Hey guys please help me on this math homework

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 cost for Zap Electric Company and Bolt Electric Company are y = 0.06r + 6.55 and y = 0.12r + 2.83

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

Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service.

The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. Hence:

y = 0.06r + 6.55

The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. Hence:

y = 0.12r + 2.83

The cost is y = 0.06r + 6.55 and y = 0.12r + 2.83

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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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Answer: 66%

Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, [tex]\frac{1}{4}[/tex] is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.

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Answer: ___________________________________________________

x = 4

Answer:

j=5

10

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

10-5=j

j=5

c

Answer:

2m + 3n + 11

Step-by-step explanation:

You cannot combine the m and the n terms, but you can combine 5 and 6

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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Answer:

2,500

Step-by-step explanation:

40 × 7 × 9

=2,500d dollars

Answer:

Yes, All the three recipes use a proportional amount of flour.

Step-by-step explanation:

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

There are three different recipes to make cookies for different amount of flour.

Recipe 1 =  3 dozen cookies and 4.5 cups of flour

Recipe 2 =  4 dozen cookies and 6 cups of flour

Recipe 3 = 5 dozen cookies and 7.5 cups of flour

Now,

To check that all the recipes in proportion, we check the amount of flour for 1 dozen cookies.

For recipes 1;

The amount of flour = 4.5 / 3

                              = 1.5

For recipe 2;

The amount of flour = 6 / 4

                              = 1.5

For recipe 3;

The amount of flour = 7.5 / 5

                              = 1.5

Clearly, All are the same amount to make 1 dozen of cookies.

So, The all recipes are in proportions.

Therefore, All the three recipes use a proportional amount of flour.

Answer:

false

Step-by-step explanation:

Credit Unions are not-for-profit financial service cooperatives

The simplified form of the expression [tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex] is [tex]\frac{5}{14}c-\frac{2}{9}d[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Therefore, let's simplify the expression as follows:

To simplify an expression means to write an equivalent expression which contains no similar terms.

his means that we will rewrite the expression with the fewest terms possible.

Hence,

[tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex]

combine like terms

[tex]\frac{6}{7}c-\frac{1}{2}c-\frac{5}{9}d+\frac{1}{3}d[/tex]

Do the arithmetic

[tex]\frac{12c-7c}{14}+\frac{-5d+3d}{9}[/tex]

[tex]\frac{5}{14}c-\frac{2}{9}d[/tex]

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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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Answer:

n = -45

Step-by-step explanation:

2/3n + 4 = -26

subtract 4 from both sides:

2/3n + 4 - 4 = -26 - 4

2/3n = -30

divide both sides by 2/3:

(2/3n)/(2/3) = (-30)/(2/3)

n = -45

Answer:

n=-45

Step-by-step explanation:

2/3n+4=-26

        -4.  -4

2/3n=-30

/2/3.    /2/3

n=-30/1 *3/2

n=-90/2

n=-45

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The number of three-letter sequences that can be made from the word "COMBINATORICS" where no 2 letters can be the same is 720 ways

The question is asking of permutation

arranging the letters without repeating a word gives

COMBINATORICS ⇒ COMBINATRS

The newly arranged word gives 10 letters and arranging 10 letters by taking 3 at a time is 10P₃

The required permutation is 10P₃

10P₃

= 10! / (10 - 3)!

= 10! / 7!

= 720

= 720 ways

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

Step-by-step explanation:

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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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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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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Answer: 3.84 , 3 41/50 , 3.789 , 3

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) 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 person has to deposit $1948.05 per year.

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

In the given question, to find the value to be added per year we will use the formula.

[tex]P= \frac{A \times \frac{r}{n}} {(1 +\frac{r}{n})^{t} - 1}[/tex]

Here A = 50,000

r (rate of interest) = 6 % or 0.06.

n = 1

t = 16

P = value deposit per year

On substituting the values,

[tex]P= \frac{50000 \times 0.06} {(1 +0.06)^{16} - 1}[/tex]

P =   3000 / 2.54- 1

 = $1948.05 .

Therefore, person has to deposit $1948.05 per year.

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It will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.

According to the question,

We have the following information:

2500 dollars is placed in an account with an annual interest rate of 9%.

We know that following formula is used to find simple interest:

Simple interest = principal*rate*time/100

Now, the simple interest on any amount will be equal to the total amount after interest minus the principal amount:

7500-2500

5000

So, we have the following expression:

(2500*9*t)/100 = 5000

Now, using cross multiplication method:

t = (5000*100)/(2500*9)

t = 200/9 years

t = 22.2 years

Now, the nearest year will be 22 years.

Hence, it will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.

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The Graph of x ≥ 3 is attach below

The definition of a linear inequality

The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.

What does a linear inequality in mathematics look like?

What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being used in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).

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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:

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