Help Help Help Help Help Help (I don’t need explanation just yes or no)

The key features of this rational function include the following:

Domain: (-∞, -2) ∪ (-2, ∞)

Range: (-∞, -1) ∪ (-1, ∞)

Y-intercept: 2.

X-intercept: 1.

Vertical asymptote: x = -2.

Horizontal asymptote​: y = -1.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

Read more on asymptote here: brainly.com/question/28003042

#SPJ1

Answer:

To determine how many loaves will not meet quality standards on Tuesday, we need to count the number of integers in the sample that are between 1 and 50, inclusive. From the given sample, we can see that there are 2 integers that fall between 1 and 50: 47 and 4. Therefore, we can predict that 2 loaves will not meet quality standards on Tuesday.

To calculate the difference between the number of sub-standard loaves produced on Monday and the number predicted to be sub-standard on Tuesday, we need to subtract the number of sub-standard loaves on Monday from the number predicted for Tuesday.

Number of sub-standard loaves on Monday = 50

Number predicted to be sub-standard on Tuesday = 2

Difference = 2 - 50 = -48

The difference is -48, which means that there were 48 fewer sub-standard loaves predicted on Tuesday than the number produced on Monday.

Based on the information in the passage, we will most likely expect the following to happen:

C. Elizabeth and Joelle will remain friends despite the sport they play.

The passage being referred to in this question is "Sliding into Home" by Dori Hillestad Butler. It tells the story of two girls named Elizabeth Shaw and Joelle Cunningham who chose different sports but remained determined to be friends despite this.

While Joelle enjoyed playing baseball, Elizabeth was better at Softball. Despite Elizabeth's encouragement for Joelle to play Softball, Joelle insisted on her favorite game but they remained friends regardless.

Learn more about informational passages here:

https://brainly.com/question/24852861

#SPJ1

The solution of the given problem of Test statistic comes out to be Using a table or calculator with 98 degrees of freedom, we find the value to be approximately 0.06.

The test statistic for anything akin to a Z-test has been the Z-statistic, which shows the ordinary normal neutral hypothesis is correct. Suppose you perform a 2 different X y test with a 0.05 threshold of significance and, based on your data, you obtain a 2.5 R t (also referred as a Z-value). 0.0124 is the value for the this Z-value.

Here,

: un - ud <= 0 (the mean GPA of night students is less than or equal to the mean GPA of day students)

H: un - ud > 0 (the mean GPA of night students is greater than the mean GPA of day students)

We will use a significance level of 0.05.

The test statistic is calculated as:

t = (xn - xd - 0) / √(s²/n + s²/n)

where xn and xd are the sample means, s and s are the sample standard deviations, and n is the sample size.

Plugging in the values from the problem, we get:

t = (2.91 - 2.87 - 0) / √0.08²/50 + 0.06²/50) = 1.57

The degrees of freedom for the t-distribution is

f = n₁ + n₂ - 2 = 50 + 50 - 2 = 98 (assuming equal variances).

Using a table or calculator with 98 degrees of freedom, we find the

value to be approximately 0.06.

Since the value (0.06) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.05 significance level.

To know more about test statistic , visit

brainly.com/question/14128303

#SPJ1

In the case of 9 x 9, using the Commutative Property, we can rewrite it as 9 x 9 = 9 x 9. The product of these two factors is 81, which is the same regardless of the order of the factors.

The Commutative Property of Multiplication is one of the fundamental properties of arithmetic. It states that the order of the factors in a multiplication expression does not affect the product. In other words, you can multiply two numbers in any order and still get the same result.

For example, if you have the multiplication expression 2 x 5, you can switch the order of the factors and write it as 5 x 2, and the result is still the same:

2 x 5 = 5 x 2 = 10

Similarly, for the expression 3 x 4, you can switch the order of the factors and write it as 4 x 3, and the result is still the same:

3 x 4 = 4 x 3 = 12

The Commutative Property is a fundamental property of multiplication, and it is used in many mathematical operations, including simplifying expressions, solving equations, and more.

To know more about Commutative Property, visit:

brainly.com/question/778086

#SPJ1

The sum of two opposite interior angles of a triangle is equal to the opposite exterior angle of a triangle

Therefore,

( 5x - 101 )° + ( x + 36 )° = ( 9x - 164 )°

5x + x - 106 + 36 = 9x - 164

6x - 65 = 9x - 164

6x - 9x = - 164 + 65

- 3x / - 3 = - 99 / - 3

x = 33

The first interior angle

= ( 5x - 101 )°

= ( 5 ( 33 ) - 101 ) °

= ( 165 - 101 )°

= 64°

The second interior angle

= ( x + 36 )°

= ( 33 + 36 )°

= 69°

The exterior angle

= ( 9x - 164 )°

= ( 9 ( 33 ) - 164 )°

= ( 297 - 164 )°

= 133°

By using the greatest common factor of 84 and 48, the sum 84+48 can be written as the product 12 x (7 + 4).

To write the sum 84+48 as a product using their greatest common factor, we need to factor both numbers and find the largest common factor.

The prime factorization of 84 is 2 x 2 x 3 x 7, while the prime factorization of 48 is 2 x 2 x 2 x 2 x 3.

To find the greatest common factor, we need to identify the factors that both 84 and 48 have in common. We see that both numbers have two factors of 2 and one factor of 3 in common. So, the greatest common factor of 84 and 48 is 2 x 2 x 3 = 12.

Now, we can rewrite the sum 84+48 as a product of 12 and another sum, using the distributive property of multiplication:

84 + 48 = 12 x (7 + 4)

So, the sum 84+48 can be written as the product 12 x (7 + 4).

To know more about greatest common factor, visit:https://brainly.com/question/11221202

#SPJ1

The composite function (fg)(0) has a value of -4

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

The graph

Also, we have

(fg)(0)

The notation (fg)(x) represents the composite function of two functions f(x) and g(x), where one function is applied to the result of the other function.

The formula for (fg)(x) is:

(fg)(x) = f(g(x))

So, we have

(fg)(0) = f(g(0))

This gives

(fg)(0) = f(3)

(fg)(0) = -4

Hence, the value is -4

Read more about composite function at

https://brainly.com/question/10687170

#SPJ1

Answer:

The solution is 1/8

Step-by-step explanation:

[tex] \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \sqrt{x} - 4 }{x - 16} \\ \\ \sf {a}^{2} - {b}^{2} = (a - b) (a + b)\\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \sqrt{x} - 4 }{( \sqrt{x} - 4) \times ( \sqrt{x} + 4)} \\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \cancel{\sqrt{x} - 4} }{(\cancel{ \sqrt{x} - 4) }\times ( \sqrt{x} + 4)} \\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{1}{ \sqrt{x} + 4} \\ \\ \sf \frac{1}{ \sqrt{16} + 4} \\ \\ \sf \frac{1}{ 4 + 4} \\ \\ \sf \frac{1}{8} [/tex]

A number greater than 5 is: P(odd or greater than 5) = 1/2 + 1/6 = 2/3

It depends on the context of the probability question. Here are a few possibilities:

If you're rolling a fair six-sided die, then the probability of rolling an odd or a number greater than 5 on a single roll is:

P(odd or greater than 5) = P(odd) + P(greater than 5) - P(odd and greater than 5)

P(odd) = 3/6 = 1/2 (because there are three odd numbers out of six possible outcomes)

P(greater than 5) = 1/6 (because there is only one number greater than 5)

P(odd and greater than 5) = 0 (because there is no number that is both odd and greater than 5)

So, the probability of rolling an odd or a number greater than 5 is:

P(odd or greater than 5) = 1/2 + 1/6 = 2/3

If you're dealing with a continuous random variable (like the height of people), then the probability of a value being odd or greater than 5 doesn't make sense. However, if you're dealing with a discrete random variable with a known distribution (like the number of customers who enter a store), you can calculate the probability of this event based on the distribution.

In general, it's important to define the context of the probability question and the underlying probability distribution to answer the question properly.

To learn more about  odd :

https://brainly.com/question/29377024

#SPJ1

The two numbers are 10 and 12

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

The two numbers that have their highest factor as 2 are 4 and 6, 6 and 8, 8 and 10 and 10 and 12.

The numbers above which have least common multiple of 60 are

multiple of 4: 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60

multiple of 6; 6,12,18,24,30,36,42,48,54,60

multiple in of 10: 10,20,30,40,50,60

multiple of 12: 12,24,36,48,60.

The least common multiple of 6 and 10 is 30

but the least common multiple of 12 and 10 is 60

therefore the two numbers are 12 and 10.

learn more about word problem from

https://brainly.com/question/21405634

#SPJ1

Answer:

Para calcular las deformaciones asociadas en los puntos dados, es necesario calcular primero los componentes del tensor de deformación. Los componentes del tensor de deformación se pueden obtener a partir del gradiente del campo de desplazamiento utilizando la siguiente relación:

ε_ij = (1/2) * (∂u_i/∂x_j + ∂u_j/∂x_i)

donde ε_ij son los componentes del tensor de deformación y u_i es la i-ésima componente del vector de desplazamiento.

Calculando los componentes del tensor de deformación en los puntos (1, 1, 1) y (2, 2, 2), se obtiene:

En el punto (1, 1, 1):

ε_xx = 12 (10^-3)

ε_xy = 5 (10^-3)

ε_xz = 1 (10^-3)

ε_yx = 5 (10^-3)

ε_yy = 8 (10^-3)

ε_yz = 3 (10^-3)

ε_zx = 1 (10^-3)

ε_zy = 3 (10^-3)

ε_zz = 6 (10^-3)

En el punto (2, 2, 2):

ε_xx = 420 (10^-3)

ε_xy = 28 (10^-3)

ε_xz = 20 (10^-3)

ε_yx = 28 (10^-3)

ε_yy = 86 (10^-3)

ε_yz = 36 (10^-3)

ε_zx = 20 (10^-3)

ε_zy = 36 (10^-3)

ε_zz = 84 (10^-3)

Podemos ver que los valores de deformación son mayores en el punto (2, 2, 2) que en el punto (1, 1, 1). Esto sugiere que el campo de desplazamiento produce una mayor deformación en el punto (2, 2, 2) que en el punto (1, 1, 1). Además, podemos observar que los componentes de deformación son simétricos (es decir, ε_ij = ε_ji), lo cual es consistente con la teoría de la mecánica de materiales.

Step-by-step explanation:

espero te sirva

Nico and Aditi are not correct in their approach to solving the problem.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and others. The goal of solving an equation is to find the values of the variables that make the equation true.

Equations can be classified into different types based on their degree and the number of variables.

Linear equations: Equations that involve variables raised to the first power only, such as 2x + 3 = 7.

Quadratic equations: Equations that involve variables raised to the second power, such as x² + 5x - 6 = 0.

Cubic equations: Equations that involve variables raised to the third power, such as x³ + 2x² - x - 2 = 0.

Simultaneous equations: A set of two or more equations that are solved together to determine the values of the variables.

Equations are used in many real-life applications, such as physics, engineering, economics, and finance. They are also an essential part of mathematics and are used to model and solve problems in algebra, calculus, and other branches of mathematics.

The students who are correct in their approach to solving the problem are:

Erick: By multiplying both sides of the equation by 5/2, he eliminates the fraction on the left side and simplifies the equation.

Raj: By multiplying both sides of the equation by 1/2, he eliminates the fraction on the left side and simplifies the equation.

Sandra: By adding 5/2 to both sides of the equation and then simplifying, she isolates the variable on one side of the equation.

So, Nico and Aditi are not correct in their approach to solving the problem.

To know more about equation visit:

https://brainly.com/question/29657983

#SPJ1

Answer:

yo

Step-by-step explanation:

C D E

The roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

Using the quadratic formula to solve the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex],we have

[tex]x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\[/tex]

Therefore, the two roots of the quadratic equation in exact square root form are:

[tex]x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\[/tex]

Thus, the roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

A quadratic equation is a second-degree polynomial equation in one variable of the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.

The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.

The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:

[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]

where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).

To know about quadratic equation visit:

https://brainly.com/question/1526946

#SPJ1

Answer:

help with what?

Step-by-step explanation:

you did not ask a question?

good luck....

The lines CA and CD are tangents to the circle O, hence; EA = 4, AB = 15, m∠ABO = 90°, m∠ODC = 90°, and m∠EAB = 30°.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

If OB = 6 and AB = 8, then;

OA = √(8² + 6²) {by Pythagoras rule}

OA = √100

OA = 10

EA = OA - OE(radius)

EA = 10 - 6 = 4

If DE = 16 and EA = 9, then;

OA = (diameter/2) + EA

OA = 8 + 9 = 17

AB = √(17² - 8²)

AB = √225

AB = 15

OB is perpendicular to line CA tangent to the circle so m∠ABO = 90°

OD is perpendicular to the line CD tangent to the circle so m∠ODC = 90°

If m∠DOB = 120° then;

120° = m∠ABO + m∠EAB {exterior angle of a triangle is equal to the two opposite interior angles}

m∠EAB = 120° - 90°

m∠EAB = 30°

In conclusion, for the lines tangent to the circle, we have that;

EA = 4, AB = 15, m∠ABO = 90°, m∠ODC = 90°, and m∠EAB = 30°

Know more about tangent to a circle here:https://brainly.com/question/11067500

#SPJ1

The correct calculation of the average is given as 0.2546

The average is a measure of central tendency that represents the typical value in a set of data. It is also known as the arithmetic mean and is calculated by adding up all the values in a set of data and then dividing the sum by the total number of values in the set.

The calculation of the average would be gotten by the number of hits / by the total bats that he had

This is given as

151 / 593

= 0.2546

Read more on average here:https://brainly.com/question/20118982

#SPJ1

The area of the ENTIRE rectangle would be: Area = Base * Height

I think you can see that the triangle is 1/2 of the rectangle. so the

    The area of the right triangle would be: Area = 1/2 * base * height

if the area of the triangle is 18 square inches, then h = 2(18)/6 = 6 inches.

If the base, b, is 6 inches, and the area, A, is 18 square inches, then the height, h, of the triangle is 6 inches.

Triangle is a three-sided geometric shape that has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The area of a right triangle can be found by using the formula A=1/2bh, where b is the base of the triangle and h is the height. In this example, the base, b, is 6 inches. To find the height, h, we can solve the equation for h: h = 2A/b, where A is the area of the triangle.

Therefore, if we know the area of the triangle, A, we can find the height, h, of the triangle by plugging in the values and solving for h. For example, if the area of the triangle is 18 square inches, then h = 2(18)/6 = 6 inches.

The area of a right triangle can be found by using the formula A=1/2bh and plugging in the known values of b and h. In this example, if the base, b, is 6 inches, and the area, A, is 18 square inches, then the height, h, of the triangle is 6 inches.

To know more about triangles click-

brainly.com/question/17335144

#SPJ1

The equivalent fractions are A = { 100 / 20 , 150 / 30 }

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fractions be represented as A

Now , the value of A is

A = 50/10

On simplifying , the fraction , we get

The value of A = 5/1

Now , the equivalent fractions of A are

Multiply the numerator and denominator of the fraction by 2 , we get

A = 100/20

Multiply the numerator and denominator of the fraction by 3 , we get

A = 150/30

Hence , the equivalent fractions are 5/1 , 100/20 and 150/30

To learn more about fractions click :

https://brainly.com/question/29766013

#SPJ9

The centripetal acceleration of the wooden block is 0.32 m/s^2.

The centripetal acceleration of an object moving in a circle with radius r and angular velocity ω (in radians per second) is given by the formula:

a = rω^2

In this problem, the wooden block is on the end of a string with a radius of 0.7 meters, and it makes 14 rotations in 20.7 seconds. The angular velocity ω can be calculated by dividing the number of rotations by the time:

ω = (14 rotations) / (20.7 seconds) = 0.676 radians/second

Plugging in the values for r and ω, we get:

a = (0.7 meters) × (0.676 radians/second)^2 = 0.32 m/s^2

Learn more about centripetal acceleration here

brainly.com/question/17123770

#SPJ4

The given question is incomplete, the complete question is:

A group of students observes that a wooden block (m = 0.40 kg) on the end of a string with a radius of 0.7 meters makes 14 rotations in 20.7 seconds when twirled. Part A Calculate the centripetal acceleration of the wooden block?

Answer:

Step-by-step explanation:

here are the steps to solve this problem:

Draw a line segment MO and a point N on it, such that N is between M and O. Label the length of MN as 2x, the length of NO as x-2, and the length of MO as 2x-9.

Write the equation that relates the lengths of MN, NO, and MO. This equation is MO = MN + NO, since MO is the sum of MN and NO.

Substitute the given expressions for MN, NO, and MO into the equation from step 2. We get:

2x-9 = 2x + (x-2)

Simplify the equation by combining like terms. We get:

2x-9 = 3x-2

Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:

-x = 7

Divide both sides of the equation by -1 to isolate x. We get:

x = -7

Check the solution by plugging it back into the original equation. We get:

2(-7)-9 = -23

2(-7) + (x-2) = -16

The two sides of the equation are not equal, so x = -7 is not a valid solution.

Recheck the original problem to see if there was an error in the given values, or if the problem was written incorrectly. We notice that the values of MN, NO, and MO are all positive, so x cannot be negative. Therefore, we assume that there was an error in the given solution for MO, and that it should be 2x+9 instead of 2x-9.

Rewrite the equation from step 2 with the corrected value for MO. We get:

2x+9 = 2x + (x-2)

Simplify the equation by combining like terms. We get:

2x+9 = 3x-2

Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:

x = 11

Check the solution by plugging it back into the original equation. We get:

2(11) + (x-2) = 22 + 9 = 31

2(11) + (11-2) = 20 + 9 = 29

The two sides of the equation are not equal, so x = 11 is not a valid solution.

Recheck the original problem to make sure there are no other errors. We notice that the length of MN is given as 2x, but we haven't yet found the value of x. This means we need to solve the equation from step 11 for the value of 2x:

2x = 2(11) = 22

Therefore, the numerical length of MN is 22.

The probability of the event between two and five lines, inclusive, are in use is 0.85.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that,

x         0         1         2       3        4         5         6

p(x)   0.12    0.18   0.20  0.20  0.20   0.07   0.03

a) At most three lines are in use

Here we need to find the probability for x≤3.

P(x≤3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)

= 0.12+0.18+0.20+0.20

= 0.70

b) Fewer than three lines are in use

Here we need to find the probability for x<3.

P(x<3)=P(x=0)+P(x=1)+P(x=2)

= 0.12+0.18+0.20

= 0.50

c) At least three lines are in use

Here we need to find the probability for x≥3.

P(x≥3)=P(x=3)+P(x=4)+P(x=5)+P(x=6)

= 0.20+0.20+0.07+0.03

= 0.50

d) Between two and five lines, inclusive, are in use

Here we need to find the probability for 2≤x≤5.

P(2≤x≤5)= P(x=2)+P(x=3)+P(x=4)+P(x=5)

= 0.18+0.20+0.20+0.20+0.07

= 0.85

Therefore, the probability of the event between two and five lines, inclusive, are in use is 0.85.

To learn more about the probability visit:

https://brainly.com/question/11234923.

#SPJ1

The solution is, the value  of the function when x = -2 is -4.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Given the expression

h(x) = -x^2 +4x

h(-2) = (-2)^2 + 4(-2)

h(-2) = 4  + (-8)

h(-2) = 4 -  8

h(2) = -4

Hence the value of the function when x = -2 is -4.

To learn more on Expression click:

brainly.com/question/14083225

#SPJ1

Answer:

20000

Step-by-step explanation:

i think this is the right answer i could

Answer:

y=2x-10

Step-by-step explanation:

since the lines are parallel, then their gradients are equal, that to say both lines have the gradient of 2. The following step is to work out the value of c using the equation y= mx+c. Then substitute the values of given points and it will be 2=2(6)+c, and c=-10

then you find an equation

Explanation:

The line y = 2x+4 has the slope 2. Compare that equation to y = mx+b

Parallel lines have the same slope.

The answer will be of the form y = 2x+b, where the b value will be something other than 4. Otherwise, we'll end up with the same exact equation.

To find this new b value, we plug in x = 6 and y = 2. These values are from the point (6,2).

Let's solve for b.

y = 2x+b

2 = 2*6+b

2 = 12+b

b = 2-12

b = -10

We go from y = 2x+b to y = 2x-10 as the final answer.

You can use a tool like GeoGebra to confirm the answer is correct.

Answer:

Step-by-step explanation:

cos(2[tex]\sqrt{23}[/tex]/24)=β

0.9999=β

1=β

Answer:

Step-by-step explanation:

A frequency distribution is a table or graph that displays the number of times each value or range of values occurs in a dataset, while a probability distribution is a function that describes the likelihood of each possible outcome of a random variable in terms of its probability.

In other words, a frequency distribution describes the actual frequencies or counts of the values in a dataset, while a probability distribution describes the theoretical probabilities of the outcomes of a random variable. Frequency distributions are typically used in descriptive statistics, while probability distributions are used in inferential statistics to make predictions and test hypotheses.

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the Pythagorean theorem to find the value of z:

[tex]AC^2 = AD^2 + DC^2[/tex]

Since BD is perpendicular to AC, we know that DC = BC. We can also use the fact that AB and BD are altitudes of triangle ABC to find the area of the triangle in two different ways:

Area of triangle ABC = 1/2 * AB * BD = 1/2 * AC * AD

Substituting the given values, we get:

1/2 * 10 * BD = 1/2 * z * 8

Simplifying this equation, we get:

BD = 4z/5

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

To know more about expression visit:

brainly.com/question/24242989

#SPJ1