How do I solve a quadratic equation using the Quadratic Formula?

Prince Edward Island in Canada has a population density that can range from less than 2 people to as many as 250 people per square mile. This is due to various factors including climate, farmland, and job opportunities.

The Canadian island with a population density that ranges from under 2 people to as many as 250 people per square mile is Prince Edward Island. This island is one of the three Maritime Provinces in Canada and is the smallest in both land area and population. But, when it comes to population density, it has a higher range than many other islands in Canada. This is due to its favorable climate, good farmland, and the job opportunities, mainly in farming and tourism, which attract a decent population.

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The equation of the given problem would be 3x + 24 = 7x - 4 and the solution is 7.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have given that "if three times a number is increased by 24, the result is 4 less than seven times the number"

Let the number be x then we have;

three times a number means 3x

seven times the number means 7x

Therefore, the equation will be;

3x + 24 = 7x - 4

Now solving for x unknown number;

3x + 24 = 7x - 4

24 + 4 = 7x -3x

28 = 4x

x = 7

Hence, the equation of the given problem would be 3x + 24 = 7x - 4, and the solution is 7.

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Answer:

Step-by-step explanation:

[tex]4-(3x-5)=6-(2x+7)\\\\/-(a+b)=-1(a+b)=(-1)(a)+(-1)(b)-\text{distributive property}/\\\\4-3x-(-5)=6-2x-7\\\\4-3x+5=6-2x-7\qquad\text{combine like terms}\\\\-3x+(4+5)=-2x+(6-7)\\\\-3x+9=-2x-1\qquad\text{subtract 9 from both sides}\\\\-3x+9-9=-2x-1-9\\\\-3x=-2x-10\qquad\text{sdd}\ 2x\ \text{to both sides}\\\\-3x+2x=-2x+2x-10\\\\-x=-10\qquad\text{change the signs}\\\\\boxed{x=10}[/tex]

Answer: [tex]x=10[/tex]

Simplify both sides of the equation

[tex]4-(3x-5)=6-(2x+7)[/tex]

[tex]4+-1(3x-5)=6+-1(2x+7)[/tex] (Distribute the Negative Sign)

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

[tex]4+-3x+5=6+-2x+-7[/tex]

[tex](-3x)+(4+5)=(-2x)+(6+-7)[/tex] (Combine Like Terms)

[tex]-3x+9=-2x+-1[/tex]

Add 2x to both sides

[tex]-3x+9+2x=-2x-1+2x\\-x+9=-1[/tex]

Subtract 9 from both sides

[tex]-x+9-9=-1-9\\-x=-10[/tex]

Divide both sides by -1

[tex]-x/-1=-10/-1\\x=10[/tex]

Answer:

Acceleration, [tex]a=-2.14\ m/s^2[/tex]    

Step-by-step explanation:

Initial speed of the airplane, u = 245 m/s

Final speed of the airplane, v = 230 m/s

The pilot takes 7 seconds to slow down to this speed. Let a is the acceleration of the plane. The change in velocity per unit time is called the acceleration of an object. It can be calculated as :

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{230\ m/s-245\ m/s}{7\ s}[/tex]

[tex]a=-2.14\ m/s^2[/tex]

So, the acceleration of the plane is [tex]-2.14\ m/s^2[/tex]. Hence, the correct option is (b).

Answer: Hello mate!

A linear equation has the form y = ax + b

where x is the variable, a is the slope and b is the x-intercept.

We want to find the pararel line to y = -2x + 10

A paralel line of this, will be another line with the same slope ( -2 in this case) and a different x-intercept; then our line has the shape of:

y = -2x + b

and we know that this line pases through the point (6,8), and with this info we could find the value of b:

8 = -2*6 + b

b = 8 + 12 = 20

then y = -2x + 20 is the pararel line that passes through the point (6.8)

Then the correct answer is the option a:

a) y - 8 = -2(x - 6) = -2x + 12

y = -2x + 12 + 8 = -2x + 20

Answer:- The quadrilateral must be a rhombus.

Explanation:-

Given :-For a craft project, two equilateral triangles are taped together to create a quadrilateral.

We know that an equilateral triangle is a triangle in which all the sides and angles are equal such that its each interior angle should be 60°.

If we join two equilateral triangle by to create a quadrilateral then the sides of the quadrilateral would be same as it was constructed by equilateral triangle.

Then the interior angle for the sides which are not joint will remain same as 60°.

But the interior angle for the vertex of quadrilateral which has formed by joining two triangles will become 60°+60°=120°.

Thus it is not a square , rectangle (no right angle )or trapezoid(quadrilateral have equal sides).

Therefore, the quadrilateral must be a rhombus.

a^2 +b^2 = (2.5sqrt(2))^2

2a^2 = 6.25 *2

a^2 = 6.25

a = sqrt(6.25)

a = 2.5

 length of each side = 2.5 units

Answer:

The answer is m∠1 = 72°

Step-by-step explanation:

One of the properties of a triangle is that all the angles of the triangle must add up to 180°.

Therefore:

m∠P + m∠O + m∠1 = 180°

Given that:

m∠P = 38° and m∠O = 70°

We can conclude that:

38° + 70° + m∠1 = 180°

m∠1 = 180° - 38° - 70°

m∠1 = 72°

Answer:

No, the given relation is not a function.

Step-by-step explanation:

Consider the given relation

[tex]\{(0.3,0.6),(0.4,0.8),(0.3,0.7),(0.5,0.5)\}[/tex]

We need to check whether the given relation is function or not.

A relation is a function if there exist a unique value of y for each value of x.

In the given relation, for x=0.3 there exist more than one value of y.

y=0.6 at x=0.3

y=0.7 at x=0.3

For one input there exist more than one output. Therefore, the given relation is not a function.

The Number in the statement is 4/5.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Ten times the square of a non zero number is equal to eighty times the number.

let the number be x.

So, 10x² = 8x

10x² - 8x= 0

2(5)(x)(x) - 2 (2)(2)(x) = 0

2x( 5x - 4)= 0

Now, 2x= 0 or 5x-4=0

x= 0 or x= 4/5

Hence, the number is 4/5.

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The length of the other diagonal, DF is 44 cm.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Since the kite has two pairs of congruent adjacent sides, we know that the diagonals of the kite are perpendicular bisectors of each other.

Therefore, we can use the Pythagorean theorem to find the length of the other diagonal DF.

Let x be the length of the other diagonal, DF.

We know that one diagonal EG has a length of 24 cm, so we can use the Pythagorean theorem to find the length of the perpendicular bisector of EG, which is half of DF.

By the Pythagorean theorem, we have:

[tex](20/2)^2 + (x/2)^2 = 24^2\\100 + (x/2)^2 = 576\\(x/2)^2 = 476\\x/2 = \sqrt(476)\\x = 2 \times 21.86\\x = 43.72\\x = 44[/tex]

Therefore,

The length of the other diagonal DF is 44 cm

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The most appropriate format for representing data depends on the intended audience, data type, and presentation purpose. Adherence to professional formatting guidelines is critical, and while figures can make data accessible, they should not duplicate table data. The effectiveness of formats such as complete sentences, tweets, Prezi, and visual figures varies based on the context.

When choosing the most appropriate format for representing data, several factors need to be considered such as the intended audience, the type of data, and the purpose of the data presentation. Complete sentences, Prezi presentations, 140 character tweets, and drawn pictures each have their own strengths in conveying information effectively and engagingly depending on these factors.

For professional or academic reports, complete sentences and structured paragraphs provide in-depth analysis and explanation. However, for social media platforms, 140 character tweets can quickly capture attention and convey key points. A Prezi can be highly engaging and visually appealing for presentations, making complex information accessible. Conversely, when displaying detailed findings, sometimes a well-illustrated figure or a clear table can speak volumes more efficiently.

Nonetheless, adhering to formatting guidelines is crucial in a professional context, as non-compliance could lead to the rejection of the report. It's also important to note that while figures are useful for making data accessible, they should not duplicate data presented in tables. When using figures, they must be clearly titled, referenced in the text, and situated conveniently in the report. If the figures are too dense, they can be relegated to an appendix.

In summary, there is no one-size-fits-all format for data presentation. Preference may vary depending on personal comfort with certain formats or the requirements of a specific assignment. Reflecting on the exercise of presenting information in various formats can elucidate which is most effective for your specific needs and audience.

Answer:

B 9.22

Step-by-step explanation:

Hello

to find the distance, you can use the distance between two points equation

Given

[tex]P1(x_{1},y_{1})\\P2(x_{2},y_{2})\\\\the\ distance(d)\\\\D=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\[/tex]

Step 1

define

[tex]P1=A=(4,3)\\P2=B=(-2,-4)\\[/tex]

Step 2

put the values into the equation

[tex]D=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\D=\sqrt{(-2-4)^{2} +(-4-3)^{2} }\\ D=\sqrt{(-6)^{2}+(-7)^{2} }\\ D=\sqrt{36+49} \\D=\sqrt{85} \\D=9.22[/tex]

the distance between the points is 9.22 ⇒B

Have a great day

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