Mathematics College

## Answers

**Answer 1**

Using **cosine law** and **sine law**, the value of angle E and D are 14° and 35° and the length of side d is 19 units

What is Law of Cosine

The **law of cosines** is a mathematical formula used to calculate the measure of a third side of a triangle when two sides and the angle between them are known. It is also used to calculate the angles of a triangle when all three sides are known. The formula is: c² = a² + b² - 2ab cos(C).

In this given problem, triangle DEF can be;

f² = e² + d² - 2(e)(d) cos(F)

But we don't know the length of side d

Using **sine law**

f / sin F = e / sin E

25 / sin 131 = 8 / sin E

sin E = 8 * sin 131 / 25

E = 13.97°

E = 14°

Using sum of angles in a **triangle**

D + E + F = 180°

D = 180 - (14 + 131)

D = 180 - 145

D = 35°

Using **cosine law**;

d² = e² + f² - 2(e)(f)cos(D)

Substituting the values into the formula;

d² = 8² + 25² - 2(8)(25)cos(35)

d = 19

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## Related Questions

Suppose a parabola has an axis of symmetry at x = -1, a maximum height of –1 and also passes through the point (0, –5). Write the equation of the parabola in vertex form.

### Answers

The **vertex form** of the **parabola** is y + 1 = - 4 · (x + 1)².

How to determine the vertex form of the equation of a parabola

Graphically speaking, **parabolae** can be generated by **quadratic equations**, whose forms are described below: (Please notice that the parabola described by statement is parallel to y-**axis** since axis of symmetry is a vertical line)

Standard form

y = a · x² + b · x + c

Vertex form

y - k = C · (x - h)²

Where:

x - Independent variabley - Dependent variablea, b, c - Real coefficient(h, k) - Coordinates of the vertex.

If we know that h = - 1, k = - 1 and (x, y) = (0, - 5), then the equation of the parabola in vertex form is:

C = (y - k) / (x - h)²

C = (- 5 + 1) / (0 + 1)²

C = - 4 / 1²

C = - 4

The equation of the **parabola** in **vertex form** is equal to y + 1 = - 4 · (x + 1)².

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3 + y = 18 for y help with problem

### Answers

**Answer: y = 15**

**Step-by-step explanation:**

**Subtract both sides by 3**

**3 + y = 18**

**y = 15**

Slopes of parallel/Purpendicular lines - What is the slope of a line parallel to the line whose equation is x + 2y = -14

### Answers

**Answer: -1/2**

Explanation:

First we solve for y.

x + 2y = -14

2y = -14 - x

2y = -x - 14

y = (-x - 14)/2

y = -x/2 - 14/2

y = (-1/2)x - 7

The equation is in slope intercept form y = mx+b

m = -1/2 = slopeb = -7 = y intercept

Parallel lines have equal slopes, but different y intercepts. This means the slope of any line parallel to this given one will have a slope of -1/2

For example, y = (-1/2)x + 10 is parallel to y = (-1/2)x - 7, since both have the same slope of -1/2 but different y intercepts.

what is solution set for 2x2+15=-11x?

A{2.5,3} C{-3,-2.5}

B[1.5,5} D{-5,-1.5}

### Answers

**Answer:**

C{-3,-2.5}

**Step-by-step explanation:**

Brainliest pls

stock prices used to be quoted using eights of a dollar. Find the total price of the transaction.

200 shares of national semi at 115 1/2

### Answers

**Answer:**

**Step-by-step explanation:**

200 x 115.5/8 = $23,100.00

A company estimates that the demand for its product fluctuates with the price it charges. The demand function is q = 450,000 – 400p where q equals the number of units demanded and p equals the price in naira. The total cost of producing q units of the product is estimated by the function C = 400,000 + 200p + 0.0005q²? (a) Determine how many units q should be produçed in order to maximize annual profit. (b) What price should be charged? (c) What is the annual profit expected to equal?

### Answers

The company should create 1 unit of production in Plant 1 in order to optimize its **earnings.**

Identify the optimal number of units to produce in order to maximize annual profit ?

The company should create 1 unit of production in Plant 1 in order to optimize its earnings.

Any extra unit above one in Plant 1 would reduce the demand for the firm's goods, which is determined by

P = 78 – 15 Q, where Q = Q1 + Q2.

For instance, the company will generate four units in Q2 if it produced two units in Q1.

The **negative demand** for the firm's goods will range from 33 units

(78 - 15 x 3, where Q = 3) to -12 units (78 - 15 x 6, where Q = 6),

depending on the production output.

The output of the company at Plant 1 (Q1) that **maximizes** its earnings is therefore 1.

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The gate code at your apartment complex is three numerical digits followed by the "#" sign. If each code

contains non-repeating digits, how many possible gate codes does your apartment complex have?

### Answers

There are 720 **possible gate codes **your **apartment complex **have.

What is algebra?

The subject matter of the math discipline of **algebra **is symbols and the **arithmetic operations **performed on them. **Variable **describes these symbols because they don't have any fixed values. We frequently notice values that are in constant flux in our day-to-day problems.

To represent these shifting values, however, is always necessary. These values are frequently represented in **algebra **with symbols like x, y, z, p, or q; these symbols are referred to as **variables**.

The gate code at your apartment complex is three **numerical digits **followed by # sign.

There are 10 **digits **(0 to 9).

Compute the number of possible gate codes if each code contains **non**-**repeating digits** as follows.

The first 3 place in the code must be filled by three **non**-**repeating digits**.

So, there are 10 possibilities for the first digit, 9 possibilities for the second digit and 8 possibilities for the third digit.

Hence, the three **non-repeating digits **can occur in 10×9×8 ways.

The three **non**-**repeating** **digits **are followed by "#" sign. The sign # can occur in only one way.

Combine the above results and obtain the number of possible gate codes as,

10×9×8×1=720

Thus, there are 720 possible **gate codes**.

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what is the distance between the pints (-1,2) and (2,6)

### Answers

**Answer:**

1

**Step-by-step explanation:**

(-1,2) and (2,6)

d=√[2-(-1)] ^+ [2-6]^

d=√3+(-4)^

d=√-1^

d=1

Edward marks exam scripts for a grade 11 extra class he charges R150 for a maths paper 1 script and R200 maths paper 2 scripts as shown below

What type of relationship is shown on the graph

### Answers

The type of **relationship **shown on the **graph **that depicts Edward's exam scripts is a Linear relationship.

What is a linear relationship ?

A straight-line link between two variables is referred to statistically as a **linear relationship** (or linear association). Both a graphical representation of a linear relationship, in which the variable and constant are connected by a straight line, and a mathematical representation, in which the dependent variable is determined by multiplying the independent variable by the slope coefficient and a constant.

Linear relationships can be represented graphically or **mathematically **as the equation y = mx + b.

Edward's cost per math paper 1 or **math paper **2 script marked will change depending on the type of paper and the number of papers. This simply means that **Edward**'s charges are increasing per paper marked which is shown a linear relationship in the attached graph.

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pls help me asap iready now

### Answers

He surveys 120 people

**the answer is there**

**60 students so. my brainly is glitchng sorry**

Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?

### Answers

Answer

Step by step explantion:

bsf= 26

Eliana:98

SS teacher=203

David=55

**Step-by-step explanation:**

m= music

bsf: m

eliana:4m-6

David:2m+3

SS teacher: 2(4m-6)+7

m+4m-6+2m+3+8m-12+7

382=15m-7

7+ +7

389=15m

/15m /15m

m=26

multiply 26 to each one of them

determine whether the three points P=(-7,6,-8), Q=(-8,4,-11), R=(-9,3,-14) are colinear by computing the distances between pairs of points

### Answers

**Answer:**

To determine whether the three points P, Q, and R are colinear, we can calculate the distances between pairs of points using the distance formula:

d(P,Q) = √((-8 - (-7))^2 + (4 - 6)^2 + (-11 - (-8))^2) = √((-1)^2 + (-2)^2 + (-3)^2) = √14

d(Q,R) = √((-9 - (-8))^2 + (3 - 4)^2 + (-14 - (-11))^2) = √((-1)^2 + (-1)^2 + (-3)^2) = √9

d(P,R) = √((-9 - (-7))^2 + (3 - 6)^2 + (-14 - (-8))^2) = √((-2)^2 + (-3)^2 + (-6)^2) = √19

If the three points are collinear, the distance between any two points should be a multiple of the distance between the other two points. Since √14, √9, and √19 are not multiples of each other, it can be concluded that the three points P, Q, and R are not collinear.

A local salesman receives a base salary of $925 monthly. He also receives a commission of 8% on all sales over $1250. How much would he have to sell in a month if he needed to have a monthly income of $2900?

He would need to sell $

to reach his needed monthly income needs.

### Answers

The salesman needs to **sell **$25937.5 to reach his needed monthly income needs.

What is commission?

**Commission**, also known as sales commission, is a payment given to employees based on the sales they make.

Given that, A local salesman receives a base salary of $925 monthly. He also receives a **commission **of 8% on all sales over $1250.

Monthly salary = fixed part + **commission **part

The fixed salary is $925.

The **commission **part is 8% on all sales over $1250

Let x = amount of sales, and x must be greater than $1250.

Then, the amount of sales over $1250 is x - 1250.

He earns 8% on that amount, so the **commission **part is 8%(x - 1250),

or 0.08(x - 1250).

Monthly salary = fixed part + **commission **part

Monthly salary = 925 + 0.08(x - 1250)

925 + 0.08(x - 1250) = 2900

0.08x = 2075

x = 25937.5

Therefore, he needs to **sell **$25937.5.

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Obtain an estimate for the following computation by rounding the numbers so that the resulting arithmetic can easily

be performed by hand or in your head. Then, use a calculator to perform the computation. How reasonable is your

estimate when compared to the actual answer?

348 +598

is O

Round the two numbers to the nearest ten. An estimate of the sum is

More

x 946 is not answer also I need help this homework math please

### Answers

**Answer: it should be 946, maybe you worded Wong**

**Step-by-step explanation:**

**o obtain an estimate for the computation 348 + 598, we can round the two numbers to the nearest ten.**

**348 rounded to the nearest ten is 350**

**598 rounded to the nearest ten is 600**

**So, our estimate for the sum of 348 + 598 is 350 + 600 = 950**

**Using a calculator, the actual computation is 348 + 598 = 946**

**Our estimate of 950 is 4 more than the actual answer of 946. This means that our estimate is slightly higher than the actual answer. This is not a big difference and it is reasonable as the numbers are rounded to nearest 10.**

Which statement is true about the graph? Select all that apply. (Lesson 3) Long Description The ratio of the rise to the run of each triangle is the same. The smaller triangle and the larger triangle shown are similar. The slope of the line is 2. The slope of the line is −2. The corresponding sides of the two triangles are not proportional.

### Answers

The **correct statements** about the **graph **are given as follows:

The ratio of the rise to the run of each triangle is the same. The smaller triangle and the larger triangle shown are similar.The slope of the line is of -2.

What are the rise and the run of a graph?

The **rise **and the **run **of a graph are defined as follows:

Rise: change in the output, that is, the change in y.Run: change in the input, that is, the change in x.

The **slope **of a line is given by the change in y divided by the change in x, hence it's equation is given as follows:

Slope = Rise/Run.

For the **first triangle**, the rise and the run are given as follows:

Rise = -6.Run = 3.

Hence the **slope **is of:

Slope = -6/3 = -2.

For the **second triangle**, the rise and the run are given as follows:

Rise = -2.Run = 1.

Hence the **slope **is of:

Slope = -2/1 = -2.

As the **ratios are the same**, the triangles are similar, the line has a slope of -2, and the corresponding sides are proportional.

Missing Information

The graph is given by the image presented at the end of the answer.

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After playing 5 games, you have 33 credits left. You play 4 more games and have 21 credits left. Write an equation that represents the number of credits y on the card after x games

### Answers

**Answer:**

5x=33y,4x=21y I hope this is helpful

find the property

plssss help

### Answers

Subtract 7 from both sides. Subtract 7 from 23 to get 16. Divide both sides by 4. Divide 16 by 4 to get** 4.**

What Is Angle Congruence’s Symmetric Property?

According to the symmetric property, if one geometric form is congruent to another, the second shape is likewise congruent to the first. The symmetric property of congruence states that for all angles A and B, if AB A B then BA B A.Transitive Property of Congruence. “If two shapes are congruent to the third shape, then all the **shapes** are congruent to each other,” asserts the transitive property of congruence.

We can solve an equation by applying the four equality properties: addition, subtraction, multiplication, and division. To get the value of an unknown variable, we simply add, subtract, multiply, or **divide** both sides of an equation.

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Use computer drawing software to construct a quadrilateral with two pairs of parallel sides and ywo angles measuring 125°. What geometric shape describes this quadrilateral

### Answers

The **geometric shape **formed is a rhombus.

What is quadrilateral?

A **quadrilateral **is a **four**-**sided **shape enclosed shape, where the sum of the internal angle is 180°.

Here,

It is mentioned in the question, we have to construct a quadrilateral with two pairs of parallel sides and two angles measuring 125°.

So, the construction of a quadrilateral is shown.

As seen in the figure, the figure is of a rhombus.

Thus, the **geometric shape **formed is a rhombus.

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Find the perimeter of triangle ABC. Round your answer to two decimal places.

2

4

6

8

10

-2

-4

-6

-8

-10

2

4

6

8

10

-2

-4

-6

-8

-10

A

B

C

### Answers

The **perimeter **of **Triangle ABC**, given the triangle in drawn in the graph, would be 40 .54 units .

How to find the perimeter ?

To find the **perimeter **of the **triangle **, you first need to find the lengths of the sides of the triangle .

The lengths would be the distance between the points A , B , and C .

The vertices are : A ( - 1 , - 8) , B ( -4 , 6 ) and C ( 4 , 9 ) .

The **distance **between the points can be found by the formula:

= √(( x₂ – x₁ )² + ( y₂ – y₁) ²)

The distance between AB is 14.3 units

The distance between BC is 8. 54 units.

The distance between AC is 17.7 units.

The perimeter is:

= 14.3 + 8. 54 + 17. 7

= 40 .54 units

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Please help me with this question.

### Answers

The **solution** of the given differential initial value problem is

**y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}**

What is initial value problem?

In multivariable calculus, an **initial value problem** is an ordinary differential equation together with an initial condition which specifies the value of the** unknown function** at a given point in the domain.

Given is the **initial value** problem -

y' = y² - 6y + 5

We can write the -

y' = y² - 6y + 5

Dividing both sides by** {y² - 6y + 5}**, we get -

y'/y² - 6y + 5 = 1

Integrating -

∫(y'/y² - 6y + 5) dx = ∫1 dx

- 1/4 log(1 - y) + 1/4 log (5 - y) = x + c{1}

Solving for **y{x}**, we can write -

y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}

The given differential equation can be solved and written as -

y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}

Therefore, the **solution** of the given differential initial value problem is

**y(x) = {e^(4x + 4c{1}) - 5}/{{e^(4x + 4c{1}) - 1}.**

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You can hire someone without experience for $13 per hour or someone with experience for $19 per hour. You believe the

experienced person increases the sales per customer by $3. Each person handles about 12 customers per hour. Should you hire the

experienced person?

a) Yes

b) No

### Answers

**Answer:**

a) Yes

The experienced person costs more per hour, but also increases sales per customer. To determine if it is more cost-effective to hire the experienced person, you would need to calculate the net gain or loss from hiring them.

You can do this by multiplying the increase in sales per customer by the number of customers per hour, and comparing that to the difference in hourly wages.

(12 customers/hour * $3/customer) - ($19/hour - $13/hour) = $36/hour - $6/hour = $30/hour

Since the net gain is positive, it is more cost-effective to hire the experienced person.

Yes that is the correct

Factor completely 640-10x^2

### Answers

**Answer:**

**Step-by-step explanation:**

640 - 10x^2 = (4x-10)(160 + 4x)

The factors of 640-10x^2 are (4x-10) and (160 + 4x).

Which of the following quadratics would have the roots of 1+ or 1- ^2.

### Answers

The **quadratic** equation for the given roots is x²-2x-1=0. Therefore, option 4 is the correct answer.

What is the solution of a quadratic equation?

The **solutions** to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic **equations**. The roots of any polynomial are the solutions for the given equation.

The **roots** of the quadratic equation are 1±√2.

Here, x=1+√2 and x=1-√2

x-1-√2=0 and x-1+√2=0

Now, (x-1-√2)(x-1+√2)=0

= x(x-1+√2)-1(x-1+√2)-√2(x-1+√2)=0

= x²-x+√2x-x+1-√2-√2x+√2-2=0

= x²-2x-1=0

Therefore, option 4 is the correct answer.

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What is the meaning of the absolute value of a number?

A.the direction a number is located with respect to zero

B. the distance a number is located from zero

C.the value of a number after it has been rounded up

D.the value of a number after it has been rounded down

### Answers

The correct answer is b.

Given f(x) = 2x – 6, find f(10)

### Answers

**Answer:**

14

**Step-by-step explanation:**

Basically, x is substituted by 10.

So if you plug that into the function, you would get

[tex]f(10)=2(10)-6[/tex]

Simplify it and you get

[tex]f(10)=14[/tex]

f(x)=2x-6

f(10)=2(10)-6

20-6

14

Nine times the difference of 5 and y

### Answers

**Answer:**

9(5 - y)

**Step-by-step explanation:**

9(?) → Nine times

(? - ?) → the difference

Nine times the difference of → 9(? - ?)

The difference of 5 and y → (5 - y)

Nine times the difference of 5 and y → 9(5 - y)

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

**Required answer: **

9(5 - y)

**Detailed explanation:**

If we have the difference of two numbers, then we're subtracting these numbers. In this case, the numbers are **5** and **y**:

[tex]\sf{5-y}[/tex]

Next, we multiply 9 times the difference, so we put 5 - y in parentheses:

[tex]\sf{9(5-y)}[/tex]

[tex]\hrulefill[/tex]

**Have a wonderful day! **

Jan-

London

Watters

Lesson 14: Fractional Lengths in Triangles and

Prisms

x3³5 OA=bhis

trange

G

Kes

ktf

421

Illustrative

73/

Cool Down: Triangles and Cubes

5

A triangle has a base of 3 inches and an area of 5 square inches. Find the height

of the triangle. Show your reasoning.

10

3

im

16-21 x 17

Fat

17

(

먹호를 30 50%

5.

### Answers

When the triangle has a base of 3** inches** and an area of 5 square inches, its height is 3.33 inches.

what is triangle ?

Since a polygon has number of sides and three vertices, it is a polygon. It is a fundamental **geometric shape**. Triangle ABC is the moniker given to a pyramid that has vertices A, B, and C. When the three factors are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three **sections **and three corners. The points where the three sides meet are known as the triangle's corners. The product of three triangle angles is 180 degrees.

given

triangle's surface area is equal to 1/2 * b*h

5 = 1/2 * 3 * h

10 = 3h

h = 3.33 inches.

When the triangle has a base of 3 inches and an area of 5 square inches, its height is 3.33 inches.

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During a spring clearance sale, Sears advertise 1/4 off the list of Model II microwave ovens and an additional 1/5 off the sale price for ovens that are scratched or dented. If the list price of a Model II is $240, what is the sale price? What is the price of a scratched one?

### Answers

**Answer:**

$180.00 sales price

$144.00 for a scratched one

**Step-by-step explanation:**

240 x .75 = 180

1/4 is 25% (100% - 25% = 75% which is .75 as a decimal)

180 x .80 = 144

1/5 is 20% (100% -20% = 80% which is .8 as a decimal)

R=1(149×109meter)2−(298×109meter)2

### Answers

**Value** of R = 1.72×10¹¹ meter

The correct option is B.

What is expression?

**Expressions** in math are mathematical statements that have a minimum of two **terms** containing **numbers** or **variables**, or both, connected by an **operator** in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

For example, x + y is an expression, where x and y are terms having an **addition** operator in between.

Given, expression

R = √[1/{1/(149×10⁹)² - 1/(298×10⁹)²}]

R = √[1/{1/(149×10⁹)² - 1/(298×10⁹)²}]

R = √[1/{(6.71×10⁻¹²)² - (3.36×10⁻¹²)²}]

R = √[1/{4.50×10⁻²³ - 1.13 × 10⁻²³}]

R = √[1/3.37×10⁻²³]

R = √2.97×10²²

R = 1.72×10¹¹ meter

Hence, 1.72×10¹¹ meter is **value** of R.

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Complete **question** is here;

how to solve this long division

### Answers

**Answer:**

**Step-by-step explanation:**

**Answer:**

0.5 is the answer

**Step-by-step explanation:**

2 clearly cannot be divided by 4

So what we have to do is put a 0 over the 2 and a decimal in the place after the 2 and bring down a 0 making it 20÷4=5

Don't forget the decimal point that was necessary to create the 20

That makes the answer 0.5