Mathematics College

## Answers

**Answer 1**

The **perimeter the polygon** using distance formula is estimated as 12 units.

Explain about the perimeter the polygon?

The perimeter of an enclosed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides. Any polygon's perimeter will always be measured in the same unit as its corresponding sides.

**Coordinate** :

A(4, 6) B(4,2) C(6,2) D(6, 6)

Using the distance formula:

AB = √(4-4)² + (6 -2)²

AB = √16

AB = 4

BC = √(4-6)² + (2 -2)²

BC = √4

BC = 2

CD = √(6 - 6)² + (2 -6)²

CD = √16

CD = 4

DA = √(4 - 6)² + (6 - 6)²

DA = √4

DA = 2

So,

perimeter the polygon = AB + BC + CD + DA

perimeter the polygon = 4 + 2 + 4 + 2

perimeter the polygon = 12 units

Thus, the perimeter the polygon using** distance formula** is estimated as 12 units.

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The correct question is-

Find the perimeter the polygon formed 7 when these points are connected: A(4, 6) B(4,2) C(6,2) D(6, 6).

## Related Questions

Please help!!!!!!!!

sec(x−20°)=cosec(x−20°)

What is x in degrees?

### Answers

**Answer: 13**

Its 13 because when you do the question it ends up being 13 degrees

we know that sec theta = cosec( 90 - theta )

sec( x - 20 ) = cosec ( x - 20 )

cosec( 90 - ( x - 20 ) = cosec ( x - 20 )

cosec ( 90 - x + 20 ) = cosec ( x - 20 )

- x + 20 = x - 20

2x = 40

x = 20

hope it helps

If MNOP is a rectangle, and m/MON = 60°, what is the value of x?

A. 30

OB. 60

C. 90

D. 45

OE 120

F. Cannot be determined

N

M

P

### Answers

This is a **contradiction**, so there is no **solution **for x. Therefore, the answer is F. Cannot be **determined**.

What is angle?

An **angle **is a measure of rotation or a figure formed by two rays called the sides of the angle, sharing a common **endpoint**, called the vertex of the angle. It is typically measured in degrees or radians and used in geometry to measure the **amount **of turn between two intersecting lines or segments.

Here,

Since MNOP is a rectangle, then opposite sides are parallel and congruent. Therefore, we have:

m/MON = 60° (1)

Since MON and NOP are congruent triangles (by the definition of a rectangle), we have:

m/NOP = 60° (2)

We know that the sum of angles in a triangle is 180°, so we can find the value of angle MNO as:

m/MNO + m/MON + m/NOP = 180°

Substituting the values from equations (1) and (2), we get:

60° + 60° + m/NOP = 180°

Solving for m/NOP, we get:

m/NOP = 60°

Therefore, angle MOP is also 60°. Since angles MOX and NOY are right angles (where X and Y are the intersections of OP with MN and PQ, respectively), we have:

angle MOX + angle NOY + angle MON + angle NOP + angle MOP = 360°

Substituting the known values, we get:

90° + 90° + 60° + 120° + 60° = 360°

Simplifying, we get:

420° = 360°

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**Answer:**

the answer is b or 60

**Step-by-step explanation:**

Algebra - Solving Equations with Roots And Powers Questions.

I cant solve these 2 equations can someone help please. Showing a step by step solution.

I compared the answer I got to these 2 questions to the answer page and I was wrong for both questions. I cant figure out how they found the answers they did.

### Answers

The **solution** are

1.) x = 3 and x = -3

2.) x=17.

**What is an algebraic equation?**

An **algebraic equation** is a mathematical statement that represents the equality of two **algebraic** **expressions** using one or more **variables**

The given equations are

[tex]\sqrt{\frac{3x^2+5}{2}}+4=8\\\sqrt{3+\frac{(4+\sqrt{x+3})^2}{6}}=3[/tex]

Solving one by one,

Let's solve each equation separately:

[tex]$\sqrt{\frac{3x^2+5}{2}}+4=8$[/tex]

Subtracting 4 from both sides, we get:

[tex]$\sqrt{\frac{3x^2+5}{2}}=4$[/tex]

Squaring both sides, we get:

[tex]$\frac{3x^2+5}{2}=16$[/tex]

Multiplying both sides by 2, we get:

[tex]$3x^2+5=32$[/tex]

Subtracting 5 from both sides, we get:

[tex]$3x^2=27$[/tex]

Dividing both sides by 3, we get:

[tex]$x^2=9$[/tex]

Taking the square root of both sides, we get:

[tex]$x=\pm 3$[/tex]

Therefore, the solutions are x=3 and x=-3.

[tex]$\sqrt{3+\frac{(4+\sqrt{x+3})^2}{6}}=3$[/tex]

Squaring both sides, we get:

[tex]$3+\frac{(4+\sqrt{x+3})^2}{6}=9$[/tex]

Multiplying both sides by 6, we get:

[tex]$18+(4+\sqrt{x+3})^2=54$[/tex]

Expanding the square, we get:

[tex]$18+16+8\sqrt{x+3}+x+3=54$[/tex]

Simplifying, we get:

x=17

Therefore, the **solution** are

1.) x = 3 and x = -3

2.) x=17.

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Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.

### Answers

Surface area of the cone = 90π

Volume of the cone = 100π Option C

**Surface area of a cone**

**Surface** area of a **cone** is the complete **area** covered by its two surfaces, i.e., circular base area and lateral (curved) surface area.

The circular base area can be calculated using area of **circle formula**.

The lateral surface area is the side-area of the cone.

πr(r + l)

where r = radius of circle

l = slanted height.

area = 5π(5 + 13)

area = 5π(18)

Area = 90π

Volume of a cone

A cone is a solid that has a circular base and a single vertex.

To calculate its volume, we need to multiply the base area (area of a circle: π × r²) by height and by 1/3:

volume = (1/3) × π × r² × h

Base area = 25π x 12 x 1/3

= 100π

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c times 30, reduced by 293 is equal to 47

### Answers

The required** **solution to the **equation** is C = 11.33.

**What is Expression?**

An expression, also known as a mathematical expression, is a** finite **combination of **symbols** that are well-formed in accordance with context-dependent principles.

According to question:

To solve for C in this equation, we can use algebraic manipulation.

The given equation is:

C * 30 - 293 = 47

First, we can add 293 to **both sides** to isolate the term with C:

C * 30 = 47 + 293

Simplifying the right side gives:

C * 30 = 340

Finally, we can divide both sides by 30 to solve for C:

C = 340 / 30

C = 11.33

Therefore, the solution to the **equation** is C = 11.33.

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Answer:

11.33

Step-by-step explanation:

how to find the 3rd root of -64

EXPLAINED!!!

### Answers

Therefore , the **solution **of the given problem of **cube root **comes out to be -4 is the third root of -64.

Describe cube root.

But since **cube root **of an integer x equals an integer y, y3 = x in mathematics. There is exactly one real cubic root, one set of transfer function cube roots, but also three distinct complex cube roots for every non-zero real integer.

The **cubic root **of an integer is the outcome of three times multiplying that number. The last cube root, the cube root, is represented by three cube roots.

Here,

We have the knowledge that: to determine the third root of -64.

=>[tex](-a)^3 = -a^3[/tex]

Consequently, we can write:

=>[tex]-64 = -4^3[/tex]

By combining both parties' third roots, we arrive at:

=> ∛(-64) = ∛(-4³)

Using the aforementioned truth, we can write:

=> ∛(-4³) = -∛4³

Today, we are aware of:

=> ∛4^3 = 4

As a result, we have:

=> ∛(-64) = -∛4³ = -4

Therefore, -4 is the third root of -64.

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M is the midpoint of R$. Rhas coordinates (2, 5). M has coordinates (6, 9). Find the coordinates of S.

### Answers

**the midpoint of the** line RS will be (4,7).

What is **spherical coordinates**?

The **coordinate **system that is most frequently employed in three-dimensional systems is called **spherical** **coordinates** of the system, represented as (r,Ф,∅ ). The surface area in three **dimensions** is **calculated** using the spherical **coordinate** system. Radial distance, polar angles, and azimuthal angle are the three numbers that these coordinates indicate. **Additionally** known as **spherical **polar **coordinates**.

M is the midpoint of R$. Rhas coordinates (2, 5). M has coordinates (6, 9).

The midpoint will be calculated by using the formula below:-

Midpoint = [ ( x₁ + x₂ ) / 2 , ( y₁ + y₂ ) / 2 ]

The given points are (2,5) and (6,9). The value of the **midpoint** will be calculated by using the **formula** above:-

Midpoint = [ ( x₁ + x₂ ) / 2 , ( y₁ + y₂ ) / 2 ]

Midpoint = [ ( 2 + 6 ) / 2 , ( 5 + 9 ) / 2 ]

Midpoint = [ ( 8 ) / 2 , ( 14 ) / 2 ]

Midpoint = [ 4 , 7 ]

Therefore, the **midpoint** of the line RS will be (4,7).

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2.4 Workout the June salary that was received by the tanker driver if he worked the entire month without fail.

### Answers

**Answer:**

pay all of his salaries ijfd jddu. dyj. fhkbdd yfgjjddd

**Answer:**

**Step-by-step explanation:**

Calculate the standard score of the given x value, x=88.9

, where x‾=82.5

, s=5.8

. Round your answer to two decimal places.

### Answers

Therefore , the solution of the given problem of test **statistics** comes out to be 1.10 is the standard result (z-score) for the given x value, x=88.9.

What is the test statistic?

The Z-statistic, which confirms the validity of the conventional null **hypothesis**, has been used as the statistical test for an analysis that resembles a Z-test. Consider running a 2 X y test with a 0.05 level of significance and getting a 2.5 R t based on your results . The** p-value** for this Z-value is 0.0124.

Here,

The algorithm for the standard score (z-score) is:

=> z = (x - μ) / σ

where the mean, the standard deviation, and x represent the raw value, respectively.

Inputting the numbers provided yields:

=> z = (88.9 - 82.5) / 5.8

=> z = 1.10

After two decimal digits of rounding, we obtain:

=> z = 1.10

Consequently, 1.10 is the standard result (z-score) for the given x value, x=88.9.

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Given that cos(x)=5/7, what is cos(−x)?

### Answers

**Answer: cos (-x) = cos x from complimentary angle properties of sine and cosine functions**

**Step-by-step explanation:**

Given:

x = 5,

r = 7,

cos (x) = x/r, &

cos (-x) = cos x from complimentary angle properties of sine and cosine functions

Then,

cos(x) = 5/7

cos(-x) = cos(x)

Therefore, cos(-x) = 5/7

using the identity cos(-x) = cos(x) we can see that cos(-x) = 5/7

Shantanu bought more apples than bananas, and he bought more bananas than cantaloupes. Furthermore, he bought more apples than bananas and cantaloupe combined.

Let

a

aa represent the number of apples Shantanu bought, let

b

bb represent the number of bananas, and let

c

cc represent the number of cantaloupes.

Let's compare the expressions

b

+

c

b+cb, plus, c and

2

a

−

b

2a−b2, a, minus, b. Which statement is correct?

Choose 1 answer:

### Answers

**According** to the given **information** the correct **statement** is b + c < 2a - b.

**What is inequality ?**

An inequality is a mathematical expression that compares two values or expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to). An inequality indicates that the values or expressions being compared are not equal, but they differ in some way.

The correct statement is

b + c < 2a - b

We know that Shantanu bought more apples than bananas and cantaloupes combined, so we can write:

a > b + c

Rearranging this expression, we get:

b + c < a

We are also given that Shantanu bought more apples than bananas and more bananas than cantaloupes, so we can write:

a > b > c

Substituting b = 2a - c into the inequality b + c < a, we get:

2a - c + c < a

Simplifying, we get:

2a < 2a

This is always false, so the statement b + c < 2a - b cannot be correct. Therefore, the correct statement is b + c < 2a - b.

Hence, **according** to the given **information** the correct **statement** is b + c < 2a - b.

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Suppose that y varies directly as the square root of x and that y =25 when x =334 what is y when x =247? Round your answer to two decimal places if necessary

### Answers

**Step-by-step explanation:**

If y varies directly as the square root of x, then we can express this relationship as:

y = k√x

where k is the constant of proportionality.

To find the value of k, we can use the initial values given in the problem:

y = 25 when x = 334

Substituting these values into the equation above, we get:

25 = k√334

Solving for k, we have:

k = 25/√334

Now we can use this value of k to find y when x = 247:

y = k√247

Substituting the value of k, we get:

y = (25/√334)√247

Using a calculator, we can evaluate this expression to two decimal places:

y ≈ 19.24

Therefore, when x = 247, y ≈ 19.24.

I need help! Please include an explanation!

### Answers

The **area** of the region bounded by the **x-axis** and the function y = f(x+4) is G 8 units.

How to calculate the area

Let's denote the **area** of the region bounded by the x-axis and the function y = f(x) as A. Then we have:

A = ∫₀^₄ f(x) dx (**integral** of f(x) from x=0 to x=4)

We want to find the area of the region bounded by the x-axis and the function y = f(x+4), which is the same as the **region** bounded by the x-axis and the function y = f(u) where u = x+4.

We can express the **area** of this region as:

∫₋₄⁰ f(u-4) du (integral of f(u-4) from u=-4 to u=0)

Using the substitution u = x+4, we can rewrite the above **integral** as:

∫₀^₄ f(u-4) du (integral of f(u-4) from u=0 to u=4). We can see that this **integral** is exactly the same as the integral we used to calculate the area A.

Therefore, the area of the **region** bounded is also 8 units².

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1. The reciprocal parent function is reflected across the x-axis, then translated 4 units right and 3 units down. Write an equation to represent the new function. Identify the asymptotes.

### Answers

The **reciprocal function's** vertical asymptote is x = 0, which after translation becomes x = 4. Hence, x = 4 is the new vertical asymptote.

How do you determine a reciprocal function's asymptote?

We must examine the polynomials' degrees in order to **accomplish **this. Suppose that m=degree of p(x)n=degree of q(x)1. The horizontal asymptote is y=0 2 if m">n>m. The horizontal asymptote is y=ab if n=m, where a and b are the lead coefficients of p(x) and q(x), respectively.

You can find the **reciprocal **parent function by using:

f(x) = 1/x

We must carry out the following changes in order to produce the new function:

The **function **must be multiplied by -1 in order to reflect along the x-axis.

4 units right translation is accomplished by substituting x with (x-4).

Translating down three units is accomplished by taking three out of the function.

Combining everything, the equation for the new **function **is as follows:

g(x) = -1/(x-4) - 3

The reciprocal function's **vertical asymptote** is x = 0, which after translation becomes x = 4. Hence, x = 4 is the new vertical asymptote.

After the modifications, the reciprocal function's horizontal asymptote, y = 0, remains constant. Hence, y = 0 is likewise the new horizontal asymptote.

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The spinner shown on the right is spun. (Assume that the size of each sector is the same.) Find each probability.

a) P(factor of 14) b) P(multiple of 7 )

### Answers

The answer of the question will be,

a)the **probability **of landing on a factor of 14 is 1, or 100%.

b)the probability of landing on a multiple of 7 is 1/4, or 25%.

What is Event?

An event is set of outcomes of **experiment **or random process. An event is a specific occurrence or a combination of occurrences that may happen when the experiment or the process is carried out.

a) To find the probability of getting a factor of 14, we need to first determine the factors of 14, which are 1, 2, 7, and 14. Assuming that each sector on the spinner is the same size, the probability of landing on any particular number is 1/4. Therefore, the probability of landing on a **factor **of 14 is the sum of the probabilities of landing on the numbers 1, 2, 7, and 14, which is:

P(factor of 14) = P(1) + P(2) + P(7) + P(14) = 1/4 + 1/4 + 1/4 + 1/4 = 4/4 = 1

So the probability of landing on a factor of 14 is 1, or 100%.

b) To find the probability of getting a multiple of 7, we need to determine the multiples of 7 that are on the spinner. Assuming that each sector on the spinner is the same size, we can see that the only multiple of 7 on the spinner is 14. Therefore, the probability of landing on a multiple of 7 is:

P(multiple of 7) = P(14) = 1/4

So the probability of landing on a multiple of 7 is 1/4, or 25%.

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The expression for the Bone mass m of a human femur of length L in terms of the outer radius R, the inner radius r and the ratio k = r/R. More generally, if the bone density is p, measured in g/cm³, then bone mass is given by the equation: M = π r² L [p − (p − 1) * k²] It may happen that p and k change with age, t. If k changes during aging 0.5 mm per year, find the rate of change of m with respect to t, At the time in which r = 40mm, 1 = 300mm, p = 2.

### Answers

**Answer:**

**Step-by-step explanation:**

The expression for the bone mass of a human femur in terms of outer radius R, inner radius r, length L, and density p is given as:

M = π r² L [p − (p − 1) * k²]

where k = r/R is the ratio of inner radius to outer radius.

To find the rate of change of bone mass with respect to time, we need to differentiate this expression with respect to time t, assuming that p and k are functions of t. Using the product rule and the chain rule of differentiation, we get:

dM/dt = π L [(2r dr/dt) p - r² dp/dt - (p - 1) (2r dr/dt) k dk/dt]

Note that the first term in the square brackets involves the derivative of r with respect to time, which we are given as -0.5 mm/year. Also, when r = 40 mm, L = 300 mm, and p = 2, we can substitute these values in the expression to get:

M = π (40 mm)² (300 mm) [2 − (2 − 1) * (40/300)²] = 3.267 x 10^6 g

We can also calculate the value of k at this point as k = r/R = 40/R.

Now, to find the rate of change of bone mass with respect to time, we substitute the given values and simplify:

dM/dt = π (300 mm) [(2)(40 mm)(-0.5 mm/year)(2) - (40 mm)² dp/dt - (2-1)(2)(40 mm)(-0.5 mm/year)(40/R)(-1/R)]

dM/dt = -6032.35 dp/dt

Therefore, the rate of change of bone mass with respect to time is equal to -6032.35 times the rate of change of density with respect to time. If the density increases with time, then the bone mass will decrease at a rate of 6032.35 times the rate of increase in density, and vice versa.

How many 5 number combinations between 1 & 69?

### Answers

There are 11,238,513 , 5 number **combinations **between 1 & 69.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

To find number of 5 number **combinations **between 1 & 69.

Now, We get;

**Numbers **of 5 number **combinations** between 1 & 69 is,

⇒ ⁶⁹ C ₅

⇒ 69! / 5! 64!

⇒ 11,238,513

Thus, There are 11,238,513 , 5 number **combinations **between 1 & 69.

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Three relationships are described below: I. The amount of time needed to mow a yard increases as the size of the yard increases. II. The amount of time needed to drive from city A to city B decreases as the speed you are driving increases. III. The income of a worker who gets paid an hourly wage increases as the number of hours worked increases and increases as the salary rate increases. What type of variation describes each relationship?

### Answers

on solving the provided question we can say that This means that as the **domain **speed you are driving increases, the amount of time needed to drive from city A to city B decreases proportionally.

what is domain?

A function's domain is the **range **of potential values that it can accept. These numbers indicate the x-values of a **function **like f. (x). The range of potential values that can be utilised with a function is known as its domain. The value that the method returns after inserting the x value **belongs** to this set. The formula for a function with y as the dependent variable and x as the independent variable is y = f. (x). When a single value of y can be successfully produced from a **value **of x, that value of x is said to be in the domain of the function.

The relationship between the amount of time needed to mow a yard and the size of the yard is an example of a direct variation. This means that as the size of the yard increases, the amount of time needed to mow the yard increases proportionally.

II. The relationship between the amount of time needed to drive from city A to city B and the speed you are driving is an example of an inverse variation. This means that as the speed you are driving increases, the amount of time needed to drive from city A to city B decreases proportionally.

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Solve the equation 2x^2 – 4x + 3 = 0 using the quadratic formula. Please show the steps.

### Answers

**Answer:**

x = 1 + (1/2)i√2 and x = 1 - (1/2)i√2

**Step-by-step explanation:**

To solve the quadratic equation 2x^2 - 4x + 3 = 0, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 2, b = -4, and c = 3.

Substituting these values, we get:

x = (-(-4) ± sqrt((-4)^2 - 4(2)(3))) / (2(2))

= (4 ± sqrt(16 - 24)) / 4

= (4 ± sqrt(-8)) / 4

= (4 ± 2i√2) / 4

= 1 ± (1/2)i√2

Therefore, the solutions of the quadratic equation 2x^2 - 4x + 3 = 0 are x = 1 + (1/2)i√2 and x = 1 - (1/2)i√2.

equation Editor Suppose Julio tosses a coin four times. What is the theoretical probability of tossing heads at least two times? Express your answer as a fraction in simplest form. (Lesson 5)

### Answers

When a coin is tossed, there are two equally likely outcomes: heads or tails. Since Julio tosses the coin four times, there are a total of 2 x 2 x 2 x 2 = 16 possible outcomes.

To determine the probability of tossing heads at least two times, we need to count the number of outcomes in which Julio gets two or more heads.

There are several ways to approach this problem, but one common method is to use the binomial distribution. If we let X be the number of heads that Julio gets in four tosses, then X follows a binomial distribution with parameters n = 4 (the number of trials) and p = 1/2 (the probability of getting heads on a single toss).

The probability of getting exactly k heads in four tosses is given by the binomial probability formula:

P(X = k) = (n choose k) p^k (1 - p)^(n - k)

where (n choose k) = n! / (k! (n - k)!) is the binomial coefficient, which gives the number of ways to choose k items from a set of n distinct items.

Using this formula, we can calculate the probability of getting two, three, or four heads in four tosses:

P(X = 2) = (4 choose 2) (1/2)^2 (1/2)^2 = 6/16

P(X = 3) = (4 choose 3) (1/2)^3 (1/2)^1 = 4/16

P(X = 4) = (4 choose 4) (1/2)^4 (1/2)^0 = 1/16

The probability of getting at least two heads is the sum of these probabilities:

P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4) = (6 + 4 + 1)/16 = 11/16

Therefore, the theoretical probability of tossing heads at least two times in four tosses is 11/16.

Work out the volume of this cone please

### Answers

**Answer: 1005.31 Cm Squared**

**Step-by-step explanation:**

What is the value of x?

Enter your answer, as a decimal, in the box. Do not round your answer.

x=

A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.

### Answers

The** value** of x is 2.70.

To find x, we can use the midpoint theorem, which states that a line segment drawn from the **midpoint** of one side of a triangle to the midpoint of another side divides that side into two equal segments. We know that segment AD is the midpoint of segment AB in this case.

So, we can use the Pythagorean theorem to calculate the length of segment AC, which is the triangle's hypotenuse. Using the values provided, we get:

AC2 = AB2 + BC2 AC2 = (2AD)2 + CB2 AC2 = 4AD2 + 7.52 AC2 = 4(32). + 56.25 ac2 = 69.25 ac = 69.25 ac = 8.32 ac (rounded to two decimal places)

The angle bisector theorem states that a line segment drawn from the vertex of a triangle to the midpoint of the opposite side divides the opposite side into segments **proportional **to the lengths of the other two sides. We know that CD bisects angle ACB and intersects AB at point D in this case.

So far, we have:

BC/AC x/3 = 7.5/8.32 x = 3(7.5/8.32) x = 2.70 (rounded to two decimal places)

As a result, the value of x is 2.70.

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Solve for x : (can be a complex number)

[tex] {x}^{2} = - 16[/tex]

### Answers

**Answer:**

**Step-by-step explanation:**

We have the equation:

x^2 = -16

Taking the square root of both sides, we get:

x = ± √(-16)

Now, the square root of a negative number is not a real number, but it can be expressed as a complex number using the imaginary unit i, where i^2 = -1.

So, we can write:

√(-16) = √(16) × √(-1) = 4i

Therefore, the solutions to the equation are:

x = ± 4i

So, the answer is x = 4i or x = -4i.

**Step-by-step explanation:**

The solution to this equation would be x = ±4i, where i is the imaginary unit, defined as the square root of -1.

In a normal distribution, 68% of the data fall within how many standard deviations of the mean? O A. Two standard deviations O B. One standard deviation O C. It cannot be determined from the given information. D. Three standard deviations

### Answers

**Answer:**

**B. One standard deviation**

In a normal distribution, approximately 68% of the data fall within one standard deviation of the mean because of the empirical rule, also known as the 68-95-99.7 rule. This rule states that in a normal distribution, about 68% of the data values will fall within one standard deviation of the mean, about 95% will fall within two standard deviations of the mean, and about 99.7% will fall within three standard deviations of the mean.

What is the surface area of the prism?

### Answers

The **surface area **of the **rectangular prism **is 888 squared centimeters.

What is the surface area of the rectangular prism?

A **rectangular prism **is simply a three-dimensional solid shape which has six faces that are rectangles.

The **surface area **of a **rectangular prism **is expressed as;

S.A = 2( wl + hl + hw )

Where w is the width, h is height and l is length

Given the data in the diagram;

Length l = 22cmWidth w = 10cmHeight h = 7cmSurface area A = ?

Plug the given values into the above formula and solve for the **surface area**.

S.A = 2( wl + hl + hw )

S.A = 2( (10 × 22) + (7 × 22) + (7 × 10) )

S.A = 2( 220 + 154 + 70 )

S.A = 2( 444 )

S.A = 888 cm²

Therefore, the **surface area **is 888 cm².

Option B) 888 cm² is the correct answer.

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A multiple choice quiz has 7 of questions each with 4 choices. Eric guesses on every question. What is the probability that he gets fewer than 5 questions correct?

### Answers

**Answer:**

the probability that Eric gets fewer than 5 questions correct is approximately 0.857, or 85.7%.

**Step-by-step explanation:**

Let X be the number of questions Eric gets correct. Since there are 7 questions and each has 4 choices, the probability of guessing any one question correctly is 1/4, and the probability of guessing any one question incorrectly is 3/4. Since Eric is guessing on every question, we can model X as a binomial random variable with n = 7 and p = 1/4.

To find the probability that Eric gets fewer than 5 questions correct, we need to calculate:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

Using the binomial probability mass function, we get:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items.

Plugging in n = 7 and p = 1/4, we get:

P(X = k) = (7 choose k) * (1/4)^k * (3/4)^(7 - k)

Therefore, we have:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (7 choose 0) * (1/4)^0 * (3/4)^7 + (7 choose 1) * (1/4)^1 * (3/4)^6

+ (7 choose 2) * (1/4)^2 * (3/4)^5 + (7 choose 3) * (1/4)^3 * (3/4)^4

+ (7 choose 4) * (1/4)^4 * (3/4)^3

≈ 0.857

Therefore, the probability that Eric gets fewer than 5 questions correct is approximately 0.857, or 85.7%.

which expression shows 1/5 more than five times a number?

### Answers

The **expression** that shows 1/5 more than **five time**s a **number **is 1/5 +5x

**What is an expression?**

Mathematical **expressions** consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: **Number/variable, Math Operator, Number/Variable **is an **expression**.

Let the number be x

1/5 more than five times a number

1/5 +5x

The expression that shows 1/5 more than five times a number is 1/5 +5x

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What is the similarity ratio of STUV to DGFE?

Simplify your answer and write it as a proper fraction, improper fraction, or whole number.

### Answers

The **similarity ratio **of STUV to DGFE is 3 if the rectangles STUV and DGFE are similar.

What are Similar Figures?

Similar figures are those figures which are having the **same shape**, but the sizes are different.

Given are two **rectangles**.

The two rectangles are similar.

The **dimensions **of the similar figures are proportional.

Side VS of the rectangle STUV is similar to the side FG of rectangle DEFG.

VS = 6 and FG = DE = 2

VS / FG = 6 / 2 = 3

This is the same for the **ratio **of sides ST and EF.

ST = 3 and EF = GD = 1

ST / EF = 3 / 1 = 3

Hence the similarity ratio is 3.

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Write an equation showing how 3/8 is a multiple of 1/8

### Answers

To show that 3/8 is a multiple of 1/8, we can write the following equation:

3/8 = (1/8) x 3

This equation states that 3/8 is equal to three times 1/8. In other words, 3/8 can be obtained by multiplying 1/8 by the integer 3. This demonstrates that 3/8 is indeed a multiple of 1/8.

**Answer: 3/8 is a multiple of 1/8 because 3x1 = 3 and 8 is common dynameter. so, it will be like what is 1/8 times 3/8 so, we get 3/8**

**Hope it helps if you got any questions ask me in comments or if I did it wrong. :D**

How much further away from guys house is the library than the cafe

### Answers

**Answer: 5/10**

**Step-by-step explanation:**