Provide the next step to derive the quadratic formula.
Step 1 : ax2+box+c=0
Step 2 : ax2+box=-c
Step 3 : x2 + b/ax=-c/a
Step 4 : ??

ABC is a right angle

ABCD is a parallelogram

Opposite sides of a parallelogram are equal

So

Opposite angles are equal

<B=<D

Hence

∆ABC and ∆CDB are congruent by SAS

The correct answer is option A which is ABCD ≅ A'B'C'D'.

The process of changing the location of the image on the coordinate system will be known as the translation.

Quadrilateral ABCD is rotated at 145° about point T. The result is quadrilateral A'B'C'D'.

ABCD ≅ A'B'C'D'is correct Since the quadrilateral remains the same even after rotation of 145 degrees. Its corresponding sides and angles will remain the same.

Thus ABCD is congruent to A'B'C'D'.

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Answer: The answer is A

Step-by-step explanation:

In a fourth-grade class, students are making cookies to learn about fractions. They are measuring using measuring cups and spoons. This learning is best described as formal standard measurement.

A standard unit of measurement is a quantifiable language that helps everyone understand the association of the object with the measurement. It is expressed in inches, feet, and pounds, in the United States, and centimeters, meters, and kilograms in the metric system.

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For random samples of size 100 from a population, the mean of the sample means from all possible samples is less than the population means.

The suggestion of the pattern means will equal the population suggest. the standard deviation of the distribution of the sample means, called the same old blunders of the suggested, is the same as the population trendy deviation divided by means of the rectangular root of the sample length (n).

The general sample suggests components for calculating the pattern mean.

The populace suggest is the mean or average of all values within the given population and is calculated by using the sum of all values within the population denoted with the aid of the summation of X divided by way of the number of values in the population that's denoted with the aid of N.

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There are 31 possible lengths for the third side.

Unknown Side +  16 > 21

Unknown Side >  5

16 + 21  > Unknown Side

37 > Unknown Side      

Unknown Side  <  37

So, the possible integer lengths range from

6 -  36  

=   36 - 6 + 1  

= 31 possible lengths

The length of the third side of a triangle has to continually be among (but not equal to) the sum and the distinction among the alternative facets. As an instance, take the example of two, 6, and seven. and consequently, the 0.33 facet length has to be extra than four and less than eight.

The regulation of Cosines to calculate the unknown aspect, then use the Law of Sines to find the smaller of the opposite angles and then use the 3 angles add to 180° to find the final attitude.

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Answer:

x = 108°

y = 72°

z = 36°

Step-by-step explanation:

   If all sides are equal in a pentagon, then it is a regular pentagon.

n = the number of sides = 5

Sum of all angles in a pentagon = (n -2) * 180

                                                     = (5 - 2)* 180

                                                     = 3 *180

                                                     = 540°

Sum of each angle of regular pentagon = 540 ÷ 5

                                                                  = 108°

  [tex]\sf \boxed{\bf x= 108^\circ}[/tex]

Linear pair: If the non common arm of adjacent angles form a straight line, then the adjacent angles are called linear pair and they add up to 180°

∠DCB + y = 180 °   {Linear pair}

  108  + y = 180

            y = 180 - 108

            [tex]\sf \boxed{\bf y = 72^\circ}[/tex]

Exterior angle property of triangle: The exterior angle equals the sum of opposite interior angles.

In Δ BCF ,

  x = y + z

Now, substitute the values of x and y , and we can find the value of z.

      108° = 72 + z

108  - 72 = z

     [tex]\sf \boxed{\bf z = 36^\circ}[/tex]

Step-by-step explanation:

so when you want to rationalize the denominator when it's in the form [tex](a-\sqrt{b})[/tex] you multiply by the conjugate which is [tex](a+\sqrt{b})[/tex] which is where the sign is the opposite. This is because it's using the difference of squares to get rid of the square root. Because [tex](a-b)(a+b) = a^2-b^2[/tex] this will remove the square root since it's going to become square and the ab - ab will cancel so there will be no square root

Multiply by conjugate

[tex]\frac{5\sqrt3}{4-\sqrt6} * \frac{4+\sqrt6}{4+\sqrt6}\\[/tex]

Simplify:

[tex]\frac{20\sqrt{3} + 5\sqrt{6 * 3}}{16-6}[/tex]

Simplify radical

[tex]\frac{20\sqrt{3} + 15\sqrt{2}}{10}\\[/tex]

You could go further and do

[tex]2\sqrt{3} + 1.5\sqrt{2}[/tex]

Answer:

The given lines are un-related.

Step-by-step explanation:

In the question two functions are given as h(t)=3t-4 and j(t)=5-t.

It is required to find whether these lines are perpendicular, parallel or neither.

Step 1 of 1

Find the slope of two lines by comparing these to the standard form.

y=mx+b

Then, [tex]$m_{1}[/tex]=3

And [tex]$m_{2}[/tex]=-1

Since, both slopes are neither equal nor reciprocal of each other.

Therefore, the lines are un-related.

Answer:

Step-by-step explanation:

13x+4/24

Rationals means that a variable would be in the denominator. In this case, only 24 is just a number

Answer:

40.6°

Step-by-step explanation:

The building and the shadow are perpendicular to each other (or intersect at a 90° angle).

Meaning that this is a triangle problem.

We are making a triangle from the building to the shadow and a diagonal line connecting the ends of both.

We need to find the angle at the top of the building. The opposite side of the angle is 84. The adjacent side is 98.

Opposite / Adjacent = Tan X

So if we go to the calculator:

[tex]tan^{-1} (\frac{84}{98}) = 40.6[/tex]

The answer is 40.6 degrees.

Answer:

16

Step-by-step explanation:

Referring to the diagram, we can use Pythagoras' Theorem to find ZY. (which is the distance from Point Y to WX)

By Pythagoras' Theorem,

[tex]c^{2} =a^{2} +b^{2} \\WY^{2} =WZ^{2} +ZY^{2} \\(16\sqrt{2}) ^{2} =16^{2} +ZY^{2} \\ZY^{2} = (16\sqrt{2}) ^{2} -16^{2} \\ZY^{2} =512-256\\ZY^{2} =256\\ZY=\sqrt{256} \\ZY=16[/tex]

The missing statement in the proof is; AB/BD = CB/EB

Similar triangles have the same corresponding angle measures and proportional side lengths.

The given proof is the triangle proportionality theorem which states that the segments formed by side DE are proportional.

The two column proof is presented as follows;

Statement                                           Reason

1. DE || AC                                             1. Given

2. ∠CAB ≅ ∠EDB        2. Corresponding angles formed between ║ lines

3. ΔABC ~ ΔDBE                  3. AA criterion for similarity

4. AB/BD = CB/EB                4. Corr. sides of similar Δs are prop.

5. AB = AD + DB                   5. Segment addition CB = CE + EB

6. (AD + DB)/(DB) = (CE + EB)/(EB)        6. Substitution Property of Equality

7. (AD)/(DB) + 1 = (CE)/(EB) + 1               7. Division

8. (AD)/(DB) = (CE)/(EB)                          8. Subtraction Property of Equality

Hence, the missing statement in the proof is; AB/BD = CB/EB

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If Eric agreed to make monthly payments of 175.00 for 36 months, the total amount of money he will pay the bank is 6,300.

Given that;

To determine the total amount of money that Eric will pay the back, we simply multiply his monthly payment and the number of months.

175.00 × 36

= 6,300

Hence, if Eric agreed to make monthly payments of 175.00 for 36 months, the total amount of money he will pay the bank is 6,300.

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Answer:

(9, 6)

Step-by-step explanation:

the given points are

(3, 2)

(6, 4)

so, can you see, how the sequence continues ?

I see immediately that for every 3 additional units of x we add 2 units of y.

so, yes, the next point in the sequence is

(6 + 3, 4 + 2) = (9, 6).

so, this point (or ordered pair) follows the same ratio or proportional relationship between x and y as the points already in the graph.

in other words, they are on the same line following the same slope ("y coordinate change / x coordinate change" when going from one point on the line to another).

The cost to drive 325 miles is $152.75.

Given: Initial cost = $39

Per mile cost= $0.35

To find: To find the total cost for 325 miles

Concept: Multiplication is the method of finding the product of two or more numbers. It is a primary arithmetic operation that is used quite often in real life.

The cost to drive 325 miles without adding the initial cost = $0.35*325 = $ 113.75

The cost to drive 325 miles while adding the initial cost = $ 113.75 +39 = $  152.75

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The difference of squares is 4m^2 - 20mn + 25n^2

Its a perfect square trinomial.

A perfect square trinomial is the square of a binomial. It follows a pattern when it is factored, so that the first and last terms are perfect squares of monomials and the middle term is twice their product. If the pattern does not fit for a particular trinomial, it is not a perfect square trinomial.

(-2m + 5n)^2

(-2m + 5n)(-2m + 5n)

4m^2-10mn-10mn+25n^2

4m^2 - 20mn + 25n^2

Thus, the difference of squares is 4m^2 - 20mn + 25n^2

Its a perfect square trinomial.

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The sampling distribution is illustrated below.

Based on the information given, the population is illustrated as 1, 4, 7. The sample without replacement will be:

Sample Mean

1 and 4. 2.5

1 and 7. 4

4 and 7. 5.5

The population mean will be:

= (1 + 4 + 7)/3

= 4

The sample mean is an unbiased estimator of the population mean.

The sampling with replacement illustrates that the mean will be:

= 36/9 = 4

Also, when n = 3, the number of samples will be:

= 3³ = 27

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Answer:

A(5 ; 8)

Step-by-step explanation:

y = 5x - 17

y = x + 3

    5x - 17 = x + 3

⇔ 5x - x = 3 + 17

⇔ 4x = 20

⇔ x = 20/4

⇔ x = 5

y = 5 + 3 = 8

So (5 ; 8)

Answer:

We can use the substitution method to solve the system of equations.

Since y = x + 3, we can substitute this expression for y in the first equation:

y = 5x - 17

x + 3 = 5x - 17

Subtracting x from both sides, we get:

3 = 4x - 17

Adding 17 to both sides, we get:

20 = 4x

Dividing both sides by 4, we get:

x = 5

Substituting this value of x into either equation, we get:

y = x + 3 = 5 + 3 = 8

Therefore, the correct ordered pair is (5, 8), which corresponds to the point where the two lines intersect.

The correct answer is (A) (5,8).

The new number in the sequence is found to be 7.

In mathematics, a sequence is a list of components, usually numbers, where the components' order is important. Here, everything fits into a predetermined pattern.

A sequence can be arranged in either ascending or descending order.

There are certain unique sequences, including the triangular number series, square number sequence, cube number sequence, geometric sequence, Fibonacci sequence, and harmonic sequence.

According to the question, the sequence follows the pattern:

Next number=2(Previous number)-2

On substituting the values,

48=2(Previous number)-2

50=2(Previous number)

Previous number=[tex]\frac{50}{2}[/tex]=25

New number=sum of digits of the previous number in the sequence

                     =2+5

                     =7

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Answer:

x = 1.48803, x= -0.821367

Step-by-step explanation:

9x²-6x=11

9x²-6x-11=0

use quadratic formula: x = [- b ± √b²- 4ac)]÷ 2a

Answer:

x =1+2{3 over 3

Step-by-step explanation:

Using the distance formula, the area of the rectangle is: 16 units².

Area of a rectangle = (length)(width).

Given the vertices:

Area = (AB)(BC)

Apply the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB and BC:

AB = √[(1−(−3))² + (3−(−1))²]

AB = √[(4)² + (4)²]

AB = √32

BC = √[(1−3)² + (3−1)²]

BC = √[(−2)² + (2)²]

BC = √8

Area = (√32)(√8) = √256

Area = 16 units²

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[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

When [tex]\bf{p^2-4p}[/tex] is subtracted from[tex]\bf{p^2+p-6}[/tex], the result is...?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

[tex]\bf{Subtract:}[/tex]

[tex]\bf{p^2+p-6-p^2-4p}[/tex]. | combine like terms

[tex]\bf{p^2-p^2+p-4p-6}[/tex] | simplify

[tex]\bf{0p^2-3p-6}[/tex] | simplify

[tex]\bf{-3p-6}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                   [tex]\bf{-3p-6}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

5p - 6

Step-by-step explanation:

p² + p - 6 - (p² - 4p) ← distribute parenthesis by - 1

= p² + p - 6 - p² + 4p ← collect like terms

= 5p - 6

For  Hasson’s Swim the data is a graph with points (6, 9.6), (8, 11.8), (10, 14), and (12, 16.2), and Michael’s Swim A 2-column table with 4 rows. Column 1 is labeled Time. Micheal won by 2 sec. This is further explained below.

Generally, a diagram that illustrates the relationship between variable quantities, usually consisting of two variables, with each variable being measured along one of a pair of axes that are intersected at right angles.

In conclusion, Micheal won by 2 sec.

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Answer:

1. Michael

2. 2 seconds  

Step-by-step explanation:

flash is the best show on netflix

Answer:

horizontal asymptote of y = -7

Step-by-step explanation:

The parent function is shown on the coordinate plane. The graph of the parent function has a horizontal asymptote (an imaginary line that the graph approaches, but never touches or intersects) of y = 0.

Since the function of g(x) = e^x - 7 is the graph of the parent function translated 7 units down, the function would have a horizontal asymptote of y = -7.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

 all real numbers greater than or equal to –3

Step-by-step explanation:

|x| has a range of all real numbers greater than or equal to zero, so f(x) = |x|-3 will have a range of ...

 all real numbers greater than or equal to -3

Answer: 36

Step-by-step explanation:

[tex]\overline{AB} \cong \overline{BC}[/tex] (Triangle ABC is isosceles)

[tex]m\angle CAB=m\angle CBA=30^{\circ}[/tex] (base angles of an isosceles triangle are congruent)

[tex]\angle MCB=90^{\circ}[/tex] (In triangle CMB, angles in a triangle add to 180 degrees)

[tex]\angle ACM=30^{\circ}[/tex] (triangle sum theorem)

[tex]MB=24[/tex] (30-60-90 triangle CMB)

[tex]AB=12[/tex] (sides opposite congruent angles in a triangle are congruent)

[tex]AB=36[/tex] (segment addition postulate)

The value of AB = 36

An isosceles triangle is a triangle with base angles equal with any two sides equal.

Analysis:

∠ACB = 120

ABC is isosceles, so ∠CAB = ∠CBA = x

x + x + 120 = 180 ( sum of angles in Δ ABC)

2x = 60

x = 30

∠AMC = 180 - ∠BMC( angles on a straight line)

           = 180 - 60 = 120

∠ACM = 180 - (30 + 120) = 180 - 150 = 30°

∠MCB = 90°

using sine rule,

12/sin 30 = AM/ sin 30

AM = 12

MB/sin 90 = 12/sin30

MB sin 30 = 12 sin 90

MB = 12/sin 30 = 12/0.5 = 24

AB = MB + AM = 24 + 12 = 36

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Answer: x+y=

Step-by-step explanation:

you would just write it out step by step explaining wht u need to do to solve the question

Answer:

Step-by-step explanation:

h² means h * h

We can start with a number like "10". 10*10 = 100, so we have to guess a bit higher.

12*12 = 144.

However, it can also be -12 * -12 since the two negative signs will cancel each other out.

So, h can be 12 or -12

Answer: +12 or -12

Step-by-step explanation:

h^2=144

taking sqrt root on both sides

h=±12

so answer is +12 or-12

When writing an informative essay about an event in history, you should:

To avoid finding it difficult to find information on your topics, pick a topic that has been well researched and has several sources of information on it. European history is well researched.

In the introduction, talk about why you think this topic is significant and include a thesis statement that would be the main logic you are producing details about.

Then divide this thesis into several points and talk about each point in a different paragraph. Use sentences that are not too long so that people don't lose interest.

Use primary and secondary information sources but make sure you reference these sources in the required format.

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Hello,

[tex]g(x) = 2x - 2[/tex]

[tex]g(-3) = 2 \times (- 3) - 2 = -6 - 2 = -8[/tex]

Answer: g(-3) = -8

Given that:

To find g(-3), insert (x = -3):

⇒ g(-3) = 2(-3) - 2

⇒ g(-3) = -6 - 2

⇒ g(-3) = -8

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