A pupil wrote:
for all numbers j and k,
(j+k)² = j² + k²
Expand and simplify (j+k)² to show that the pupil is wrong.

The value of x in the rectangle is  -5 + 5√3.

A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides are parallel to each other.

Therefore, the area of a rectangle can be found as follows:

area of a rectangle = lw

where

Therefore,

length = x + 10

width = x

Hence,

50 = x(x + 10)

50 = x² + 10x

x² + 10x - 50 = 0

using quadratic formula,

[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

a = 1

b = 10

c = -50

Therefore,

x = [tex]\frac{-10+\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex]  and x =  [tex]\frac{-10-\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex]

Hence,

x = -5 + 5√3 and x = -5 - 5√3

Therefore, we can't use negative values

The value of x = -5 + 5√3

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a) Continuous random variable

b) Discrete variable

c) Discrete random variable

d) Continuous random variable

e) Continuous random variable

f) Continue random variables

A variable is something whose value changes.

A discrete variable is a variable whose value can be obtained by counting.

Example: Number of students in attendance

Number of red marbles in a jar

A continuous variable is a variable whose value is determined by measurements.

Example: Height of a student in a class

Weight of a student in a class

Random variable : A random variable is a variable whose value is the numerical result of a random phenomenon.

Random variables can be discrete or continuous.

A discrete random variable X has a countable number of possible values.

Example: Let X be the sum of two dice.

A continuous random variable X takes all values at a specific number interval.

On the basis of above definition we can easily evaluate that the given examples are random variable, continuous random variable or Discrete variable.

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Answer:

Step-by-step explanation:

Slope of a straight line is the gradient of that line.

Formula for gradient is rise over run. Meaning: m = (y2 - y1) / (x2 - x1)

To use this formula, you need 2 points of the straight line. They have already given you one: (8, -3). For the second one, we consider the equation of the line. The y-intercept is given too: -4.

Now, keep in mind, the y intercept is the point of the line that passes from x = 0. Meaning, the point where the line touches the y axis, and at y axis, x = 0. So our second point is (0, -4).

Now as we have 2 points, (8, -3) and (0, -4), we put the values in the formula: m = (y2 - y1) / (x2 - x1) = (-4 - (-3)) / (0 - 8) = -1 / -8 = 1 / 8

For the given fees charged by two fitness clubs , number of months required by two fitness clubs to pay the same total amount is equal to      10 months.

As given in the question,

Number of fitness club  = 2

Let 'x' represents the number of months

Charges for a month membership charged by Mike's Fitness center is equal to $30.

Charges for a month membership charged by All-Day Fitness club is equal to $22 plus $80 initiation fee.

Required equation when two clubs have same amount of charges is given by:

30x = 22x + 80

⇒ 30x -22x = 80

⇒ 8x = 80

⇒ x = 10 months

Therefore, number of months required by two fitness clubs to pay the same total amount is equal to 10 months.

The complete question is:

Mikes fitness center charges $30 per month for a membership. All-Day fitness club charges $22 per month plus an $80 initiation fee for a membership. After how many months will the total amount paid to the two fitness clubs be the same?

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Answer:

-1, 0, 1

Step-by-step explanation:

The unit rate for three dollars for 2 1/2 hours of work will be $1.2 using the concept of unitary method.

The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. The unitary technique is a method for determining the value of any necessary quantity by first obtaining the value of the unit (one) quantity.

Here,

$3 for 2.5 hours of work,

1 hour will cost $x,

3/2.5=x/1

2.5x=3

x=$1.2

Using the unitary technique, the unit rate for three dollars for two and a half hours of labour will be $1.2.

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The mean is 63.12 using the data given.

Given that,

Calculate the dataset's mean using the output from the following calculator, rounding to the nearest 100th if necessary.

1-Var-Stats

[tex]\bar x[/tex] = 63.1428571429

∑x = 442

∑x² = 28266

Sₓ = 7.71208081364

σₓ = 7.13999942834

n = 7

minX = 48

Q₁ = 58

Med = 66

Q₃ = 69

maxX = 69
​Mean value is defined as sum of all data values divided by the total number of data values

Using the given data output

We get,

Mean = 63.14 (rounded to 2 decimals)

Therefore, The mean is 63.12 using the data given.

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Answer:

c) divide both sides by 8

hope this helps!

Answer:

Its the 3 option

Answer:just add if i am right?

Step-by-step explanation:

Answer:

-6 is the y-intercept, as in the point that crosses the y axis

Answer: Slope=7/9

Step-by-step explanation:

m=[tex]y_{2} - y_{1} / x_{2} - x_{1}[/tex]

We can insert your equation to get:

m=8-1/10-1

Simplify:

m=7/9

Two approximations of the area of the region between the graph are

(9, 11)

Given;

To calculate two approximations of the area of the region between the graph of the function and the x-axis across the given interval, use the left and right endpoints and the specified number of rectangles. rectangles f(x) = 2x + 3, [0, 2], 4

The graph is positive and the width of each subinterval will be,

a = 0, b = 2, n = 4

Δx = b-a/n = 2-0/4

     = 0.5

Now for different values;

x → f(x) = 2x+3

x₀ = 0 → f(x₀ ) = 2x+3 = 2(0)+3 = 3

x₁ = 0.5 → f(x₁) = 2x+3 = 2(0.5)+3 = 4

x₂ = 1.0 → f(x₂) = 2x2+3 = 2(1) +3 = 5

x₃ =1.5 → f(x₃) = 2x+3 = 2(1.5)+3 = 6

x₄ = 2 → f(x₄) = 2x+3 = 2(2)+3 = 7

The area by using the approximation using 4 approximating rectangles and right endpoints is given by,

A ≈ R₄ = ∑f(x) Δx = ( ƒ(x1)Δx + ƒ (x2)Δx+ ƒ (x3)Δx + ƒ (x4)Δx)

          = 0.5 (4 + 5 + 6 + 7)

          = 0.5 × 22

          = 11

The area by using the approximation using 8 approximating rectangles and left endpoints is given by.

A ≈ L₄ = ∑f(x) Δx = ( ƒ(x0)Δx + ƒ (x1)Δx+ ƒ (x2)Δx + ƒ (x3)Δx)

          = 0.5 (3 + 4 + 5 + 6)

          = 0.5 × 18

          =9

Thus, 9 < Area < 11.

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For a box given a sudden push up a ramp and the friction between the box and the ramp is not negligible, the diagrams which best represent the directions of the actual forces acting on the box as it moves upward after the push is Option A.

Friction refers to the force of resistance in the relative motion of solid surfaces in contact and sliding or rolling against each other. Frictional forces are affected by the surface texture and the amount of force impelling them together and the angle and position of the object. The actual forces acting on the box will be the normal force (always perpendicular to the surface), weight force (acting downward) and frictional force (acting opposite to the direction of push).

Note: The question is missing options which are provided in the figure.

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Dr. Ellison's equation that f(2) = 5/3 is wrong

From the question, we have the following equation that can be used in our computation:

y = -3x + 7

This equation can be expressed as a function

So, we have

f(x) = -3x + 7

In Dr. Ellison's equation, we have

f(2) = 5/3

This means that

x = 2

So, we have

f(2) = -3 * 2 + 7

Evaluate

f(2) = 1

The calculated value is different from Dr. Ellison's equation

Hence, the solution is wrong

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Tickets for a ball game are $69 for Primary Level seats and $39 for Porch Level seats. A total of $804 was spent on the tickets by a group of 16 friends who attended the game.

How many tickets were purchased for the Main Level and the Terrace Level?

No. of tickets for the Main Level = X

No. total price = 804 = 39(16 - X) + 69X = 624 - 39X + 69X = 624 + 30X 30X = 804 - 624 = 180 X = 180/30 = 6

No. of Terrace Level Tickets = 16 - X

Main Level Tickets Prace = 69X

Terrace Level Tickets Prace = 39X

Total Price = 804 = 39(16 - X) + 69X = 624 - 39X + 69X =of tickets for the Main Level, X = 6

No. of tickets for the Terrace Level: 16 - X = 16 - 6 = 10 Check:39x10 + 69x6 = 390 + 414 = 804

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Answer:

Slope: 1

Step-by-step explanation:

If you take 2 points on the graph, for example (0,3) and (-3,0), you can find the slope. Use the rise over run method (y2-y1/x2-x1). 0-3=-3 and -3-0=-3. After I did that, I divided it: -3/-3=1.

Answer:

20800 dollars

Step-by-step explanation:

15600*(1/0.75)

=20800

the original price was 20800 dollars.

weirdly expensive computer though

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Infinity is denoted by ∞.

∞ = 1/0

∞ times x is ∞

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Infinity is denoted by ∞.

∞ = 1/0

Now,

∞ times x = ∞

Whatever we multiply with infinity will always give us infinity.

Thus,

∞ times x is ∞

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Answer:

4(y+3)(y+5)

Step-by-step explanation:

4y^2+32y+60 = 4(y^2+8y+15) = 4(y+3)(y+5)

y^2+8y+15 = (y+3)(y+5)

LCD = 4(y+3)(y+5)

For the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 } .

As given in the question,

Given function is equal to :

h(x) = x² +5

Domain of the function h(x) = x² +5 maps by the set { -2, -1, 0, 1, 2 }

Range of the function h(x) = x² +5 is represented by the set as follow :

Substitute the value x = -2, -1, 0, 1, 2 in the function h(x) = x² +5 we get,

h(-2) = (-2)² + 5

       = 9

h(-1) = (-1)² + 5

       = 6

h(0) = (0)² + 5

       = 5

h(1) = (1)² + 5

       = 6

h(2) = (2)² + 5

       = 9

Range of the function is represented by the set : { 5, 6, 9 }

Therefore, for the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 }.

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Answer:

[tex]2^{\frac{4}{3}}[/tex]

Step-by-step explanation:

we do the reverse of what is in the photo

Denominator of exponent is 3 and numerator 4

2^4/3

hopes this helps please mark brainliest

Answer:

y>-1.3

Step-by-step explanation:

y+2.1>0.8

 -2.1.   -2.1

   y>-1.3

Hopes this helps please mark brainliest

Answer:

Hi! Okay so the Inequality form would be: Y>-1.3

and the Interval Notation would be: (-1.3, ∞)

Sorry if it doesn't work btw

Step-by-step explanation:

Answer: x=1    x=-2   x=-1/3

Step-by-step explanation:

[tex]f(x)=3x^3+4x^2-5x-2\\\\3x^3+4x^2-5x-2=0\\\\3x^3+(-3x^2+7x^2)-5x-2=0\\\\(3x^3-3x^2)+7x^2-5x-2=0\\\\3x^2(x-1)+7x^2+(-7x+2x)-2=0\\\\3x^2(x-1)+(7x^2-7x)+(2x-2)=0\\\\3x^2(x-1)+7x(x-1)+2(x-1)=0\\\\(x-1)(3x^2+7x+2)=0\\\\x-1=0\\\\x=1\\\\3x^2+7x+2=0\\\\3x^2+(6x+x)+2=0\\\\(3x^2+6x)+(x+2)=0\\\\3x(x+2)+(x+2)=0\\\\(x+2)(3x+1)=0\\\\x+2=0\\\\x=-2\\\\3x+1=0\\\\3x=-1\\\\[/tex]

Divide both parts of the equation by 3:

[tex]\displaystyle\\x=-\frac{1}{3}[/tex]

1. The first figure posses the SSS property.

2. The second figure posses the ASA property.

3. The third figure posses the hypotenuse length property.

4. The fourth figure posses the SAS property.

Given:

1. The first figure shows the SSS property.

Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.

hence the two triangles are congruent.

2. The second figure posses the ASA property.

Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.

hence the two triangles are congruent.

3. The third figure posses the hypotenuse length properety.

RHS criterion stands for right angle-hypotenuse-side congruence criterion. Under this criterion, two triangles are congruent, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle.

hence the two triangles are congruent.

4. The fourth figure posses the SAS property.

Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.

hence the two triangles are congruent.

Hence we get the required answer.

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After solving the word problem,  the change in the number of shares of stock he owns, is x-96.

In the given question we have to find  the change in the number of shares of stock he owns.

As given that Eric owns shares of a certain stock. If he sells off 8 shares each month for a year.

Let Eric owns x shares of a certain stock.

If he sells off 8 shares each months for a year.

So as we know that in a year have 12 months.

In 1 month = 8 shares sells

12 months = 12×8 shares sells

12 months = 96 shares sells

So in a year Eric sells 96 shares and he have total x shares.

So the remaining shares are x-96.

Hence, the change in the number of shares of stock he owns, is x-96.

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Answer:

-2 ( 12x - 1 )

Step-by-step explanation:

1) Simplify the equation

To simplify the equation, we have to get rid of any brackets. To do this multiply the term to left of it with everything inside the bracket

Now we can plug these numbers into our equation

2) Collect like terms

The equation we are left with from the previous step would be 10-8-24x

The terms that are similar are 10 and -8.

To collect like terms simplify the terms down to one term

3) Find common factor and simplify

What we are left with from the previous step is -24x+2

To find the common factor you have to find a number that goes it both numbers which for 2 and 24 would be 12.

Hope this helps, have a great day!

Answer:

12oz box of cereal for $3.50 is the better buy

Step-by-step explanation:

12oz=$3.50

36oz = $10.50

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

18oz=$5.40

36oz=$10.80

Answer:

the is 20 because you need to multiple