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The nature of the roots for y=2x²- 5 is there are 2 distinct real roots.

What is the nature of roots?

The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant

Δ > 0 means there are 2 distinct real roots.

Δ = 0 means there are 2 equal real roots or 1 distinct real root.

Δ < 0 means there are no real roots, but 2 complex roots.

Here,

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b² - 4ac

Substitute the values of a, b, and c.

Evaluate the given equation to find the discriminant, we get

= 0 - 4×2×(-5)

= 41

> 0

Since the discriminant is greater than 0

Hence, there are 2 distinct real roots.

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Answer:

164 minutes

Step-by-step explanation:

$8 + $0.06m = $17.84

To isolate the m, first bring the eight to the other side

0.06m = 9.84

then divide both sides by 0.06

m = 164

The coordinates of G' after the rotation = (6, 5)

In this question we have been given a point G, located at (-5, 6) is rotated 270° counterclockwise.

We need to find the coordinates of G' after the rotation.

a point (-5, 6) is located in the second quadrant.

First 90° counterclockwise rotation gives (-6, -5)  because x & y are interchanged and in Quadrant III both coordinates will be negative.

Second 90° counterclockwise rotation yields (5,-6) because x & y are interchanged and in Quadrant IV the y coordinate will be negative.

Last 90° counterclockwise rotation yields (6, 5) because x & y are interchanged and in Quadrant I both coordinates will be positive.

Therefore, the coordinates of G' after the rotation = (6, 5)

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Part a: Monthly percent rate = y/x

Part b:  APR = y/x × 12.

For the given question;

Average daily balance sheet of Suzanne's is  x dollars.

Finance charges = y

Part a: monthly percentage rate

Finance charge = Monthly percent rate × Average daily balance

Monthly percent rate = Finance charge/Average daily balance

Monthly percent rate = y/x

Part b: APR

Thus,

For 12 months.

APR = y/x × 12

Thus, the value of APR for the period of 12 months is APR = y/x × 12 .

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Answer:

(-11/24)

Step-by-step explanation:

  3         5

------- - -------

  8         6

 3(3)    5(4)

------- - -------

 8(3)     6(4)

  9        20       - 11

------- - ------- = -------

  24      24        24

I hope this helps!

If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your working memory.

A cognitive apparatus known as working memory has a finite capacity and can only temporarily store information. It is crucial for reasoning, decision-making, and behaviour direction. When working on a long-division problem, kids use their working memory abilities to retain the long-division steps. Other instances include keeping track of complicated instructions, taking notes in class, recalling an argument while someone else is speaking, or performing mental calculations. In contrast to long-term memory, which stores a large amount of knowledge over a lifetime, working memory is the little amount of information that may be kept in mind and used to carry out cognitive tasks. One of the most often used concepts in psychology is working memory.

Given,

If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your:

d) Working memory

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do you mean 712 or 7.12?

If for 712 it is 1808.48

if for 7.12 it is 18.0848

The two-column table to prove ∠ABC ≅ ∠DBE using the angle addition postulate is presented as follows;

Statements  [tex]{}[/tex]                                                  Reasons

1. ∠ABD is a right angle   [tex]{}[/tex]            1. Given

∠CBE is a right angle

2. ∠ABD are complementary  [tex]{}[/tex]    2. Definition of complementary angles

3. ∠CBE are complementary  [tex]{}[/tex]     3. Definition of complementary angles

4. ∠ABC ≅ ∠DBE   [tex]{}[/tex]                       4. Congruent complements theorem

The angle addition postulate states that the when two angles are placed side by side such that they share a common ray, the measure of the angle formed by the two angles is the sum of the measure of the individual angles.

∠ABD = ∠ABC + ∠CBD (angle addition postulate)

∠ABD = 90° (definition of right angle)

∠ABC + ∠CBD = 90° (substitution property of equality)

∠ABC and ∠CBD are complementary (definition of complementary)

Similarly

∠CBE = ∠CBD + ∠DBE (angle addition postulate)

∠CBE = 90° (definition of right angle)

∠CBD + ∠DBE = 90° (substitution property of equality)

∠CBD and ∠DBE are complementary (definition of complementary)

∠ABC is a complementary angle to ∠CBD and ∠DBE is a complementary angle to ∠CBD

Therefore;

∠ABC is congruent to ∠DBE (congruent complements theorem)

The congruent complement theorem states if an angle ∠A is a complement to an angle ∠C and if an angle ∠B is also a complement of angle ∠C then ∠A is congruent to ∠B.

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The expression x³ + 3x² - 10x + 24 cannot be factorized

From the question, the polynomial is given as

x3+3x2−10x+24

Rewrite the polynomial properly

So, we have the following representation

x³ + 3x² - 10x + 24

Next, we represent the above expression on a graph

From the attached graph, we can see that the polynomial expression only cross the x-axis at x = -5.569

This implies that the expression cannot be factored

So, we cannot further rewrite the given expression

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If a polynomial is divisible by another then that will be a factor of the polynomial. The value of c such that the given polynomial p(x) = 4x³ + cx² + x + 2 is divisible by (x + 2) is 8.

An algebraic factor is the multiplication of two algebraic terms.

That term could be in the form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given polynomial,

p(x) = 4x³ + cx² + x + 2

Divide  4x³ + cx² + x + 2 by (x+2)

First quotient = 4x²

Then, (4x³ + cx² )- (4x³ + 8x²)

Now in order to become it zero c must be the same as 8.

c = 8

Then, the second quotient = 1

(x + 2) - (x + 2) = 0

So, 4x³ + cx² + x + 2 = (x + 2)(4x² + 1)

Hence "The value of c such that the given polynomial p(x) = 4x³ + cx² + x + 2 is divisible by (x + 2) is 8".

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The Ratio of money made by Jackie and Liana by selling lemonade is 2/3

What does a math ratio mean?

Definitions: If b is not equal to 0, then an ordered pair of numbers a and b, denoted as a/b, is a ratio. A proportion is an equation that equalizes two ratios. You could, for instance, write the ratio as follows: 1: 3 in the case of 1 boy and 3 girls.

How is a ratio calculated?

By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B). You are multiplying information A by information B, as indicated by this. For instance, if A is 5 and B is 10, your ratio will be 5/10.

Given that

Jackie earn = $24

Liana earn = $36

Ratio of their earning = 24/36 = 2/3

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The probability that a woman has a malignant tumor in her breast is 7.5%. ie 75

Let  + = mammogram result is positive

B = tumor is benign

M = tumor is malignant.

Note that Bc = M.

given that P(M) = .01,

so P(B) = 1 − P(M) = 0.99.

We are also given the conditional probabilities

P(+ | M) = .80 and

P(− | B) = .90, where the event − is the complement of +

P(+ | B) = .10

Bayes’ formula:-

P(M | +) = P(+ | M) P(M) / (P(+ | M)P(M) + P(+ | B)P(B))

= 0.80 × 0.01 / (0.80 × 0.01 + 0.10 × 0.99)

=0.075

So the chance would be 7.5%. ie 75

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Answer: .................................................

how many ways can the seating be arranged?

answer = 128 ways

correct or what???

The given expression is proved by the necessary changes.

cosec 2A + cosec 4A = cot A - cot 4A​

Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A

Taking LHS  :

⇒Cosec 2 A + Cot 4 A

⇒Cosec 2 A + ( Cot 2 A )2

⇒Cosec 2 A + ( Cosec 2 A - 1 )2    (  we know:1+ Cot 2 θ =  Cosec 2 θ )

⇒Cosec 2 A +  Cosec 4 A  + 1  - 2 Cosec 2 A

⇒ Cosec 4 A  + 1  - Cosec 2 A

⇒ Cosec 4 A  + 1  - ( 1 + Cot 2 A)

⇒ Cosec 4 A  + 1  -  1 - Cot 2 A

⇒ Cosec 4 A  - Cot 2 A

or cosec2A+cosec4A=cotA-cot4A

Hence Proved.

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The graph of x - y = 6 that shows the x and y-intercepts is in the attachment below.

For a linear graph, the x-intercept is point where the line intercepts the x-axis of a graph, of which the value of y is zero at this point. On the other hand, the y-intercept is the point where the line intercepts the y-axis and the value of x at this point is zero.

Given the equation x - y = 6, determine the x and y-intercepts.

To find the x-intercept, substitute y = 0 into the equation x - y = 6:

x - 0 = 6

x = 6

The x-intercept is (6, 0).

To find the y-intercept, substitute x = 0 into the equation x - y = 6:

0 - y = 6

-y = 6

y = -6

The y-intercept is (0, -6).

This means the line will cut the x-axis at 6, and also cut the y-axis at -6. The graph of the equation x - y = 6 is shown below.

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Answer:

128

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]14^2+x^2=18^2 \\ \\ 196+x^2=324 \\ \\ x^2=128 \\ \\ x=\sqrt{128}[/tex]

The equation which has infinitely many solutions from the given answer choices is; Choice A: -76x+76=-76x+76 and Choice B: 76x + 76 = 76x + 76.

It follows from the task content the the equation with infinitely many solutions among the given answer choices is to be determined.

An equation of the type; a(1)x + b(1) = a(2)x + b(2) is said to have infinitely many solutions if; a(1) = a(2) and b(1) = b(2).

Hence, the equations which have infinitely many solutions among the given answer choices are; Choice A: -76x+76=-76x+76 and Choice B: 76x + 76 = 76x + 76.

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The 4.89 hours after midnight did the temperature first hit 63 degrees.

A sinusoidal function can be used to mimic the daily variation in outdoor temperature. Assume you are aware that the daily average temperature starts at 9 am and swings between 60 and 70 degrees throughout the day.

We have to find to two decimal places, how many hours after midnight did the temperature first hit 63 degrees.

Max T=70 and Min T=60

D = (Max + Min)/2

   = 70+60/2

   = 65

A = Max- D

   = 70 - 65

   = 5

Since,

Period is 24 hours,

So,

W = 2π/24

   = π/12

The function will be:

T(t) = 5 Sin (π/12(t-C)) + 65

Given average temperature occurs at 8 am so,

T(9)=65

Solving this we get

C=9

Hence,

T(t)= 5Sin(π/12( t-9))+65

Now,

We need to find t such that T(t)=63

63=5Sin(π/12( t-9))+65

t = 4.89 hours.

Therefore, The 4.89 hours after midnight did the temperature first hit 63 degrees.

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The equation that models the total amount of money y you pay if you buy x yards of fabric is y = 9.50x - 6

Given,

You have a coupon for a $6 discount at a fabric shop. You purchase fabric for $9.50 per yard.

We have to find an equation that models the total amount of money y you pay if you buy x yards of fabric.

Here,

The equation for the situation be like;

y = 9.50x - 6

Where,

y is the total amount paid

x is the number of yards of fabric you bought

That is,

The equation that models the total amount of money y you pay if you buy x yards of fabric is y = 9.50x - 6

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We see BC is in the middle of the lines AB and BD, therefore mABC + mCBD = mABD.

We're given mABD = 75, mABC = 40.

Therefore, mCBD = mABD - mABC = 75 - 40 = 35.

Answer:

∠CBD = 35°

Step-by-step explanation:

We are told in the question that m∠ABD = 75° and m∠ABC = 40°. We are then asked what the value of m∠CBD is.

As we can see from the diagram, ∠ABD is made up of the angles ABC and CBD. Therefore:

∠ABD = ∠ABC + ∠CBD

⇒ 75° = 40° + ∠CBD

⇒ 75° - 40° = 40° + ∠CBD - 40°       [

⇒ 35° = ∠CBD

∴ ∠CBD = 35°

The answer is 3/25π m/h.

acc to our question-

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

hence,The answer is 3/25π m/h.

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They will require 4 (4/11) days to complete the remaining work together.

Time is the duration during which any activity or work happens or continues.  Work is a task or set of activities to achieve a certain result

It takes Ann alone 10 days to translate a document.

Ann's work in one day = 1/10

In 2 days = 2 / 10

Work left = 8 / 10

Ben alone now takes 12 days to translate a document.

Ben's work in one day = 1/12

We will now use addition.

Combined work of both Ann and Ben in 1 day = 1 / 10 + 1 / 12 = 11 / 60

Time taken to complete the rest of the work = 8 / 10 ÷ 11 / 60

= 48 / 11 = 4.4 days.

As a result, they need 4 (4/11) days to finish the remaining work together.

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An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Divide both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore, the correct representations of the inequality is  an open circle is at 5 and a bold line starts at 5 and is pointing to the right r

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The area of the triangle is A. 17.5yd².

Using this formula to find the area

Area = 1/2 ( b × h)

Where:

b = base = 5

h = Height = 7

Hence,

Area = 1/2 (5 ×7)

Area = 1/2 (35)

Area = 1× 35/2

Area = 35/2

Area = 17.5yd²

Therefore the correct option is A.

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Answer:

y = 12

Step-by-step explanation:

We'll use the form of an equation of a straight line of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are told the slope, m, is -2.

That leads to:  y = -2x + b

y = -2x + b

B, the y-intercept, can be found by using the given point (3,28) in the equation (it falls on the line, so must be a valid solution to the equation.  Use the given x and y in the equation and solve for b:

            y = -2x + b

           28  = -2*(3) + b

           28  = -6 + b

b = 34

The equation is y = -2x + 34

Use this to find y when x = 11:

  y = -2(11) + 34

  y = -22 + 34

  y = 12

y is 12 when x is 11

     See the attached graph.

The actual roots ordered from least to greatest is -45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

Rational roots are roots of a quadratic equation which can be expressed as a ratio or are elements of rational numbers.

Since we have that the possible rational roots are  ±1, ±3, ±5, ±9, ±15, and ±45.

We list the actual roots as follows

+1, -1, +3, -3, +5, -5, +9, -9, +15, - 15, +45 and -45

Since we require the actual roots from least to greatest knowing that the largest negative number is the least and tha largest positive number is the greatest, rearranging, we have

-45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

So, the actual roots are -45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

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