Solve Similar Triangles (advanced)

Solve for X.

Solve Similar Triangles (advanced)Solve For X.

Answers

Answer 1

Given:

[tex]m\angle B=90^\circ, m\angle D=90^\circ, AB=x, BD=9, BC=1, DE=5[/tex].

To find:

The value of x.

Solution:

In triangles ABC and ADE,

[tex]\angle B\cong \angle D[/tex]              (Right angles)

[tex]\angle A\cong \angle A[/tex]              (Common angles)

[tex]\Delta ABC\sim \Delta ADE[/tex]              (AA property of similarity)

We know that the corresponding sides of similar triangles are proportional. So,

[tex]\dfrac{AB}{AD}=\dfrac{BC}{DE}[/tex]

[tex]\dfrac{x}{x+9}=\dfrac{1}{5}[/tex]

On cross multiplication, we get

[tex]5x=x+9[/tex]

[tex]5x-x=9[/tex]

[tex]4x=9[/tex]

[tex]x=\dfrac{9}{4}[/tex]

[tex]x=2.25[/tex]

Therefore, the value of x is 2.25 units.


Related Questions

I help in the next 5 min also if you could explain how to sove it would help a ton!!!
find the value of x 4 2x 3 and x+5

Answers

Answer: x4 2x 3 is 126x power of 3 + 5

In the expression 34% of 60, what
operation does the word "of" mean?

Answers

Answer:

Means to Multiply

Step-by-step explanation:

34% times 60

An art teacher has 6 1/4 gallons of paint to pour into containers. If each container holds 1/2 gallon, what is the maximum number of full containers they can fill.

Answers

12 is the answer because 6 x 2 = 12

When two rotations are performed on a single figure, does the order of the rotations sometimes, always, or never affect the location of the final image? Explain.

Answers

When two rotations are performed on a single figure, the order of the rotations never affect the location of the final image.

What is the rotation?

In mathematics, rotation is defined as that of the circular movement of an object around with a center, an axis, or a fixed point. Since rotations are rigid transformations, the size, length, shape, and angle measurements of the figure are maintained.

Precession, nutation, and intrinsic rotation are the names of these rotations. The rotation of the earth on its axis is one of the greatest instances of rotation in nature.

There are broad guidelines for rotations of 90, 180, and 270 degrees around the origin that are both clockwise and anticlockwise. Counterclockwise. X and Y are rotated by 90 degrees that means (x , y) ----> (-y , x); Rotation of 180 degrees: (x, y) —- (-x , -y); Rotation of 270 degrees: (x, y) —- (y , -x).

Here two times rotation means 180 degrees that means no change in the final image.

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Using a number line, find both the intersection and the union of the following
intervals:
(-3,∞) and (4,∞)

Answers

Answer:

The intersection of the two intervals = 4, 5, 6,.......∞ = (4, ∞)

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-3, ∞)

Step-by-step explanation:

The given intervals are;

First interval  = (-3, ∞)

Second interval  = (4, ∞)

Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,∞

The second interval includes 4, 5,.....,∞

Which gives the intersection as 4, 5, 6,.......∞

The union is the interval that combines the two sets of intervals which is given as follows;

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,∞

How do you plot a coordinate plane?

Answers

We can plot in the coordinate plane if an ordered pair is known to us.

What is coordinate plane?

The space or plane in where location of points is represented by a pair of numerical terms with respect to some reference lines or reference direction is called coordinate plane.

How do we plot a coordinate plane?

let we have some pair of numerical terms such as A (4, 9) and B (6, 10)

that is needed to plot in the coordinate plane.

At first, we will plot the point A (4, 9)

we will start from the origin and move horizontally along the direction of X axis up to 4 unit. In the next, start again and move up vertically in the direction of y axis up to 9 unit. And we will draw a point at the final location.

By the same way, we can plot the point B.

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(look at photo)
iready level h compare functions quiz

Answers

Answer:

So I would say when the number of classes is lower fishing is less expensive and when the number of canoeing classes is lower it's less expensive

Step-by-step explanation:

You have to make sure to pay attention to the label and the points in the graph and the table

tell which number is greater 56%, 5.6.

Answers

Answer:

5.6

Step-by-step explanation:

56% = 0.56

5.6 > 56%

Find the product using any method. (Please help me on this!)

Answers

Answer:

The answer is (4x² - 36x + 81)

Step-by-step explanation:

Given(2x - 9)²Property Used(a - b)² = a² - 2ab + b²

So,

(2x - 9)² = (2x)² - 2(2x)(9) + (9)²

(2x - 9)² = 4x² - 36x + 81

Thus, The product of (2x - 9)² is (4x² - 36x + 81)

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answers

Answer:

Option B

Step-by-step explanation:

Given quadratic equation is,

12a² + 9a + 7 = 0

By comparing this equation with standard quadratic equation,

hx² + kx + c = 0

h = 12, k = 9 and c = 7

By using quadratic formula,

a = [tex]\frac{-k\pm\sqrt{k^2-4hc}}{2h}[/tex]

  = [tex]\frac{-9\pm\sqrt{9^2-4(12)(7)}}{2(12)}[/tex]

  = [tex]\frac{-9\pm\sqrt{81-336}}{2(12)}[/tex]

  = [tex]\frac{-9\pm\sqrt{-255}}{24}[/tex]

  = [tex]\frac{-9\pm i\sqrt{255}}{24}[/tex]

a = [tex]\frac{-9+ i\sqrt{255}}{24},\frac{-9- i\sqrt{255}}{24}[/tex]

Therefore, Option B will be the correct option.

Kate can mow lawns at a constant rate of 4/5 lawns per hour. How many lawns can Kate mow in 20 hours?

Answers

Answer:

16 lawns

Step-by-step explanation:

set up a proportion:

(4/5 ÷ 1) = (x÷20)

cross-multiply:

5x = 80

x = 16

Kate can mow lawns at a constant rate of 16 lawns in 20 hour.

What is Multiplication?

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

Given that;

Kate can mow lawns at a constant rate of 4/5 lawns per hour.

Now,

Since, Kate can mow lawns at a constant rate of 4/5 lawns per hour.

Hence, In 20 hours;

Kate can mow lawns = 20 × 4/5

                                 = 16 lawns

Thus, Kate can mow lawns at a constant rate of 16 lawns in 20 hour.

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Find the measure of the indicated angle. Need help please.
I need explanation

THANK YOU

Answers

Answer:

I think I got the answer. See picture attached : )! Also sorry if my handwriting is bad! I hope this gives you a better understanding,have a good day!

Find the missing side

Answers

Answer:

Step-by-step explanation:

[tex]\sqrt{61}[/tex]

A mysterious metal medallion has a mass of 3,088 grams. Water is poured into a graduated glass container with a 10-by-10 cm square base with a water level of 53.0 cm. The medallion is dropped into the container and the water level rises to 54.6 cm. Find the volume and the density of the medallion.​

Answers

Answer:

Look at my in the photo

Step-by-step explanation:

A tore i having a ale on almond and jelly bean. For 5 pound of almond and 2 pound of jelly bean, the total cot i $12. For 3 pound of almond and 8 pound of jelly bean, the total cot i $31. Find the cot for each pound of almond and each pound of jelly bean

Answers

b = $3.5 the cost of each pound of jelly beans.

a = $1, the cost of each pound of almonds

What is the elimination method?

The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.

Here,

We let a be the almond and b be the jelly bean.

5a + 2b = $12....(1)

3a + 8b = $31....(2)

...Solving by elimination method.

5a = 12 - 2b

a = (12 - 2b)/5

Now, we put the value of a in equation(2)

3a + 8b = $31

3(12 - 2b)/5 + 8b = 31

(36 - 6b)/5 + 8b = 31

36 - 6b + 40b = 155

34b = 155 - 36

34b = 119

b = $3.5 the cost of each pound of jelly beans.

a = $1, the cost of each pound of almonds.

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Click on the solution set graphic until the correct one is displayed.

Answers

Answer: I can't answer that because it's not a question

Step-by-step explanation:

What is the area? ……square millimeters

Answers

Answer:320

Step-by-step explanation:

for any square or rectangle the formula for area is l*w means length times width so for this particular square the length is 16 and the width is 20 so multiply the two and you get 320 hope this helps

What does it mean to solve an equation by substitution?

Answers

The value of a variable from one equation is substituted in the other equation when using the substitution method.

The graphic approach and the algebraic method are the two main categories into which simultaneous linear equations can be solved. One of the categories of the algebraic approach is the substitution method. The algebraic approach to solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Steps for Substitution method:

Simplify the given equation by expanding the parenthesisSolve one of the equations for either x or ySubstitute the step 2 solution in the other equationNow solve the new equation obtained using elementary arithmetic operationsFinally, solve the equation to find the value of the second variable

Therefore in the Substitution method, The value of a variable from one equation is substituted in the other equation.

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HELLPP MEE ! I NEED HELP FAST
NO LINKS PLEASE:D

Find the volume of the figure. Use 3.14 for p. If necessary, round your answer to the nearest tenth.

A. 4083.6 ft^3
B. 75.6 ft^3
C. 1361.2 ft^3
D. 160.1 ft^3

Answers

Your answer is option C. Hope I answered it on time

Answer:

the answer is C I hope you got this answer

Please help me, I don’t get what I am supposed to be doing to find the answer.

Answers

Answer:

A=0 B=2/3 C= 1/4 D=1/6 E=1/12 F=1

Step-by-step explanation:

P means the probability

A there is no 0 so the p will be 0

B there is 8/12 odd numbers so simplified is 2/3

C  there are 3/12 3s so simplified is 1/4

D there are 2/12 2s so simplified is 1/6

E there is 1/12 1s

F all numbers are less than 6

URGENT!! 25 POINTS!!!!!

What is the equation shown
by the following graph?

Answers

Answer:

denominator - 6234 is math

Step-by-step explanation:

I want to know why B is the correct answer.

Answers

Answer:

Choice B. 2395.83 cm^3

Step-by-step explanation:

V = [tex]\frac{lwh}{2}[/tex] = [tex]\frac{(25)(12.5)(23)}{2}[/tex] = 2395.83333 = 2395.83cm^3

Answer:

oki! hope this explanation will help you! my last answer was deleted sooo...

Step-by-step explanation:

To find the volume of the pyramid, the formula is 1/3 x height x base

In this case...

the height:23 cm

the base:312.5 [tex]cm^{2}[/tex]

and the equation is 1/3 x 23 x 312.5

which will be 2395.8333333(and more 3!)

We round it in the hundreths place and get 2395.83(aka option B) as the answer!

Whats 3x+1? for in high school its really hard to solve none of my friend cant do it

Answers

As per the zeros of the function, the value of the function 3x + 1 is  x = -1/3.

Zeros of the function in math is defined as the values of the variable of the function such that the function equals 0.

Here we have given the function 3x + 1.

Now, we have to equate the function with zero, in order to solve it, then we get,

=> 3x + 1 = 0

Now, we have to subtract 1 on both sider to individualize the x value then we get the rewritten expression as,

=> 3x = -1

Now, we have to divide each side by 3, then we get the value of x as,

=> x = -1/3

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Please help
u have to the Pythagorean Theorem

Answers

Answer:

13.7

Step-by-step explanation:

[tex]x^2 + 30^2 = 33^2[/tex]

[tex]x^2 + 900 = 1089[/tex]

[tex]x^2 = 189[/tex]

[tex]x = \sqrt{189}[/tex]

[tex]x = 13.7[/tex]

How to solve and answer?

Answers

Answer:

I believe the answer is 3

Step-by-step explanation:

because NO and KL are parallel, they have the same length which is 3 as given in the question description. We also know that KL and NM have the same length. Therefore, NM is also 3.

Que es un variable? (De matemáticas)

Answers

Answer:

[tex]\huge\boxed{Que \ es \ un \ variable \ ?\hookleftarrow}[/tex]

✐ En matemáticas, una variable es un símbolo que funciona como marcador de posición para expresiones o cantidades que pueden variar o cambiar; se utiliza a menudo para representar el argumento de una función o un elemento arbitrario de un conjunto. Además de los números, las variables se utilizan comúnmente para representar vectores, matrices y funciones.

Making connections between arithmetic sequences and linear function


Use the graph or the formula to write the equation of the line in a slope intercept form

Answers

The equation of line passing through (-9,-10) and(7,-3) will be y = (7/16)x - 1

What is slope?

Slope is a measure of the steepness of a line, and it is also known as the "gradient." It is a ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. It is often represented by the letter "m" in the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

What is the formula to find the equation of line given the two points?

The formula to find the equation of a line given two points is:

y - y1 = m(x - x1)

where (x1,y1) and (x2,y2) are the coordinates of the two points on the line, and m is the slope of the line, which can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

m = (y2 - y1) / (x2 - x1)

where (x1,y1) and (x2,y2) are the coordinates of the two points.

so the slope m = (-3 - (-10)) / (7 - (-9)) = 7/16

We can use point slope form to get the equation of the line passing through the two points:

y - y1 = m(x - x1)

so the equation of the line is y - (-10) = (7/16)(x + 9)

=> y = (7/16)x + (-10) + (9 * 7/16)

=> y = (7/16)x - 1

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write a linear equation that passes through the points (2,-7) and (4,-9) and has a slope "-5"

Answers

Step-by-step explanation:

a line passing through 2 points get a slope just by these 2 points.

all we can do is to verify that the given slope is the same as the slope defined by the 2 points.

the slope is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

for our 2 points that gives us

x changes by + 2 (from 2 to 4).

y changes by -2 (from -7 to -9).

the slope is therefore

-2/+2 = -1

the question asks for a slope of -5.

that is a contradiction. there is no line possible to pass through both points and have a slope of -5.

What is the equation of the line graphed below?

Answers

Answer: -2/3x is the slope and the beginning amount is 5 so the equation would be -2/3x+5.

Step-by-step explanation:

Once you find the slope using the formula rise/run you will get 2/3 but since the slope is going downwards it would be -2/3 which gives you the mx. Now to find the beginning amount look where the line intersects the graph which will give you the equation.

What is the variable in 2x 3 7?

Answers

The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms only x is the variable.

What is an equation?

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms.

if we solve the above equation, we get

2x + 3 = 7

or, 2x = 7 - 3

or, 2x = 4

or, x = 2

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