simplify x
\( {x}^{2} + 6x - 12\)
​

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

Slope = 15/13

Step-by-step explanation:

(13 - - 2)/(8 - - 5) = 15/13

Answer:

15/13 or 1 2/13

Step-by-step explanation:

1. To find the slope of a line given two points, you can use the formula \(\frac{y_2-y_1}{x_2-x_1}\)

and plug in the corresponding values to get it.

2. (Solving)

Therefore, the slope is 15/13 or 1 2/13.

On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667

A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.

red die, there are 3 numbers greater than 3 out of 6 numbers

Probability (A) = 3/6 = 1/2.

green die, there are 2 numbers less than 3 out of 6 numbers

Probability (B) = 2/6 = 1/3.

events are independent

P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)

16.67% probability = 0.1667

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Answer:

The answer is false and is not

Explanation:

Given the equation -

Substitute x = 2 in the equation

Thus, the equation is false. When the equation is false, meaning that the coordinate x-term isn't passed by the line. (Rather say that the point is not the part of the graph.)

The equation is false is our first answer.

If the equation is false, that means the given value is not part of the graph, thus making the x-value not the solution.

A number line was used to draw and label a figure for Points X and Y that lies on CD as shown in the image attached below.

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

A number line can be defined as a type of graph with a graduated straight line which contains numerical values (positive and negative numbers) that are placed at equal intervals along its length.

A number line would be used to draw and label a figure for Points X and Y that lies on CD as shown in the image attached below.

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Answer: 62

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

First, use trigonometric function to find RT.

θ = 60°

Opposite = 2√3

Hypotenuse = RT

Apply SOH:

Sin θ = Opp/Hyp

Plug in the values

Sin 60° = 2√3/RT

RT*Sin 60° = 2√3

Divide both sides by Sin 60°

RT = 2√3/sin 60°

RT = 2√3 × √3/2 (sin 60° = √3/2)

RT = (2√3 × √3)/2

RT = (2 × 3)/2

RT = 3

✔️Find x

θ = 45°

Opposite = x

Adjacent = 3

Apply TOA:

Tan θ = Opp/Adj

Substitute

Tan 45° = x/3

3 × Tan 45° = x

3 × 1 = x (tan 45° = 1)

3 = x

x = 3

Answer:

you take 5/6 and multiply it by 4/1.

which gives you 20/6

then reduce it by dividing the top number by the bottom number

 which gives you 3 with a remainder of 2

you then place the remainder over the

This tells you he practicedfor 3 2/6

Step-by-step explanation:

Answer:

The correct set of image points for trapezoid WXYZ is:

(second option) OW(4, 2), X'(3, 4), Y'(1, 4), Z'(0, 2)

Step-by-step explanation:

Add

1/5+3/10=5/10

Find common denominator

1/5+3/10=1*2/5*3+3*1/10*1=2/10+3/10

10 is the least common multiple of denominators 5 and 10. Use it to convert to equivalent fractions with this common denominator.

Add

2/10+3/10=2+3/10=5/10

Simplify

5/10=1/2

5 is the greatest common divisor of 5 and 10. Reduce by dividing both the numerator and denominator by 5.

Answer:

number is 2

Step-by-step explanation:

let the number be n then 8 times the number is 8n, subtract 1 from this and

8n - 1 = 15 ( add 1 to both sides )

8n = 16 ( divide both sides by 8 )

n = 2

that is the number is 2

Answer:

Its 2√10/5. So B.

Step-by-step explanation:

I did it on paper.

Number of car sold are 98.

Number of trucks sold are 66.

Given,

Dealer 1 sold 164 cars and trucks and dealer 2 sold 229 cars and trucks .

Let number of cars sold are x.

Let number of cars sold of y .

Now,

For dealership 1 equation will be,

x + y = 164  ......(1)

For dealership 2 equation will be,

As the cars are sold twice and trucks are sold half .

2x + y/2 = 229......(2)

Solving 1 and 2,

y = 66

x = 98

Thus number of car sold are 98.

Thus number of trucks sold are 66.

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The ordered pair could be removed to make this relation a function is (4,-2).

What is an ordered pair?

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

The numeric values in an ordered pair can be integers or fractions.

Here,

A function is when each input has one output. So, for every x there is one y. The x values can not repeat.

But in the given value x is repeating so the ordered pair (4, -2) can be removed.

Hence, the ordered pair could be removed to make this relation a function is (4,-2).

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So,

The temperature was -10 degrees in the morning. Given that it dropped 15 degrees by midnight, we could substract 15 to -10 to find the temperature at midnight:

The temperature at midnight was -25 degrees.

b. Clearly,

c. The absolute value of the morning temperature is:

That's because:

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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Answer:

c

Step-by-step explanation:

you replace x with the firat number because it is (x,y) then you replace y with the second number, and since c would equal 7 = 7, it would be true. C is the answer

Answer:

Length of rectangular strip = 12

area of rectangular strip =   2*12 = 24

Area of square =  x^2 = 12^2 = 144

Step-by-step explanation:

Area of square x^2

area of rectangle is given by length * width

Length of rectangular strip = x

width of rectangular strip = 2

area of rectangular strip =  length * width = 2*x = 2x

Area of square piece of paper when  rectangular strip is taken away from it

= Area of square - area of rectangular strip

= \(x^2 -2x\)

It is given that Area of square piece of paper when  rectangular strip is taken away from it is 120 square units.

Thus,

\(x^2 -2x = 120\\=> x^2 -2x -120 = 0\\=> x^2 -12x +10x-120\\=> x(x-12) +10(x-12)\\=> (x+10)(x-12) = 0\\\\\)

Thus,

either x+10 = 0 or x -12= 0

x = -10 or x = 12

but length cannot  be negative hence neglecting x = -10

hence value of x is 12.

Hence,

Length of rectangular strip = 12

area of rectangular strip =   2*12 = 24

Area of square =  x^2 = 12^2 = 144

Answer: =−36x−54

Step-by-step explanation:

=(9)(−4x+−6)

=(9)(−4x)+(9)(−6)

Answer:

-36x - 54

Step-by-step explanation:

Distribute 9 to all terms within the parenthesis. Multiply:

9( -4x - 6) =

9(-4x) = -36x

9(-6) = -54

-36x - 54 is your answer.

~

Answer:

40

Step-by-step explanation:

"The minimum number of hours is the distribution was 23."

So the lowest number of hours per week is 23

"The range was 17."

So from 23 we add 17 more hours to get the full range.

23 + 17 = 40

The maximum number of hours in the distribution is 40.

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Answer:

2x

Step-by-step explanation:

5, 10, 20, 40, 80

each step is multiplying by 2, therefore the sequence is 2x

Answer:

45

scalene

acute

Step-by-step explanation:

Answer: The triangle classified by the sides is 59 degrees.  The triangle is classified by the angel is 1

Step-by-step explanation:

A parallelogram has opposite sides parallel and equal in length. A rectangle has four right angles and opposite sides equal in length. A rhombus has opposite sides equal in length and opposite angles equal.

A parallelogram is a quadrilateral with opposite sides parallel and equal in length. In a parallelogram, the statement "Opposite sides are parallel and equal in length" is always true.

A rectangle is a parallelogram with four right angles. In a rectangle, the statement "Has four right angles" is always true.

A rhombus is a parallelogram with all sides equal in length. In a rhombus, the statement "All sides are equal in length" is always true.

A square is a rectangle with all sides equal in length. In a square, both the statement "Has four right angles" and "All sides are equal in length" are always true.

So, by looking at these properties, you can determine the type of quadrilateral for which a given statement is always true.

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Answer:

18.63

Step-by-step explanation:

B i guess

Answer:

I don't know the answer what is the answer

The required length of each panel would be 1 feet.

Given that,
A mural is 7  feet long and is divided into 7 equal-length panels. How many feet long is each panel to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
The required length of each panel = total length of the panel / 7
                                                     = 7 / 7 = 1 feet

Thus, the required length of each panel would be 1 feet.

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Answer:

b= infinity

Step-by-step explanation:

Because is b>1 than b can be 2, 3, 44, 100, 1000, 100000000213981623 and higher. There is no way to find the exact number though.

Answer: D

Step-by-step explanation: x is a variable, and so is the number of tractors he sells. he is going to get paid $1000 for sure each month.

So 150x(the number of tractors) + 1000(his pay each month)

Answer:

blue and white

Step-by-step explanation:

yes swag forever