-x^2 +x+6=0 (Please solve by completing the square, and show steps)

Que knows that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.

To determine the undiscovered side of a right-angled triangle, utilize the Pythagoras theorem.

The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c2 = a2 + b2, where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.

So, we have:

Height of 6 and bas of 9 units of the right triangle.

Pythagorean formula:

c=√a²+b²

Now, insert values and calculate as follows:

c = √a²+b²

c = √9²+16²

c = 18.35 units

Therefore, we know that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.

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Complete question:

A right triangle has a base of 9 and a height of 16. Calculate hypotenuse.

20 cannot be represented in exponential form as it's a whole number and it's not in the form of a base number raised to a power.

Exponential notation is typically used to express a number as a product of the base number raised to a power. For example, the number 8 can be written as 2³ (2 raised to the power of 3) or 8 can be written as [tex]10^{0.8[/tex].

In mathematics, exponential notation is used to represent large or small numbers in a more manageable form. The number 20 is not considered large or small as it's a whole number, it is not in the exponential form

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Answer:

1 1/2 cups of flour.

Step-by-step explanation:

You can work this as a proportion:

1/4 cup → 1/6 of a cake

x cups  → 1 cake

Cross-multiply.

(1/4 cup)(1 cake) = (x cups)(1/6 cake)

Solve for x.

x = 6(1/4) = 1 1/2 cups

Answer: The distance is 8.

Answer:

x = 3

y = 4
Step-by-step explanation:

The opposite sides of a parallelogram are always equal.

From the above statement, we get two equations-

[tex]4x+6 = 7x-3[/tex] and [tex]4y-3=3y+1[/tex]

Solving for x:

[tex]4x+6=7x-3\\6=3x-3\\9=3x\\3=x[/tex]

Solving for y:

[tex]4y-3=3y+1\\y-3=1\\y=4[/tex]

Therefore , the solution of the given problem of expression comes out to  be the first number plus twice the second number, or the summation of the numbers c and d.

An algebraic expression must be checked by replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is identical to 6, since 7 + 8 = 15. If we know the values of the variables, we can replace them with those values and evaluate the expression.

Here,

Assuming that:

The formula is as follows:

= c + 2d

Here, the real numbers are c and d.

c should be the first number.

The following number is d.

A digit is a mental construct that can be employed in the counting, measuring, and naming of objects. The numbers include 1, 2, 56, etc. as an example.

the two-fold sum between the first and second numbers.

In term of c and d, or

the product of c and d divided by two

The first number plus twice the second number, or the summation of the numbers c and d, is what the mathematical equation c + 2d means in verbal form.

Therefore , the solution of the given problem of expression comes out to  be the first number plus twice the second number, or the summation of the numbers c and d.

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Answer:

4x-10=3x+12

4x+3x= 12+10

7x= 32

x= 32÷7

x=4.571

The expression of an exponential function f that has a slope of 12 of a line from the point (0, f(0)) to the point (2, f(2)) is the exponential function;

An exponential function is a function that includes the argument as an exponent, index or power of a constant.

The points on the function are; (0, f(0)), and (2, f(2))

The required slope between the points x = 0, and x = 2 is 12

Therefore;

(f(2) - f(0))/(2 - 0) = 12

f(2) - f(0) = 12 × (2 - 0) = 24

The

The exponential function can be presented in the form;  f(x) = a·bˣ

When x = 0, we get; f(0) = a·b⁰ = a

When x = 2, we get; f(2) = a·b²

f(2) - f(0) = a·b² - a = 24

a·(b² - 1) = 24

Let a = 3, and b = 3, we get;

3 × (3² - 1) = 24

Therefore, possible values of a and b are; a = 3, and b = 3

The exponential function is therefore;

The slope of the line that extends from the point (0, f(0)), to the point (2, f(2), is therefore;

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3x² is a second-degree polynomial, also known as a quadratic equation.

A polynomial is a mathematical expression that consists of constants, variables, and exponents. This polynomial can be represented as an equation in the form of ax^2 + bx + c, where a, b, and c are constants, and x is an unknown. In this case, a = 3, b = 0, and c = 0. In this case, the polynomial is 3x², which contains one constant (3) and one variable (x) with an exponent of 2. To calculate the value of this polynomial, we can substitute a value for x and then solve. For example, if x=2, then 3x² = 3x2 = 3(2)2 = 3(4) = 12.

Therefore, when x=2, 3x² = 12.

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The rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).

One way to think of a function is as a rule that assigns or maps each member of a set, x, to the same value, y, known as its image.

x → Function → y

Functions are frequently denoted by a letter, such as f, g, or h. F(x) = x2+ 5 is the formula for the function that squares a number and adds a 3. A function's impact on specific values can be demonstrated using the same idea.

Given that  f(x) =  √(x² - 2)

And g(x) = -2f(x+5)

Substitute the function f(x) =  √(x² - 2) in g(x) = -2f(x+5)

g(x) = -2(√(x² - 2))(x+5)

g(x) = (-2x - 10)(√(x² - 2))

Thus, the rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).

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The amount of money you must pay at the gas station could be represented using the variables y = price in dollars, x = gas in gallons, and a proportionality constant, k: y = kx.

Mrs. Tenon has spent $5 on 25 party favours.

Equation form of proportional relationships is written as y=kx.

If you substitute $5 for y and $25 for x in the formula for the proportional relationship above, you can find the value of the proportionality constant, or k.

$5=k(25)\sk=$5/25\s=0.2

0.2 is the proportionality constant. Thus, each party favour costs $0.20.

Let's say there are r party favours and the cost is c. c=0.2r

In the equation above, 40 should be substituted for r to get the price of 40 party favours: c=0.2 (60) = 12.00.

As a result, the cost for 40 guests is $ 8.00, and the cost for 60 party favours is $ 12.00.

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On solving the provided question, we can say that multiplication of polynomial  3(8 + ) is 24+3

A polynomial is an algebraic expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of variables and coefficients.

For example, in the expression , x is the variable and coefficients of  and  are 1 and 2 respectively.

When we are asked to do multiplication of polynomials, we multiply term by term in the brackets until every term is multiplies with another in different bracket.

Like in 3(8 + ), we first multiply 3 with the first term inside the bracket, which is 8 and then we multiply 3 with the second term, which is b and maintaining the plus sign as it is.

So the answer is

(3)(8)+(3)()

=24+3

Hence, the answer is 24+3.

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Answer:

F=4

Step-by-step explanation:

1+3(4f-7)=28

3×4f= 12f

3×-7= -21

ADD THE LIKE TERMS

1+-21= -20

now you have 12f-20=28

at 20 to both sides

12f=48

divide 12 from both sides

48/12=4

F=4

The distance between points (7, 4) and (3, 4) is 4 units.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by,

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, Are two points (7, 4) and (3, 4).

Therefore, By the distance formula the distance between the two points

(7, 4) and (3, 4) would be,

[tex]D = \sqrt{(3 - 7)^2 + (4 - 4)^2[/tex].

[tex]D = \sqrt{(-4)^2 + (0)^2[/tex].

[tex]D = \sqrt{(16[/tex].

D = 4.     (negative 4 is inadmissible).

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Answer: look it up

Step-by-step explanation:

Answer: 34

Step-by-step explanation:

Answer: 14

Step-by-step explanation:

So on solving the provided question we can say that here all angles of of a quadrilateral = 30, so, each will be 90

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here all angles of of a quadrilateral = 30

so, each will be 90

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[tex]\displaystyle n\hat A[/tex] is the number of squares of arrays present.

An arrangement of objects, images, or numbers in rows and columns is called an array. Arrays are a convenient representation of the concept of multiplication. This array has 4 rows and 3 columns. This can also be described as a 4 x 3 array. Arrays are a way of representing multiplication and division using rows and columns. Rows represent the number of groups. The columns represent the number of each group or the size of each group. The number 24 can be represented as a 6-by-4 array (6-by-4) because 6-by-4 = 24. It can also be represented as a 2 by 12 array, since 2 by 12 = 24.

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Each measure of the angle when the total measure of the angles is (n−2)·180° and n is 8 will be 235°.

From the information, the total measure of the angles is (n−2)·180°, where n=8. The term regular means all interior angle measures are the same.

It should be noted that in Mathematics, the value of the sum of angles is Illustrated in this case. We can determine each angle measure from the total angle measure thus:

(n - 2) × 180

n = 8

It should be noted that n in this case simply means the number of sides

= (n - 2) × 180

= (8 - 2) × 180

= 1080°

Each measure of the angle will be:

= 1080° / 8

= 135°

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180

since it's a rectangle it wil have 4 sides hence to find breadth we need to make it a square so all 4 sides will be equal hence 54 minus 3 times 2 and the length of the rectangle is 3 cm longer than the breadth of the rectangle making the perimeter into 48 after the equation 48 divide by 4 equal 12 . so now we know that the breadth of the rectangle is 12 we can add 3 to 12 to find the length of the rectangle and use 12 times 15 to find the area of the rectangle

Answer:

12.73%

Step-by-step explanation:

24 + 32 = 56(veggie sandwich)

112 + 150 = 262

262 + 64 = 326

326 + 58 = 384

384 + 56(veg sand) = 440

440 = total number of students

Divide 100 by 440 and you get 0.23

Multiply that by 56 and you get 12.73%

:)

The requried equation used to find the total cost of care of dogs is given as, 1. y = 35x  for 0 ≤ x ≤3 2. y = 35 + 25x for 3 < x. None of the op[tions are correct.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Emma takes care of dogs while their owners are on vacation. She charges $35 for each of the first 3 days she takes care of a dog and $25 for each day thereafter.

Two equations will be formed,
1. y = 35x  for 0 ≤ x ≤3
2. y = 35 + 25x for 3 < x

Thus, the requried equation used to find the total cost of care of dogs is given as, 1. y = 35x  for 0 ≤ x ≤3 2. y = 35 + 25x for 3 < x. None of the op[tions are correct.

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Prime multiples of number 3 is number 3 itself as other multiples of three are representing composite numbers.

As given in the question,

Given number is equal to :

3

Multiples are those numbers which we get when we multiply the given number by any other integer.

Multiples of three are equal to :

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

............... so on.

When we multiple 'n' by three we get 3n.

All other multiples have more than two factors that is one , three , and at least number itself.

So other multiples of three are composite numbers.

Prime multiples has only two factors one and number itself.

3 represents the prime multiple.

Therefore, three is the only number which is the prime multiple of 3.

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Since FE bisects <DFG, then the value of x and measure of <DFG are:

a. x = 24

b. m<DFG = 106^o

An angle bisector is a straight line constructed in such a way that it divides a given angle into two equal measures.

Thus given that FE bisects <DFG, this implies that;

i. m<DFE ≅ m<EFG

So that,

3x - 19 = 2x + 5

collect like terms to have;

3x - 2x = 19 + 5

x = 24

To solve for x, the value of x is 24^o.

ii. To determine the measure of DFG;

m<DFG = (3x - 19) + (2x + 5)

             = (3(24) - 19) + (2(24) + 5)

             = 53 + 53

             = 106

m<DFG = 106^o

The measure of <DFG is 106^o.

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Since 1 bowl can fill 6 muffins, it's fraction is 1/6  would Luca put in each muffin cup

Luca i making 12 jumbo muffin to ell at a bake ale.

He ha 2 bowl full of batter

Number of sections batter was divided  = 12

We need to find the fraction of a cup of muffin content in each muffin.

Now according to given data Batter was divided in 12 sections of the pan.

So we can say the number of muffins baked = 12

Now we know that;

bowl content in each muffin can be calculated by dividing bowl content in the batter with the number of sections batter was divided.

Find out how much muffins is needed for 1 bowl.

2 bowls = 12 muffins

1 bowl = 12 ÷ 2 = 6 muffins

Since 1 bowl can fill 6 muffins, it's 1/6 r would Luca put in each muffin cup

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A graph of the line with slope -3 passing through the point (4, -1) has been plotted in the image attached below.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At point (4, -1), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1) = -3(x - 4)

y + 1 = -3x + 12

y = -3x + 12 - 1

y = -3x + 11

Next, we would use an online graphing calculator to plot the above linear equation in slope-intercept form as shown in the graph attached below.

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The statement which best describes the triangle or triangles, if any, that can be formed with the sides measuring 60 centimeters, 100 centimeters, and 40 centimeters include the following: A. No triangle.

In Mathematics, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of triangles that can be formed would be determined as follows:

60 + 40 > 100 (False and no triangle).

In conclusion, we can logically deduce that the two (2) short side lengths does not exceed the long side lengths and as such no triangle can be formed with the sides measuring 60 centimeters, 100 centimeters, and 40 centimeter.

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Complete Question:

Which best describes the triangle or triangles, if any, that can be formed with the sides measuring 60 centimeters, 100 centimeters and 40 centimeter?

A. No triangle

B. One unique scalene triangle

C. infinitely small similar scalene triangles

D. Two unique scalene triangles.

No, These both expressions are not equal to each other.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expressions are,

⇒ 12(8y - 16k) and 16(2y - 4k)

Now, We can check both expressions as;

⇒ 12 (8y - 16k)

⇒ 12 × 8 (y - 2k)

⇒ 96 (y - 2k)

⇒ 16 (2y - 4k)

⇒ 16 × 2 (y - 2k)

⇒ 32 (y - 2k)

Thus, We get;

⇒ 96 (y - 2k) ≠ 32 (y - 2k)

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The range of y = log subscript 8 baseline x is all real numbers.

The range is a set of all the defined values of y-correspond to the domain. In this case, to find the range of the function y = log subscript 8 baseline x, we need to draw the graph of the function.

The graph is attached.

Now, because of the base of the logarithm is 8 > 1; so, the graph is raising and passes through the point (1,0).

So, the domain of this function is:

x > 0

And, the range of this function is:

y ∈ (–∞,∞)

or all real numbers.

Hence, the range of y = log subscript 8 baseline x is all real numbers.

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Answer:

All real answers

Step-by-step explanation:

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