Do you always need three congruent corresponding parts to prove triangles congruent?

The trigonometric ratio is sin 10° = h/109

Which ratios in trigonometry are there?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). The branch of geometry known as trigonometry examines the sides and angles of a right-angled triangle.

What three types of trigonometry are there?

Three crucial trigonometric functions—sine, cosine, and tangent—are represented by the abbreviations sin, cos, and tan. tan

Given that :

Hypotenuse = 109 ft

Height = h

Hence sin = height / Hypotenuse

sin 10° = h/109

Learn more about trigonometric ratio

https://brainly.com/question/24349828

#SPJ1

Answer:

Let x=1

-5*x+8=y

-5*1+8=y

-5+8=y

3=y
Another

Let x=-1

-5*(-1)+8=y

5+8=y

13=y

There are multiple endings I suppose this is a point of intersection question that needs to be done on graph

Answer:

5 hours

Step-by-step explanation:

Time = 200÷40 = 5 hours.

The range of the graph is [-4, 11).

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.

In the given graph,

The value of the x coordinate varies from -8 to 11.

And the values of x shows the domain,

Therefore, domain is (-8, 11).

The y coordinate varies from -4 to 11.

And the values of y coordinate shows the range.

The value of y at 11 is open circle, So it shows open interval.

And at -4 it shows close interval.

So the range of the graph will be [-4, 11)

To know more about Graph on:

https://brainly.com/question/17267403

#SPJ1

a. The scatter diagram indicates that the Number of Defective Parts found increases with Line Speed

b. The regression model is Y = 27.5 - 0.3·X

c. When the line speed is 25 feet per minute, the number of expected defective parts is 20 defective parts.

According to the Question:

The give data is presented as follows'

Line Speed;                   20,   20,    30,    30,    40,    40,    50,     50

Number of Defective;   23,    21,     19,     16,     15,     17,     14,       11  

Now,

1. From the scatter diagram there is an apparent correlation between increase line speed and the number of defective parts found.

2. The equation for linear regression by the least squares method is presented as follows;

   Y = a + b·X

Where;

b = N ∑XY - (∑X) (∑Y) / N ∑X² - (∑X)²     -------------------- (1)

and

a = ∑Y - b ∑X / N                          ---------------------------- (2)

Now, after calculation, we have;

∑X = 280, ∑Y = 136, ∑X² = 10,800, ∑XY = 4,460, (∑X)² = 78,400, N = 8

Putting in equation (1) and (2), we get;

b = (8×4460 - 280×136) / (8×10,800 - 78,400) = -0.3

and,

a = (136 - (-0.3)×280)/8 = 27.5

Therefore, we have the linear regression as follows;

                 Y = 27.5 - 0.3·X

Therefore, when the line speed is 25 feet per minute, we have;

Y = 27.5 - 0.3 × 25 = 20

The number of defective parts expected to be found when the line speed is 25 feet per minute, Y = 20 defective parts.

Learn more about Scattered Diagram:

https://brainly.com/question/29120900

#SPJ4

Answer:

Both lines intersect at the point (2, 10)

See the attached image

The slope of the line which is perpendicular to the given line is (-6/5).

Describe the negative reciprocal.

The negative reciprocal of a number, let's say "n," is "- (1/n).

We are aware of a line's equation in slope intercept form, y = mx + b, as well as the fact that perpendicular lines have slopes that are reciprocal to each other's negative values.

The slope intercept form of the line 15x - 18y = -486 can be expressed as,

-18y = -15x - 486.

- y = (-15/18)x - (486/18).

- y = (-5/6)x - 27.

y = (5/6)x + 27.

The slope of the supplied line is (5/6), making the perpendicular line's slope (-6/5).

learn more about slope here :

brainly.com/question/3605446

#SPJ4

To find the actual size of an item, multiply the scale factor by the size of the item in the drawing

The scale factor is the ratio of the measurement of the new figure to the measurement of the original figure

Here, we are drawing an item on the paper, the size of the object on the paper maybe less than or greater than of original item

The dimensions of the actual item will be equal to the product of scale factor and the dimensions of the item on drawing.

If the scale factor is greater than 1, then the actual size will be greater than drawing, if the scale factor is between 0 to 1, then actual size will be less than drawing

Therefore, to find the actual size multiply the scale factor and size of drawing

Learn more about scale factor here

brainly.com/question/29464385

#SPJ4

The roots of the given equation are √5, - √5, 2i, and - 2i      

The values of a variable for which the provided polynomial equals zero are referred to as a polynomial's roots. If n is the root of a polynomial p(x), then p(n) will be equal to zero.

Here we have

x⁴- x²- 20 = 0  

To find the roots of the Equation factorize the given equation

=>  x⁴- x²- 20 = 0    

Let t = x²

=>  t²- t - 20 = 0  

Split the middle term

=> t²- 5t + 4t - 20 = 0  

=> t(t - 5) + 4(t - 5) = 0

=> (t - 5) (t + 4) = 0

=> (t - 5) = 0   and  (t + 4) = 0

Take t - 5 = 0

=>  t = 5  =>  x² = 5

=> x = ±√5          

Take (t + 4) = 0

=> t = - 4 => x² = -4

=> x = ± √- 4                  

=> x = ± 2i         [ ∵ - 1 = i² ]

Therefore,

The roots of the given equation are √5, - √5, 2i, and - 2i                    

Learn more about the Roots of a polynomial at

https://brainly.com/question/29491359

#SPJ1

The correct interpretation regarding the y-intercept of the least squares regression line is given as follows:

For a car weighing 0 lbs we would expect a fuel efficiency rating of 68.17 mpg.

For a function, the y-intercept represents the value assumed by the output of the function when the input of the function assumes a value of zero.

For the least squares regression line in this problem, the input variable and the output variable are defined as follows:

The y-intercept in this problem has a value of:

68.17.

Meaning that when the weight is of 0 pounds, the fuel efficiency is of 68.17 mpg.

The missing part of the problem is of:

"For this data set, X represents the weight of each car in hundreds of pounds, and Y represents the predicted fuel efficiency of each car in miles per gallon (mpg). Note that 68.17 is reasonable value for the y-intercept of the least squares regression line. Which of the following is the most appropriate interpretation of the y-intercept?"

More can be learned about the y-intercept of a function at https://brainly.com/question/24363347

#SPJ1

The smallest and largest possible range in the histogram summarizes the percentage of people in each state and the District of Columbia who identify as Hispanic or Latino is 0 - 4.9 and 45 - 49.9 respectively.

As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

The histogram summarizes the percentage of people in each state and the District of Columbia who identify as Hispanic or Latino,

The Hispanic or Latino percentage of the population is shown in the x-axis, whereas the frequency of the population is shown in the y-axis.

Calculate the smallest possible range by considering the graph,

The smallest possible range = 0 - 4.9

Calculate the largest possible range by considering the graph,

The largest possible range = 45 - 49.9

To know more about percentages:

https://brainly.com/question/26080842

#SPJ1

Answer:

skewed right

Step-by-step explanation:

I am not sure about the numbers, but it's skewed right i had the same question

Answer:

a) The factored form of the function Hs= -16s2+96s is Hs = -16(s-3)(s-2).

b) The two factors in the factored form of the function, -16(s-3)(s-2), represent the maximum height of the baseball and the time at which the baseball reaches its maximum height. The first factor, -16, represents the maximum height of the baseball, since a negative value multiplied by the product of two positive values will always be negative. The second factor, (s-3)(s-2), represents the time at which the baseball reaches

or

a) Hs = (-16s + 48)(s - 2)

b) The factor (-16s + 48) represents the initial height of the baseball when it is hit, and the factor (s - 2) represents the time it takes for the baseball to reach its maximum height.

Answer:

Step-by-step explanation:

x-y=-6          (1)..

6x-3y=9       (2)...

First, multiply (1) by 6:

6x-6y=-36

Now subtract the whole eqaution:

 6x-6y=-36

- 6x-3y=9

----------------------

-3y = -45

y=15

Now substitute y into one of the equations:

x-15=-6

x=9

So the answer is x=9, and y=15.

The answer to this Question based on Length is Yes he can easily make a bow with that

What is Length?

Length is a measurement of distance or size. It is the greatest of the three linear dimensions and is often denoted by the letter “L”. Length is commonly used to measure the size of objects, the distance between two points, or the magnitude of a displacement. Length can be measured in a variety of units such as inches, feet, meters, kilometers, or miles. Length is also used to determine the area of a two-dimensional shape, the volume of a three-dimensional shape, and the circumference of a circle. Length is an important concept in mathematics, physics, engineering, and other scientific disciplines. Length can also be used to describe how long something lasts, such as the length of a movie or a song.

we can see that length of henry ribbon that is available is 6 1/4 feet long ribbon which means 25/4 feet ribbon
= 6.25 feet of ribbon
whereas length of ribbon he needs is 1 1/12 feet ribbon to make a bow which is equal to

13/12 = 1.08 feet ribbon and he has 6.25 feet available hence he can easily make a bow with that

To learn more about Length:

https://brainly.com/question/8552546

#SPJ1

The possible outputs of the function for different values of [x] are given below.

Given is the following function -

h(x) = 32x - 1

We can write the output for the given function as -

[x]            h(x) = 32x - 1                   h(x)                             

1               {32 x 1 - 1 = 31}                   31

2              {32 x 2 - 1 = 63}                 63  

3              {32 x 3 - 1 = 95}                 95

4              {32 x 4 - 1 = 127}                127

Therefore, the possible outputs of the function for different values of [x] are given above.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ1

Answer: X = -12

Step-by-step explanation:

-4x-16=32

We move all terms to the left:

-4x-16-(32)=0

We add all the numbers together, and all the variables

-4x-48=0

We move all terms containing x to the left, all other terms to the right

-4x=48

x=48/-4

x=-12

Answer:

x=12

Step-by-step explanation:

Given,

4x-16=32

4x=32+16(We transpose LHS to RHS)

4x=48

x=48/4

x=12

Hence, the answer is 12

Answer:

y = 2x + 7

Step-by-step explanation:

Use the formula y - y1 = m(x - x1)

Step-by-step explanation:

formula =y-y1=m(x-x1)

a group of nine people are attending the movies together . now 40320 ways can the nine be seated together in a row by combination.

(a) The two people who insist on sitting side-by-side can be seated in 1 way. The remaining 7 people can be seated in 7! ways. Therefore, the total number of ways in which the 9 people can be seated together in a row is 1 x 7! = 40320.

(b) In this case, the two people who do not like each other can be seated in (7-1)! ways. The remaining 7 people can be seated in 7! ways. Therefore, the total number of ways in which the 9 people can be seated together in a row by combination is (7-1)! x 7! = 40320.

Learn more about combination here

https://brainly.com/question/28720645

#SPJ4

The interval is [4, 6], and the compound inequality is 2 ≤ x < 5 as indicated on the number line.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign.

It is an illustration of inequity.

This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

So, the blue line runs from 12 and then to 5.

The solid dot at position 2 denotes inclusion, whereas the hollow dot at position 5 denotes exclusion.

Now,

x  ≥ 2 and x < 5

Combine:
2 ≤ x < 5

Therefore, the interval is [4, 6], and the compound inequality is 2 ≤ x < 5 as indicated on the number line.

Know more about inequality here:

https://brainly.com/question/28964520

#SPJ1

Answer:

Step-by-step explanation:

6x^2-2x+1=0

6*6=36

36x-2x+1=0

34x+1=0

subtract 1 on both sides

34x=-1

divide both sides by 34

x=-0.0294117647059

Answer:

46

Step-by-step explanation:

because it is ...... maybe

Answer:

5.2 or 5:12

Step-by-step explanation:

1.3*4 = 5.2 or 5:12. That's a pretty fast mile.

Assume that you have laid out the namecards for 14 people, and you want to hide 4 golden tickets, at most one under each namecard. The total number of ways = 784

From the question, we have

The total number of people in each party = 8

The total number of winners in each party = 2

The total number of ways of selecting two winners from 8 people  = P(8,2) = 28

The total number of ways of selecting two winners from each political party = 28*28 = 784

The total number of ways = 784

Multiplication:

To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly.

The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.

Complete question:

In celebration of Chinese new year, you are arranging name cards for 16 people to sit around this table. Since the cards are placed on the rotating lazy Susan, the specific chair of a guest does not matter, only who is to their left and right. That is, two namecard arrangements are considered different iff there is a guest whose person on their right or left changes. Now when you hide four golden tickets under the placed name cards, you want to ensure that each party has two winners. In how many ways can you choose to do so?

To learn more about multiplication visit: https://brainly.com/question/5992872

#SPJ4

Answer:

Step-by-step explanation:

the second one

By using the concept of probability, it can be calculated that

Probability that the hand contains exactly two face cards = [tex]\frac{209}{833}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

From the set of five cards, two cards can be chosen in [tex]{5 \choose 2}[/tex] ways = 10 ways

Number of face cards = 12

Number of non face cards = 52 - 12 = 40

Probability that the hand contains exactly two face cards = [tex]{5 \choose 2}\times \frac{12}{52} \times \frac {11}{51} \times \frac{40}{50} \times\frac{39}{49}\times \frac{38}{48}\\[/tex]

[tex]\frac{209}{833}[/tex]

To learn more about probability, refer to the link-

https://brainly.com/question/24756209

#SPJ1

The completed relative frequency table is given by the image shown at the end of the answer.

First we look at the row total of people who like to fly, which is of 70%, hence:

Amount those who can drive, we have that:

Amount those who cannot drive, we have that:

Thus the total frequency of the second row is given as follows:

0.17 + 0.13 = 0.30.

The table is given by the image shown at the end of the answer. I don't know if the values are the same but you will have to follow the same procedure to obtain the missing values.

More can be learned about relative frequency at https://brainly.com/question/1809498

#SPJ1

Answer:

I took the test

the answer is in the image below

Step-by-step explanation:

Answer: y= -8x + 9.5

Step-by-step explanation:

The equation for slope intercept form is y=mx+b

b is the y-intercept; we see that it is located at (0, 9.5), so b is 9.5

The slope is rise/run

We see that the y decrease by 8 and x increases by 1, so the slope is -8/1

So the answer is y= -8x + 9.5