Solve for X, Similar triangles

Solve For X, Similar Triangles

Answers

Answer 1

Answer:

x = √75

Step-by-step explanation:

We can write out all relations of each triangle here using the Pythagorean theorem (there are 3 triangles total). The triangles are ABD, BCD, and ABC.

For triangle ABD:

AB² = AD² + BD²

AB² = (AC - DC)² + BD²

y² = (15 - 5)² + BD²

y² = 100 + BD²

For triangle BCD:

x² = BD² + 5²

x² = BD² + 25

For triangle ABC:

15² = x² + y²

225 = x² + y²

From here we can substitute into the equation ABC. We can substitute x² and y² with our first and second equations.

225 = BD² + 25 + 100 + BD²

225 = 2BD² + 125

100 = 2BD²

50 = BD²

We don't need to solve for BD, we can substitute it into our equation for triangle BCD to solve for x.

x² = BD² + 25

x² = 50 + 25

x² = 75

x = √75


Related Questions

51×59 evaluate and answer​

Answers

51 multiply by 59 is 3009
51 multiply by 59 and evaluate and you should get 3,009 plz mark brainliest

Calculator
Given j | k and mZ1 = 40".
8/1
What is mZ6?
7/2
k
Enter your answer in the box.
63
54
mZ6 =

Answers

Answer:

65 oop

Step-by-step explanation: o0iiutdgc vhy

Find the slope of the line graphed below.

Answers

Answer:

-2/3

Step-by-step explanation:

rise over run is 4/-6 = -2/3

find the circumcenter

Answers

Answer: (0, -2)

Step-by-step explanation:

what is the rate of change between the points (0,0) and (2,100)?

Answers

I think you can google this

Answer:

The answer is 50.

Step-by-step explanation:

How many of the numbers between 8 and 65 are a multiple of 7?
A) 5
B) 6
C) 7
D) 8

Answers

Answer:

8 is the answer.

8 numbers between 8 and 65 are a multiple of 7

What is the zero of f ?

Answers

A line is y-y1=m(x-x1)
So, F = y-8=-4(x+3)
Simplify so y= -4x-12+8
Y=-4x-4
Then to find “the zero” which I’m assuming is x and y intercepts.

Plug in a 0 for x and y=-4
Plug in a 0 for y and x=-1

So (0,-4) (-1,0)

Hope this helps!! If so please give us brainliest!!

Please answer correctly !!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!

Answers

Answer: Angle MNO

Step-by-step explanation: Supplementary angles equal 180, or a straight line.

Answer: 14

MNJ is angle 13 so angle 14 is the other angle that makes a straight line or 180°.

Write an algebraic expression for the verbal expression.
5 times a number n
Idk what to do

Answers

Answer:

5 x n

Step-by-step explanation:

This is the answer because:

1) 5 times a number n is just 5 times n

Hope this helps!

13 points hurry fast answer both number 19 and 20 plz with an explination!!!!!!!

Answers

Answer:

I don't get it

Step-by-step explanation:

but okay!!!!?!!?!?!?

4)_Slope = 4; contains (-5, - 13)
I need help please

Answers

Answer:

The equation of the line with slope = 4 and point (-5, -13)

will be:

[tex]y=4x+7[/tex]

Step-by-step explanation:

Given

slope = m = 4point = (-5, -13)

As the point-slope form of the equation of line is

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where m is the slope.

substituting the values m = 4 and the point (-5, -13)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-\left(-13\right)=4\left(x-\left(-5\right)\right)[/tex]

[tex]y+13=4\left(x+5\right)[/tex]

subtract 13 from both sides

[tex]y+13-13=4\left(x+5\right)-13[/tex]

[tex]y=4x+7[/tex]

Therefore, the equation of the line with slope = 4 and point (-5, -13)

will be:

[tex]y=4x+7[/tex]

Three Linear Variables​

Answers

Answer:

23 yellow, 30 pink and 12 blue balls

Step-by-step explanation:

Let the number of yellow, pink, blue, and black balls be y, p, b, and x respectively.

From 1st sentence:

y +p +b +x= 90

"60 of them are not pink"

➜ y +b +x= 60

Given that 25 are black, x= 25.

"67 of them are not yellow"

➜ p +b +x= 67

Subst. x= 25 into the above equations:

y +p +b +25= 90

y+ p +b= 65 -----(1)

y +b +25= 60

y +b= 35 -----(2)

p +b +25= 67

p +b= 42 -----(3)

I will rewrite the 3 equations for better clarity:

y +p +b= 65 -----(1)

y +b= 35 -----(2)

p +b= 42 -----(3)

(1) -(2):

p= 65 -35

p= 30

(1) -(3):

y= 65 -42

y= 23

Substitute p= 30 and y= 23 into (1):

23 +30 +b= 65

b= 65 -53

b= 12

Thus, there 23, 30 and 12 yellow, pink and blue balls respectively.

Please hurry!!
If a gas with a pressure of 1 atm and a volume of 2 L is put into a 5 L container, what happens to the pressure?
A. Increase
B. Decreases
C. Remains the same
D. Not enough information

Answers

Answer:

A

Step-by-step explanation:

The gas will increase

Have a great day

I would love your guys help! Thanks! I will give 75 points! Just look at the picture! I just need the answer to 1.

Answers

Answer:

its 0.12

Step-by-step explanation:

**PLEASE HELP I NEED IT WITHIN 20 MINUTES**

These are Trig Ratios and you can read the instructions to solve question 15 & 16 (if you can please show the work it would be greatly appreciated)

Answers

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[1][2]) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis.

Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their side lengths are proportional. Proportionality constants are written within the image: sin θ, cos θ, tan θ, where θ is the common measure of five acute angles.

The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function (called inverse trigonometric function), and an equivalent in the hyperbolic functions as well.[3]

The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extending these definitions to functions whose domain is the whole projectively extended real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) is often used. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane (from which some isolated points are removed).

Contents

Right-angled triangle definitions Edit

A right triangle always includes a 90° (π/2 radians) angle, here labeled C. Angles A and B may vary. Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle.

Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.

In this section, the same upper-case letter denotes a vertex of a triangle and the measure of the corresponding angle; the same lower case letter denotes an edge of the triangle and its length.

Given an acute angle A = θ of a right-angled triangle, the hypotenuse h is the side that connects the two acute angles. The side b adjacent to θ is the side of the triangle that connects θ to the right angle. The third side a is said to be opposite to θ.

If the angle θ is given, then all sides of the right-angled triangle are well-defined up to a scaling factor. This means that the ratio of any two side lengths depends only on θ. Thus these six ratios define six functions of θ, which are the trigonometric functions. More precisely, the six trigonometric functions are:[4][5]

sine

{\

if you could help me with this i would be very thankful

Answers

Answer:

Δ QRS is an obtuse triangle ⇒ according to its angle

Δ QRS is an isosceles triangle ⇒ according to its sides

Step-by-step explanation:

In Δ QRS

∵ m∠Q = 8x - 17

∵ m∠R = 19x + 4

∵ m∠S = 5x + 1

→ The sum of the interior angles of a Δ is 180°

m∠Q + m∠R + m∠S = 180°

→ Substitute their values in the equation above

8x - 17 + 19x + 4 + 5x + 1 = 180

→ Add the like terms

∴ (8x + 19x + 5x) + (-17 + 4 + 1) = 180

∴ 32x + (-12) = 180

∴ 32x - 12 = 180

→ Add 12 to both sides

∵ 32x - 12 + 12 = 180 + 12

∴ 32x = 192

→ Divide both sides by 32

∵ [tex]\frac{32x}{32}[/tex] = [tex]\frac{192}{32}[/tex]

x = 6

→ Substitute the value of x in each measure of angles to find them

∵ m∠Q = 8(6) - 17 = 48 - 17

∴  m∠Q = 31°

∵ m∠R = 19(6) + 4 = 114 + 4

∴  m∠R = 118°

∵ m∠S = 5(6) + 1 = 30 + 1

∴  m∠S = 31°

m∠R > 90°

∴ ∠R is an obtuse angle

Δ QRS is an obtuse triangle

m∠Q = m∠S

→ In any Δ if two angles are equal in measures, then the two sides

  opposite to these angles are equal in length and the Δ is isosceles

RQ = RS

Δ QRS is an isosceles triangle

The regular cost for tickets to an outdoor concert is $10 per person. If the temperature is above 90°F, the venue offers a discount of $4 off per person. Today the temperature is 35°C. What is the total cost for a group of 12 people to go to the outdoor concert today? A. $6 B. $10 C. $72 D. $120

Answers

Answer:

C. $72

Step-by-step explanation:

What is the prime factorization of 23
Thank you

Answers

Answer:

9 is the prime of it

Answer:

Prime factorization: 23 is prime. The exponent of prime number 23 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 23 has exactly 2 factors.

can u create an algebraic equation to describe the relationship between the term value and its position in the pattern given below :

termnumber: term value:
1 . 3
2. 12
3. 21
4. 30



term value:3,12,21,30.​

Answers

Answer:

t(n+1) = t(n) +9

Step-by-step explanation:

Let the Term position be represented by n.

and term value is represented by t.

so term value at any position can be represented by t(n).

Here look closely

t(1)=3, t(2)=12, t(3)=21, t(4)=30

By examining, we notice that the next term is 9 more than the previous one.

e.g

t(2)= t(1)+9

       3+9

t(2)=12

t(3) = t(2)+9

t(3) = 21

we can represent them in mathematical form as:

t(n+1) = t(n) +9

.) One mile is equal to about 1.6 kilometers. If the distance between two cities is 8 kilometers, then how many how many miles is that equal to?

Answers

Answer:

5

Step-by-step explanation:

8/1.6 = 5 divide the two and get the answer!

Brainliest please!

Answer:

5 miles

Step-by-step explanation:

divide 8 by 1.6

Identify the function shown in this graph.



A.
y
=
1
2
x
+
1
y=
2
1
​ x+1

B.
y = –2x – 1

C.
y = –2x + 1

D.
y = 2x – 1

Answers

Answer:

b

Step-by-step explanation:

B.................

I am having a party. I purchase:
x pizzas, y 12-packs of soda, and zcupcakes for a party. If each pizza costs $7.50, each 12-pack of soda costs $3.25, and each cupcake cost $0.75, write an equation for the total cost, t,in terms of x, y and z.

Answers

Answer:

Explanation:

(7.5)x + (3.25)y + (0.75)z = t

Help me I will give u brainlest

Answers

Answer:

(4,0)

Step-by-step explanation:

plz give brainliest!

Answer:

4,0

Step-by-step explanation:

How many lines of symmetry

Answers

Answer:

Zero lines of symmetry

Step-by-step explanation:

What is the sum of all integers that are multiples of 4 from 1 to 150? *Show your solution*

Answers

There's a pretty simple formula to follow: count of multiples [tex]*[/tex] average of the multiple.

To find the average, we take the smallest multiple of 4 which is in the range of 1 and 150 which is 4 of course. And the largest would be 148 since that's the only number in the range. So now average them: [tex]\frac{4 + 148}{2} = \frac{152}{2} = 76[/tex]

Now we find the count of the multiples which is in the range of 1 to 150. To do that, we use this formula:

[tex]\frac{\text{largest multiple} - \text{smallest multiple}}{n} \\[/tex]

Here, [tex]n[/tex] is 4 so this would be:

[tex]\frac{148-4}{4} = \frac{144}{4} = 36[/tex]

This would give you the exclusive count of all the numbers, but we want the inclusive count so, we simple add 1 so the count would be [tex]37[/tex]

Now following the 1st formula we get: [tex]37 * 76 = 2812[/tex]

So the answer would be 2812! :D

And here's the check too:

What is 40 to the 3rd power

Answers

Answer:

64000

Step-by-step explanation:

sorry if wrong

Answer:

64000

Step-by-step explanation:

The Mariana Trench in the Pacific Ocean the deepest known place in any of the world's oceans. Which of the following numbers would be the most reasonable estimate for its depth?

Answers

Step-by-step explanation:

what is the numbers to choose from

Please help! Thanks thO!

Answers

Answer:

8

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle

7x - 4 + 9x + 4 = 128° add like terms

16x = 128 divide both sides by 16

x = 8

If A=,[2 5 7],find the value of
[1 4 9]
[8 3 6]
a23+a12-a32 matrix.​

Answers

Answer:

THE CORRECT ANSER OF THIS QUESTION IS 5.

Step-by-step explanation:

Here,

a23=6

a12=5

a32=6

Now,

a23+a12-a32

=6+5-6

=5

What is the modulus and argument after (StartRoot 3 EndRoot) (cosine (StartFraction pi Over 18 EndFraction) + I sine (StartFraction pi Over 18 EndFraction) ) gets raised to the 6thpower?


ill give brainiest :3

Answers

Answer:

On the test I took the correct answer is c

Step-by-step explanation:

I took the test

The modulus= 27 and Argument = π/3

What is Argument?

The angle inclining from the real axis in the direction of the complex number shown on the complex plane is known as the argument of a complex number.

Given:

z = √3 (cos (π/18) + i sin (π/18))[tex]^{6[/tex]

Now, z = [tex](\sqrt{3}) ^6[/tex] (cos (π/18) + i sin (π/18))[tex]^{6[/tex]

z = 27 (cos (π/18) + i sin (π/18))[tex]^{6[/tex]

As, A complex equation can be expressed as:

z [tex]= |z |e^{i\theta[/tex]

where z= Modulus and [tex]\theta[/tex] is an argument

and, [tex]e^{i\theta =[/tex] cos (π/18) + i sin (π/18)

Then, z = 27 ([tex]e^{i(\(\pi/18)}^6[/tex])

and  [tex]e^{i\theta =[/tex] [tex]e^{i(\(\pi/18)}^6[/tex]

Now comparing

[tex]i\theta =i \pi/18[/tex] x 5

[tex]\theta = \pi/3[/tex]

Learn more about Argument here:

https://brainly.com/question/20053440

#SPJ2

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