How many solutions does the equation have 2x y 5 and 4x 2y 10?.

Answers

Answer 1

The answer is the equation can have many solutions. the given equation is the linear equation that may have infinitely many  solutions.

The equation given in the question is  

2x + y – 5 = 0  

4x + 2y – 10 = 0  

For the given equation it can be written as:  

[tex]a_{1} x+ b_{1}y - c_{1} = 0[/tex]

[tex]a_{2} x+ b_{2}y - c_{2} = 0[/tex]

Here, [tex]a_{1}[/tex] = 2, [tex]b_{1}[/tex] = 1, [tex]c_{1}[/tex] = −5  

[tex]a_{2}[/tex]= 4, [tex]b_{2}[/tex]= 2,  [tex]c_{2}[/tex]= −10

So, according to the question given for the equation:

[tex]\frac{a_{1} }{a_{2}} = \frac{2}{4} = \frac{1}{2}[/tex]

[tex]\frac{b_{1} }{b_{2}} = \frac{1}{2}[/tex] and

[tex]\frac{c_{1} }{c_{2}} = \frac{-5}{10} = \frac{1}{2}[/tex]

⇒  [tex]\frac{c_{1} }{c_{2}} = \frac{b_{1} }{b_{2}} = \frac{c_{1} }{c_{2}}[/tex]

From the above solution, we see the end result for the equation given so, we can say that this given equation can have infinitely many solutions.

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Related Questions

If m∠DBE = (8x - 7)°, m∠DBC = (10x - 6)° , and m∠EBC = 29° , find m ∠ABD.

Answers

The unknown angle in the intersected line is as follows:

m∠ABD  = 46 degrees.

How to find angles in intersecting lines?

The lines intersected to form different angles. The angles are as follows:

m∠DBE = (8x - 7)°,

m∠DBC = (10x - 6)°

m∠EBC = 29°

The unknown angle ∠ABD can be found as follows:

∠ABC = 180(sum of angles on a straight line)

Therefore,

m∠DBC = m∠DBE +  m∠EBC

Hence,

10x - 6 = 8x - 7 + 29

10x - 8x = -7 + 6 + 29

2x = 28

x = 28 / 2

x = 14

Let's find the angle  m ∠ABD.

m∠DBC = 10x - 6 = 10(14) - 6 = 140 - 6 = 134 degrees

m∠ABD + m∠DBC = 180

m∠ABD  = 180 - 134

m∠ABD  = 46 degrees.

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Your rectangular claroom rug ha an area of 110. 5 quare feet. What i the perimeter of the rug?

Answers

The perimeter of the rug that has 110.5 square feet area is 43 ft

What is the area?

Area is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2

To solve this geometry exercise the equation and procedure we will use is:

P = (2*L) + (2*W)A = L * W

Where:

P= perimeterL= lengthW= widthA = area

Information about the problem:

L = ?P = ?W = 13 ft (check the image attached)A = 110.5 ft^2

Clearing the width from the rectangle area formula, we get:

A = L * W

W = A / L

W = 110.5 ft^2 / 13 ft

W = 8.5 ft

With the width calculated we get the perimeter of the rectangular classroom:

P = (2*L) + (2*W)

P = (2*13 ft) + (2*8.5 ft)

P = 26 ft + 17 ft

P = 43 ft

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What is the binomial factor of the polynomial x³ Y³?.

Answers

The binomial factor for the given expression is x = 4.

In mathematics, a binomial is an expression that is made up of two terms. The binomial factor of an expression is the part of the expression that is written in the form (x - a)^n, where a is a constant and n is a positive integer.

The binomial factor of x³ is x³. The equation x³ = 64 is not a binomial equation, as it does not have the form (x - a)^n = 0, where a is a constant and n is a positive integer. If you are trying to solve for x in the equation x³ = 64, one solution is x = 4. However, there are also three other solutions, which are the cube roots of 64 that are not real numbers (they are complex numbers).

Hence, The binomial factor for the given expression is x = 4.

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19. Which can be used to find the product: 398 x 5? A 400-2 X 5 B (400 x 5) - (2 x 5) C (400 x 5) + (2 X 5) D (400 x 5) -2​

Answers

The product of  398×5 is equal to (400-2)×5

What Is Distributive Property?

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Given here: The product of two numbers as 398×5

Now 398 can be rewritten as 400-2

Thus the expression 398×5 =(400-2)×5 ( Using distributive property)

                                1990   = 1990

Thus they are also equivalent.

Hence, The product of  398×5 is equal to (400-2)×5

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What does it mean when your solving a linear equation and you get 2=2

Answers

Answer:

When you solve a linear equation and get 2=2, this means that the equation is true and there is no solution. This is because both sides of the equation are equal, so there is no value that can satisfy both sides of the equation at the same time.

give me brainiest

Answer: It means that the equation is balanced and both sides have the same value (they are equal)

Find the difference. Show each step for full credit. Use ^ for exponents, for instance, x^2 means x

3n3+ 4n2– 9 and -2n3+ 4n – 9^323

Answers

5n³ + 4n² -4n + 720 is the difference between these two given expressions.

What are Systems of equations?

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation 3n³+ 4n²– 9 and -2n³+ 4n – 9³

We need to find the difference between These given Systems of equation

Difference = 3n³+ 4n²– 9 -( -2n³+ 4n – 9³)

Difference = 3n³+ 4n²– 9 + 2n³- 4n + 9³

Difference = 5n³ + 4n² -4n + 720

therefore, The difference between these two given equations is 5n³ + 4n² -4n + 720.

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What is the formula for log A log B?.

Answers

The formula for the logarithmic function  log A ± log B is given by

log A  + log B = log ( AB )

log A  - log B = log ( A / B )

As given in the question,

For the given logarithmic function is given by :

Addition of two logarithmic function represents the multiplication of two numbers.

log ( A × B ) = log A + log B

Example : log ( 6 )

= log ( 2 × 3 )

= log 2 + log 3

Subtraction of two logarithmic function represents the division of two numbers.

log ( A ÷ B ) = log A - log B

Example :

log ( 5 ÷ 2 ) = log 5 - log 2

Therefore, the formula of the logarithmic function  log A ± log B is given by :

log A  + log B = log ( AB )

log A  - log B = log ( A / B )

The above question is incomplete, the complete question is:

What is the formula for logarithmic function log A ± log B?.

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find the missing side lengths 65 √2 x y 45°?​

Answers

Answer:

x = 65

y = 65

Step-by-step explanation:

This is a special right triangle with angle measures as follows:

90° - 45° - 45°

The side lengths are represented respectively as follows:

a√2 - a - a

The side length that sees angle measure 90°, hypotenus,   is given as 65√2.

The legs are congruent because this is a isosceles triangle at the same time so each = 65.

What is cos concept?.

Answers

For Trigonometric ratios, the values of sin, cos, and tan are defined by the ratio of sides of a right-angled triangle. The cosine of an acute angle in a right triangle is calculated using trigonometry.

By dividing the measurements of the side that it is adjacent to by the hypotenuse of the triangle.

The neighboring  base-to-hypotenuse ratio is known as the cos function. It aids in determining the triangle's side lengths regardless of the provided angle.

If the angle between the neighboring side and the hypotenuse of a right triangle is, we can write this using the cos function.

In a right-angled triangle, We calculate their values by the ratio

Cos = Base of the right-angled triangle/ Hypotenuse of the right-angled triangle.

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solve for a side in right triangles

Answers

Answer:

AC ≈ 4.28

Step-by-step explanation:

using the tangent ratio in the right triangle

tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{AC}[/tex] ( multiply both sides by AC )

AC × tan35° = 3 ( divide both sides by tan35° )

AC = [tex]\frac{3}{tan35}[/tex] ≈ 4.28 ( to the nearest hundredth )

How do you decide whether to use substitution or elimination to solve a system?.

Answers

When deciding whether to use substitution or elimination to solve a system of linear equations, it is important to consider the size and complexity of the system.

Substitution is generally recommended for systems with two equations and two variables, as it can be a simpler and quicker approach. For larger systems with more equations and/or variables, elimination may be a better option as it can reduce the number of steps required to solve the system.

When using either method, it is important to keep track of all the steps you take and double check your work for accuracy. Additionally, both methods involve solving for one variable in terms of the others, so if you are dealing with an equation that already has only one unknown variable, then substitution could be the best approach. Ultimately, it is important to assess each situation individually and decide which method would be most effective.

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Suppose that c and d vary inversely and that d=4/3 when c = 9. Write a function that models the inverse variation and find d when c = 3.

Answers

The equation for the inverse variation is:

d = 12/c

And evaluating that we can see that when c = 3, d = 4.

How to find the inverse variation equation?

A genearl inverse variation equation can be written as:

y = k/x

Where k is a constant.

Here we know that there is an inverse variation between c and d, then we can write:

d = k/c

We know that d = 4/3 when c = 9, replacing that we will get:

4/3= k/9

9*(4/3) = k

12 = k

Then the equation is:

d = 12/c

Now we can evaluate this in c = 3 so we get:

d = 12/3

d = 4

When c =3, d = 4.

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Select the correct answer from each drop-down menu.
A veterinarian's office recorded one particular week that they had 50 patients. The table shows the recorded number of dogs.
Monday Tuesday Wednesday Thursday Friday
7
4
5
5
2
Use the given data to complete the sample proportion and confidence intervals for this situation.
Percentage of patients that were dogs
90% confidence interval
95% confidence interval

Answers

1. The correct answer is 46 percent, 2. The correct answer is .07, 3. The correct answer is (34%,58%), 4. The correct answer is (32%,60%)

What is standard error?

The term "standard error" is used to refer to the standard deviation of various sample statistics, such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.

The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

1. Let's calculate the percentage or proportion of patients that were dogs:

p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46

The correct answer is 46%

2. Let's estimate the standard error, using the given formula, this way:

S.e = √ (0.46 * 0.54)/50 = √0.049 = 0.07

The correct answer is .07

3. Let's calculate the confidence limits of the 90% confidence interval, this way:

Confidence limits = proportion +/- 1.645 * standard error

Confidence limits = 0.46 +/- 1.645 * 0.07

Confidence limits = 0.46 +/- 0.12

Confidence limits = 0.34, 0.58

The correct answer is (34%,58%)

4. Let's calculate the confidence limits of the 95% confidence interval, this way:

Confidence limits = proportion +/- 1.96 * standard error

Confidence limits = 0.46 +/- 1.96 * 0.07

Confidence limits = 0.46 +/- 0.14

Confidence limits = 0.32, 0.60

The correct answer is (32%,60%)

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Car A travels 60 miles per hour for 1½ hours; Car B
travels 40 miles per hour for 2 hours. What is the
difference between the number of miles traveled by
Car A and the number of miles traveled by Car B ?
F.
0
10
H.
80
90
K. 170

Answers

One is a head of the other

How do u solve this?

Answers

Answer:

-f(x)

Step-by-step explanation:

Figure H is just Figure G reflected across the x-axis meaning that you just have to slap a negative symbol in front of whatever function gave you Figure H.

Find each product mentally show the steps you used 9 x44

Answers

Answer:

396

Step-by-step explanation:

I found this answer by using standard multiplication but mentally.

4x9 is 36

and 4x9 is also 36, but for the sake of this way of solving we must add a zero the end of this answer making it 390

Now you have to add these two together:

    36

+ 360

  396

Hope this helps :)

What is the nature of roots of quadratic equation x² 5x 14 0?.

Answers

The nature of roots of the equation x² + 5x + 14 = 0 are of the form x = (-5 ± √(-31))/2, which are complex numbers and not real.

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants, and x is the variable. The nature of the roots of a quadratic equation can be determined by the discriminant, which is the value of b² - 4ac.

In this case, the quadratic equation is x² + 5x + 14 = 0. To find the nature of the roots, we need to find the discriminant, which is b² - 4ac:

Discriminant = 5² - 4 * 1 * 14 = 25 - 56 = -31

The discriminant can be used to determine the nature of the roots:

If the discriminant is greater than 0, the roots are real and distinct.

If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).

If the discriminant is less than 0, the roots are complex and not real numbers.

In this case, the discriminant is negative, so the roots of the equation x² + 5x + 14 = 0 are complex. The roots can be found by factoring the equation into (x + a + bi)(x + a - bi), where a and b are real numbers, and i is the imaginary unit (i² = -1).

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How do you know if a log function is increasing or decreasing?.

Answers

A logarithmic function is increasing when the base, b of the function is greater than one i.e., b>1 , and the function is decreasing when the base b lies in the interval (0,1).

Logarithmic functions are inverses of exponential functions, and any exponential function can be expressed in logarithmic form. The form of the equation is y = log₂x. This can be read as "y is equal to the logarithm of x, base 2" or "y is equal to the logarithm of base 2, x". In exponential function form, x = 2ʸ.

If the base of the logarithmic function is greater than 1, then the graph becomes increasing. A function whose value decreases to zero more slowly than any nonzero polynomial is called a logarithmically decreasing function.

The graph of logarithmic functions always passes through a point i.e., (1,0).

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g3(7+h) using the Distributive Property
Helpppppp

Answers

The value of the equation is A = 21g + 3gh

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = g3 ( 7 + h )   be equation (1)

On simplifying the equation , we get

Applying the distributive property , we get

A = g3 ( 7 ) + g3 ( h )

A = 21g + 3gh

Therefore , the value of A is 21g + 3gh

Hence , the equation is A = 21g + 3gh

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Let the random variable X repreent the number of automobile that are ued
for official buine purpoe on any given workday. The probability
ditribution for company A
x 1 2 3
f(x) 0. 3 0. 4 0. 3
and for company B
x 0 1 2 3 4
f(x) 0. 2 0. 1 0. 3 0. 3 0. 1
a) Find mean and variance of company A and B
b) Show that the variance of the probability ditribution of
company B i greater thna A

Answers

The Mean of both the company is 2 while the variance of companies A and B is 0.6 and 1.6 respectively.

Here we have the probability distribution of both companies A and B

a)

We need to find the mean and variance of the companies.

Mean = E(X) = ∑xp(x)

Variance = E(X - Mean)²

Hence the mean of Company A will be

= [1 X 0.3] + [2 X 0.4] + [3 X 0.3]

= 0.3 + 0.8 + 0.9

= 2

Now Variance will be

0.3[1 - 2]² + 0.4[ 2 - 2]² + 0.3[3 - 2]²

= 0.3[1] + 0.4[0] + 0.3[1]

= 0.3 + 0.3

= 0.6

Now for Company B, we get mean to be

[0 X 0.2] + [1 X 0.1] + [2 X 0.3] + [3 X 0.3] + [4 X 0.1]

= 0 + 0.1 + + 0.6 + 0.9 + 0.4

= 2

The variance of Company B will be

0.2[0 - 2]² + 0.1[1 - 2]² + 0.3[2 - 2]² + 0.3[3 - 2]² + 0.1[4 - 2]²

= 0.2[4] + 0.1[1] + 0.3[0] + 0.3[1] + 0.1[4]

= 0.8 + 0.1 + 0 + 0.3 + 0.4

= 1.6

b)

Here we see that the value of the variance of company B is greater than A

Hence proved.

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Complete Question

Let the random variable X represent the number of automobiles that are used for official business purposes on any given workday. The probability distribution for company A

x         1         2         3

f(x)    0.3     0.4      0.3

and for company B

x         0         1         2         3         4

f(x)    0.2       0.1     0.3      0.3      0.1

a) Find the mean and variance of companies A and B

b) Show that the variance of the probability distribution of company B is greater than A

*URGENT*

i’m so confused when it comes to this, please help

Answers

The value of w has been solved to be 57.7 m.

What are trigonometric functions?

Trigonometric functions are set of functions which can be applied so as to determine the unknown value of a side or angle of a right triangle. Some of the basic functions are: Sine, Cosine, Tangent etc.

In the given question, to solve for w let us applying sine function of the angle.

Sin θ = opposite/ hypotenuse

We have;

Sin θ = opposite/ hypotenuse

Sin 25 = 10/ w

w = 10/ sin 25

  = 57.6877

w = 57.7 m

The value of w is 57.5 m.

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How many real solutions are there?.

Answers

The sign of the discriminant [tex]b^{2}-4ac[/tex] of a quadratic equation determines how many real solutions there are to that quadratic equation.

The value of the expression is the discriminant of a quadratic equation in standard form : This quantity specifies how many different ways a quadratic problem can be solved.

Solutions to quadratic equations can be 0, 1, or 2. If the discriminant has a positive value, then there are two genuine solutions for x, and the graph of the solution has two different x-intercepts. There is only one actual solution for x if the discriminant's value is zero, which means that the solution's graph only has one x-intercept.

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Kaylee is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $2.50. Kaylee spent $12.50 altogether at the carnival and the number of rides she went on is twice the number of games she played. Graphically solve a system of equations in order to determine the number of games Kaylee played, x, and the number of rides Kaylee went on, y

Answers

To graphically solve a system of equations, we can plot the equations on a coordinate plane and find the point of intersection, which represents the solution to the system.

The first equation represents the total cost of the games, which is:

x(1.25) = 1.25x

The second equation represents the total cost of the rides, which is:

y(2.50) = 2.50y

The third equation represents the total cost of all games and rides, which is:

x(1.25) + y(2.50) = 12.50

We can also represent the fourth equation as the number of rides she went on is twice the number of games she played:

y = 2x

We can plot the first equation on the coordinate plane by treating x as the x-coordinate and 1.25x as the y-coordinate. We can plot the second equation in the same way, treating x as the x-coordinate and 2.5y as the y-coordinate.

We can plot the third equation as a line by treating x as the x-coordinate and 12.5-1.25x-2.5y as the y-coordinate.

Finally, we can plot the fourth equation as a line by treating x as the x-coordinate and 2x as the y-coordinate.

We can then find the point of intersection of the three lines, which represents the solution to the system of equations.

The point of intersection is the point (5,10) which means that Kaylee played 5 games and went on 10 rides.

5. In the circle, arc AD = 79, and

Answers

A circle is a closed two-dimensional shape because every point in the plane that makes up a circle is evenly separated from the "centre."

What are the 2 standard equation of circle?

The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the centre at all angles.

The two foci are located in the middle of a circle, a particular type of ellipse.

a circle's equation, represented as (xh)2+(yk)2=r2, where r is the radius and (h,k) is the centre. The equation for the circle, which has a radius of 1, is x2+y2=1. Its centre is at the origin. x2+y2+cx+dy+e=0 is the formula for the equation of a circle.

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The lateral height of a cone is 6 inches and the area of the base of the cone is 49π in². It requires 1.5 minutes to paint the cone. The area of the base is doubled. How long will it take to paint this cone if it can be painted at the same rate? Use π≈3.14. Enter your answer, rounded to the nearest tenth, in the box. min

Answers

It would take 4.0 minutes to paint the cone.

solving for how long will it take to paint this cone if it can be painted at the same rate:

The original radius of the cone is √(49/π) inches

= √(49/3.14)

= √(15.7)

= 3.5 inches.

The new base area is 2 * 49π

= 98π square inches.

The new radius is √(98/π)

= √(98/3.14)

= √(31.4)

= 5.6 inches.

The new lateral surface area is π * 5.6 * 6

= 33.6 * π square inches.

The new total surface area is 33.6π + 98π

= 131.6π square inches.

Since it takes 1.5 minutes to paint the original cone, it would take

1.5 * (131.6/33.6) = 4.0 minutes to paint the new cone.

Hence, it would take 4.0 minutes to paint the cone.

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Brian paid a total of $46.44 for a jacket at a department store. The jacket was on sale for 20% off the regular price, and he used a coupon for an additional $5.00 off of the discounted price. Brian had to pay 8% sales tax on the cost of the jacket after any discounts and coupons.

Select the equation where p represents the original price of the jacket and the solution of that equation.

A.
1.08(0.8p - 5) = 46.44
The original price of the jacket was $60.00.
B.
1.08(0.8(p - 5)) = 46.44
The original price of the jacket was $60.00.
C.
1.08(0.8(p - 5)) = 46.44
The original price of the jacket was $58.75.
D.
1.08(0.8p - 5) = 46.44
The original price of the jacket was $58.75.

Answers

The equation, where p represents the jacket's original price, and the equation's solution is A. 1.08(0.8p - 5) = 46.44. The original price of the jacket was $60.00.

What is an equation?

An equation is a mathematical statement showing that two mathematical expressions are equivalent or equal.

Equations are depicted using the equation symbol (=).

The total cost paid by Brian = $46.44

The discount on offer = 20%

Amount after the initial discount = 0.8p (1 - 20%)

Additional coupon = $5

Amount after the additional coupon = 0.8p - 5

Total discount = 20% + $5

Sales tax = 8%

Amount paid after the sales tax = (0.8p - 5)(1.08)

Original price = p

p = $60

1.08(0.8p - 5) = 46.44

1.08(0.8 x 60 - 5) = 46.44

1.08(43) = 46.44

46.44 = 46.44

Thus, Option A is correct.

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When constructing the incenter of a triangle, why do you first construct the angle bisectors of two angles? select the true statement.

Answers

The intersection of angle bisectors are equidistant from the sides of the triangle.

The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors.

What about angle bisectors is true ?

According to the angle bisector theorem, a point is equally distant from both sides of an angle if it is on the angle's bisector.

According to the converse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally distant from its sides.

According to the given information

Angle bisector intersection points are evenly spaced from the triangle's sides.

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What is the solution to the system of equations y 3x 2 5x 2y 15 40 19?.

Answers

The solution to the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55).

In the given question, we have to find the solution to the system of equations y = -3x - 2 and 5x + 2y = 15.

The given equations are:

y = -3x - 2...................(1)

5x + 2y = 15...................(2)

Now solving the equation 2 by substituting the value of y from the equation 1.

5x + 2(-3x - 2) = 15

5x - 6x - 4 = 15

-x - 4 = 15

Add 4 on both side, we get

-x = 19

x = -19

Now putting the value of x in equation 1.

y = -3(-19) - 2

y = 57 - 2

y = 55

Hence, the solution to the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55).

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The complete question is:

What is the solution to the system of equations y = -3x - 2 and 5x + 2y = 15?

What is the conjugate of 4 3i?.

Answers

The complex conjugate of 4 − 3i is;

4 - (-3i) = 4 + 3i .

Now, According to the question:

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.

Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.

The complex conjugate of a + bi is a - bi

So,  the complex conjugate of 4 − 3i is;

4 - (-3i) = 4 + 3i .

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For a project in his Geometry class, Jevonte uses a mirror on the ground to measure
the height of his school's flagpole. He walks a distance of 10.85 meters from the
flagpole, then places a mirror on flat on the ground, marked with an X at the center.
He then steps 1.15 meters to the other side of the mirror, until he can see the top of
the flagpole clearly marked in the X. His partner measures the distance from his
to the ground to be 1.65 meters. How tall is the flagpole? Round your answer to the
eyes
nearest hundredth of a meter.
1.65 m
1.15 m
(Diagram is not to scale.)
10.85 m-

Answers

Using the formula for angle of depression if the mirror is at a distance of 10.85 meters from the flagpole, then the height of the flagpole is 15.56 meters.

What is angle of depression?

An angle formed between a horizontal line and the line connecting an object and the observer's eye is referred to as the angle of depression. Two variables, namely height and distance, affect this angle.

The height of the school's flagpole = h

The distance from flagpole to mirror = 10.85 m

The distance from mirror to other side = 1.15 m

The height of Jevonte eyes' to the ground = 1.65 m

Let the angle of depression from Jevonte's point of view be represented by θ. Then apply the required trigonometric function -

tan θ = opposite / adjacent

tan θ = 1.65/1.15

tan θ = 1.4347

θ = tan^-1 (1.4347)

θ = 55.12°

For the given mirror, the angle of incidence is equal to that of reflection. Then apply the required trigonometric function -

tan θ = opposite / adjacent

tan 55.12° = h/10.85

1.4347 = h/10.85

h = 1.4347 × 10.85

h = 15.56

Therefore, the height value is obtained as 15.56 m.

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