Mathematics High School

## Answers

**Answer 1**

**Answer:**

The speed in yards per year is 60.8.

**Step-by-step explanation:**

To convert the speed from inches per day to yards per year, we need to first convert the speed to inches per year and then convert the units to yards per year.

First, we can convert the speed to inches per year by multiplying the speed by the number of days in a year:

Speed (inches/day) * Days per year = Speed (inches/year)

6 inches/day * 365 days/year = 2190 inches/year

Next, we can convert the units to yards per year by dividing the speed in inches per year by the number of inches per yard:

Speed (inches/year) / Inches per yard = Speed (yards/year)

2190 inches/year / 36 inches/yard = 60.8 yards/year

Rounding to the nearest 10th, we have:

60.8 yards/year ≈ 60.8 yards/year

Therefore, the speed in yards per year is 60.8.

## Related Questions

if you were to integrate around the curve in the opposite direction, what would be the value of the line integral?

### Answers

both directions can be chosen as positive in this example. The right-hand rule solves these **ambiguities**. The resultant remains the same at 3.2 *10^4 Tm

It is **possible **for the line integral to go around the loop in either **direction **(clockwise or counterclockwise), the vector area dS to point in either of the two normal directions and Ienc, which is the net current passing through the **surface **S, to be positive in either direction—but both directions can be chosen as positive in this example. The right-hand rule solves these ambiguities.

The resultant remains the same at 3.2 *10^4 Tm

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Why do we need to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number?

### Answers

**The statement would no longer be true if you did not flip the signs.**

Example: 1 **<** x **<** 2 multiplied by (-1) equals -2 **<** x **<** -1, because you can't have a number that is greater than -1, and less than -2 at the same time.

Establish the identity.

(csc 0+1)(csc 0-1) = cot 0

a. Multiply and write the left side expression as the difference of two squares: ?

b. The expression from the previous step is equivalent to cot 0 using what?

OA. Cancellation Property

OB. Quotient Identity

OC. Pythagorean Identity

OD. Reciprocal Identity

OE. Even-Odd Identity

pls help asap i can’t pass this class without passing this test

### Answers

To establish the given identity, we need to first multiply the left side of the equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.

The left side of the given equation can be written as:

(csc0+1)(csc0-1)

We can then apply the difference of squares formula to this expression to get:

(csc0+1)(csc0-1) = (csc0+1)(csc0-1)

Now, we can see that this expression is equivalent to cot 0 using the Pythagorean Identity. This identity states that the sum of the squares of the cosecant and cotangent of an angle is equal to 1. In this case, since (csc0+1)(csc0-1) = cot 0, we can use the Pythagorean Identity to rewrite the left side of the equation as (csc0^2 + cot0^2) = 1, which is equivalent to cot 0.

Therefore, the given identity is established using the Pythagorean Identity. This means that the correct answer is C. Pythagorean Identity.

Mustafa walks 15 km east and then 10 km south. How far is Mustafa from the starting point? Is in which direction

### Answers

**Answer:**

25 kilometres West direction

You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 44 pieces of clothing (shirt, pants, socks, or hat) and 3 33 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?.

### Answers

The** probability** of ending up with an orange hat is 1/12. It is because here are twelve possible outcomes.

What is Probability?

**Probability** is a branch of mathematics in which the **chances** of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting **heads** or **tails** in the launch of a coin to the chance of error in research.

It is represented mathematically as;

Probability = Number of Expected outcomes / Total number of outcomes

From the question, we can have the following outcomes;

Clothing = 4

Colors = 3

Pr (pick a clothing) = 1/4

Pr (pick a color) = 1/3

Pr (picking an orange hat) = 1/4 x 1/3

Pr (picking an orange hat) = 1/12.

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work out the surface area

### Answers

**Answer:**

a = 120 cm2

**Step-by-step explanation:**

The prism has 5 sides:

2 triangles, base: 3 hight: 4, each

3 rectangles, 3x9, 5x9 and 4x9

Add the areas on each side to the total area:

[tex]a=(2)\frac{(3)(4)}{2} +(3)(9)+(5)(9)+(4)(9)=12+27+45+36[/tex]

[tex]a=120cm^{2}[/tex]

Hope this helps

The table shown below gives the approximate enrollment at the University of Michigan every fifty years. How many more students were enrolled at the University of Michigan in 1950 than in 1900?

### Answers

Answer:

2.33*10^4

Step-by-step explanation:

Let's subtract the enrollment in 1900 from the enrollment in 1950.

2.7*10^4 - 3.7*10^3

= 27*10^3 - 3.7*10^3

= (27-3.7)*10^3

= 2.33*10^3

2.33*10^4 students.

aahan has a job that guarantees him the same fixed salary increase every year. after 4 years, he makes $56,785; after 9 years, he makes $60,210. what is the equation of the line that would graph his salary over time?

### Answers

The** equation of line** that would graph his salary over time will be;

⇒ y = 1/685x - 38.89

**What is Equation of line?**

The equation of line in **point-slope form** passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

After 4 years, he makes $56,785; after 9 years, he makes $60,210.

Now,

Since, After 4 years, he makes $56,785; after 9 **years**, he makes $60,210.

Hence, The equation of **line **passes through the **points **(56,785, 4) and

(60,210, 9).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (9 - 4) / (60210 - 56785)

m = 5 / 3425

m = 1/685

Thus, The **equation of line **with slope 1/685 is,

⇒ y - 4 = 1/685 (x - 56,785)

⇒ y - 4 = 1/685x - 42.89

⇒ y = 1/685x - 42.89 + 4

⇒ y = 1/685x - 38.89

Therefore, The** equation of line** that would graph his salary over time will be;

⇒ y = 1/685x - 38.89

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Which number line shows the solution to the inequality -2(3x - 1) < 8?

### Answers

**Answer: B**

**Step-by-step explanation:**

1. multiply (-3x+1) by -2 to get -6x+2 -> **-6x+2<8**

2. then subtract 2 from both sides, -6x+2 *-2 *< 8 *-2* -> **-6x<6**

3. divide both sides by -6, when dividing an inequality, the inequality symbol switches so you'd have **x > -1**

so the answer would be **B**

Which of the following are possible side lengths

for a triangle?

A. 8, 16,4

B. 3, 6, 9

C. 3, 12, 10

### Answers

**Answer:**

C. 3, 12, 10

---------------------------

According **triangle inequality theorem** the sum of any two sides of a triangle is greater than the third side.

**Apply** this to our options, add up the two shortest sides and compare with the longest side.

Option A8 + 4 < 16, **no**, it is **impossible to build a **triangle.

Option B3 + 6 = 9, no, it is **impossible to build a **triangle.

Option C3 + 10 > 12, **yes**, possible triangle.

Suppose you walk at the rate of 210 ft/min. You need to walk 10,000 ft.

How many more minutes will it take you to finish if you have already walked 550 ft?

### Answers

**Answer:**

**Step-by-step explanation:**

**210x550=115500**

**115,500 divide 10,000=11.55?**

A boa constrictor slithers 2/6 kilometers in 4/5 hours. What is the distance the boa constrictor travels in 16 hours?

### Answers

**10 kilometres**

Explanation

1/3 + 4/5 = 5/8

5÷8 = 0.625

0.625 * 16 = **10**

A radioactive isotope has a half life of 1 month. It begins with 500 grams. After 8 months, how many grams would it have. Round to the nearest two decimal places.

### Answers

**Answer:**

t1/2=1m => 30days

A0=500g =0.5kg

t=8m = 240days

A=?

λ=ln2÷t1/2

λ=0.6931÷30

λ=0.0231033333

A=A0×e^-λ×t

A=0.5×e^-0.0231033333×240

A=1.953125grams

Establish the identity.

(csc0+ cot 0)(csc0- cot0) = 1

a. Multiply and write the left side expression as the difference of two squares: ?

b. The expression from the previous step is equivalent to 1 using what?

O A. Reciprocal Identity

O B. Quotient Identity

O C. Pythagorean Identity

O D. Cancellation Property

O E. Even-Odd Identity

pls help asap i can’t pass this class without passing this test

### Answers

To answer this question, we need to first multiply the left side of the given equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.

The left side of the given equation can be written as:

(csc0+ cot 0)(csc0- cot0)

We can then apply the difference of squares formula to this expression to get:

(csc0+ cot 0)(csc0- cot0) = (csc0+ cot 0)(csc0- cot0)

Now, we can see that this expression is equivalent to 1 using the Cancellation Property. This property states that if two numbers or expressions are equal, then their corresponding parts are also equal. In this case, since 1 = (csc0+ cot 0)(csc0- cot0), we can cancel out the corresponding parts on both sides of the equation to get 1 = 1.

Therefore, the correct answer is D. Cancellation Property.

Simplify 5r + 4p - 8r + 6

### Answers

**Answer: -3r+4p+6 or 4p-3r+6**

**Step-by-step explanation:**

**Combine like terms**

**5r-8r=-3r**

**4p**

**6**

**-3r+4p+6**

**Answer:**

–3r + 4p + 6

**Step-by-step explanation:**

5r + 4p – 8r + 6

= 5r – 8r + 4p + 6

= –3r + 4p + 6

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What’s the value of -(-20)

### Answers

**Answer:**

20

**Step-by-step explanation:**

When you have two minuses, it will result in a plus.

**Answer:**

it's 20

**Step-by-step explanation:**

i just hv to know the sign

x+6/-2= 5

what is x

### Answers

**Answer:**

**Step-by-step explanation:**

x - 3 = 5

(x -3) +3 = 5+3

x - 3 + 3 = 8

so,

x = 8

a quantity with an initial value of 800 grows exponentially at a rate of 5.5% every 10 minutes. what is the value of the quantity after 30 minutes, to the nearest hundredth?

### Answers

940 is the initial value, to the closest hundredth, after 30 minutes when amount that starts out at 800 **increases **exponentially at a rate of 5.5% every 10 **minutes**.

Given that,

An **amount **that starts out at 800 increases **exponentially **at a rate of 5.5% every 10 minutes.

We have to find what is the quantity's value, to the closest hundredth, after 30 minutes.

We know that,

**Formula **is

S=a(r+1)ⁿ

Here,

S is initial value

a is 800

r is 5.5%

n is time 30/10

800×(5.5%+1[tex])^{30\div10}[/tex]

=939.3931

Therefore, 940 is the quantity's **value**, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

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Answer:

939.39

Step-by-step explanation:

find the curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1).

### Answers

The **curvature **of r(t) = 3t, t2, t3 at the point (3, 1, 1) is 0.178

In this question we need to find the **curvature **of r(t) = <3t, t^2, t^3> at the point (3, 1, 1).

The **derivative **of r(t) with respect to t is:

r'(t) = <3, 2t, 3t^2>

The **point **(3, 1, 1) corresponds to t = 1,

and r′(1) = <3, 2(1), 3(1)^2>

r'(1) = <3, 2, 3>

|r'(1)| = √(3^2 + 2^2 + 3^2)

|r'(1)| = √(9 + 4 + 9)

|r'(1)| = √(22)

|r'(1)| = 4.69

Now, r''(t) = <0, 2, 6t>

and r′'(1) = <0, 2, 6(1)>

r''(1) = <0, 2, 6>

r′(1) × r′′(1) = <0, 4, 18>

|r′(1) × r′′(1) |

= √(0^2 + 4^2 + 18^2)

= √(16 + 324)

= √340

= 18.44

So, the **curvature **of r(t) would be,

κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3

k(1) = 18.44 / 4.69³

k(1) = 0.178

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7. find and describe a case in which the land surface of an area in the u.s. has subsided due to groundwater withdrawal. if possible, give an estimate of how many feet the land surface subsided.

### Answers

an instance where a region's u.s. land surface has changed subsided due to groundwater withdrawal. The** land surface in the Central Valley **has subsided by as much as **30 feet in distance** some areas due to unsustainable groundwater withdrawals.

The most famous **case of land subsidence** due to groundwater withdrawal in the United States is the Central Valley of California. The land surface in the Central Valley has subsided by as much as **30 feet distance** in some areas due to **unsustainable groundwater** withdrawals. In addition to land subsidence, the unsustainable withdrawals have caused significant groundwater depletion, **surface water contamination**, and reduced agricultural productivity.

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Find the distance between the two points rounding to the nearest tenth (if necessary).

(0,7) and (4,9)

### Answers

Use the distance formula.

d = √((x2-x1)²+(y2-y1)²)

plug in your points

d = √((4-0)²+(9-7)²)

d = √(16+4)

d = √20

d = 4.472135955

distance = 4.5 (rounded to the nearest tenth)

Siddhu bought an mp3 player that typically costs $120 when it was on sale for 20% off. He had to pay 7% sales tax on the sale price. How much did Siddhu pay for the mp3 player in all?

### Answers

**Answer:**

$102.72

**Step-by-step explanation:**

If the mp3 player typically costs $120 and was on sale for 20% off, then the sale price would be 120 * (1 - 0.2) = $96.

If Siddhu had to pay 7% sales tax on the sale price, then the total tax he paid would be 96 * 0.07 = $6.72.

Therefore, Siddhu paid a total of 96 + 6.72 = **$102.72** for the mp3 player when it was on sale with the sales tax included.

if a lawyer charges 120 an hour(or any fraction of an hour) how much is a mill for 3 hours and 20 minutes?

### Answers

If a lawyer **charges** 120 an hour then the bill for 3 hours and 20 minutes will be **400**

**Bill:** A bill is the printed or written statement of the money owed for goods or services.In later** Latin**, bulla became billa, and in English billa became bill. The word can still refer to various official **documents**, such as a proposed law that is brought before parliament, although it is now most commonly used for documents that request **payment** of money.

One hour = 60 minutes

3 hours and 20 minutes = 3×60 +20

= 180+20=200

Here, one hour=60 minutes charges 120

1 minute charges = 120/60

= 2

200 minute charges = 2×200=400

Therefore If a lawyer charges 120 an hour then the bill for 3 hours and 20 minutes will be** 400.**

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If your parabola has a vertex going through the point (2,13), the axis of symmetry would be?

### Answers

The axis of **symmetry** of the **parabola** would be x = 2

How to determine the axis of symmetry

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

Vertex = (2, 13)

Rewrite the **vertex **as follows

So, we have the following representation

(x, y) = (2, 13)

Remove the **y-coordinates**

This gives

x = 2

This represents the axis of symmetry

Hence, the **axis **of symmetry is x =2

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Solve.

27) The cost of having a car towed is given by the

linear function C(x) = 3x + 65, where C(x) is in

dollars and x is the number of miles the car is

towed. Find the cost of having a car towed 7

miles.

2/2

### Answers

**Answer:**

It will cost $86.00 for the care to be towed 7 miles.

**Step-by-step explanation:**

C(x) = 3x + 65 Substitute in 7 for x

C(7) = 3(7) + 65

C(x) = 21 + 65

C(x) = 86

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**8****6**** ****Dollars**

**Step-by-step explanation:**

It is given that

[tex]c(x) = 3x + 65 \\ [/tex]

Since,x is the number of miles the car is towed which in this case is 7

So, If we input 7 in the function C(x)

[tex]c(7) = 3 \times 7 + 65[/tex]

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**T****h****u****s****,**

**[tex]c(7) = 21 + 65 \\ because \: 3 \times 7 = 21 \\ [/tex]**

**and**** ****so****,**

**[tex]c(7) = 86 \\ because \:21 + 65 = 86[/tex]**

**and**** ****so****,**

**c****(****7****)**** ****=**** ****8****6**

**We**** ****also**** ****know**** ****that**** ****C****(****x****)**** ****is**** ****the**** ****cost**** ****of**** ****having**** ****the**** ****car**** ****towed**** ****which**** ****is**** ****equal**** ****to**** ****8****6**** ****for**** ****the**** ****case**** ****of**** ****towing**** ****the**** ****car**** ****7**** ****miles**

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If BA BD, the value of x is:

4.

9.

10.

None of these choices are correct.

### Answers

Because angles ABC and CBD sum up to a 90° angle, their measures must sum up to 90.° So, we can create the following equation:

5x+4x=90

Simplify by combing lien terms:

9x=90

Divide both sides by 9:

x=90/9

x=10

Let’s check this answer:

5(10)+4(10)?=?90

50+40?=?90

90=90

Therefore, x=10

ELYSE OWNS 2,000 SHARES OF A

CORPORATION THAT PAYS A QUARTERLY

DIVIDEND OF $0.51 PER SHARE. HOW MUCH

SHOULD SHE EXPECT TO RECEIVE IN A YEAR?

### Answers

Using the **mathematical operations** of multiplication, if Elyse owns 2,000 shares of a corporation that pays a quarterly **dividend** of $0.51 per share, she should expect yearly **dividends** of $4,080.

What are mathematical operations?

**Mathematical operations** involve the use of **operands** and **mathematical operators** to solve mathematical problems.

Mathematical operations follow the **PEMDAS** rule, which states that Parentheses, Exponents, **Multiplication**, and Divisions in that order should be solved first before Additions and Subtractions.

The number of shares owned = 2,000

Quarterly dividend per share = $0.51

Quarters in a year = 4

Yearly dividends = $4,080 (2,000 x $0.51 x 4)

Thus, applying the **multiplication operation**, the annual **dividend** Elyse should receive is $4,080.

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is (x+1) a factor of polynomial x^3+2x^2-19x-20

### Answers

**Answer:**

**Step-by-step explanation:**

3

the questions are on the picture

### Answers

**Answer:**

(i) x = 17 cm

(ii) 360 cm²

(iii) 14400 cm³

(iv) 4000 cm²

**Step-by-step explanation:**

You want the **slant side length**, **end area**, **volume**, and **total surface area** of an isosceles **trapezoidal prism** with end **bases 16 cm and 32 cm** and end **height 15 cm**. The **length** of the prism is **40 cm**.

(i) Slant side

The* *slant side of the base is the hypotenuse of a right triangle that has legs of 15 cm and (32 -16)/2 = 8 cm. You recognize these numbers as belonging to the {8, 15, 17} Pythagorean triple, so you know the slant side is 17 cm.

If you don't recognize that triple, you can figure the side length as ...

x = √(15² +8²) = √(225 +64) = √289

** x = 17 . . . centimeters**

(ii) End area

The area of the end trapezoid is given by ...

A = 1/2(b1 +b2)h = 1/2(32 +16)(15) = 360 . . . cm²

**The area of the end surface is 360 cm²**.

(iii) Volume

The volume of the prism is given by ...

V = Bh

where B is the area of the base, and h is the length between bases.

V = (360 cm²)(40 cm) = 14400 cm³

**The volume of the prism is 14400 cubic centimeters**.

(iv) Surface area

The total surface area is the sum of the areas of the two bases and the lateral area. The lateral area is the product of the perimeter of the base and the length of the prism.

total area = 2 · base area + lateral area

total area = 2 · 360 cm² + (32 + 17 + 16 + 17 cm)(40 cm)

total area = 720 cm² + 3280 cm² = 4000 cm²

**The total surface area of the prism is 4000 square centimeters**.

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In the diagram below, angle f is congruent to angle i. Enter segments in the blanks provided that would result in a true equation.

### Answers

The **segments in the blank** provided is GH/FH=IH/JH so that the **equation is true**

What are the 4 characteristics of similar triangles?

Similar **triangles differ** in size but have the same form. Corresponding angles are identical in **comparable triangles.** Similar triangles have corresponding sides that have the same ratio. The ratio of the square of any two of their corresponding sides to any identical triangle's area is the same.

What are the 3 types of triangle similarity?

The triangle similarity criteria are:

AA (Angle-Angle)

SSS (Side-Side-Side)

**SAS **(Side-Angle-Side)

In the given question

<GHP=<IHJ (vertically opposite angles)

<JIH=<HPG (alternate angles)

From AA similarity critera

triangles JHI ~ triangle GHP

Hence

GH/FH=IH/JH

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