An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 11 inches, and the length of the base is 6 inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.

The proof that the angles m<1 = m<4 is shown below

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

Measure of angles

The angle measurements are then given as

m<1 + m<2 = 90 and m<3 + m<4 = 90

The relationship to prove is also given as

m<1 = m<4

Using the above as a guide, we have the following:

Subtract the equations m<1 + m<2 = 90 and m<3 + m<4 = 90

This gives

m<1 + m<2 = 90

-(m<3 + m<4 = 90)

Evaluate the difference

m<1 + m<2 = m<3 + m<4

When both sides of the angle equations are compared, we have:

m<1 = m<4

m<2 = m<3

Ignoring the second equation, we have

m<1 = m<4

Hence, the measure of the angles has been proved

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Work Shown:

[tex]\left(3\text{x}^2\text{y}^5\right)^3\\\\\left(3\right)^3\left(\text{x}^2\right)^3\left(\text{y}^5\right)^3\\\\27\text{x}^{2*3}\text{y}^{5*3}\\\\27\text{x}^{6}\text{y}^{15}\\\\[/tex]

Explanation:

The outer exponent 3 is "distributed", so to speak, to each term inside the parenthesis. This isn't the actual distribution rule. But we can think of it as such. This is what's happening in the second step.

So we'll cube the coefficient 3 to get 3^3 = 27, and we'll cube x^2 to get x^6, and finally cube y^5 to get y^15.

I used the rule [tex](a^b)^c = a^{b*c}[/tex] for the third step.

The constant term that should be used to complete the square? x2 - 5x + _____ = 7 is 25/4

What is quadratic equation ?

A quadratic equation in the variable x is of the form. ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. • Roots of a quadratic equation : A real number α is said to be a root of the. quadratic equation ax2 + bx + c = 0, if aα2 + bα + c = 0.

Given:

x^2-5x+c=7, the constant term c will be obtained using the formula:

c=(-b/2a)²

The quadratic equation in its generic form is:

ax^2 + bx + c

To complete squares we must add the following term:

(b / 2) ^ 2

The equation is:

ax^ 2 - 5x + k = 7

By completing squares we have:

x ^ 2 - 5x + (-5/2) ^ 2 = 7 + (-5/2) ^ 2

Rewriting:

x ^ 2 - 5x + 6.25 = 7 + 6.25

Hence, A constant term should be used to complete the square is 25/4 or 6.25.

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Answer:

4 7

Step-by-step explanation:

Need to find the x and y: The Graph asking in question is attached below:

A graph is a type of data structure used to represent relationships between different objects. It consists of nodes, which are connected by edges. The nodes represent the objects, while the edges represent the relationships between them. Graphs can be used to represent many different types of information, such as road networks, social networks, and even computer networks. Graphs can be used to solve a variety of problems, such as finding the shortest path between two nodes, or finding the most efficient way to route data throughout a network. Graphs can be represented in a variety of ways, such as in the form of a table, a map, or a diagram. In addition, graphs can be used to represent abstract concepts such as relationships between individuals.

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Answer:

11/10

Step-by-step explanation:

33/10 - 22/10

Answer: what

Step-by-step explanation:

On solving the provided question, we can say that - by the help of unitary method the value of 9 units will be

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

cost for the 12 classes = $72

cost of 1 unit = $6

cost of 9 units = $54

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The reference angle of 7pi/4 is pi/4

The acute angle formed by the terminal arm or side and the x-axis is known as the reference angle.

There is always a positive reference angle. The reference angle is, in other words, the angle formed by the terminal side and the x-axis. It must always be positive and less than 90 degrees.

considering angle 7 pi/4, the angle is pi/4 away from 2 pi.

7 pi/4 + pi/4 = 8 pi/4 = 2 pi

We can therefore conclude that 7 pi/4 is an angle on the third quadrant and the reference angle is pi/4.

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Answer:y=

Step-by-step explanation:Firstly let's find the slope which is (7-7)/(4-(-3))=0. Using the point slope formula y-y1=m(x-x1) we plug in one of the points and simplify y-7=0(x-4). Simplifying and solving for y gives us y=

Answer:A two-way table, also known as a contingency table, is a way to organize and present categorical data in a tabular format. It can be used to show the relationship between two categorical variables, such as whether a student lives with a grandparent and the number of people who live in their home.

Based on the information you provided, the two-way table would look like this:

More than 4 people | 6 | 10

4 or fewer people | 4 | 30

It should be noted that the information you provided does not add up to 50 students.

Total for students living with grandparents: 10,

Total for students with more than 4 people: 6+10 =16.

Let me know if this table is incorrect and I'll provide you with more information

Step-by-step explanation:

Miguel only wins $2 in one of the six tournaments, and he only loses $1 in the other five.

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a large group of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

We identify the chips so that we can check all six events. Let's say two chips each have a designated 1: R1 and B1 (as if they were red and blue). Let's now consider all possible combinations.

There are 4 options for the first chip, and 3 options remain for the second chip.

There are 12 combinations as a result. There are just six combinations since we don't care about the sequence; for instance, R1, 3 is the same as R1, 3 to us. (R1, B1), (R1, 3), (R1, 5), (B1, 3), and (B1, 5) are the combinations (3,5) Miguel only wins $2 in one of the six tournaments, and he only loses $1 in the other five.

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For this problem, we know that the line's function is equal to 3 if X isn't 0. That means that for every X that isn't 0, we'll have a line at y = 3 (since we know that g(x) is just fancy for y!). We're also given that if X is equal to 0, it must be at y = 4.

Therefore, your graph should have a straight line through y = 3 EXCEPT at x = 0! At x = 0 you should just have a shaded dot at y = 4.

Step-by-step explanation:

first of all, if he continuously earns only $160 per month (or at least in that dimension), then he will not have to pay any income tax.

but to do the exercise :

100% = $160

1% = 100%/100 = 160/100 = $1.60

10% = 1% × 10 = 1.6 × 10 = $16

he earns after tax

160 - 16 = $144

FYI :

when we combine all the calculations above into one sequence, then we know

100% - 10% = 90%

and 90% of 100% is 100% × 0.9

and so he earns after tax

160 × 0.9 = $144

a) The patient weight in pounds is 234 lbs.

b) The patient weight in kilograms is 106.36 Kg.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

The patient’s weight is 245 lbs.

Each week patient loses = 1 Kg

So, In 5 week patient loses = 5 Kg

As, 1 kg = 2.2 lbs

In 5 week patient loses = 11 lbs

a) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs.

                                                                      = 234 lbs.

b) The weight of the patient after 5 weeks =  234 lbs.

The weight of the patient after 5 weeks in Kg

= 234 lbs x 1 kg per 2.2 lbs.

= 106.36 kg

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Answer:

[tex]4x^2+4vx + v^2[/tex]

Step-by-step explanation:

[tex](2x+v)^2 \\(2x)^2+2(2x)(v)+(v)^2\\4x^2+4vx + v^2[/tex]

x = 3/4 is the correct solution of the given expression.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

The expression Lin tried to solve
8(x-3)+7=2x(4-17)

Simplifying the expression,
8x - 24 = 2x(-13)
8x - 24 = -26x
8x+26x = 24
32x = 24
x = 24/32
x = 3/4

Thus, x = 3/4 is the correct solution of the given expression.

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To find the sum or difference we must know what k is however you can simplify the expression by rewriting and removing the parenthesis furthermore collecting the like terms to get the solution.

Attached photo shows the steps to the solution :P

Answer:

The scale of the model is (21 ft / 3 in) = 7 ft / 1 in. So an 84 foot building would be (84 ft / 7 ft) * 1 in = 12 inches tall in the model.

Step-by-step explanation:

hope it helps

Answer:

588 inches

Step-by-step explanation:

First, find the scale factor of the model by dividing the height of the real building by the height of the model: 21 ft / 3 inches = 21/3 = 7

7 inches/ft

Then, multiply the scale factor by the height of the 84 foot building to find the height of the model: 7 inches/ft * 84 ft = 7*84 = 588

588 inches

Therefore , as a result, we may state that the stated trapezoid angles x = 110°, which is the solution to the problem.

A trapezoid is a quadrilateral that has at least one connected pair of sides. It has the name trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. The trapezoid's base is made up of its parallel sides. A closed, flat shape having two neighboring sides and four successive sides is called a trapezoid. The parallel walls and base of the trapezoid are commonly referred as as the parallel sides and the legs, respectively.

Here,

Given : 110°

and 90°

To find the value of x ,

Thus,

The value of angle opposite to x :

=> 110° + y =180°

=>y =180°-110°

=>y = 70°

thus, x value is

=> x + 70° =180°

=> x =110°

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The formula is written as (3x+9)(x+9) of + 36x + 81 = 0. A second-degree polynomial equation can be used to define quadratics.

Multiplying a variable by itself is the mathematical operation known as "squaring," which is frequently used to refer to a quadratic issue. This vocabulary is based on the notion that a square's area is equal to the sum of its side lengths. The word "quadratic" derives from the Latin quadratum, which meaning square.

here ,

[tex]= + 36x + 81 = 0\\= 3x^2 + 27x + 9x + 81\\= 3x(x+9) + 9(x+9)\\= (3x+9)(x+9)\\= 3(x+3)(x+9)[/tex]

factorized form is [tex](3x+9)(x+9) of + 36x + 81 = 0 .[/tex]

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Rami's glass is fuller than Will's glass by 1/8

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

Rami's glass is 1/2 full. Will's glass is 3/8 full.

Convert the fractions to decimal

This gives

Rami's glass is 0.5 full. Will's glass is 0.375 full.

0.5 is greater than 0.375

So, Rami's glass is fuller

To do this, we calculate the difference

So, we have

Difference = 0.5 - 0.375

Evaluate

Difference = 0.125

Rewrite as

Difference = 1/8

Hence, it is 1/8 fuller

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Answer:

3 stacks of paper can be purchased.

Step-by-step explanation:

Start by setting up the inequality:

15 = 3.79x

Now that you have set up the inequality, go to solve the inequality.

You should get the answer 3.958 (rounded). Since Mr. Valentino can not by a half stack of paper, drop the decimal so we are left with 3.

I would describe the graph as a straight line increasing, with money on y and stacks of paper on the x axis

The value of the x is 10.

What is the exterior angle theorem?

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.

We have given,

angles of the triangle:

Interior angles :

∠D = 2x + 7,

∠E = 26°,

Exterior angle:

∠C = 6x - 7

To find x = ?

few common properties about the angles of a triangle:

A triangle has 3 internal angles which always sum up to 180 degrees.

It has 6 exterior angles and this theorem gets applied to each of the exterior angles.

Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.

Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.

So,

∠C  = ∠D + ∠E

6x - 7 = 2x + 7 + 26,

6x - 7 - 2x - 7 = 26,

4x - 14 = 26,

4x = 40

x = 40/4

x = 10,

Hence, the value of the x is 10.

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Answer:

3 feet

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem. Let's call the distance from the tent pole to the rope x. We can set up the following equation:

x^2 + 12^2 = 15^2

Solving for x, we get:

x = sqrt(15^2 - 12^2)

x = sqrt(9)

x = 3

Therefore, the distance from the tent pole to the rope is 3 feet.

A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
When a system of linear equations consists of an infinite number of solutions then this equation should be dependent and consistent as well, and this system is said to be a system of equivalent equations.

Thus, A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.

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The next step in the series is, shown in Option C.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

There are three steps are shown.

Now, In first step, only one line shown.

In second line the line is left to first line.

And, So on.

Hence, The next step in the series is, shown in Option C.

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The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

Given equations ,

[tex]x^{2}[/tex] + 81 = 0  ,[tex]x^{2}[/tex]-22 = -26 , 3[tex]x^{2}[/tex]-18=21 ,2[tex]x^{2}[/tex] +15 = -13

What is Quadratic equation ?

quadratic equation can be defined as the equation which is in the form of a[tex]x^{2}[/tex]+bx + c = 0 .

where a,b,c are constants .

By solving we get ,

[tex]x^{2}[/tex] +81 = 0

[tex]x^{2}[/tex] = -81

x = 9i , -9i

[tex]x^{2}[/tex] - 22 = -26

[tex]x^{2}[/tex] = -26 + 22

[tex]x^{2}[/tex] = -4

x = 2i,-2i

3[tex]x^{2}[/tex] - 18 = 21

3[tex]x^{2}[/tex] = 18+21

3[tex]x^{2}[/tex] = 39

[tex]x^{2}[/tex] = 13

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex]

2[tex]x^{2}[/tex] +15 = -13

2[tex]x^{2}[/tex]  = -13-15

2[tex]x^{2}[/tex]  = -28

[tex]x^{2}[/tex]  = -14

x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i

Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

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