f(x) = 11 – x Find the range of f for x > 4.​

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:200 is a perfect square

Step-by-step explanation:

because when divided by two it give a whole number being divided

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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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

Answer:

15 weeks.

Step-by-step explanation:

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

how many ways can the seating be arranged?

answer = 128 ways

correct or what???

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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Answer: Campbell to Hillsboro to Richmond to Winchester

(Note: Not taking the Washington route)

Step-by-step explanation:

Form Campbell all the way to Richmond have no other choices, From Richmond to Winchester has two choices, 12.2 mi +5.2 mi or 15.7 mi

12.2+5.2=17.4 mi while the other choice is only 15.7 mi

So taking the 15.7 mi option is faster

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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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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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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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 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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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 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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do you mean 712 or 7.12?

If for 712 it is 1808.48

if for 7.12 it is 18.0848

Price of one pair of socks are $5.00

The total of 5 sisters each bought scarves and 2 pairs of socks.

Socks price variable defined as x.

Total scarves bought by the sisters are:

5 × 1 = 5

Total socks bought by the sisters are:

5 × 2 = 10

Equation for total bill:

$125.00 = 5 × $15.00 + 10 × x

$125.00 = $75.00 + 10x

10x = $125.00 - $75.00

10x = $50.00

x = $50.00/10

x = $5.00

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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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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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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 largest area that may be surrounded by fencing is 61776.13 m².

A building's side will have a rectangular storage room built into it. The remaining three corners of the space need security fencing.

The maximum area is enclosed within 703ft of fencing.

Let x = width

     L = length

The perimeter with 3 sides;

L + 2x = 703

L = (703 - 2x)

Let, Area = x * L

Now, replace L with (703 - 2x);

A = x * (703 - 2x)

A = 703x - 2x²

To get the max area by finding the axis of symmetry;

x = -b/2a

In this equation a = -2; b = 703

x = -703 / (2*-2)

x = 175.75m, ( width for the max area )

To get the max area, x=175.75;

A = -2(175.75²) + 703(175.75)

A = -61776.12 + 123552.25

A = 61776.13 m² is a max area

Hence, The maximum area that can be enclosed with 703ft of fencing is 61776.13 m².

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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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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!

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]

Sarah can run = 100 metres.

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The p-value for a Z of 1.34 for a two-tailed test is 0.18025. Since the worth of p is greater than 0.05, we has fail to reject the null hypothesis.

What is hypothesis testing?

In hypothesis testing, we'll find to know whether we should reject or fail to reject some hypothesis.

To hold the decision, we should always compare the p-value in the test statistic to the significance level we have chosen to use the test. If the p-value is a smaller amount than the significance level, we'll reject the null hypothesis. Otherwise, we'll fail to reject the null hypothesis.

This calculations will tells you whether you ought to reject or fail to reject a null hypothesis based on the value of the test , the format of the test are going to be (one-tailed or two-tailed), and therefore the significance level you have chosen to use.

One-tailed or two-tailed ?

Value of the test statistic

1.34

Decision Rule say that : fail to reject the null hypothesis

The p-value for a Z of 1.34 for a two-tailed test is 0.18025. Since the worth of p is greater than 0.05, we has fail to reject the null hypothesis.

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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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