What is the longest triangle side called?

The solutions to the quadratic function y = x² + 4x + 3, using the quadratic formula, are given as follows:

x = -1 and x = -3.

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

In which the leading coefficient a must assume a value different of zero.

The solutions to the quadratic function ax² + bx + c = 0 are obtained using the quadratic formula, as follows:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The quadratic function for this problem is defined as follows:

x² + 4x + 3 = 0.

Hence the coefficients are:

a = 1, b = 4, c = 3.

The first solution is:

[tex]x = \frac{-4 - \sqrt{4^2 - 4(1)(3)}}{2} = -3[/tex]

The second solution is:

[tex]x = \frac{-4 + \sqrt{4^2 - 4(1)(3)}}{2} = -1[/tex]

This problem was incomplete, hence the quadratic formula is used to solve y = x² + 4x + 3, as an example.

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To verify the inverse we can use Horizontal Line Test.

Suppose F is a function.

F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.

If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.

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Answer: Thirty-eight thousand two hundred.

Step-by-step explanation: You'd get Thirty-eight thousand two hundred because the standard form is writing out the number using letters. So, we should break this down:

38,000 + 200 is a good strategy to divide big numbers.

So, 38,000 = Thirty-eight thousand

And 200 = two hundred

So, combine it and you get Thirty-eight thousand two hundred or Thirty-eight thousand and two hundred. (it's the same thing)

Answer:

Jane has 251

Step-by-step explanation:

Stickers Initially = 27 Jane bought stickers on 1st day = 3 Remaining days = 13 Each next day she bought 2 more stickers than the previous day, so: Stickers bought in the last 2 weeks (14 days) = n+(n+2)+(n+2+2)+(n+2+2+2)+.............+(n+2(13))here n =3 So:Stickers bought in the last 2 weeks (14 days) = 3+5+7+9+11+13+15+17+19+21+23+25+27+29Stickers bought in the last 2 weeks (14 days) = 224 At Present Jane has Total Stickers = Stickers Initially+ Stickers bought in the last 2 weeks (14 days)At Present Jane has Total Stickers = 27+224

Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).

A ratio or fraction in math displays how many times one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3 or decimal 1.333).

Here,

Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.

A statistical data's confidence interval can be expressed as.

=> x+/-zr/√n

=> Knowing that;

Average Sample x = $70.00

$17.50 is the standard deviation.

n = 60 samples were used.

95% confidence interval

95% confidence interval for z = 1.96

substituting our current values;

$70.00+/-1.96($17.50/√60)

$70.00+/-1.96($2.259240285287)

$70.00+/-$4.428110959163

$70.00+/-$4.43

= ( $65.57, $74.43)

Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).

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A trapezoid will appear smaller than the original trapezoid if it is dilated with a scale factor between 0 and 1.

An open, flat shape with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.

What three characteristics do trapezoids have? An isosceles trapezoid has equal base angles and diagonals. The midpoints of the two opposing sides are parallel to the point where the diagonals intersect. An isosceles trapezoid has opposite sides that are congruent to one another or have the same length.

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In fraction form, this is 6.375/8.5, or 3/4.In decimal form, this is 0.75.

Fraction is a mathematical expression which represents a part of a whole. It consists of a numerator and a denominator which are separated by a fraction bar. The numerator is the number of parts and the denominator is the total number of parts in the whole. Fractions can be used to represent parts of a whole number or parts of a physical object. Fractions can also be used to express ratios or rates.

To solve on paper, we can use the following equation:

Pears = 8.5 kg - (3/4 x 8.5 kg)

Pears = 8.5 kg - (6.375 kg)

Pears = 2.125 kg

Therefore, the farmer sold 2.125 kg of pears at the farmer's market in fraction form, and 0.75 in decimal form.

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The solution of given triangle is 32°.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal.

Given,

∠BAC=52°

since, ΔBAC is isosceles triangle hence opposite angle will be equal.

∠BAC+∠ABC+∠ACB=180°

2∠BCA=180°-52°

∠BCA=128/2

∠BCA=64°

also,

∠BCA+∠DCA=180°

∠ACD=180°-64°

∠ACD=116°

since,

ΔACD is isosceles triangle, hence opposite angle is equal

∠ACD+∠CAD∠ADC=180°

2∠CAD=180°-116°

∠CAD=64/2

∠CAD=32°

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Answer:

16a^4

Step-by-step explanation:

Answer:

16a^4

Step-by-step explanation:

The expression (2a)^4 can be written in exponential form as 2^4 * a^4. Using the laws of exponents, we can simplify this to:

2^4 = 2 * 2 * 2 * 2 = 16

a^4 = a * a * a * a

So, (2a)^4 = 16a^4

The axis of symmetry of the function f(x) = -( x 9 )( x 21) is x = 15.

The axis of symmetry of a parabola is a line that divides the parabola into two exact mirror images. In this case, the parabola is defined by the quadratic function f(x) = -(x-9)(x-21). To find the axis of symmetry, we can take the average of the x-coordinates of the two solutions, which are 9 and 21. The average of 9 and 21 is 15, so the axis of symmetry is x = 15. This means that the parabola is symmetrical about the line x = 15, and the vertex of the parabola is located at the point (15,0).

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The equation to determine the length and the width of the rug is

21 = W² - 4W.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

A quadrilateral is a rectangle.

A rectangle's opposing sides are equal and parallel to one another.

Each vertex of a rectangle has a 90° internal angle.

360° is the total of all interior angles.

The diagonals cut each other in half.

The diagonals are all the same length.

The Pythagorean theorem may be used to determine the length of the diagonals.

A rectangle is also referred to as a parallelogram since its sides are parallel.

While all parallelograms are rectangles, not all rectangles are parallelograms.

The length of the rug is l ft

Then the width of the rug will be l-4 ft

So the are will be l*(l-4) = [tex]l\x^{2} - 4l[/tex]

We know area is 21

so the equation is 21 = [tex]l\x^{2} - 4l[/tex]  (Option a)

And after solving the equation the lenght is7m and breadth is 3 m.

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Answer: 47

Step-by-step explanation:

4.72 / .1= 47

47

Check the picture below.

The value of y is 15 and angle is 68°

A triangle is a polygon with three edges and three vertices.

Given that, a triangle KLM

We have, KL = MK

We know that, In a triangle, sides opposite to equal angles are equal, therefore,

∠ M ≅ ∠ L

5y-19 = 56

5y = 75

y = 15

We know, Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

∠ M + ∠ L + ∠ K = 180°

56° + 56° + ∠ K = 180°

∠ K = 180° - 112°

∠ K = 68°

Hence, the answers are; ∠ K = 68° and y = 15

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The nature of the roots of the equation x^2 - 5x + 7 = 0 : no real roots

Consider given quadratic equation: x^2 - 5x + 7 = 0

Comparing given quadratic equation with the standard form of quadratic equation i.e., ax^2 + bx + c = 0

a = 1, b = -5, c = 7

First we find the discriminant:

D = b^2 - 4ac

D = (-5)^2 - 4(1)(7)

D = 25 - 4(7)

D = 25 - 28

D = -3

Since, the discriminant D < 0

Therefore, there are no real roots of this equation.

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Answer:

Slope = -1 or (-1/1)

Step-by-step explanation:

slope = m

Point 1: (0, 2); Point 2: (2, 0)

           (x₁, y₁)                (x₂, y₂)

        y₂ - y₁       0 - 2        -2

m = ----------- = ---------- = ------- = -1 or (-1/1)

        x₂ - x₁       2 - 0        2

I hope this helps!

Answer:

-1, 0, 4

Step-by-step explanation:

2f - 8 ≤ 6f + 4

-4f ≤ 12

f ≥ 12/-4  **flip the inequality when you divide by a negative number

f≥ -3

Check all the answers that are ≥ -3

Answer: To find the length of an object in a scale drawing, you need to use the scale to convert the length on the drawing (measured in inches) to the actual length (measured in feet).

The scale of the drawing is given as 0.5 inches = 10 feet, which means that 1 inch on the drawing represents 10 feet in reality.

So, if the length of the object on the scale drawing is L inches, then the actual length of the object in feet would be:

Length (ft) = (Length (in) * 10 ft/0.5 in) = (L*20)

To find the actual length of the object in feet, you need to know the length of the object in inches from the scale drawing.

Once you have that measurement, you could then simply multiply it by 20.

Step-by-step explanation:

The values of x and y in the Simultaneous equation are 4 and 30 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 and 4x − 4y = 4.

y = -5x + 50 equation 1

y = 5x+ 10 equation 2

subtract equation 1 from 2

5x-(-5x) +10-50 = 0

10x -40 = 0

10x = 40

x = 40/10

x = 4

substitute 4 for x in equation 2

y = 5(4)+10

y = 20+10

y = 30

Therefore the value of x and y are 4 and 30 respectively

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The types of 3 triangles are called-

Scalene triangle:

Isosceles triangle:

Equilateral triangle:

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Hello there!

Answer:

x = 39 2/7

Step-by-step explanation:

-14 - 14(x - 26) = -200

- 14 + 14 - 14(x - 26) = -200 + 14

-14(x - 26) = -186

-14(x - 26)/(-14) = -186/(-14)

x - 26 = 93/7

x - 26 + 26 = 93/7 + 26

x = 275/7

x = 39 2/7

Translation is a rigid transformation. As such, it preserves sizes and angles. Isometric is an alternative way to say the size is preserved. Hence; B, C and E are the correct choices.

A triangle is a three-sided polygon. A closed shape consisting of three straight lines and three corners. The sum of the three angles of a triangle is always 180 degrees. Triangles come in a variety of shapes and sizes and can be classified according to their angles and sides. The most common type of triangle is the right triangle, which has 90 degree angles.

Translation is the transformation that happens when we move the image without changing anything in it. Therefore, the shape, size, and orientation remain the same.

In this case the triangle ABC has been transformed to A'B'C'. This means that the triangle has been moved in one direction to form a new triangle A'B'C' without changing its size or orientation. This is an example of translation transformation.

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The complete question is follows:

Triangle ABC was translated to form A’B’C’. Which describes the transformation? Check all that apply

A. It is non rigid

B. The size is preserved

C. It is rigid

D. The angles are not preserved

E. It is isometric

The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expressions are given below.

(2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²)

Simplify the expression (2.3 × 10⁴) × (1.5 × 10⁻²), then the value of the expression will be given as,

⇒ (2.3 × 10⁴) × (1.5 × 10⁻²)

⇒ 345

Simplify the expression (3.6 × 10⁻⁵) ÷ (1.8 × 10²), then the value of the expression will be given as,

⇒ (3.6 × 10⁻⁵) ÷ (1.8 × 10²)

⇒ 2 × 10⁻⁷

The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.

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The two companies will be equal in cost when 21.428 miles are driven.

How do you calculate the cost of rent?

The weekly rental amount is divided by 7 to determine the daily rental rate, then multiplied by 365 (days per year) to determine the yearly rate, and finally divided by 12 to determine the monthly rental amount. For example, a property is advertised as $200 per week, ($200 divided by 7) is $28.57 for the daily rate.

We can set up an equation to represent the cost of renting a car from each company in terms of the number of miles driven, and then solve for the number of miles at which the cost is the same for both companies.

Let x be the number of miles driven.

The cost of renting from Sunshine Rental Company is given by:

Cost1 = 17 + 0.5x

The cost of renting from Rent Me company is given by:

Cost2 = 20 + 0.36x

We can set the two equations equal to each other, and solve for x:

17 + 0.5x = 20 + 0.36x

0.14x = 3

x = 21.428 miles

Hence, the two companies will be equal in cost when 21.428 miles are driven.

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Answer:

You need to combine like terms

x=-1.5

y=8

the answer is in the picture below

The predicted height if the man with shoe-size 10 is 427.09 cm.

We get the answers using the following steps.

a. The equation of the line of best fit is: y = 42x - 19.81

b. The slope, 42, represents the rate of change of the height variable with respect to the shoe size variable. It means that for every 1-unit increase in shoe size, we can expect a 42-unit increase in height.

c. The y-intercept, -19.81, is the point where the line of best fit crosses the y-axis. It represents the height when the shoe size is 0. It means that if a man has 0 shoe size, his height would be -19.81, both of which is impossible.

d. To predict the height of a man with a shoe size of 10.5, we substitute x = 10.5 into the equation of the line of best fit:

y = 42x - 19.81

y = 42(10.5) - 19.81

y = 447.9 - 19.81

y = 427.09

So, a man with a shoe size of 10.5 would have a predicted height of 427.09 cm

It's worth noting that this is just a predicted value and it might not be accurate. The line of best fit is calculated based on the given data set, it might not be accurate for other data points.

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Answer:

[tex]80^{\circ}[/tex]

Step-by-step explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%" (percent sign). Percentages are used to express how much of something there is in relation to the whole. For example, if a student answers 80% of the questions correctly on a test, it means they answered 80 out of 100 questions correctly.

A tax is a financial charge imposed by a government on individuals, businesses, or other entities to raise revenue for government spending. Taxes are typically based on a percentage of income or sales, and can be levied on various forms of income, including wages, salaries, and profits. The purpose of taxation is to fund government programs and services, such as roads, schools, and national defense. Taxes can also be used to redistribute wealth and influence economic behavior.

The amount withheld from the student's pay last year in federal tax is $6675 x 0.1 = $667.50

The amount withheld from the student's pay last year in state tax is $6675 x 0.03 = $201.25

The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75

So the answer is A. 867.75

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