery.

let x represent how many more hours edna's phone can operate without running out of battery.

Then

x + 6 ≤ 18

x ≤ 12

Thus,required inequality is x ≤ 12.

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Answer: Actually kinda ez not gonna lie. y = 11.547, x = 23.094

Step-by-step explanation: we know that y * square root of 3 = 20. 20/ root 3 is 11.547. Hypotenuse is 2 times y. This gives us x = 23.09

Answer:

  neither

Step-by-step explanation:

You want to know if the graphed function is even or odd. It appears to be a cubic with a y-intercept of about 40.

Even functions are symmetrical about the y-axis. A function is even if ...

  f(x) = f(-x)

Even polynomial functions have terms that are all even powers of the variable.

Odd functions are symmetrical about the origin. A function is odd if ...

  f(x) = -f(-x)

Odd polynomial functions have terms that are all odd powers of the variable.

The graphed polynomial function has a non-zero added constant (the y-intercept value), so has both even and odd terms. It is neither even nor odd.

The graph is neither symmetrical about the y-axis, nor symmetrical about the origin.

The trigonometrical ratios of the triangle are:

sin∠X = x/z

cos∠X = y/z

tan∠X = x/y

sin∠Y = y/z

cos∠Y = x/z

tan∠Y = y/x

We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent or tan = sin/cos

The opposite is the side the angle of consideration is facing

The hypotenuse is the side the right angle  is facing

The adjacent is the side left after determining the opposite and hypotenuse

Thus, we have the following trigonometric ratios in the triangle:

sin∠X = x/z

cos∠X = y/z

tan∠X = x/y

sin∠Y = y/z

cos∠Y = x/z

tan∠Y = y/x

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On solving the provided question, we can say that the probability of guessing the sequence 2^99 possible combinations.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true.

As soon as you realize there are more heads than tails, you realize you require at least 50 of them, and you ask 100 people to select 50 locations for them to go.

Considering that you have 250 options for the remaining coins, there are a total of (100 pick 50) + 250 combinations that are feasible.

There are 299 potential options if you simply inquire as to whether the first coin will land on heads.

Asking whether there are more heads than tails is preferable because, according to Wolfram Alpha, 299 is larger than (100 pick 50) + 250.

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The sequence will be; 8/49, 14/49, 20/49, 26/49

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We are given that the sequence as;

8/49, 2/7, 20/49, 26/49

so, we can see the pattern as the denominator is the multiple of 7.

So multiply the second term by 7.

2/7 = 14/49

therefore, the sequence will be;

8/49, 14/49, 20/49, 26/49

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Since X, Y, and Z are independent random variables, the probability of one event occurring has no bearing on the likelihood of the other events. In this instance, the probabilities of X, Y, and Z are 30%, 40%, and 20%, respectively.

We must take into account the possibility that both events could occur simultaneously when determining the likelihood that either X or Y will occur. The occurrences where both X and Y occur would be doubly counted if we just added the probabilities of X and Y. To circumvent this, we employ the following formula for the chance of two events occurring together:

P(X or Y) = P(X) + P(Y) - P (X and Y)

This formula takes into account the fact that we must deduct the probability of X and Y's intersection (i.e., the likelihood that they both occur) from the total of each variable's individual probabilities.

Given that X and Y are independent events, P(X and Y) = P(X) * P(Y) = 0.3 * 0.4 = 0.12 is known.

P(X or Y) is therefore equal to P(X) + P(Y) - P(X and Y) = 0.3 + 0.4 - 0.12 = 0.68 = 68% 

 So, according to option most approximately option is A.

Therefore, 70% would be the most accurate response.

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A student at Big Sky Middle School are more likely to get a t-shirt than a student at High Peaks High School.

(a) To calculate the probability of getting a t-shirt if you are a student at the middle school, we divide the number of t-shirts being given away by the number of students at the school.

Probability of getting a t-shirt at the middle school = 40 / 350 = 4/35 = 0.114 or 11.4%.

(b) To calculate the probability of getting a t-shirt if you are a student at the high school, we divide the number of t-shirts being given away by the number of students at the school.

Probability of getting a t-shirt at the high school = 75 / 800 = 3/32 = 0.094 or 9.4%.

(c) From the above calculations, it is clear that you are less likely to get a t-shirt if you are a student at the high school (9.4%) than at the middle school (11.4%).

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As per the given ratio, the diameter for the circle A is 8 cm.

The term diameter in math is defined as a straight line that goes from one side to the other side of a circle, passing through the center

Here we have given that Circle A is in the interior of circle B. The diameter of circle B is 16 cm.

And we need to find  the diameter of circle A in which the ratio of the shaded area to the area of circle A is 3:1.

While we looking into the given diagram, here we know that the area of the shaded region plus the area of circle A equals the Area of Circle B.

As we know that since the shaded area of the circle, 3:1,

And here we also have

=> 3x + x = 64π

When we simplify this one then we get,

=> 4x = 64π,

Then the value of x = 16π.

Here we have to directly we get

=> π x p² = 16π,

Then the value of

=> r² = 16

=> r = 4.

Here we must know that length can't be negative!

Therefore the diameter of circle A is

=> 4* 2 = 8 cm.

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Answer:

-8

Step-by-step explanation:

(-2)^3 X (-2)^7 / 3X 4^6

= (-8) X (-128) / (3 X 4096)

= 1024 X -128 / 12288

= -128/12

= -8/1

So the final answer is -8

Answer:

1.398101×10^6

Step-by-step explanation:

(-2)^3×(-2)^7/3 ×4^6

=4194304/3

=1.398101×10^6

Answer: x = 1

Step-by-step explanation: 4(1-x) = 6(x-1)

 -  4-4x = 6x-6

 -  6x-4x = 6-4

 -  2x = 2

 - x= 1

On solving the provided question we can say that the polynomial is x² + 6x + 8  by factorization are x(x-5) - 1(x-5) ⇒ (x-1)(x-5) ⇒ x = 5, 1

A number or other mathematical object is factored, or written as the product of numerous factors—typically smaller or simpler things of the same kind—in mathematics. For instance, the integer 15 is factorized as 3 5, which is the factorization of the polynomial x2 – 4. Factorization in mathematics refers to the breakdown of a number into smaller numbers that are multiplied together to produce the original number. Factorization is the division of a number into its factors or factors. 12 is multiplied by 3 and 4 as an example.

the polynomial is

by factorization are

x(x-5) - 1(x-5)

(x-1)(x-5)

x = 5, 1

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Answer: 4.2

Step-by-step explanation: First, you'd need to re-arrange the decimals so, you can get 4.65.........

Then, you round up to get about 4.7

Another way is to round up the decimals, so your new equation:

[tex]\frac{21}{5}[/tex]

Then, you'd divide to get 4.2. This way is more of an estimate than the 1st way; the 1st way is an exact answer [rounded] I hope this helped.

Answer:

  4.64

Step-by-step explanation:

You want an estimate of the quotient 21.4/4.6.

Multiplication and division by 5 are simplified by the relation ...

  5 = 10/2

Here, the denominator is about 5, so the quotient is about ...

  21.4 × 2/10 = 42.8/10 = 4.28 ≈ 4.3 . . . . . a first estimate; known to be low

We notice that 4.6 is 0.4 less than 5, which is 0.8/10 = 0.08, or 8% less. That means the actual quotient will be on the order of 8% more than 4.3.

A closer estimate would be ...

  4.3 + 0.08 · 4.3 = 4.3 +0.344 ≈ 4.64

An estimate of the quotient is 4.64.

__

Additional comment

To compute our "error correction," we rounded 4.28 up to 4.3, about 2 parts in 400, making that number (4.3) be about 0.5% high. The estimate of 1/0.92 ≈ 1.08 turns out to be about 0.7% low. This means an even better estimate would add 0.2%, or about 0.009, to the estimate we have, making it about 4.653. These second-order corrections are also slightly off. The actual quotient rounds to 4.652.

Doubling a number is so easy that we elected to keep all of the digits of the numerator when we did the division by 5. This gave a more satisfying 4.3 instead of 4 as the first estimate.

Answer:

1000

Step-by-step explanation:

\log _{10}\left(5\right),\:500,\:2\log _{10}\left(5\right),\:2+\log _{10}\left(4\right),\:32+\log _{10}\left(4\right),\:8

The rate of change of the hypotenuse is 9.5 inches per second.

The rate of change of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem. The theorem states that for a right triangle with sides of length a, b, and c (where c is the hypotenuse), a2 + b2 = c2.

In this case, we know that the two legs are 3 inches and 4 inches, and that the short leg is increasing by 7 in/sec and the long leg is growing at 9 in/sec.

Using the Pythagorean theorem, we can calculate the rate of change of the hypotenuse. We can set up the equation as follows: c2 = 32 + 42, where c is the hypotenuse. Solving for c, we get: c = √(32 + 42).

To calculate the rate of change of the hypotenuse, we need to take the derivative of the equation. Taking the derivative of the equation, we get: c' = (7/2) * (3/c) + (9/2) * (4/c).

Plugging in our values, we get: c' = (7/2) * (3/5) + (9/2) * (4/5). Simplifying, we get: c' = 9.5 in/sec.

Therefore, the rate of change of the hypotenuse is 9.5 inches per second.

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