How Do I Simplify: 5/3+i

Sides of the given Right angle Triangle are 7.5,12.5,10.

The Pythagoras Theorem defines the relationship between a triangle's perpendicular, hypotenuse, and base. The right-angled triangle theorem is another name for this. The Pythagoras theorem states that a triangle is said to be right-angled if the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be said in the following way:

If Angle equals 90° then Hypotenuse = Perpendicular∧2+ Base∧2.

The base is the side that the right angle is connected to, the neighboring side of the right angle is connected to the hypotenuse by the perpendicular, and the side that the angle is opposite to is known as the hypotenuse. The legs of the hypotenuse are another name for the base.

Given

Tan(B) = [tex]\frac{3}{4}[/tex]=[tex]\frac{NE}{BE}[/tex]

⇒BE=10;

NB^2=NE^2+BE^2;

⇒NB^2=156.25

⇒NB=12.5

Sides of the given Right angle Triangle are 7.5,12.5,10.

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Null Hypothesis: The actual mean is equal to the company's claim of 5 hours.Alternative Hypothesis: The actual mean is less than the company's claim of 5 hours.

Null and alternative hypotheses are applied for evaluating statistical theories. In contrast to the null hypothesis, which is a test's default assumption, the alternative hypothesis indicates how your research anticipates an effect or link between variables.

Null hypothesis: The null hypothesis states the expected outcome. In the given situation, the expected outcome is that the actual mean is equal to the company's claim of 5 hours.The alternate hypothesis conveys the null hypothesis' complete opposite.In this case, the alternative hypothesis is that the actual mean is less than the company's claim of 5 hours.

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Answer: c≈44°

Step-by-step explanation:

cos(c)=0,7193

c=arccos(0.7193)

c≈44°

The value of x is 5.

The value of y is 40°.

It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

A composite figure that has three triangles.

Two equilateral triangles.

One isosceles triangle.

We see that,

Both equilateral triangles have the same sides and the same angles.

5x - 1 = 24

5x = 24 + 1

5x = 25

x = 5

We see that,

Let the opposite angle of 6y° = m

6y° + 60 + 60 + m = 360

6y + 120 = 360

6y = 360 - 120

6y = 240

y = 40°

Thus,

x = 5 and y = 40°

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To get rid of the split infinitive move the term that separates the infinitive from the split position.

In the given question we have to explain, how we remove split infinitives.

As we know that,

Split infinitives are grammatical constructions in which the "to" and "infinitive" halves of what is more often referred to as the to-infinitive in modern linguistics are separated by an adverb or adverbial phrase.

When an adverb is inserted between the word "to" and the infinitive verb, a split infinitive results. Move the term that separates the infinitive from the split position to get rid of the split infinitive.

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Answer:

Below

Step-by-step explanation:

Find the slope between the two given points

  (y1-y2) / (x1-x2)     <====  does not matter which you assign as point 1 or 2

(-3-5) / (0-4) = -8/-4 = 2

now set up equation using point-slope form  (use either point)

  y-5  = 2 (x-4)      re-arrange

   y -5  = 2x - 8

   2x - y  = 3

Answer:

D. -30

Step-by-step explanation:

Let's say 0 is sea level. If the diver is 30 feet below 0, then they would by 30 below 0, or -30.

The last sentence of the proof is Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex]. Hence, option b is the correct answer to this question.

We have that △ABC and △CBD are right-angled triangles.

We have to prove [tex]a^{2} + b^{2} = c^{2}[/tex].

We are given the proof too.

Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA.

Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA.

The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as

[tex]a^{2}[/tex] = cf and [tex]b^{2}[/tex] = ce.

Adding [tex]b^{2}[/tex] to both sides of the first equation, [tex]a^{2}[/tex] = cf, which results in the equation [tex]a^{2} + b^{2} = cf +b^{2}[/tex].

Because [tex]b^{2}[/tex] and ce are equal, ce can be substituted into the right side of the equation for [tex]b^{2}[/tex], resulting in the equation [tex]a^{2}+b^{2}[/tex] = cf + ce.

Applying the converse of the distributive property results in the equation  [tex]a^{2}+b^{2}[/tex]= c(f + e).

Now Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex] .

Hence, the last sentence of this proof is Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex].

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The complete question is -

Which is the last sentence of the proof?

a. Because f + e = 1, [tex]a^{2} + b^{2} = c^{2}[/tex].

b. Because f + e = c, [tex]a^{2} + b^{2} = c^{2}[/tex].

c. Because [tex]a^{2} + b^{2} = c^{2}[/tex], f + e = c.

d. Because [tex]a^{2} + b^{2} = c^{2}[/tex], f + e = 1.

Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).

Answer: option b

Step-by-step explanation:

Yes, three equations are needed to find the values of three variables. Then only it will have a unique solution. The  solution of three variable equation is also known as the ordered triple.  

There must be 3 equations, If there are 3 variables.

Lets consider  A,B,C as our equations and x, y, and z as the variables.

We will now follow these following steps:

1) By using C, first write z in terms of x and y. Then, Replace z with its equivalent in B.

2) Then write y in terms of x.

3) In A, replace y with its equivalent and replace z with its equivalent then solve A for x. Now you should know the value of x. You should have written y in terms of x so plug x and you will find y.

4)Finally, you should have written z in terms of x and y so you can find the value of z.

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$15 = 1.25x + 2.50y

x number of games, y = number of rides

Graphing this will show a line with coordinates (x, y) on it who 'fit' in this equation to make it = 15

I graphed points where both x and y are whole numbers.

These are answers to the equation that make it = 15.

Graph the line 2x = y   (2 times the number of games is the number of rides)

Where the lines intersect is where number of rides is twice taht of games, and the price is 15.

Visually, we can determine that they intersect at (2.4, 4.8)

To verify that this is correct, plug them into the first function to see if this gives you 15.

It does equal 15.

While these are not whole numbers, they do make the equations true, but in the real world we would not have numbers like this.

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Step-by-step explanation:

1.6a+4 when a=1/3 is 6

2.5a-2/3=0.133

RIP BRO

Answer:

(3,-1)

Step-by-step explanation:

you have a graph and poin is (0,1) you have 0+3 to make 2 on the horizontil line and they y = -2 so you go down 2 to make (3,-1)

Answer:

(3, -1)

Step-by-step explanation:

Graphical Translation is about shifting the coordinates by a certain value towards the left/down (x and y coordinates respectively) for negative signs and towards the right/up (x and y coordinates respectively) for positive signs.

Eg. x is shifted by + 3 units, y is shifted by - 1 unit from the point (9 , 3) , the resulting coordinate will be:

(9 + 3, 3 - 1) = (12, 2)

Given from the question:

x is shifted by + 3 units and y is shifted by - 2 units,

Therefore, the resulting coordinates will be:

(0 + 3, 1 - 2) = (3, -1).

Answer:

-13???

Step-by-step explanation:

Answer: −28+15=-13

Step-by-step explanation: -28 + 15 = -13

Answer:

y = 3 ; x = -3

Step-by-step explanation:

[x + 1 x y = 1/3x + 1] y = 3

SUBSTITUTE

[ x + 1 x 3 = 1/3x + 1

SIMPLIFY

[ x + 3 = 1/3x + 1]

ISOLATE X FOR X + 3 = 1/3X + 1: X = -3

In the given triangle, length of side AD is 5 unit and length of side AB is 7 unit.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

In triangle ABC,

BC is perpendicular bisector or side AC.

The length of side AC = 10, BC = 7,

Since, BD is a perpendicular bisector of AC,

Therefore, D will be midpoint of AC.

AD = DC = AC /2 = 10/2 = 5.

By angle bisector property,

AB/BC = AD / AC

AB / 7 = 5/5

AB = 7

The length of side AB is 7 and Side AD is 5.

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The probability that next ice cream cone sold is a chocolate chip ice cream cone is 0.052. The result is obtained by dividing the chocolate chip ice cream cone sold by the total ice cream from the previous week data.

Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

The previous week data shows that

To estimate the probability that will happen in the future, we use the data happened in the past.

The probability that the ice cream cone sold for chocolate chip variant is

P(A) = n(A) / n(S)

P(A) = 52 / 997

P(A) = 0.052

Hence, the probability of next selling a chocolate chip ice cream cone is 0.052.

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Answer: 52/997

Step-by-step explanation: I checked on khan

The constant of proportionality is 0.25

Using the unitary approach, you can solve problems by first figuring out the value of a single unit, then multiplying that value by the number of units you need.

According to the given information

Applying Unitary Method

Pages have a direct relationship with time.

N ∝ t

N = k × t

k is constant of proportionality

Time taken to read 15 pages = 60 minutes

Time taken to read 1 page = [tex]\frac{15}{60}[/tex]

                                            = 1/4

1/4 is constant of proportionality

k = 0.25

The constant of proportionality is 0.25

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The complete statements are

The complete question is added at the end of this solution

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

Garrick's plant:

Zan's plant:

Garrick's plant is shorter than Zan's plant and the difference in heights is

Actual difference = 100 mm - 10 mm = 90 mm

Measured difference = 88 mm - 8 mm = 80 mm

The percentage errors are calculated using

Percentage errors = Difference/Actual measurement * 100%

So, we have

Garrick's actual error = (10 - 8)/10 *100% = 20%

Zan's actual error = (100 - 88)/10 * 100% = 12%

Hence, Garrick's measurement was 20% off and Zan's was 12% off.

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Answer:

Step-by-step explanation:

hey buddy thts supper easy just match the d and b

The area of the given triangle will be A = 4.52 units².

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

As per the given,

P(4,6), Q(8,5), and R(5,9)

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

PQ = [tex]\sqrt {\left( {4 - 8 } \right)^2 + \left( {6 - 5 } \right)^2 }[/tex]

PQ = √17 = 4.12

PR = [tex]\sqrt {\left( {4 - 5 } \right)^2 + \left( {6 - 9 } \right)^2 }[/tex]

PR = √5 = 2.25

QR = [tex]\sqrt {\left( {8 - 5 } \right)^2 + \left( {5 - 9 } \right)^2 }[/tex]

QR = √18 = 4.25

The area will be as, √(S(S - PQ)(S - QR)(S - PR)

Where, S = (4.12 + 2.25 + 4.25)/2 = 5.31

Area = √(5.31(5.31 - 4.12)(5.31 - 4.25)(5.31 - 2.25)

A = 4.52 units²

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Answer:

6.5 square units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7cm}\underline{Area of a triangle}\\\\$A=\dfrac{x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $(x_1,y_1), (x_2,y_2)$ and $(x_3,y_3)$ are \\ \phantom{ww}\;\;\; vertices of the triangle. \\\end{minipage}}[/tex]

From inspection of the given diagram, the vertices of the triangle are:

Substitute the vertices into the formula to solve for area:

[tex]\implies A=\dfrac{4(5 - 9) + 8(9 - 6) + 5(6 - 5)}{2}[/tex]

[tex]\implies A=\dfrac{4(-4) + 8(3) + 5(1)}{2}[/tex]

[tex]\implies A=\dfrac{-16 + 24 + 5}{2}[/tex]

[tex]\implies A=\dfrac{13}{2}[/tex]

[tex]\implies A=6.5 \; \sf units^2[/tex]

Therefore, the area of triangle PQR is 6.5 square units.

Answer:

It is impossible to prove that AABC = ADEF with the information given. In order for us to prove that these two figures are congruent, we would need to know the measures of all the angles in both figures and the lengths of all the sides. Since we only have the measures of some of the angles and the lengths of two sides, we cannot prove that the figures are congruent.

The simplified form of the compound inequality - 3a < 6 Or a - 5< - 2

is a > 3 Or a < 3.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, - 3a < 6 Or a - 5< - 2.

∴ 3a > 6  Or a < - 2 + 5.

a > 6/3 Or a < 3.

a > 3 Or a < 3.

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The algebraic expression for 8 less than a number is x - 8

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations

Let the number be x.

The algebraic expression for 8 less than a number will be:

x - 8.

The expression is x - 8.

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The completed two-column table used to prove that ΔSUV ≅ ΔTVU, can be completed as follows;

        Statements         [tex]{}[/tex]                        Reasons

1.    [tex]\overline{SU}[/tex] ≅ [tex]\overline{TV}[/tex]                                         Given

2.   ∠TSU ≅ ∠STV [tex]{}[/tex]                               Given

3.   [tex]\overline{UV}[/tex]║[tex]\overline{ST}[/tex]        [tex]{}[/tex]                                  Given

4.   ∠TSU ≅ ∠SUV[tex]{}[/tex]                               Alternate Interior Angles Theorem

5.   ∠TVU ≅ ∠STV[tex]{}[/tex]                               Alternate Interior Angles Theorem

6.   ∠STV ≅ ∠SUV [tex]{}[/tex][tex]{}[/tex]                              Transitive Property of Congruence

7.   ∠TVU ≅ ∠SUV[tex]{}[/tex]                               Transitive Property of Congruence

8.    [tex]\overline{UV}[/tex]    ≅ [tex]\overline{UV}[/tex]                               [tex]{}[/tex]    Reflexive Property of Congruence

9.    ΔSUV ≅ ΔTVU         [tex]{}[/tex]                    SAS                            

Two triangles such  as ΔSUV and ΔTUV are congruent when the three sides of triangle ΔSUV are congruent to the three sides of triangle ΔTUV.

The details of the reasons used to prove the congruency of the triangles are as follows;

Alternate Interior Angles Theorem

The alternate interior angles theorem states that the alternate interior angles formed by two parallel lines, such as [tex]\overline{UV}[/tex] and [tex]\overline{ST}[/tex] and their common transversals, [tex]\overline{TV}[/tex] and [tex]\overline{SU}[/tex], are congruent.

Transitive Property of Congruence

The transitive property of congruence states that two shapes are congruent to themselves if both shapes are congruent to a third shape.

Reflexive Property of Congruence

The reflexive property of congruence states that a shape, line, or angle is congruent to itself.

SAS

SAS, is an acronym for Side-Angle-Side congruency postulate, which states that, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

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With the help of simple mathematical operations, we know that the publisher can sell a maximum of 12 yearbooks.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

The order of operations refers to the rules that govern how to solve an expression with several operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, the maximum number of books that can be sold are:

24 + 475 = 499

Now, the publisher can receive not more than $6100. Then,

6100/499 = 12.22

Therefore, with the help of simple mathematical operations, we know that the publisher can sell a maximum of 12 yearbooks.

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If x and y are two numerical variables, they will have a negative correlation. As the value of x declines, the value of y tends to do the same.

Statistics uses the terms correlation or dependency to describe any statistical relationship between two random variables or bivariate data, regardless of whether it is causal or not. When two variables are negatively correlated, one drops when the other grows.Therefore, if the value of x decreases, the value of y will decrease as well.A negative correlation between x and y means that when x increases, y decreases, and when x decreases, y also decreases. This is expressed by the formula y = -x.

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The Piecewise function is

f(x) = [tex]\left \{ \right.[/tex] 0,    x<5

          5,     5<x<11

          7,      11<x< 16

A function that is defined piecemeal is one that has numerous subfunctions, each of which applies to a distinct interval in the domain. Instead of being a property of the function itself, piecewise definition is a means to express the function.

A piecewise function is a function that is constructed from bits of various functions across various time intervals.

Given:

let x be the age of person.

We have,

let f(x) represents the piecewise function

f(x) = [tex]\left \{ \right.[/tex] 0,    x<5

          5,     5<x<11

          7,      11<x< 16

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straightforward random sampling With simple random sampling (SRS), each sampling unit of a population has an equal chance of being included in the sample.

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