find x with two triangles

Answers

Answer 1

Answer:

x=12

Step-by-step explanation:

Given that there is only one expression given in each triangle, if we only use the information in a single triangle, there is no way to set up an equation that we could solve to find the expression. (For this situation, at best we could use the triangle sum theorem to say that the three angles in one triangle added to 180°, but since we don't know the other two angles, that's 3 unknowns with only 1 equation... that's not solvable)

The only way to solve this problem is to make a relationship of some sort between the two triangles.

Proving a relationship between triangles - option 1

You may have a theorem about the Third angles of two triangles... "Given two arbitrary triangles, [tex]\triangle ABC[/tex] and [tex]\triangle D E F[/tex], if [tex]\angle A \cong \angle D[/tex] and [tex]\angle B \cong \angle E[/tex], then [tex]\angle C \cong \angle F[/tex] "

If you have this, then the third angles are congruent.

In a more general situation of a similar problem (one in which you don't know two of the angles to begin with), it might be easier to prove triangle congruence, or triangle similarity.

Other Relationships between triangles

There are two main relationships between triangles: similarity and congruence.

Most people learn about congruence first.

In the situation for this problem, the two triangles happen to be congruent (we'll prove it shortly), which implies that all corresponding angles between shapes are congruent (and all corresponding sides between shapes are congruent).

For the purpose of solving for things related to angles, proving that the two triangles are similar is enough to know that angles between triangles are congruent (sides wouldn't necessarily be equal, but would be proportional, and since we're not solving for anything related to side lengths, proving that the triangles are similar would be enough).

Proving a relationship between triangles - option 2 - congruence

Notice that the triangle on top has two angles with markings (a single mark, and a double mark), and one side with a marking (a single tick). These three pieces are in a configuration of ASA (the side is between the two angles).

Looking at the bottom triangle, it also has angles and sides with corresponding markings, and they are also in an ASA configuration.

Thus, by ASA congruence, these triangles are congruent triangles.

Knowing the triangles are congruent (even though we only used 3 parts), the rest of the corresponding parts (including the third angles) are also congruent.

Proving a relationship between triangles - option 3 - Similarity

For similarity, the process is similar to proving congruence, however the theorems we have for proving similarity are different.

SSS, SAS, or AA similarity.

Since the triangles in our problem do have two angles that are congruent, by AA similarity, the triangles are "similar".

Knowing the triangles are similar (even though we only used 2 parts), the last set of corresponding angles are also congruent.

Building our equation

Since the third angle of each triangle is congruent, by definition of congruent angles, the measures of each of those two angles are equal, and so we can build an equation knowing that the two expressions are equal to each other:

[tex]3x-7=2x+5[/tex]

Solving for x

From there, we need some algebraic properties equality to solve for x.

Subtract 2x from both sides...

[tex](3x-7)-2x=(2x+5)-2x\\x-7=5[/tex]

add 7 to both sides...

[tex](x-7)+7=(5)+7\\x=12[/tex]

Extension

Knowing the value for x, we could solve for the measure of the angles, if that had been requested. Simply substitute 12 back into the expressions for the angle measure (the results should be the same for both angles, since they were congruent angles)

[tex]3(12)-7\\36-7\\29[/tex] [tex]2(12)+5\\24+5\\29[/tex]

So, if we had been asked, the measure of the angle is 29°

Related Questions

Bacteria colonies can increase by 73%
every 2 days. If you start with 55 bacteria
microorganisms, how large would the
colony be after 10 days?
Future Amount = [?] microorganisms
←time
Hint: Future Amount = 1(1+r) periods
↑
initial growth
amount rate
Round to the nearest whole number.

Answers

The size of the colony after 10 days is 852.

What is the size of the colony after 10 days?

The growth rate of the colony can be represented with an exponential equation with the form:

FV = P(1 + r)^n

Where:

p = present population r = rate of growth n = growth factor = 10 days / 2 days = 5

55(1.73)^5 = 852

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2x+3y=4 cual es la respuesta??

Answers

Answer:

y = 2/3x + 4/3

Step-by-step explanation:

Voy a suponer que necesitas resolver para y.

2x + 3y = 4

3y = -2x + 4

y = -2/3x + 4/3

10. A Chemical balance needs to weigh 237 grams using weights of 50 grams , 20 grams , 10 grams and 1 gram . How many of each weight is needed ?

Answers

Answer:

237 grams

50 * 4

= 200

4 weight of 50 g

1 weight of 20g

1 weight of 10g

7 weight of 1g

in quadlateral wxyz wc equals 2X +5 and CY equals 3X +2 what must x equal

Answers

The value of x in the given quadrilateral is; x = 3

How to find the angle in a quadrilateral?

The diagonals of a parallelogram bisect each other.

Thus, from the image attached, we can say that;

WC = CY.

Thus;

2x + 5 = 3x + 2

Subtract 2x from each side to get;

5 = x + 2

Subtract 2 from each side to get;

5 - 2 = x + 2 - 2

x = 3

The complete question is;

In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?

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Please help !!! I will give 20 points to the correct answer!!

Answers

-2x + 11 =31
-2x =31 - 11
-2x = 20
X = 20/2
X = 10

What is the area of this triangle?

Answers

Answer:

sum of all sides

Step-by-step explanation:

x1y2 + x3y3 + x1y1

There are two colored marbles and one white marble in a box. Julie mixes the marbles and then Sam draws two marbles at random without replacement. If the two marbles match, Sam wins; otherwise, Julie wins. Does each player have an equal chance of winning? Will adding another white marble give each player an equal chance of winning? What if a game with the same rules was played using three colored marbles and one white marble?

Answers

at first there are three marbles for Sam to pick from. the possibility of drawing a colored marble is 2/3. if Sam picks one of the colored marbles, the possibility of therefore (if he'd drawn the colored marble) drawing the second colored marble is 1/2. for the possibility of those happening consequently, we have to multiply the possibilities. 2/3 * 1/2 is 2/6 is 1/3. which means Sam wins in 33.333...% cases. Julie has a better chance of winning.

adding a white marble would change the possibilities to 1/2 and 1/3 consequently, meaning Sam wins in 1/2 * 1/3 = 1/6 = 16.7% cases, which is even less fair.

adding a colored marble would change the possibilities to 3/4 and 2/3 consequently, meaning Sam wins in 3/4 * 2/3 = 6/12 = 50% cases, which finally makes the game fair.

A regular polygon has n sides.
How many pairs of parallel sides does the polygon have if:
a) n is odd?
b) n is even?

Answers

The number of pairs of parallel sides of the polygon have no parallel sides if n is odd and n/2 pair of parallel sides if n is even.

What is a polygon?

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

A regular polygon has n sides.

Then the number of pairs of parallel sides of the polygon will be

IF n is odd, then none of the sides are parallel.

If n is even, then the number of pair of parallel sides will be n / 2.

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The Gross Domestic of a country in the first quarter of 2014 was $1.3299×10×8.
GPD=$

Answers

The GDP of the country for 2014 is $5.3196 × 10⁸.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given the Gross Domestic of a country in the first quarter of 2014 was $1.3299×10⁸. Therefore, the GDP of the country for that year will be,

GDP = 4 × (Gross Domestic for a single quarter)

= 4 × ($1.3299×10⁸)

= $5.3196 × 10⁸

Hence, the GDP of the country for 2014 is $5.3196 × 10⁸.

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A football teams offense T is found by adding the total passing yardage P to the total rushing yardage R; that is, T=P+R. During the 2012 regular football season, the teams total offense was 4559 yards. The teams passing yardage was 3069 yards. How many yards did the team gain by rushing during the season?

Answers

The team gain 1490 yards by rushing during the season.

What is football yardage?

Football yardage is the number of yards that a team or player manages to move the ball forward toward their opponent's end zone.

According to the question,

A football teams offense T is found by adding the total passing yardage P to the total rushing yardage R,

i.e. T=P+R

In 2012,

The teams total offense was 4559 yards.

The teams passing yardage was 3069 yards.

By using the formula

T=P+R

T = 4559 yards , P = 3069 yards

Put the values in the above equation;

4559 = 3069 - R

4559 - 3069 = R

R = 1490 yards

Therefore , 1490 yards the team gain rushing during the season.

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Find the x-intercept of the line whose equation is 8x + 2y = 4.

Answers

Answer: (I am copying and pasting my answer from the same question you did before in case you are waiting for an answer on this instead.)

1/2

Step-by-step explanation:

To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.

8x+2y = 4 ➨ 8x+2*0 = 4

Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:

8x = 4

Now I will divide both sides by 8, which isolates our x.

x = 1/2

The x-int is 1/2.

Answer:

(0.5 , 0) or (1/2 , 0)

Step-by-step explanation:

Any x-intercept must be at (x,0), so we substitute y=0 into the equation.

8x + 2(0) = 4

8x = 4

x = 1/2 = 0.5

Therefore, the x-intercept is at (0.5 , 0) or (1/2 , 0)

To prove triangles similar, we only need to prove corresponding angles congruent OR corresponding sides are proportional. However, with a quadrilateral we need to prove corresponding angles congruent AND corresponding sides are proportional. Explain in your own words why it takes more to prove that quadrilaterals are similar. Include examples demonstrating how “just angles” or “just sides” is not enough.

Answers

It takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc.

What is a quadrilateral?

It should be noted that a quadrilateral simply means a shape that has four sides and four angles.

In orde to prove that triangles are similar, we only need to prove corresponding angles congruency.

On the other hand, it takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc. This makes them more elaborate.

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where are mc donalds

Answers

Answer:

all over the world

Step-by-step explanation:

use g00g!e maps

Answer:

Not in Russia

Step-by-step explanation:

McDonald's left Russia following the violations of human rights

A table lamp emits light in the shape of a hyperbola. If the hyperbola is modeled by the equation 25x2 – 144y2 + 3,600 = 0, which of the following equations represents the boundaries of the light?

y equals five twelfths x and y equals negative five twelfths x
y equals twelve fifths x and y equals negative twelve fifths x
y equals five thirteenths x and y equals negative five thirteenths x
y equals thirteen fifths times x and y equals negative thirteen fifths times x

Answers

Answer:

(a) y = 5/12x and y = -5/12x

Step-by-step explanation:

Given the equation of a hyperbola 25x² – 144y² + 3,600 = 0, you want the equations of the asymptotes.

Standard form

Dividing by 3600 and doing a little rearrangement, we have ...

(y/5)² -(x/12)² = 1 . . . . . standard form equation of a hyperbola

Asymptotes

The equation of the asymptotes is ...

(y/5)² -(x/12)² = 0

Solving for y gives ...

(y/5)² = (x/12)²

y/5 = ±x/12 . . . . . . take the square root

y = ±5/12·x . . . . . . . matches the first choice

Additional comment

The equation of a hyperbola with vertices on the y-axis is often written as ...

y²/a² -x²/b² = 1

We have written it in the above form to better show the scale factors applied to x and y.

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14. The probability my daughter will eat her dinner without complaining is 5/7. The probability she will eat
her dinner and do her homework all without complaining is 2/7. What is the probability she will do her
homework without complaining given that she ate her dinner without complaining?

Answers

Probability helps us to know the chances of an event occurring. The probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Let eating dinner without complaining be A, and doing homework without complaining be B.

Given the probability my daughter will eat her dinner without complaining is 5/7. So, we can write,

P(A) = 5/7

Also, The probability she will eat her dinner and do her homework all without complaining is 2/7. So, we can write,

P(A∩B) = 2/7

Now, the probability she will do her homework without complaining given that she ate her dinner without complaining is,

[tex]P(B|A)= \dfrac{P(A\cap B)}{P(A)}[/tex]

[tex]= \dfrac{\dfrac{2}{7}}{\dfrac57}\\\\\\= \dfrac25[/tex]

Hence, the probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.

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Two candidates ran for class president. The candidate that won received 80% of the 320 total votes. How many votes did the winning candidate receive?

pls help

Answers

Answer:

256

80÷100×320=256

80÷100=0.8

0.8×320=256

Somebody help please!!

Answers

The correct answer is 19

4. At what coordinates does the terminal side of a -420° angle intersect the unit circle?

Answers

Answer:

[tex]\left(\dfrac{1}{2},-\dfrac{\sqrt{3}}{2}\right)[/tex]

Step-by-step explanation:

An angle is co-terminal with the same angle that has any multiple of 360° added to it.

The angle -420° is co-terminal with (-420° +720°) = 300°. The attached unit circle chart shows the coordinates of the terminal side of that angle.

These coordinates are ...

(x, y) = (cos(300°), sin(300°))

(x, y) = (1/2, -√3/2)

Mrs. Hilt owns a house on a lot shaped like a rectangle. The perimeter
of the lot is 60 feet. What is the length and the width of the lot?

Answers

Answer:

2l + 2w = 60

Step-by-step explanation:

Janelle and Jacob are considering a $130,000 mortgage for 30 years at 4.8%. With this information, their monthly payment
would be $682.06.
If they make only the minimum payment each month, what is the total payback of this loan?
How much of this total payback is interest?

Answers

30 years = 360 monthly payments
Total payback = 360 x $682.06 = $245,541.60
Interest = 245,541.60 - 130,000 = $115,541.60

The mean amount of time it takes a kidney stone to pass is 12 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N

b. Find the probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it.

c. Find the minimum number for the upper quarter of the time to pass a kidney stone.
days.

Answers

The probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it is 0.15866 , the minimum number for the upper quarter of the time to pass a kidney stone days is 14.4 .

What is Probability ?

Probability is the measure of likeliness of an event to happen

Let X denote the time to pass the kidney stone.

The random variable X follows normal Distribution

mean = 12 days days

standard deviation = 4 days

The distribution of X is X - N ( 12 , 4)

The probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it is

P ( X > 16) = 1 - P( X ≤ 16)

= 1 - P( Z ≤ (16-12)/4)

= 1 - P ( Z ≤ 1 )

= 1 - 0.84134

= 0.15866

P( X < x₀) = 0.75

[tex]\rm P ( \dfrac{x - \mu }{\sigma} < \dfrac{x_0 -13}{6}) = 0.75[/tex]

[tex]\rm \phi (\dfrac { x_o - 12}{4}) = 0.75[/tex]

Using the excel function the z score for the area 0.75 is

z - score = 0.6745

[tex]\rm \dfrac {x_o - 12}{4} = 0.6745[/tex]

x₀ = 0.6 * 4 + 12

x₀ = 14.4

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On Sunday, there were 22 inches of snow. The weather finally began to warm up and by Monday afternoon there were 19 inches. Then on Tuesday, there were 16 inches. If the snow continues to melt the same number of inches every day complete the equation to model the snowmelt if d represents the number of days after Sunday.

Answers

Answer:

22-3d=x

Step-by-step explanation:

where d is the days that it melts and the amount of snow x is the snow that is left.

Jacob spends 13/4 dollars to paint 9/3 square feet. Find the cost to paint a
square feet per dollar.

Answers

The cost to paint a is 12/13 square feet per dollar.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Jacob spends 13/4 dollars to paint 9/3 square feet.

[tex]\dfrac{\dfrac{9}{3}}{ \dfrac{ 13}{4}} = \dfrac{9}{3} \times \dfrac{ 4}{13}\\\\= \dfrac{ 36}{39}\\\\= \dfrac{ 12}{13}[/tex]

Hence, the cost to paint a is 12/13 square feet per dollar.

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find the measure of angle ACB

Answers

Answer:

angle ACB=45º

Step-by-step explanation:

angle 135º lies on a straight line

a straight line = 180º

thus, angle ACB= 180-135=45º

Rectangle LMNP is rotated, using the origin as the center of rotation, to form rectangle L’M’N’P’. What is the angle of rotation? On a coordinate plane, rectangle L M N P has points (negative 2, 5), (1, 5), (1, 4), (negative 2, 4). Rectangle L prime M prime N prime P prime has points (2, negative 5), (negative 1, negative 5), (negative 1, negative 4), (2, negative 4).

Answers

Answer: 180 degrees

Step-by-step explanation:

A rotation of 180 degrees about the origin maps [tex](x,y) \longrightarrow (-x, -y)[/tex].

Answer:

180

Step-by-step explanation:

took the test

Please help meeeeeeeeee

Answers

Answer:

a, b, d

Step-by-step explanation:

its one of those

Answer:

A, the first one

A piecewise function g(x) is represented by the graph.

Which functions represent a piece of the function? Select three options.

g(x) = −2x, −2 < x < 0
g(x) = −2, x < −2
g(x) = x − 2, −2 < x < 1
g(x) = −2x + 6, x ≥ 1
g(x) = + 1, –2 ≤ x < 1

Answers

For different function different results are shown below.

What is Function?

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

We have been given a graph of piecewise function. Using that we have to select the function from given choices which is represented by graph.

g(x) = −2x, −2 < x < 0

Answer:

NO. Because g(x) = −2x has negative slope so that means it goes downward also there is no y-intercept in g(x) = −2x but the only graph that has y-intercept in given graph goes upward so that can't be answer.

g(x) = −2, x < −2

Answer:

YES. Because g(x) = −2 is a horizontal line which is only on the left side of x=-2. Graph of this part is present in given graph. So yes it is answer.

g(x) = x − 2, −2 < x < 1

Answer:

NO. Because g(x) = x−2 has y-intercept at y=-2 and slope 1 so that means graph of g(x)= x-2 must be going upward and crossing at y=-2 but there is no such graph. Hence this can't be answer.

g(x) = −2x + 6, x ≥ 1

Answer:

YES. Because g(x) = −2x+6 satisfies the graph which is going downward.

g(x) = x/2+ 1, –2 ≤ x < 1

Answer:

YES. Because g(x) = x/2+ 1 satisfies the graph which is going downward.

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Answer: i think this is the answer sorry if i am wrong.

g(x) = −2, x < −2,

g(x) = −2x + 6, x ≥ 1,

g(x) = x/2 + 1, –2 ≤ x < 1

Step-by-step explanation:

Here is the graph

Flying against the jetstream, a jet travels 1710 miles in 3 hours. Flying with the jetstream, the same jet travels 5820 miles in 6 hours. What is the rate of the jet in still air and what is the rate of the jetstream

Answers

The rate of the jet against jetstream will be 570 miles per hour and the rate of the jet in still air will be 970 miles per hour.

What is speed?

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

Flying against the jetstream, a jet travels 1710 miles in 3 hours. Flying with the jetstream, the same jet travels 5820 miles in 6 hours.

The rate of the jet against the jetstream will be calculated as:-

V = [tex]\dfrac{1710}{3}[/tex] = 570 miles per hour

The rate of the jet in still air will be calculated as:-

V = [tex]\dfrac{5820}{6}[/tex] = 970 miles per hour.

Therefore the rate of the jet against jetstream will be 570 miles per hour and the rate of the jet in still air will be 970 miles per hour.

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Find equation in slope intercept form of the line passing through the points with given coordinates (-3,-4), (0,-3)

Answers

Answer:

Step-by-step explanation:

→ Find the gradient

( -3 --4 ) ÷ ( 0 --3) = 1/3

→ Write into format

y = 1/3x + c

→ Substitute in a coordinate pair

-3 = 0 + c

→ Solve for c

c = -3

→ Write into format

y = 1/3x - 3

Write an equation for the polynomial graphed below

Answers

The expression for the polynomial graphed will be y(x) = (x + 3)(x - 1 )(x - 4 ).

How to factor the polynomial?

From the graph, the zeros of the polynomial of given graph are:

x = -3

x = 1

x = 4

Equate the above equations to zero

x + 3 = 0

x - 1 = 0

x - 4 = 0

Multiply the equations

(x + 3)(x - 1 )(x - 4 ) = 0

Express as a function gives;

y = (x + 3)(x - 1 )(x - 4 )

Hence, the factored form of the polynomial will be y = (x + 3)(x - 1 )(x - 4 ) .