Solve for x trigonometry

The pair of triangles in option A, C and D are congruent triangles.

What is triangle?

A triangle is a polygon with three edges and three vertices. It's one of the introductory shapes in figure. A triangle with vertices A, B, and C is denoted triangle Alphabet. In Euclidean figure, any three points, whennon-collinear, determine a unique triangle and contemporaneously, a unique aeroplane.

What is congruent triangle?

SSS: When all three sides are equal to each other on both triangles, the triangle is harmonious. AAS: If two angles and anon-included( you can suppose of it as outside) side of one triangle are harmonious to the corresponding corridor of another triangle, also the triangles are harmonious.

A) In the given figure, two angles and one side of the one triangle is equal to two angles and one side of the other triangle

By AAS consonance, two triangles are harmonious.

B) In the given figure, one angle and one side is equal

So, two triangles aren't harmonious

C) Then, two sides and one included angle of the one triangle is equal to two sides and one included angle of the other triangle

D) Then, two angles and one included side of the one triangle is equal to two angles and one included side of the other triangle.

thus, the brace of triangles in option A, C and D are harmonious triangles.

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Answer:

B) Observational

Explanation:

Observational studies are studies where the researchers only observe the variables and don't make changes. When the political pollster reports the percentage, it only observes the decision of the people but they can't change what makes a person select one candidate or the other.

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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Answer:

900

Step-by-step explanation:

4500/5

Answer:

See below

Step-by-step explanation:

Square objects have four sides of equal length

so the perimeter of the drawing will be   4 * 2.5 = 10 inches

  area of drawing = 2.5 x 2.5 = 6.25 in^2

the actual object will have side lengths

       2.5 in  / 1 inch/ 5mm = 12.5 mm

   four sides each 12. 5 mm = 50 mm

      area of object = 12.5 x 12.5 = 156.25 mm^2

Answer:

5

Step-by-step explanation:

when we calculate mean

mean= 4+4+5+5+6+6/6

=30/6

=5

This might help you

Answer:

C

Step-by-step explanation:

A six back has a value of 35 cents per bun,

you may find this by dividing 2.10 by 6  and getting .35 per

while a 8 pack 3.12 divided by 8 is .39

so it is more economical or correct to get C. 8 six packs for 35 cents a bun

Answer:

23/27

Step-by-step explanation:

The square root of 529 is 23

while the square root of 729 is 27

Answer:

23/27

Step-by-step explanation:

529=23^2

729=27^2

sqrt{529/729} =sqrt{\(23^{2}\)/\(27^{2}\)}

= 23/27

The equation of the halfpipe is  Option A , (0, 20); Y equals one over eighty times x squared plus 20.

The equation of the halfpipe is  Y = X²/80 +20.

What is parabola ?

The equation of parabola is given by  

(X-h)² = 4p(Y-k)²

In this case h = 0

So we get  

Y = X²/4P +k

Focus point is (h, p+k) , (p+k) = 40

Hence h, k = (0,20)

P = 40-k = 20

Equation Y = X²/80 +20

Therefore, the equation of the halfpipe is  Y = X²/80 +20

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The complete question is -

A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?

(0, 20); y equals one over eighty times x squared plus 20

(0, 20); y equals one over eighty times x squared minus 20

(0, 10); y equals one over forty times x squared plus 10

(0, 10); y equals one over forty times x squared minus 10

Answer:

The correct option is;

69 cm

Step-by-step explanation:

The z-score, or standard score is a measure of how far a data is from the mean

The z-score, is given by the relation;

\(z = \dfrac{x- \mu}{\sigma}\)

Z = Standard score

x = Value observed

μ = The mean height of the plants = 52.5 cm

σ = Standard deviation = 7.2 cm

Given that the z-score = 2.25, we have;

\(2.25 = \dfrac{x- 52.5}{7.2}\)

Therefore, x = 7.2 × 2.25 + 52.5 = 68.7 cm ≈ 69 cm

Therefore, the minimum required height for this type of plant to be displayed in the main lobby is 69 cm.

Answer: 38 teachers.

Step-by-step explanation:

Let the share ratio be x.

So, quantity of teachers = 2x, quantity of male students = 17x,

quantity of female students = 18x.

17x+18x=665

35x=665

Divide the left and right sides of the equation by 35:

х=19.

2x=2*19

2x=38.

The product of sums form:

F = (A' + D' + A'D)B + (A' + D')C'

To put the function F into a product of sums form, we need to distribute and simplify the expression using Boolean algebra laws and theorems. Let's work through it step by step:

F = A’(B + C’ + DB) + D’(C’ + B)

Distribute A' to the terms inside the parentheses:

F = A'B + A'C' + A'DB + D'(C' + B)

Distribute D' to the terms inside the parentheses:

F = A'B + A'C' + A'DB + D'C' + D'B

Group similar terms:

F = A'B + D'B + A'DB + A'C' + D'C'

Apply the distributive law to factor out B:

F = (A' + D' + A'D)B + A'C' + D'C'

Apply the distributive law to factor out C':

F = (A' + D' + A'D)B + (A' + D')C'

Finally, we have the function F in the product of sums form:

F = (A' + D' + A'D)B + (A' + D')C'

Throughout the process, we used the distributive law to distribute the negations (') and to factor out common terms.

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The component form of a vector refers to breaking the vector into components with unit vectors denoting the direction of each component. The general component form angled vectors in a two-dimensional space is given by:

\(\vec v=|v|cos\theta\hat{x}+|v|sin\theta\hat{y}\)

where |v| is the magnitude of the vector component and theta is the angle of the vector.

Using the magnitude and angle given for vector u we can write its component form :

\(\vec u=|u|cos\theta_u \hat{x}+|u|sin\theta_u \hat{y}\\\vec u=|5|cos(9)\hat{x}+|5|sin\(9) \hat{y}\\\vec v=5cos9_u\hat{x}+5sin9_u\hat{y}\)

Doing the same for v

\(\vec v=|v|cos\theta_u \hat{x}+|v|sin\theta_u \hat{y}\\\vec v=|1|cos5_u \hat{x}+|1|sin5_u \hat{y}\\\vec v=1cos5_u\hat{x}+sin5_u\hat{y}\)

Now adding both vector together

\(\vec u+\vec v=(5cos9_u\hat{x}+5sin9_u\hat{y})+(cos5_u\hat{x}+sin5_u\hat{x})\\\vec u+\vec v=(5cos9_u\hat{x}+cos5_u\hat{x})+(5sin9_u\hat{y}+sin5_u\hat{y})\)

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2x-6.3=39.2

2x-6.3+6.3=39.2+6.3

2x=45.5

2x=45.5

2x/2 = 45.5/2

x=22.75

x=22.75

Option-C is correct that is the algebraic expression of the function F = (x +y +z').(x +y' +z').(x' +y +z) from the circuit in the picture.

Given that,

We have to find what is the algebraic expression of the function F.

In the picture we can see the diagram by using the circuit we solve the function F.

We know that,

From the circuit for 3 - to - 8 decoder,

D₀ = \(\bar{x}\bar{y}\bar{z}\)

D₁ = \(\bar{x}\bar{y}{z}\)

D₂ = \(\bar{x}{y}\bar{z}\)

D₃ = \(\bar{x}{y}{z}\)

D₄ = \({x}\bar{y}\bar{z}\)

D₅ = \({x}\bar{y}{z}\)

D₆ = \({x}{y}\bar{z}\)

D₇ = xyz

We can see bubble after D₀ to D₇ in the circuit,

So, Let A = \(\bar{D_1}\) = \(\overline{ \bar{x}\bar{y}{z} }\) = x + y + \(\bar{z}\)

Now, Let B = \(\bar{D_3}\) = \(\overline{ \bar{x}{y}{z} }\) = x + \(\bar{y}\) + \(\bar{z}\)

Let C = \(\bar{D_4}\) = \(\overline{ {x}\bar{y}\bar{z} }\) = \(\bar{x}\) + y + z

Now, Output F = A.B.C

F = (x + y + \(\bar{z}\)).(x + \(\bar{y}\) + \(\bar{z}\)).(\(\bar{x}\) + y + z)

F = (x +y +z').(x +y' +z').(x' +y +z)

Therefore, The algebraic expression of the function F = (x +y +z').(x +y' +z').(x' +y +z).

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The question is incomplete the complete question is -

What is the algebraic expression of the function F.

Option-

a. F = (x+y+z)(x+y'+z)(x'+y+z')(x'+y'+z)(x'+y'+z')

b. F = (x'+y'+z')(x'+y+z)(x+y+z')(x'+y+z)(x+y+z)

c. F = (x +y +z').(x +y' +z').(x' +y +z)

d. F = (x' +y' +z').(x +y +z').(x +y +z)

Answer:

the ratio is 4/5

Step-by-step explanation:

27 pennies all together. just divide the number of each group by the same thing till you no longer get a whole number. like 3÷12 and 3÷15. Do it till you get the smallest whole number for each

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Answer:

C. 39

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

A = y = 1.5   x =  -2\<x,< 3  

B = y = 0.2   x =  -2<x < 2

C = y = -1.2  x =  -2< x\< 3

D = y =  1.2   x = - 2< x < 2

Hence, the probability that both defective bulbs will be selected is 0.1630

We are given that a box containing 24 light bulbs. 2 light bulbs are defective.

Now if a person selects 10 bulbs at random, without replacement.

We are required to find the probability that both defective bulbs will be selected.

Since there are two defectives, therefore two defective can be chosen in(2,2) ways.

Also since 10 bulbs are selected, the remaining 8 bulbs can be selected in (22,8)

Also, the total number of ways 10 bulbs can be selected is:

\(^{22}C_8\\\)

Therefore, the probability that both defective bulbs will be selected is:

\(=\frac{(^2c_2)(^{22}C_2)}{^{24}C_10}\\\\=1.630.\)

rounded to 4 decimal places

Hence, the probability that both defective bulbs will be selected is 0.1630

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Using the Pythagorean Theorem, the length of the base is: 15 units.

The Pythagorean theorem is used to find any of the length of the legs or hypotenuse of a right triangle if we know any two measures of its side. The theorem is given as: the square of the hypotenuse = sum of the squares of the legs of the right triangle.

It can be expressed as c² = a² + b², where c is the longest side of the right triangle.

Note: The hypotenuse is the longest side of the triangle.

Thus, given the triangle in the image below, where:

c = 25

a = 20

b = length of the base

The expression that would be appropriate for this situation would be written based on the Pythagorean Theorem, which is:

b = √(c² - a²)

Substitute

b = √(25² - 20²)

b = 15 units

The length of the base is: 15 units.

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Answer:

oouu I'm in 7th grade science and I already did this I can help!

Step-by-step explanation:

In triangle ABC. In triangle DBC

AB. = DB.

[Given]

<ABC. = <DBC

[Given]

BC. = BC

[Common side]

Hence,

As two sides and one angle of triangle ABC and triangle DBC are equal.

Triangle ABC is congruent to Triangle DBC

The expression {xyz | x, z ∈ σ ∗ and y ∈ σ ∗ 1σ ∗ , where |x| = |z| ≥ |y|} represents a set of strings that can be formed by concatenating three substrings: x, y, and z.

The strings in the set must satisfy the following conditions:

Intuitively, this set represents all the strings that can be formed by taking a "core" string of length |y| and adding some arbitrary strings before and after it to create a longer string of the same length. The single symbol at the end of y is meant to separate y from the rest of the string and ensure that y is not empty.

For example, if σ = {0, 1}, then one possible string in the set is "0011100", where x = "00", y = "111", and z = "00". This string satisfies the conditions because |x| = |z| = 2, |y| = 3, and y ends in the symbol "1" from σ. Other strings in the set could be "0000110", "1010101", or "1111000", depending on the choice of x, y, and z.

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The area covered by the pool and the cement walkway is 304  square feet. The width of the walkway would be 5 feet

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be represent the width of the walkway.

The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway =  25+ x + x = 25 + 2x

The total width of the pool and the walkway = 10 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 304  square feet. This means that;

(25 + 2x)(10 + 2x) = 304

250 + 50x + 20x + 4x^2 = 304

4x^2 + 70x + 250 - 304 = 0

4x^2 + 70x - 54 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

Thus The width cannot be negative.

Therefore, the width of the walkway is 5 feet.

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The value of the smaller number (x) is approximately 6.67 (rounded to two decimal places).

To solve this problem, let's call the smaller number x and the larger number y.
According to the given information, the sum of the two numbers is 20, so we can write the equation: x + y = 20.
It is also given that one of the numbers (y) is twice the other number (x).

In equation form, we can write: y = 2x.

To find the value of the smaller number (x), we can substitute the value of y from the second equation into the first equation:
x + 2x = 20
Combining like terms, we get:
3x = 20
Dividing both sides by 3, we find:
x = 20/3
So, the value of the smaller number (x) is approximately 6.67 (rounded to two decimal places).

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Answer:

S=2t

or

T=1/2 S

Answer:

im pretty sure it would be 9 bc there are 3 dif colours and 3 dif finishes and u j count the table

Step-by-step explanation:

Answer:

its 2

Step-by-step explanation:

for a fact the product of two rational numbers is rational in that statement is always true

Answer:

600 words.

Step-by-step explanation:

If Johanna can type 120 words in 3 minutes, and the problem is asking us to find how many words she can type in 10 minutes at the same unit rate, we'll have to start by solving how many words she can type in 1 minute:

\(\frac{120}{3}\)

Dividing 120 words into 3:

\(=60\) words per minute.

Now that we know how many words Johanna types in one minute (per minute), we can multiply the words per minute by 10 (minutes):

\(60\) × \(10=600\) words in 10 minutes.

_

We can check our work by dividing 600 words into 10 minutes to see if we achieve the same unit rate of 60 words per minute:

\(\frac{600}{10}\)

\(=60\) words per minute.

Since we have the same unit rate, our answer is correct!