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Base of the Sail is 12 feet and Height of the Sail is 5 feet

What is Right Angle Triangle?

A right triangle or right-angled triangle, or more technically an orthogonal triangle, historically known as a rectangled triangle, is a triangle with one right angle (that is, a 90-degree angle) and two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Solution:

Accroding to the Question,

Let, Base = x and Height = y

x = 7 + y

Using the Pythagorous Theorem

[tex]Base^{2} + Perpendicular^{2} = Hypotenuse^{2}[/tex]

[tex]x^{2} + y^{2} = 13^{2}[/tex]

Using the above mentioned relation

49 + y^2 + 14y + y^2 = 169

2y^2 + 14y - 120 = 0

Discriminant = 34

y = 5, -12

The length of a sail can not be neegative, therefore y = 5

From the equation 1, x = 12

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The total spent to paint the mural which is circular with a diameter of 45 feet will be $100.67.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The longest line which can be drawn inside the circle will be the diameter.

The perimeter of the circle = 2πr where r is the radius of the circle.

As per the given,

Diameter = 45 feet  so radius 45/2 = 22.5 feet

Area of circle = πr² = π(22.5)² = 1590.43 feet²

Since one gallon covers  300 square feet.

Number of gallons needed to cover the whole area,

1590.43/300 = 5.30

Cost of one gallon = $18.99

Total spend = 5.30 × 18.99 = $100.67

Hence "The total spent to paint the mural which is circular with a diameter of 45 feet will be $100.67".

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The expression (9.12n 4.3) (8 + 13.6n) are subtracted to yield (12.3 + 4.48n).

What is an algebraic expression?

An algebraic expression is a type of mathematical expression that uses variables and constants.

Algebraic expressions are evaluated by changing the variables to numbers or values.

What in mathematics is a polynomial?

Sums of terms of the form k⋅xⁿ, when k is any variable and n is a positive number, compensate polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.

Detailed explanation:

We begin by solving the equation = 9.12n - 4.3 - 8 - 13.6n. Next, we remove the comparable terms using the formula = - 12.3 - 4.48n.

Therefore, the simple answer to the formula is -(12.3 + 4.48n).

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Angela is a real estate broker option c.

Real Estate Broker;

A real estate broker represents the buyer or seller when looking for the appropriate home. A broker often works for a larger company that helps home sellers and home purchasers select the best and most affordable housing alternative.

A real estate broker is a licenced real estate professional in their own right, as opposed to only being a licenced real estate agent. Like an agent, a real estate broker possesses knowledge that can assist clients with real estate transactions and the sale or acquisition of real estate.

Here,

Angela works as a real estate broker. In order to ascertain the couple's demands for a new home and the size of a property they can afford, Angela meets with them. As a result, choice C is accurate.

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The distance between the two airlines changing at 3:00 p.m is 374mi/hr

Here, the trajectory of the 2 planes will form a right angle at the airport.

Let 'a' be the distance of the east bound plane travelled past the airport and b be the distance of the south bound plane travelled past the airport and c is the horizontal distance between the two planes

a² + b² = c²

differentiating both sides with respect to time

2a da/dt + 2b db/dt = 2c dc/dt

The speed of both airlines is given,

da/dt = 520mi/hr and  db/dt  = 560mi/hr

At 12 pm the east bound plane has been flying post airport

at 3 pm, the distance = 3 x da/dt = 2(520) = 1560

At 1 pm the east bound plane has been flying post airport

at 3 pm, the distance = 2 x db/dt = 2(560) = 1120

c = √(a² + b²)

c = √(1560² + 1120²)

c = 1920.41

fast is the distance between them changing dc/dt

dc/dt = (3a da/dt + 2b db/dt)/2c

= (1560 x 520+ 1120x560)/1920

dc/dt = 374

Therefore, the distance between them changing at 3:00 p.m is 374mi/hr

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Answer:

3.5 tons

Step-by-step explanation:

We can use the information we already have to figure out how much 1 ton is. In the equation: 8,000/4 will give us how many pounds per ton. The answer to that is 2,000 pounds per ton. So, if we divide the number of tons the female elephant is by how many pounds a ton is, we use the equation: 7,000/2,000, which equals 3.5 tons.

Answer:

false

Step-by-step explanation:

Credit Unions are not-for-profit financial service cooperatives

Answer:

$15.99

Step-by-step explanation:

Let y = the total cost

Let x = the cost of the combo

4x + 5 = 68.96  Subtract 5 from both sides

4x = 63.96  Divide both sides by 4

x = 15.99

Answer:

2,500

Step-by-step explanation:

40 × 7 × 9

=2,500d dollars

The objective function is z = 13x+8y

From the question, we have

A student earns $13 per hour for tutoring and $8 per hour as a teacher's aid.

x = the number of hours each week spent tutoring and

y= the number of hours each week spent as a teacher's aid.

the objective function is z = 13x+8y

Addition:

Addition is the process of combining two or more things. In mathematics, adding is the process of calculating the sum of two or more numbers. It is a basic mathematical operation that is applied frequently in daily life. We regularly use addition when dealing with money, calculating our food expenses, or calculating the time. However, for larger numbers, we divide the numbers into columns using their respective place values, such as ones, tens, hundreds, thousands, and so on. One-digit numbers can be added simply to solve addition issues.

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Answer:

4x - 5y = -18

Step-by-step explanation:

y+2=4/5(x+7)

5(y + 2) = 5 × 4/5(x + 7)

5y + 10 = 4x + 28

5y = 4x + 18

4x - 5y = -18

The case of the velocity vectors, v₁ and v₂ that yield the largest absolute value of Δv = v₂ - v₁ is the case of option B. b

A velocity vector provides an indication of s particle's speed and direction of motion.

The vectors in the question can be expressed using vector notation as follows;

a) [tex]\vec{v_1}[/tex] = i + j

[tex]\vec{v_2}[/tex] = i + j

Δv = v₂ - v₁ is therefore;

v₂ - v₁ = i - i + j - j = 0

Δv = 0

b)  [tex]\vec{v_1}[/tex] = i + j

[tex]\vec{v_2}[/tex] = -i - j

Δv = v₂ - v₁ is therefore;

v₂ - v₁ = i - (-i) + j - (-j) = 2·i + 2·j

Δv = 2·i + 2·j

c)  [tex]\vec{v_1}[/tex] = i + j

[tex]\vec{v_2}[/tex] = i - j

Δv = v₂ - v₁ is therefore;

v₂ - v₁ = i - i + j - (-j) = 2·j

Δv = 2·j

d)  [tex]\vec{v_1}[/tex] = i + j

Comparing the vertical and horizontal lengths of the arrows, indicates;

[tex]\vec{v_2}[/tex] ≈ -1.2·i - 0.5·j

Δv = v₂ - v₁ is therefore;

v₂ - v₁ = i - (-1.2·i) + j - (-0.5·j) = 2.2·i + 1.5·j

Δv = 2,2·j + 1,5·j

Option (b) and (d) have the largest values, however, their magnitudes are;

b) |Δv| = √(2² + 2²) = 2·√2 ≈ 2.83

d) |Δv| = √(2.2² + 1.5²) ≈ 2.66

Therefore, option b has the largest absolute value for Δv = v₂ - v₁

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Answer: 4[tex]\frac{n}{4}[/tex]

Step-by-step explanation:

The exponential function for the given graph having points (2, 16) is f(x) = [tex]4^{x}[/tex].

The exponential function is a type of mathematical function that can be used to determine whether something is increasing or decreasing exponentially, such as population, money, or price. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base.

Exponents are used in exponential functions, as the name indicates.

The given point on the graph is (2, 16).

The given function is f(x) = [tex]a^{x}[/tex]

From graph, (x, y) = (2, 16)

Put the value of (x, y) = (2, 16) in f(x) = [tex]a^{x}[/tex]

16 = a²

a = √16

a = 4

So, the function is

f(x) = [tex]4^{x}[/tex]

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The number of coins that are in Jacob's collection is 50

information from the problem

Jacob has a coin collection

He keeps 5 of the coins in his box, which is 10% of the collection

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

10%

= 10 percent

= 10 / 100

= 0.1

The factor 0.1 of the total number of coin is 5

let the total number be x

0.1 * x = 5

0.1x = 5

x = 5 / 0.1

x = 50

The total number of coins is 50

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The solution to the x/-3≤ 3 inequality is x ≤ -9.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

Given,

Inequality:

x/-3 ≤ 3

Cross multiplying:

x ≤ 3× -3

x ≤ -9

The solution to the x/-3≤ 3 inequality is x ≤ -9.

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Answer:

j=5

10

[tex] 10 \geqslant j + 5[/tex]

10-5=j

j=5

c

Answer: 300%

Step-by-step explanation:

Multiplying something by 3 is the same as 300% of that number

20 x 3 = 60

60 = 300% x 20

The indices (8.1)(8.1²)⁴ simplifies to 8.1⁹

Index is the power or exponent which is raised to a number or a variable. For example, in number 3², 2 is the index of 3. The plural form of index is indices

Given:  (8.1)(8.1²)⁴

To simplify these indices, we are going to apply one of the indices, which is expressed below:  (4³)² = 4³ ˣ ² = 4⁶. We basically multiply the powers

We also need another law which is expressed below:

3⁶ x 3⁴ = 3⁶⁺⁴ = 3¹⁰

If two indices with the same base (in case 3) are being multiplied, you can simplify by taking one of the bases and then add the powers  

Thus, to simplify (8.1)(8.1²)⁴:

(8.1)(8.1²)⁴ = (8.1)(8.1)²ˣ⁴

           =  (8.1)(8.1)⁸

            = 8.1¹ × 8.1⁸

            = 8.1¹⁺⁸

            =   8.1⁹

Therefore, (8.1)(8.1²)⁴ simplifies to 8.1⁹. The 4th option is the answer

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If the required reserve ratio is 10 percent, currency in circulation is $1,200 billion, checkable deposits are $1,600 billion, and excess reserves total $2,500 billion

Given that

Reserve ratio is 10 percent

Currency in circulation is $1,200 billion

Checkable deposits are $1,600 billion

Excess reserves total $2,500 billion

Here we are calculating M1 measure of money supply

C: Currency in circulation

D: Checkable Deposits

M1=C+D = 1200+1600= 2800

C: Currency in circulation

D: Checkable Deposits

Currency Deposit Ratio= C/D = 1200/1600 = 0.75

ER: Excess Reserves

CD: Checkable Deposits

Excess Reserve Ratio= ER/CD= 2500/1600 = 1.56

The formula for the M1 money multiplier is:

M1 money multiplier= M1/MB

M1 money multiplier= C+D / R+C

M1 money multiplier= C+D / q∗D+ER+C

M1 money multiplier= (1,200+1,600) / (0.1∗1,600+2,500+1,200)

M1 money multiplier= 0.73

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The car selling price is $34.30

From the question, we have

Selling price = 40* 95/100*95/100*95/100

=$34.30

The car selling price is $34.30

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

[tex](x^2+7)(x^2-5)[/tex]

Answer: ___________________________________________________

x = 4

Answer:

slope is 3

If you need the formula lmk

Answer: 3

Step-by-step explanation:

calculate the slope by subtracting the y coordinates, subtracting the corresponding x coordinates, then dividing y by x.

(10-1)/(3-0)=9/3=3

The value of x : 56

What is Angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

Given,

∠A = (2x - 6)°

∠B = 74°

Since, we have to find the value of x

we have to find it by Linear equation

∠A + ∠B = 180°

Substituting the values we have

(2x - 6)° + 74° = 180°

2x - 6 + 74 = 180

2x + 68 = 180

2x = 180 - 68

2x = 112

x = 112/2

x = 56

The value of  ∠A = 56 - 6 = 60°

Hence, The value of x = 56

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(a) By expanding, the derivative of the polynomial is f'(x) = 12x² - 6x + 8

(b) Using the product rule, the derivative of the polynomial is f'(x) = 12x² - 6x + 8

(c) The expressions for the derivative in (a) and (b) are the same

From the question, we are to determine the derivative of the given polynomial.

The given polynomial is f(x) = (x² + 2)(4x - 3)

(a) By expanding the polynomial, we get

f(x) = (x² + 2)(4x - 3)

f(x) = x²(4x - 3) +2(4x - 3)

f(x) = 4x³ - 3x² + 8x - 6

∴ f'(x) = 12x² - 6x + 8

(b) By using the product rule

f(x) = (x² + 2)(4x - 3)

g(x) = x² + 2

and

h(x) = 4x - 3

Thus,

g'(x) = 2x

h'(x) = 4

From the product rule

f'(x) = g(x).h'(x) + h(x).g'(x)

f'(x) = (x² + 2)(4) + (4x - 3)(2x)

f'(x) = 4x² + 8 + 8x² - 6x

Collect like terms

f'(x) = 4x² + 8x² - 6x + 8

∴ f'(x) = 12x² - 6x + 8

(c) The expressions are the same

Hence,

The derivative is f'(x) = 12x² - 6x + 8

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The parabola equation in its vertex form is f(x) = -3(x - 5)² + 9

From the question, we have the function to be

f(x) = 3x²

Also, we have the vertex to be given as

Vertex = (5, 9)

A quadratic function takes the form:

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

So, we can rewrite f(x) = 3x² as follows

f(x) = 3(x - 0)² + 0

By comparing the equations, we have

a = 3

Also, by comparison, we have

(h, k) = (5, 9)

Substitute a = 3 and (h, k) = (5, 9) in f(x) = a(x - h)² + k

So, we have

f(x) = 3(x - 5)² + 9

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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a) The Factor of -4x² + 12x is 4x( -x +3)

b) The multiplication of (4.8x)(4x) is  19.2x²

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:

-4x² + 12x

Now, factorizing

4x²= 2 x 2× x × x

12x = 2 ×2× 3 × x

So, the factor can be

-4x² + 12x

= -2 x 2× x × x + 2 ×2× 3 × x

= 4x( -x +3)

and, (4.8x) ×4x

= 4.8 × 4 × x × x

= 19.2x²

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8. The value of x is 9

9. The value of x is 9

10. The value of x is 36

11. The value of x is 8

From the question, we are to determine the value of x in the given diagram.

8.

2x + 12 = 5x - 15

Collect like terms

12 + 15 = 5x - 2x

27 = 3x

3x = 27

Divide both sides by 3

3x/x = 27/3

x = 9

9.

8x - 63 = 4x - 27

Collect like terms

8x - 4x = -27 + 63

4x = 36

Divide both sides by 4

4x/4 = 36/4

x = 9

10.

(3x - 18)° = 90°

3x - 18 = 90

Add 18 to both sides

3x - 18 + 18 = 90 + 18

3x = 108

Divide both sides by 3

3x/3 = 108/3

x = 36

11.

Since the angles are complementary, we can write that

(3x)° + (8x + 2)° = 90°

3x + 8x + 2 = 90

11x + 2 = 90

Subtract 2 from both sides of the equation

11x + 2 - 2 = 90 -2

11x = 88

Divide both sides by 11

11x/11 = 88/11

x = 8

Hence, the value of x is 8

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