Mathematics High School

## Answers

**Answer 1**

The **equation **of a **straight **line passing through the given point and slope is y - y1 = m(x - x1).

What is the simple definition of slope?

The slope of a line is a measure of its **steepness**. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Let the given point be (x1,y1).

slope be m.

we know that,

Line **equation **passing through point is:

y - y1 = m(x - x1)

where m = slope and (x1,y1) = given point.

Therefore The equation of a straight line passing through the given **point **and **slope **is y - y1 = m(x - x1).

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## Related Questions

A sculptures height will be 563 ft find the height in meters. 1 meter = 3.28 ft

### Answers

**Answer:**

≈171.646341 meters

**Step-by-step explanation:**

(563ft/x m)(3.28ft/1 m)

Answer should be around 171.646341 meters

You can also round to whichever decimal place the question asks for.

Which function is an example of exponential growth?

A a(x) = 0.5(1.2)x

B b(x) = 2.4(0.86)x

### Answers

**Answer:**

A

**Step-by-step explanation:**

I think you mean

A a(x) = 0.5(1.2)^x

B b(x) = 2.4(0.86)^x

an exponent to a base larger than 1 will make the function result grow exponentially (getting bigger and much bigger with growing x).

an exponent to a base between 0 and 1 will make the function result shrink and shrink dramatically with growing x.

If Sarah Hsu earns a $60,840 annual salary, what is her weekly salary?

A. $1,216.80

B. $2,535.00

C. $2,340.00

D. $1,170.00

### Answers

D $1170

$60,840 divided by 52 =

D.1,170.00 dollars a week

3. Given the triangles are congruent with 4SK, HK TS, and JR, write a congruence

statement, and find the values of a and b.

H

51

(7b-10)

(6a-3)

83

R

T

Congruence Statement

### Answers

The **congruency statement** that states the congruency between the **triangles** ΔHJK and ΔRST is; Triangle ΔHJK is congruent to ΔRST according to SAA congruency rule.

b = 8a = 9

What are congruent triangles?

Two triangles are **congruent** if they have all three sides of one **triangle** congruent to the **three** sides of the other triangle.

The specified parameters of the **relationship** between the **angles** and the **lengths** of the sides of the triangles are;

∠S ≅ ∠K

[tex]\overline{HK}[/tex] ≅ [tex]\overline{TS}[/tex]

∠J ≅ ∠R

The relationship between the relative positions of the specified congruent sides and angles of the two triangles are;

Angles ∠S and ∠R and segment [tex]\overline{TS}[/tex] in triangle ΔRST are congruent to angles ∠K and ∠J and side [tex]\overline{HK}[/tex] in triangle ΔHJK

The **congruence** statement is therefore;

**Triangles** ΔHJK is congruent to ΔRST by SAA **Side**-**Angle**-**Angle** **congruency** rule.

The measure of angle m∠R in the diagram is 83°, therefore;

m∠R = 83°

∠J ≅ ∠R

m∠J = m∠R (definition of congruency)

m∠J = m∠R = 83°

m∠J = 83°

51° + 83° + (7·b - 10)° = 180°

(7·b - 10)° = 180° - (51° + 83°) = 46°

7·b = 46 + 10 = 56

b = 56 ÷ 7 = 8

b = 8

m∠K = (7·b - 10)°

Therefore; m∠K = (7 × 8 - 10)° = 46°

m∠S = m∠K by definition of congruency, therefore;

m∠S = m∠K = 46

Therefore; 83° + 46° + (6·a - 3)° = 180°

(6·a - 3)° = 180° - 83° - 46° = 51°

6·a - 51 + 3 = 54

a = 54 ÷ 6 = 9

a = 9

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please help with this and explain please

### Answers

The statement (2, 4) is the** intersection **of the two lines, explains that the point (2,4 ) is the solution.

How is the solution to the system of equations found?

Let us consider the given equations of two lines .

-6x + 4y = 4

y = -3x + 10

Rewriting the above **linear equations**,

6x = 4y -4 ---(1)

3x = -y + 10 ---(2)

Multiplying equation (2) by 2,

6x = 4y -4 ---(1)

6x = -2y + 20 ---(3)

Applying subtraction (1) - (3)

6y -24 = 0

6y = 24

y = 4

Substituting the value of y in equation (1)

6x = 4y -4

6x = 16 -4

6x = 12

x = 2

Thus, the system of equations has the **solution** of (x, y) as (2,4).Since the solutions are found by calculating the intersection point of the two lines , Option D is correct.

What are **linear equations?**An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line.Both linear equations with one variable and those with two variables exist. A linear equation is expressed using the linear equation formula. A mathematical equation resembles a balance scale with identical weights on either side.

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What does M =+ 1 signify for plane mirror?

### Answers

M= +1 shows the **image **is **erect **and **same size **of object

What is Magnification?

Magnification is the **process **of enlarging something's apparent size rather than its **actual size**. This enlargement is measured in terms of a calculated quantity known as "magnification." The term "minification" or "de-magnification" is frequently used to describe a reduction in size when this number is less than one.

Given:

M= +1

Then, we know that Magnification =+1 signifies that the **image **formed in a **plane mirror **is of **same size **as the object.

**Positive sign **in the value of magnification signifies that image formed by a plane mirror is **erect**.

The **erect **image is **upside**.

Hence, M= +1 shows the **image **is **erect **and **same **size of **object**

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a random sample of packages delivered by a company were tracked if they were delayed or on time and whether they were sent in-state or out-of-state. the relative frequency table displays the data gathered. in-state out-of-state total delayed 4% 36% 40% on time 39% 21% 60% total 43% 57% 100% based on the given information, what is the likelihood of a package being sent out-of-state, given that it was on time? 53% 37% 35% 21%

### Answers

Answer:36

Step-by-step explanation:

Let f(x) represent the linear parent function.

Which descriptions match the given transformations?

Drag and drop the answers into the boxes..

f(x) - 15

15f (x)

f(x) is translated 15 units up.

f(x) is translated 15 units left.

f(x) is translated 15 units down. f(x) is vertically compressed by a factor of 15.

f (x) is vertically stretched by a factor of 15.

### Answers

The given **transformation** of a function f(x) - 15 and 15 f(x) represents "f(x) is **translated** 15 units down and f(x) is vertically **stretched** by a factor of 15" respectively.

What are the transformation rules for the translation and dilation of a function?

The **translation** transformation rule for a function is

1) f'(x) = f(x) + a; Vertical translation by 'a' units up.

f'(x) = f(x) - a; Vertical translation by 'a' units down.

2) f'(x) = f(x + a); horizontal translation by 'a' units left

f'(x) = f(x - a); horizontal translation by 'a' units right.

The **dilation** transformation rule for a function is

1) f'(x) = a f(x);

If a > 1, vertical stretch by a factor of 'a' units

If 0 < a < 1, vertical compression by a factor of 'a' units

2) f'(x) = f(ax);

If a > 1, horizontal compression by a factor of 'a' units

If 0 < a < 1, horizontal compression by a factor of 'a' units.

Calculation:

It is given that f(x) represents the linear parent function.

The transformed functions are given as

f(x) - 15 and 15 f(x)

The transformation f(x) - 15 is a vertical **translation** of the function f(x) by 15 units **down**.

The transformation 15 f(x) is a vertical **stretch** by a factor of 15 units.

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What is capital in business?

### Answers

Anything that provides value or **advantage** to its owners, such as a factory and its equipment, intellectual property like** patents**, or the financial assets of a company or an individual, can be referred to as capital.

While money in and of itself might be considered capital, the term capital is typically used to refer to money that is being used for investments or productive purposes. To manage a firm day-to-day and finance its future **expansion**, capital is, in general, a crucial element.

Business capital can be acquired through debt or **equity funding**, as well as from the operations of the business. Capital is typically obtained from:

cash held personally

family and close friends

financial backers

Corporations with **venture capital** (VC)

either the federal, state, or municipal governments

Private financing

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What is value of I²?

### Answers

The **value **of I^2 (I squared) is -1.

**What in mathematics is a complex number?**

Math: **Complex Numbers**. **Complex numbers **are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the **value **(-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).

I is a symbol that is used to represent the imaginary unit, which is the **square root **of -1. In other words, I^2 = sqrt(-1)^2 = (-1)^(1/2)^2 = -1.

In mathematics, the imaginary unit is used to represent the **complex numbers**, which are numbers that have both a real part and an imaginary part. The real part is a normal number (like 3, 5, or -2), and the imaginary part is represented by I. For example, the **complex number** 3 + 2I has a real part of 3 and an imaginary part of 2I.

In mathematical notation, the imaginary unit is usually written as I or i, and the **complex numbers** are written in the form a + bI, where a is the real part and bI is the imaginary part. For example, the **complex number** 3 + 2I could be written as 3 + 2i.

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HI temperature change:

equation:

Explain your reasoning

### Answers

The **temperature change **between the relevant **cities **is -18°C and the equation is t = -5°C - 13°C

The temperature change between the relevant cities

From the question, we have the following parameters that can be used in our computation:

London = +13°C

Beijing = -5°C

The temperature change

This is calculated as

The **temperature change **= Beijing - London

The equation

Substitute the known values in the above **equation**, so, we have the following representation

The temperature change = -5°C - 13°C

Evaluate

The temperature change = -18°C

The reasoning

The **difference **is taken because the movement is from London to Beijing

Hence, the temperature change is -18°C

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HELP ME PLEASE

Express in logarithmic form for the base.

x^(y) = P

### Answers

The **equation **as a **logarithm **is y = logₓ(P)

How to express the equation as a logarithm?

From the question, we have the following parameters that can be used in our computation:

x^(y) = P

Rewrite properly

So, we have

x^y = P

Take the **logarithm **of both sides

So, we have the following representation

log(x)^y = log(P)

Next, we have

y log(x) = log(P)

**Divide **both sides by log(x)

y = logₓ(P)

Hence, the **equation **is y = logₓ(P)

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**Answer:**

[tex]y=\log_{x}P[/tex]

**Step-by-step explanation:**

Given equation:

[tex]x^y=P[/tex]

Take **log **with **base x **of both sides:

[tex]\implies \log_{x}x^y=\log_{x}P[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ac^n=n\log_ac[/tex]

[tex]\implies y\log_{x}x=\log_{x}P[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies y(1)=\log_{x}P[/tex]

Simplify:

[tex]\implies y=\log_{x}P[/tex]

A country's population in 1990 was 154 million.

In 2001 it was 159 million. Estimate

the population in 2005 using the exponential

growth formula. Round your answer to the

nearest million.

P= Aekt

### Answers

Using the **exponential** growth formula, the **population** in 2005 was 161 million.

The **equation** f(x) = a(1 + r)^x can also be used to compute exponential growth, where: The function is represented by the word f(x). The initial value of your data is represented by the a variable. The growth rate is represented by the r variable. To calculate **growth** rates, divide the difference between the starting and ending values for the period under study by the starting value.

Growth factor = (159/154) for the eleven-year period between 1990 and 2001.

The population growth might thus be described by the exponential equation

p(t) = 154(159/154)^(t/11), where t is the **number** of years since 1990.

The model forecasts a population of... p(15) = 154(159/154)^(15/11)

= 160.86 = 161 million

In 2005, there were about 161 million people living there.

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**Correct Question:**

A country's population in 1990 was 154 million. In 2001 it was 159 million. Estimate the population in 2005 using the exponential growth formula. Round your answer to the nearest million.

In an examination, a score of 154 is 44 %. What is the maximum score for the examination

### Answers

**Answer:**

350

**Step-by-step explanation:**

154/0.44 = 350

Answer: 350

Check: 44% of 350 = 0.44 × 350 = 154

The solution is 350

The maximum **score **for the examination is given by the **equation **A = 350

**What is an Equation?**

**Equations **are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an **equation**. The "=" sign and terms on both sides must always be present when writing an **equation**.

Given data ,

Let the **equation **be represented as A

Now , the value of A is

The **score **of the examination = 154

The percentage of the **score **154 = 44 %

So , the **equation **will be

**score **of the examination = 44 % of the maximum **score **A

Substituting the values in the **equation **, we get

154 = ( 44 / 100 ) x A

On simplifying the **equation **, we get

A ( 0.44 ) = 154

Divide by 0.44 on both sides of the **equation **, we get

A = 154 / 0.44

A = 350

Therefore , the value of A is 350

Hence , the maximum **score **is 350

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A contractor has 75 feet of safety rail. The foreman is going to install it in such a way that the work area is divided into two congruent rectangles. The table represents the total fenced area, a(s), depending on the length of the shared side, s. The equation a(s) = 37. 5s − 1. 5s2 models the function represented in the table. Fill in the blank to complete the restricted domain of the function. D = {0 ≤ s ≤

### Answers

The **answer** is **D** = {0 ≤ s ≤ **50**}.

The restricted domain of the function **represents** the **set** of all possible input **values** (in this case, the length of the shared side, s) that result in a valid output value (the total fenced area, a(s)).

In this case, the contractor has 75 feet of safety rail, so the **length** of the shared side (s) cannot be **greater** than **50** feet. This is because the shared side is being used to divide the work area into two **congruent** rectangles, so the length of each rectangle (s) plus the length of the shared side (s) must be equal to 75 feet. Therefore, the maximum value of s is 50 feet.

**Additionally**, the length of the shared side (s) cannot be **less** than **0** feet, as a length of 0 feet would mean that no fencing is being used to divide the work area.

Therefore, the restricted **domain** of the **function** is: **D** = {0 ≤ s ≤ **50**}

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Where is the center of the curve X² y² 2x 4y 31 0?

### Answers

The** center** of the curve X² + y² + 2x + 4y = 31 is (x₀, y₀) = (**-1, -2.5**).

To **calculate **the center of the curve, we need to solve the equation for x₀ and y₀.

First, we move all terms with x and y to the **right side** of the equation:

X² + y² - 2x - 4y = -31

Then, we divide both sides by 2 to isolate the x and y terms:

(X² + y²)/2 - x - 2y = -31/2

Next, we take the partial **derivatives **of both sides of the equation with respect to x and y to find the centers of x and y:

(2x - 2)/2 = -1

(2y - 4)/2 = -2.5

Solving for x and y, we get:

x₀ = -1

y₀ = -2.5

Therefore, the center of the **curve** X² + y² + 2x + 4y = 31 is (x₀, y₀) = (-1, -2.5).

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How does the graph of G x 3x 2 compare to the graph of F x )= 3x?

### Answers

We can **graph **the following **function **using the concepts of **translation**.

The required graph can be **plotted **as translating the function f(x) 2 units down.

So as to translate a function f(x) for one unit down we can **subtract **a unit , let say a , from the given function ,f(x) - a.

Let g(x) be f(x) translated down to 2 units

Therefore the graph of g(x) is a translation of f(x) 2 units down.

We can perform the translation of graphs using methods such as **shifting**, **scaling**, or reflecting.

There are two parts of a graph its **ordinate **and its **abscissa**.

The x-coordinate, acts as a separation from the y-axis, that allows us to find a point using a coordinate pair, this is known as the abscissa.

The ordinate, or y-coordinate, is the other part of a **graph **. This tells about the **distance **from x-axis and is above or below the surface.

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find the slope y=-4/3x+4

### Answers

The slope for y=-4/3x+4 is 12/(3x+4)^2

given the nine-sided regular polygon $a 1a 2a 3a 4a 5a 6a 7a 8a 9$, how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set $\{a 1, a 2, \dots, a 9\}$?

### Answers

The total number of distinct **equilateral triangles** in the plane of the polygon A₁, A₂,A₃,A₄,A₅,A₆,A₇,A₈,A₉ with at least two vertices in the set {A₁, A₂,......,A₉} is 84 x 9 = 756.

Given the nine-sided regular **polygon** A₁, A₂,A₃,A₄,A₅,A₆,A₇,A₈,A₉ the question is how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set {A₁, A₂,......,A₉}.

To answer this question, we must first consider the number of ways in which we can select three distinct points from the set. Since the set contains nine distinct points, we can select three distinct points from the set in Computing Binomial CoefficientsC(n, r) where n is 9 and r is 3 . We get C(9, 3)=84

Now, we must consider the number of distinct equilateral triangles that can be formed in the plane of the polygon with at least two **vertices** in the set. Since the regular polygon A₁,A₂,A₃,A₄,A₅,A₆,A₇,A₈,A₉ has nine sides, there are nine distinct equilateral triangles that can be formed in the plane of the polygon with at least two vertices in the set.

Therefore, the total number of distinct equilateral triangles in the plane of the polygon A₁, A₂,A₃,A₄,A₅,A₆,A₇,A₈,A₉ with at least two vertices in the set {A₁, A₂,......,A₉} is 84 x 9 = 756.

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What is AAS and AES?

### Answers

Atomic absorption spectroscopy (AAS) is a **analytical technique** used to determine the concentration of certain elements in a sample. And,Atomic emission spectroscopy (AES) is a analytical technique used to determine the elemental composition of a sample.

Why do we need AAS?

There are many reasons why AAS might be used, including:

To identify the presence of certain elements: AAS can be used to detect the presence of **trace elements** in a sample, even at very low concentrations. This can be useful for identifying the presence of elements that might be harmful or toxic, such as heavy metals.To quantify the concentration of elements: AAS can be used to determine the concentration of elements in a sample with high accuracy. This is useful for a variety of purposes, such as measuring the concentration of nutrients in soil or water, or determining the purity of a chemical compound.To analyze a wide range of elements: AAS can be used to analyze a wide range of elements, including both metallic and non-metallic elements. This makes it a useful technique for analyzing samples that may contain a diverse range of elements.Why do we need AES?

There are many reasons why AES might be used, including:

To identify the presence of certain elements: AES can be used to detect the presence of trace elements in a sample, even at very low concentrations. This can be useful for identifying the presence of elements that might be harmful or toxic, such as heavy metals.To quantify the concentration of elements: AES can be used to determine the concentration of elements in a sample with high accuracy. This is useful for a variety of purposes, such as measuring the concentration of nutrients in soil or water, or determining the purity of a chemical compound.To analyze a wide range of elements: AES can be used to analyze a wide range of elements, including both metallic and non-metallic elements. This makes it a useful technique for analyzing samples that may contain a diverse range of elements.To analyze samples quickly and easily: AES is a relatively fast and easy technique to use, making it a popular choice for many applications. It can be used to analyze samples in the laboratory or in the field, and does not require the sample to be in a particular form or condition.

In AAS, a sample is introduced into a flame or an electric arc, which causes the atoms in the sample to become excited and emit light at specific wavelengths. The emitted light is then passed through a monochromator, which filters out all wavelengths except for a specific one. The amount of light absorbed at this wavelength is then measured, and the absorption is used to determine the concentration of the element being analyzed.

In AES, a sample is introduced into a flame or an electric arc, which causes the atoms in the sample to become excited and emit light at specific wavelengths. The emitted light is then passed through a monochromator, which filters out all wavelengths except for a specific one. The intensity of the emitted light at this wavelength is then measured, and the intensity is used to determine the concentration of the element being analyzed.

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What method would you choose to solve the equation 2x 2 7 9 prime explain why you chose this method?

### Answers

I would use the **square root method** because there is a **power **of 2 and **constants **without a **variable power **of 1.

What is **square root method**?

The "best" method to solve a quadratic equation when there are only x² terms is the **square root method**. That suggests that nowhere in the equation there is any x term being raised to the first **power**.

The **constants **are kept on the other side of the equation while the x2 terms are generally collected on one side of the equation.

Taking the **square roots **of both sides to solve for the value of x is the logical next step after completing the previous step. When you find the **square root **of a **constant**, you must always add the "±" symbol.

2x² - 7 = 9

2x² = 9 + 7

2x² = 16

x² = 16/2

x² = 8

x = √8

x = 2√2

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-2(-4x+5)+6x distributive property in algebraic expressions factoring and distribution

### Answers

**Answer:**

14x - 10

**Step-by-step explanation:**

-2(-4x+5)+6x

8x -10 + 6x

14x - 10

Question 14 of 20:

Select the best answer for the question.

14. Solve the following problem: 28-18-10.

Ο Α. 0

OB. 8

O C. 18

O D. 10

### Answers

**Answer:**

**Step-by-step explanation:**

28-18=10

10-10=0

**Answer:**

**Step-by-step explanation:**

28-18-10= 0

suppose the ratio of lev's age to mina's age is $1 : 2$ and the ratio of mina's age to naomi's age is $3 : 4$. if the sum of all three of their ages is between $30$ and $50$, then how old is mina? assume all ages are whole numbers.

### Answers

Assuming that all ages are whole numbers, following the given **ratios**, then Mina is 12 years old.

If the **ratio **of Lev's age to Mina's age is 1:2, this means that for every 1 year of Lev's age, Mina is 2 years old.

If the ratio of Mina's age to Naomi's age is 3:4, this means that for every 3 years of Mina's age, Naomi is 4 years old.

Let L be Lev's age, M be Mina's age, and N be Naomi's age.

L : M = 1 : 2

M : N = 3 : 4

L + M + N = X, where X is between 30 and 50

Find M in terms of L. Since the ratio of L to M is 1 : 2, this means that M = 2L. Substitute this expression for M in the second equation.

M : N = 2L : N = 3 : 4

This means that 3N = 4(2L) or N = 8L / 3.

Substitute the expression for M, and N in terms of L to the equation L + M + N = X.

L + 2L + 8L/3 = X

17/3 L = X

Since 30 ≤ X ≤ 50, then

30 ≤ 17/3 L ≤ 50

90/17 ≤ L ≤ 150/17

Solve for Mina's age, M.

M = 2L

180/17 ≤ M ≤ 300/17

10.6 ≤ M ≤ 17.6

Assuming that all ages are **whole numbers**, Mina's age should be a multiple of 2 and 3 between 10.6 and 17.6. Hence, Mina's age is 12.

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Is touching the x-axis a zero?

### Answers

When the **x - axis** is **touched**, the value of y would be a zero.

Where does the y - axis intercept the x - axis ?

The points on a graph where the graph crosses the two axes are known as the intercepts (x-axis and y-axis). The **x-coordinate** is the location where the graph crosses the **x-axis, **and the y-coordinate is the location where the graph crosses the y-axis.

The line's **intersection **with the x axis is known as the x intercept. Y = 0 at this point. Set y=0 and then solve for x to find the x-intercept. Set x=0 and then solve for y to obtain the y-intercept.

This means that when the x - axis is touched, the **y value **of the point would therefore be zero.

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help me on this please

### Answers

The **coordinates **of L are (2a, 0)

What are coordinates?

The **coordinates **are a point use to represent a certain position of a certain thing, represented as (x, y).

Given that, a **right triangle **Δ JKL, in which J is (0, 0) and K (2a, 2b)

When plotting the **graph **(refer to the attached figure)

We can see, L lies on x-axis and in a line with x value as 2a and as it is lying on the x-axis then the y value is 0,

Therefore, by the graph we can say the **coordinates **of L are (2a,0)

Hence, L's **coordinates **is (2a, 0)

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at noon a tank contained of 10cm of water after seven hours it contained 7cm of water what is the pendent decrease

of water in the tank

### Answers

The **pendent decrease **of water in the tank is **30%**.

We have been given that at noon a tank contains 10 cm of water after several hours it contains 7 cm of water.

**What is percentage?**

Rather than being stated as a fraction, a **percentage** is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the **percentage.**

To find the **decrease percent** we will use formula:

[tex]\text { Decrease percent }=\frac{\text { Original value-new value }}{\text { Original value }} \times 100[/tex]

Upon substituting our given values in above formula we will get,

Decrease **percentage **of water in the tank [tex]$=\frac{10-7}{10} \times 100$[/tex]

Decrease percentage of water in the tank [tex]$=\frac{3}{10} \times 100$[/tex]

Decrease percentage of water in the tank [tex]$=3 \times 10=30$[/tex].

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You want to borrow 7500 to buy a used boat. First century bank will lend you the money at 15 percent for 12 months. Fidelity savings and loan will lend you the money at 10 percent for 24 months

### Answers

The **future value** or the overall cost of the loan would be $8,625 for First Century Bank and $9,075 for Fidelity Saving and Loan. Hence the First Century bank would be a preferable option for the loan.

Based on the provided information, the **present value** (PV) of the loan is $7500. In order to determine the overall cost of the loan, the **future value **(FV) of the loan is calculated. The Future Value is the implied value of an asset as of a specific date in the future based upon a growth rate assumption.

FV = PV(1 + i)^n

Where i is the interest rate and n is the number of compounding period (years)

For First Century Bank, where i = 15% and n = 1

FV = 7500 (1 + 0.15)^1 = $8625

For Fidelity Savings and Loan, where i = 10% and n = 2

FV = 7500 (1 + 0.1)^2 = $9075

As the First Century bank will cost less, it would be a preferable option for the loan.

Note: The question is incomplete. The complete question probably is: You want to borrow 7500 to buy a used boat. First century bank will lend you the money at 15 percent for 12 months. Fidelity savings and loan will lend you the money at 10 percent for 24 months. How much will each loan cost and which would be preferable option?

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How do you know if a coefficient is positive or negative?

### Answers

A** coefficient** is a numerical value that is used to indicate the strength of a relationship between two variables in a mathematical equation. we can find if they are negative or positive by observing the** sign** in front of them.

Generally speaking, positive coefficients indicate a **positive** relationship between the two **variables**, meaning that as one variable increases, the other variable increases as well. Negative coefficients, on the other hand, indicate a **negative** relationship between the two variables, meaning that as one variable increases, the other variable decreases.

In addition to the sign of the coefficient, the magnitude of the coefficient can also be used to determine the strength of the relationship between the two variables. A larger coefficient indicates a **stronger** relationship, while a smaller coefficient indicates a **weaker** relationship.

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Find the length of the arc. Round to the nearest tenth.

60°

7 mi

### Answers

I think it’s 7.33 mi

Hope that helps