Find the equation of the graphed line.

The value of the discriminant of the given expression x² + 4x +40 = 0  is equal to -144.

As given in the question,

Given expression is equal to :

x² + 4x +40 = 0

Standard formula of the discriminant for the general quadratic equation

ax² + bx + c = 0 is given by :

Discriminant is represented by  'D'

D = b² - 4ac

Here b = 4 , a = 1 and c = 40

Substitute the value in the formula we get,

D = 4² - 4(1)(40)

⇒D = 16 - 160

⇒ D = -144

Therefore , the value of the discriminant of the given expression x² + 4x +40 = 0 is equal to -144.

The above question is incomplete ,the complete question is :

What is the value of discriminant x² + 4x +40 = 0?

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When the sides and angles of two triangles match that triangle is congruent and When the angles of two triangles match that triangle is similar.

When the sides and angles of two triangles match, the triangles are said to be congruent. When the angles of two triangles match, the triangles are said to be similar. Thus, two triangles can be superimposed side to side and angle to angle.

Hence, when the sides and angles of two triangles match that triangle is congruent and When the angles of two triangles match that triangle is similar.

If two triangles have an equal number of comparable angles and sides, they are said to be similar. Similar figures are items that have two or more figures with the same shape but varying sizes.

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Answer:

860 cards

Step-by-step explanation:

[tex]\frac{5}{100} =\frac{43}{x}[/tex]

43 cards only represents 5% of the total cards sold on Mother's Day. So create proportions and solve for the number of cards that represents 100%.

5x = 43*100

5x = 4300

x = 860

Answer:

D. y = 2

Step-by-step explanation:

It can't be A because this is the equation for the slope is undefined.

It can't be B because this equation has no y-intercept!

It can't be C because the equation is y=mx + b. And we see that this equation has a slope of 2, so it is wrong.

So, the answer is D

This is a geometric sequence since common difference is same between previous and next term.

The sum of arithmetic sequence is know as arithmetic series.

The general formula to find arithmetic series is:

[tex]S_{n} =\frac{n}{2} [2a_{1} +(n-1)d][/tex]

Since 8 17 26 and 35 have a common difference that is d=9 always between previous and next term so given sequence is arithmetic sequence.

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We need to solve this question using Arithmetic Progression concept. Yes the given sequence is Arithmetic and value of d is 3.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...

The n-th term of the sequence (a n) is provided by: If the first term of an arithmetic progression is a and the common difference between each succeeding component is

{a {n}=a+(n-1)d},

If the AP contains m terms, then a m denotes the final term, which is provided by:

{a {m}=a+(m-1)d}.

The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.

The given sequence is -3,0,3,6,....

 We know that an=a + (n-1)d where d is the common difference

  ⇒ 0= -3 + d

∴ d=3

So hence proved that the given sequence is arithmetic.

We need to solve this question using Arithmetic Progression concept. Yes the given sequence is Arithmetic and value of d is 3.

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The domain and range of g(x) = |x - 3| are all real numbers and all positive real numbers while the domain and range of the function h(x) = x - 3 are all positive real numbers.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

As per the given function,

g(x) = |x - 3|

Since it is a mode function thus the value of the function will always positive.

Thus, the range will be [0, ∞) or all positive real numbers.

In the function h(x) = x - 3 here we have negative real numbers as well as positive thus the range of it will be all real numbers.

Hence "While the domain and range of the function h(x) = x - 3 are all positive real numbers, those of g(x) = |x - 3| are all real numbers and all negative real numbers.".

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The probability from the odds is 3/7

The value of the odds is given as

Odds = 3 to 4

Represent the odds as a fraction

So, we have the following representation

Odds = 3/4

To convert the odds to probability, we make use of the following equation

Probability = Odds/(1 + Odds)

Substitute the known values in the above equation, so, we have the following representation

Probability = (3/4)/(3/4 + 1)

Evaluate the sum

Probability = (3/4)/(7/4)

Evaluate the quotient

Probability = 3/7

Hence, the probability is 3/7

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Answer:

y=90 degrees

Step-by-step explanation:

x+y+70=180 degrees  ==> these three angles make up a triangle, and the

                                         the total sum of angles in a triangle is 180 degrees

Notice that y is on a straight line?

Straight lines are 180-degree angles called straight angles.

Hence:

(180-y)+x+70=180  ==>  these three angles also make up a triangle, and the

                                        the total sum of angles in a triangle is 180 degrees

180-y+x+70=x+y+70  ==> since both expressions equal 180, they both are

                                         equal to each other

180-y+x+70 + y = x+y+70 + y ==> add y on both sides to isolate y to one side

180 - y + y + x + 70 = x + y + y + 70  ==> simplify

180 + x + 70 = x + 2y + 70

180+x+70 - x = x+2y+70 - x  ==> subtract x on both sides to eliminate x

180 + x - x + 70 = x - x + 2y + 70  ==> simplify

180 + 70 = 2y + 70

180 + 70 - 70 = 2y + 70 - 70 ==> subtract both sides by 70 to simplify the equation

180 = 2y

y = 180/2

y = 90 degrees

Answer:

r = 6 feet

Step-by-step explanation:

Ler r represents the radius

Hence perimeter = edge speed times 3second

2 times 3.14 times r = 12.56 times 3

r = 6 feet

What is Clustering method in unsupervised learning?

An method known as unsupervised learning discovers patterns in untagged data. The idea is to compel the computer to create a clear representation of its surroundings and then produce innovative material from it through imitation, which is a crucial learning method for people.

There are several ways to evaluate the performance of a clustering method in unsupervised learning. Some common evaluation metrics include:

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Answer:

$58.50

Step-by-step explanation:

1.2 kg = 1200g

To get from 200 to 1200, we time 6, so we take $9.75 times 6 to get the price.

$9.75 times 6 = $58.50

So, the cost of 1.2kg cheese is $58.50

The answer is $58.50

I have attached the explanation! :)

It is a quadratic equation, indeed.  7x =2x²

A quadratic equation is any equation of the form where x is a variable, b, and c are any real values, and a 0.

As is common knowledge, the formula for the quadratic equation's roots is the discriminant formula

By replacing, we can create the following equation given the information in the question:7x =2x²

2x^2-7x=0

This is a quadratic equation because, as we can see, x has a power of two.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

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The term (7 + 3x) is a factor of the quadratic equation 3x² + 7x  .

A number is called a factor of the quadratic equation if that number satisfies the equation .

the term is given as : 7 + 3x ,

solving it we get ; 3x = - 7

So , x = -7/3 .

to check whether it is a factor , we substitute the value of x in the equation ,

we get , 3x² + 7x

= 3(-7/3)² + 7(-7/3)

= 49/3 - 49/3

= 0

Therefore , Yes , (7 + 3x) is the factor of 3x² + 7x  .

The given question is incomplete , the complete question is

Is (7 + 3x) is a factor of the quadratic equation 3x² + 7x  ?

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A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number, 8 is divisible by 2 and 4 other than itself and 1, so 8 is not a prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction.

factor of 8 = 2x2x2,

since 8 is divided by 2, so it is not a prime number.

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Answer:

£135

Step-by-step explanation:

70% of £450

=£315

£450-£315=135

Answer: [tex]p + 254 \leq 471[/tex]

Step-by-step explanation:

The number of people in the theater plus 254 )the number of people already in the theater) must be less than or equal to the maximum amount allowed to be seated, 471.

So, [tex]p + 254[/tex] represents the number of people in the theater.

471 is the maximum amount of people.

So, p + 254 must be less than or equal to [tex]p + 254[/tex].

Therefore, we can say that:

[tex]p + 254 \leq 471[/tex]

Answer:

85

Step-by-step explanation:

Think of mean as the average of a set of values. In this case, we have to find the average of Danielle's scores. To do this, add all of the values together and divide it by the number of values we have:

We have 11 scores so we will divide all of them by 11:

[tex]\frac{84+85+83+86+80+85+86+88+89+86+83}{11} = \frac{935}{11} = 85[/tex]

The answers for the given proof of a parallelogram are explained below:

A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. The Euclidean parallel postulate, or one of its equivalent formulations, is a necessary precondition for both the congruence of opposite sides and opposite angles, and neither condition can be demonstrated without using it. In contrast, a quadrilateral with just one set of parallel sides is referred to as a trapezoid or trapezium in British or American English. A parallelepiped is the parallelogram's three-dimensional counterpart.

1) CPCTC(corresponding parts of congruent triangles are congruent)

2) Reflexive property

3) Corresponding angles theorem converse(If corresponding angles are equal then the lines are parallel)

4) Alternative angles theorem converse(If alternative angles are congruent then the lines are parallel)

5) SSS

6) Given.

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The effect of good debt to ones credit score is that is would increase it. That is option B.

A credit score is defined as the expression that can be used to show a customer's worth regarding the payment of their debts.

A customer's credit score can be rated as follows:

A good debt is the ability of a customer to quickly pay off their debt which has been noted as one of the qualities that raise their credit score.

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The value 1 is the multiplicative identity of any number.

In the field of mathematics, the 1 value can be described as the multiplicative identity of any number which has any mathematical value. 1 value describes that when any number is multiplied by the digit 1, the result that arises is the number itself. Hence, value 1 represents the multiplicative identity.

Based on the 1 value, we know that any mathematical expression, digit, or value when multiplied by the digit 1 has an answer that is the same value. As this property is common to all the numbers when multiplied by 1, hence it is referred to as 1 value.

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Answer:

To find a, you'll put the value 8.3 as x in the equation to get the value of y which is equal to a. For the second point you'll put -10.2 as the value of y in the equation to get x which is equivalent to b.

Step-by-step explanation:

every point represents an ordered pair of (x, y) values.

if the point is on the given line (or any other form of curve/ function), then these x and y values make the functional equation true. if the equation turns out to be false with these values, then the point is not on that functional curve.

so, we need to find a and b to make the equations true.

(8.3, a)

3×8.3 - 4a + 24 = 0

24.9 + 24 = 4a

48.9 = 4a

a = 48.9/4 = 12.225

(b, -10.2)

3b - 4×-10.2 + 24 = 0

3b + 40.8 + 24 = 0

3b + 64.8 = 0

3b = -64.8

b = -64.8/3 = -21.6

83% of pupils passed the test as a group.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

It is claimed that two ratios are in proportion if they are the same. A/B Equals C/D if the four elements are a, b, c, and d in that order. The terms a and d are referred to as extremes, whereas b and c are referred to as medium terms. The ratio equates the product of extremes to the product of means.

Results in total: 65% of the review was finished.

The desired results were 55% exam pass.

The percentage is as follows:

p = 55/65 x 100%

  = 82.3%.

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The complete table is given and rate of change is 1 per 28 pair of jeans.

How quickly something evolves over time is referred to as its rate of change (ROC).

Given, of the 84 pair of jeans only 3 are defected.

And rate of change is constant.

And 1 defected pair of jeans is 84 /3 = 28.

That means,

total number of jeans = n x 28

Where n is the number of defected pair of jeans.

So, for n = 3,6,8,12,15

Then, number of jeans =84, 168, 224, 336, 420.              

The table is given in the image.

The basic formula for the rate of change is:

Rate of change = (Change in quantity 1) / (Change in quantity 2)

In every 28 pair of jeans there is one defected jeans.

Therefore, the complete table is given and rate of change is 1 per 28 pair of jeans.              

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No, 4 is not a linear expression.

A linear expression is an algebraic expression involving two or more variables, where the highest power of each variable is one. Linear expressions can be written in the form of an equation, such as y = 2x + 5. In this equation, y and x are variables, and 2 and 5 are constants. The highest power of each variable is one, so this is a linear expression. In contrast, 4 is a constant and does not involve any variables, so it is not a linear expression.

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The race result will not be disqualified due to an illegal wind.

In order to determine whether the wind velocity during the race was legal, we need to compare the wind velocity w to the legal wind speed limit of 5 km/hr. In this case, the wind velocity is given as 5ij km/h, which is purely vertical wind. The direction of the wind is not relevant in this case, since the race is run in the direction of the vector v, which is a purely horizontal direction. Since the wind velocity w is purely vertical and the race is run in a purely horizontal direction, the wind velocity w has no effect on the race result. Therefore, the race result will not be disqualified due to an illegal wind.

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The probability that 5 people sit in the correct order in either direction clock or anti-clock is equal to the probability of any one of the orders occurring, which is 1/2, or 50%.

To calculate the probability that they sit in the correct order in both directions, you would multiply the probability of each event occurring. Since the probability of either event occurring is 1/2, the probability of both events occurring is (1/2) * (1/2) = 1/4, or 25%. This means that there is a 25% chance that the 5 people will sit in the correct order in both directions around the table.

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The triangles are congruent if two angles and the excluded side of one triangle match equivalent areas in another triangle, it is known as the AAS similarity theorem.

Angle-Angle-Side is abbreviated as AAS.

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

AAS congruence can be demonstrated with a few simple methods.

If and only if the corresponding sides and angles are in proportion, two triangles are said to be comparable.

Similar to how there are particular ways to demonstrate triangle congruence (SSS, ASA, SAS, AAS, and HL), there are particular ways to demonstrate triangle similarity.

Therefore, the triangles are congruent if two angles and the excluded side of one triangle match equivalent areas in another triangle, it is known as the AAS similarity theorem.

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The adjusted trial balance for revenue in the accounting worksheet is 20,000.

Trial balance in the accounting worksheet is a financial report where the credit entries and debit entries are listed which is used to audit the accounting system of business or organization internally. It is used to confirm that the sum of all credits and debits must be equal.

Here we have the credit of 15,000 for revenues.

Then the trial balance is adjusted with a credit of 5000.

If we have two debits or credits, we will add them.

So the adjusted trial balance = 15,000 + 5,000 = 20,000

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There are a few ways to find discontinuities in a function. One way is to look for places where the function is not defined or where it produces an undefined result, such as division by zero. Another way is to look for places where the function exhibits a sudden change in behavior, such as a jump or a sharp turn.

To find discontinuities more formally, you can use mathematical techniques such as limits or derivatives. If you are familiar with these concepts, you can use them to identify discontinuities in a function.

For example, if you are trying to find the discontinuities of a function f(x), you can consider the limit of the function as x approaches a certain value, say x=c. If the limit of the function as x approaches c from both the left and the right is different, then there is a discontinuity at x=c. Similarly, if the derivative of the function is not defined at a certain value of x, then there is a discontinuity at that point.

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if you are trying to find the discontinuities of a function f(x), you can consider the limit of the function as x approaches a certain value, say x=c. If the limit of the function as x approaches c from both the left and the right is different, then there is a discontinuity at x=c. Similarly, if the derivative of the function is not defined at a certain value of x, then there is a discontinuity at that point.