LEVEL 3

Record the letters

in your triangle from

left to right.

Example:

ABCDEFGHI

Enter the correct 9 letter sequence (no spaces) Use all capital letters *

Answer:

To solve a right triangle, we can use the Pythagorean theorem, which states that the sum of the squares of the two smaller sides equals the square of the largest side. In this triangle, we have:

a^2 + b^2 = c^2

Plugging in the values we have:

18.7^2 + b^2 = 46.4^2

Solving for b, we have:

b = √(46.4^2 - 18.7^2)

b = √(2159.36 - 349.69)

b = √1809.67

b = 42.6 cm (rounded to the nearest tenth)

Next, we can use the tangent function to find angles A and B:

tan(A) = a/b = 18.7/42.6 = 0.439

A = tan^-1(0.439) = 24° 26' (rounded to the nearest minute)

And, using the Pythagorean theorem:

c^2 = a^2 + b^2 = 18.7^2 + 42.6^2 = 346.69 + 1809.67

B = 90° - A = 90° - 24° 26' = 65° 34' (rounded to the nearest minute)

So the solution is:

a = 18.7 cm

b = 42.6 cm

c = 46.4 cm

A = 24° 26'

B = 65° 34'

C = 90°

Step-by-step explanation:

The value of sin B rounded to the nearest hundredth is 0.80.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

The right triangle represented in the question is given below.

We know that sine of an angle in a right angled triangle is the ratio of it's opposite side to hypotenuse.

In the triangle ABC, AB is the hypotenuse and AC is the opposite side of B.

Sin B = AC / AB

Sin B = b / c

Sin B = 20 / 25

Sin B = 0.8

Hence the value of sine of B is 0.8.

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In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:

{x | -8 <= x < 17}

An explanation of set builder notation?

A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | },  where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.

In this instance, the set consists of all numbers higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint

-8 <= x < 17,where x is a real value. This implies that x must exceed or equal to -8 and must be less than 17 to be a part of the set.

As a result, in set builder notation, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows:  {x | -8 <= x < 17}

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The option B is a linear function. The solution has been obtained by using the properties of a linear function.

What is a linear function?

A function is referred to as linear if it can be represented on a graph as a straight line. Typically, the highest degree of this polynomial function is 1 or 0. Despite the fact that linear functions can be expressed in both calculus and linear algebra.

We are given four functions.

It is clearly visible that option A is not a linear function because the degree of the function is 2.

Option B is a linear function because we obtain a straight line on the graph.

Also, option C is not a linear function because the degree of the function is greater than 1.

Similarly, option D is also not a linear function because it's graph is not a straight line.

Hence, option B is a linear function.

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Answer:

x = -4°

Step-by-step explanation:

We know that,

→ Sum of angles of straight line is 180°.

Now we have to,

→ Find the required value of x.

Forming the equation,

→ (54°) + (7x + 154°) = 180°

Then the value of x will be,

→ 7x + 154° + 54° = 180°

→ 7x + 208° = 180°

→ 7x = 180° - 208°

→ 7x = -28°

→ x = -28° ÷ 7

→ [ x = -4° ]

Hence, the value of x is -4°.

Answer: I think x = -4

Step-by-step explanation: I used a calculator.

Answer:

y = 18 + b

Step-by-step explanation:

Add 18 to both sides

y = 18 + b

Answer:5.5

Step-by-step explanation:

Example: Add 1/4 + 2/4

Solution: Let us add these fractions using the following steps.

Step 1: Check if the denominators are the same. (Here, the denominators are the same, so we move to the next step)

Step 2: Add the numerators and place the sum over the common denominator. This means (1 + 2)/4 = 3/4

Step 3: Simplify the fraction to its lowest form, if needed. Here, it is not needed. So, the sum of the given fractions is, 1/4 + 2/4 = 3/4

The angle AED of arc AD of the circle is calculated to be equal to 8100/πr

We shall use the formula:

arc length = (arc angle/360) × 2 × π × radius

where arc angle is measured in degrees and radius is the distance from the center of the circle to the point on the circle where the arc begins.

If AD = 45 and r the radius, we evaluate the arc angle m ∠AED as follows:

(arc angle/360°) × 2 × π × r

by cross multiplication;

arc angle AED = (360 × 45)/2πr

2 can divide 360° to give;

arc angle AED = (180 × 45)/πr

arc angle AED = 8100/πr

Therefore, the angle AED of arc AD of the circle is calculated to be equal to 8100/πr

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Since the triangles are congruent. Then The size of angle Q is 47°

Congruent Angle:

Congruent angles are often used in architecture, construction, design, and art. Isometrics have the same angular measurements. For example, a regular pentagon has 5 sides and 5 angles, each measuring 108 degrees. Regardless of the size or scale of a regular polygon, the angles are always congruent.

Here is a list of rules for the congruence of angles.

1. The only condition for two angles to be congruent is if the measurements of the angles agree.

2. The lengths and orientations of the two sides of this congruent angle are not important.

According to the Question:

It is given that :

B = 6 cm, 12 cm and 9 cm

A = 47°

R' = 29°

If the triangle is congruent, then all the three sides and angles will be same.

Therefore,

Angle Q = Angle A

Therefore, Angle Q = 47°

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To make the concentration of 50% syrup,

she needs to add 0.5 lb of sugar.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

Emma has half a pound of sugar.

To make the concentration of 50% syrup:

Let n be the required amount.

In decimals, 50% is 0.5.

Applying the percentage formula;

we get,

[tex]\frac{0.5}{n + 0.5} \cdot 100 = 50[/tex]

Applying cross multiplication,

we get,

[tex]\frac{0.5}{n + 0.5} = 0.5[/tex]

0.5 = 0.5(n + 0.5)

1 = n + 0.5

n = 1 - 0.5

n = 0.5 lb.

Therefore, she would have 0.5 + 0.5 = 1 pound of sugar.

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The number that is most likely an irrational number is given as follows:

D. 4.279458105...

Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.

Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.

For this problem, the option D gives the irrational number, as it is the lone non-repeating decimal. For the others, we have that:

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A and C are equivalent expressions for a given expression.

What does an expression mean?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is -4y+8.

Given options are:

A. -4(y-2)

By simplifying it we will get -4(y-2) = -4y+8

So, both are equivalent.

B. -4(-2+4y)

By simplifying it we will get -4(-2+4y) = 8-16y

So, both are not equivalent.

C. (2-y)4

By simplifying it we will get (2-y)4 = 8-4y

So, both are equivalent.

D. 4(-y+8)

By simplifying it we will get 4(y-8) = 4y-32.

So, both are not equivalent.

A, and C are equivalent expressions for a given expression.

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The amount invested in the account that earns 10% interest is $4,000 and the amount invested in the account that earns 11% interest is $3,000.

The system of equations that represent the information in the question is:

a + b = 7000 equation 1

0.1a + 0.11b = 730 equation 2

Where:

a = amount invested in the account that earns 10% interest

b = amount invested in the account that earns 11% interest

The elimination method would be used to solve the equations.

Multiply equation 1 by 0.1

0.1a + 0.1b = 700 equation 3

Subtract equation 3 from equation 2

0.01b = 30

Divide both sides of the equation by 0.01

b = 30 / 0.01

b = 3000

Substitute for b in equation 1:

a + 3000 = 7000

a = 7,000 - 3000

a = 4000

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Answer:

(-8 + 35x) / 5x or -8 / 5x + 7 (same)

Step-by-step explanation:

(-32x^8 + 140x^9) / 20x^9 =

= -32x^8 / 20x^9 + 140x^9 / 20x^9 =

= -8 / 5x + 7 =

= (-8 + 7 * 5x) =

= (-8 + 35x) / 5x

Answer:

x=4

Step-by-step explanation:

-6x = -6-18

-6x = -24

-6x/-6 = -24/-6

x =4

The equation Distance = Speed × Time can be used to calculate the time spent in both city and highway. The sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.

Distance is a numerical measurement of the distance between two objects in physical space. It is commonly measured in meters, kilometers, or miles. Angles, such as degrees of longitude and latitude, can also be used to calculate distance.

Distance may be estimated mathematically using methods such as the Pythagorean theorem. When studying the movement of things, such as in physics and engineering, and estimating the speed of objects in motion, distance is a significant component.

Since you know the total distance traveled and the average speed of the vehicle in both city and highway, you can use the equation

Distance = Speed × Time

to solve for the time spent in both city and highway.

For time spent in city:

35 mph × C = 995 miles

C = 995 miles/35 mph = 28.43 hours

For time spent in highway:

60 mph × H = 995 miles

H = 995 miles/60 mph = 16.58 hours

Therefore, the sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.

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Answer:

$105

Step-by-step explanation:

Let x be the amount of money Carolina has in her checking account. Then, her savings account has x + $30. The total amount of money in both accounts is $180, so we can write the equation:

x + (x + $30) = $180

Expanding the left-hand side:

2x + $30 = $180

Subtracting $30 from both sides:

2x = $150

Dividing both sides by 2:

x = $75

Therefore, Carolina has $75 in her checking account and $75 + $30 = $105 in her savings account.

Here are the steps to complete the budget, as described in the instructions:

Calculate totals for each type of expense and for each month:

Calculate net income for each month:

Add another column to calculate the percentage of total expenses for each category:

Create two different unique charts:

Label each page tab according to the chart:

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Answer:

option (A).

Step-by-step explanation:

The equivalent expression to the given radical expression, when the denominator has been rationalized and x > 5, is 2(√x + √x - 5), or option (A).

The values of p for which the equation (p+1)x² + 4px +9=0 has equal roots:

p =  (36 ± 59.8)/32

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

The quadratic equation,

(p+1)x² + 4px +9=0

So, for equal roots, we have:

(4p)² - 4 x (p + 1) x 9 = 0

Solving for p, we get:

16p² - 36 p -36 = 0

This is a quadratic equation, and we can find the roots using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a = 16, b = -36, and c = -36.

Plugging in the values into the formula, we get:

p = (36 ± 59.8)/32

Thus, the values of p for which the equation (p + 1)x² + 4px + 9 = 0 have equal roots are  (36 ± 59.8)/32.

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Answer:

324

Step-by-step explanation:

To evaluate (a) f(f(2)), we first evaluate f(2) which is 52-4 = 6. Then, we evaluate f(6) which is 56-4 = 26. So, f(f(2)) = 26.

To evaluate (b) g(g(3)), we first evaluate g(3) which is 23^2 = 18. Then, we evaluate g(18) which is 218^2 = 324. So, g(g(3)) = 324

we get two possible solutions: L = 6 and W = 4. Therefore, the length of the land could be 6 meters.

If the rectangular plot has length L and width W, then we know that 2L + 2W = 20 since 20 meters of wire mesh were used. We also know that L × W = 24 since the area of the plot is 24 square meters. Solving these two equations simultaneously, We have the equations:

2L + 2W = 20

L × W = 24

From the first equation, we can solve for L in terms of W:

2L = 20 - 2W

L = 10 - W

Substituting this into the second equation, we get:

(10 - W) × W = 24

Expanding the brackets, we get: 10W - W² = 24

Rearranging and setting equal to zero, we get: W² - 10W + 24 = 0

We can solve this quadratic equation by factoring: (W - 6) × (W - 4) = 0

So the possible solutions for W are: W = 6 or W = 4

If W = 6, then L = 10 - W = 4, so the rectangular plot has dimensions 4 meters by 6 meters. If W = 4, then L = 10 - W = 6, so the rectangular plot has dimensions 6 meters by 4 meters. Therefore, the length of the land is 6 meters. because the length is assumed as the longer side of a shape or an object.

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Complete Question

To enclose a rectangular plot of 24 m², 20 m of wire mesh were used, what is the length of the land?

A parent function is the most fundamental function that still satisfies the criteria for a specific type of function. When considering the linear functions that make up a family of functions, for instance, the parent function would be y = x. The simplest function is this linear one.

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Answer:

Therefore, z = 1 + i.

Step-by-step explanation:

Given that the argument of z + 1 is pi/6 and the argument of z - 1 is 2*pi/3, we can use the fact that the argument of a complex number is equal to the angle between the positive x-axis and the line connecting the origin to the complex number in the complex plane.

Let's call the complex number z = a + bi. Then, z + 1 = a + (b + 1), and z - 1 = a - (b - 1).

Using the argument values given, we have:

arg(z + 1) = pi/6, so the line connecting the origin to z + 1 makes an angle of pi/6 with the positive x-axis.

arg(z - 1) = 2pi/3, so the line connecting the origin to z - 1 makes an angle of 2pi/3 with the positive x-axis.

From the above information, we can sketch the complex plane and find the location of the complex number z. We then have two equations for a and b in terms of the argument of the complex numbers:

a = (z + 1 + z - 1)/2 = 1

b = (z + 1 - z - 1)/2 = 1

Therefore, z = 1 + i.

Answer: I believe that the answer is 8x.

Step-by-step explanation:

My explanation is that since x equals a random value, we can still add 5 and 3 to get 8.

I hope this helps!

Using the proportions of the side lengths of the pair of similar triangles, we have:

1. x = 35

2. x = 20; y = 23.3

3. x = 11

4. x = 9

5. x = 10

Triangles that are similar to each other, will have side lengths that are proportional to each other.

Therefore, using proportions, we would have:

1. x/14 = 40/16

Cross multiply:

16x = 40 * 14

16x = 560

x = 560/16

x = 35

2. x/12 = 15/9

9x = 12 * 15

9x = 180

x = 20

y/14 = 15/9

9y = 210

y = 23.3

3. (x + 5)/24 = 36/54

Cross multiply:

54(x + 5) = 36 * 24

54x + 270 = 864

54x = 864 - 270

54x = 594

x = 11

4. 20/28 = 15/(2x + 3)

Cross multiply:

20(2x + 3) = 28 * 15

40x + 60 = 420

40x = 420 - 60

40x = 360

x = 9

5. 24/28 = x + 8 / 3x - 9

Cross multiply:

24(3x - 9) = 28(x + 8)

72x - 216 = 28x + 224

72x - 28x = 216 + 224

44x = 440

x = 10

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Answer:

(a) To determine the mean and standard deviation of Y, we need to find the expected value and standard deviation of the number of defects that can be sold by Company F. Since the number of defects that can be sold is equal to X if X is less than or equal to 2, and equal to 2 if X is greater than 2, we can use the following formula to find the expected value of Y:

E(Y) = P(X = 0) × 0 + P(X = 1) × 1 + P(X = 2) × 2 + P(X > 2) × 2

E(Y) = 0.58 × 0 + 0.23 × 1 + 0.11 × 2 + 0.03 × 2

E(Y) = 0.23 + 0.22 + 0.03

E(Y) = 0.48

To find the standard deviation of Y, we can use the following formula:

Var(Y) = P(X = 0) × (0 - E(Y))^2 + P(X = 1) × (1 - E(Y))^2 + P(X = 2) × (2 - E(Y))^2 + P(X > 2) × (2 - E(Y))^2

Var(Y) = 0.58 × (0 - 0.48)^2 + 0.23 × (1 - 0.48)^2 + 0.11 × (2 - 0.48)^2 + 0.03 × (2 - 0.48)^2

Var(Y) = 0.58 × 0.2304 + 0.23 × 0.1024 + 0.11 × 0.0304 + 0.03 × 0.0304

Var(Y) = 0.1333

The standard deviation of Y is the square root of the variance:

StdDev(Y) = √Var(Y)

StdDev(Y) = √0.1333

StdDev(Y) = 0.3663

So, the mean and standard deviation of Y are 0.48 and 0.3663, respectively.

(c) To find the mean and standard deviation of the selling price for the fat quarters sold by Company G, we need to find the expected value and standard deviation of the price, taking into account the discount for each defect. We can use the following formula to find the expected value of the price:

E(Price) = $5.00 - $1.50 × E(Defects)

E(Price) = $5.00 - $1.50 × 0.40

E(Price) = $5.00 - $0.60

E(Price) = $4.40

To find the standard deviation of the price, we can use the following formula:

StdDev(Price) = $1.50 × StdDev(Defects)

StdDev(Price) = $1.50 × 0.66

StdDev(Price) = $0.99

So, the mean and standard deviation of the selling price for the fat quarters sold by Company G are $4.40 and $0.99, respectively.