Which side is opposite of 30 in a 30 − 60 − 90 triangle?

Step-by-step explanation:

Pythagoras :

c² = a² + b²

the only problem : we don't know which one of the 3 expressions is the longest side (= c = Hypotenuse).

let's try with 8x -21

(8x - 21)² = (3x - 7)² + (6x)²

64x² - 336x + 441 = 9x² - 42x + 49 + 36x²

19x² - 294x + 392 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 19

b = -294

c = 392

x = (294 ± sqrt(86436 - 4×19×392))/(2×19) =

= (294 ± sqrt(56644))/38 =

= (294 ± 238)/38

x1 = (294 + 238)/38 = 532/38 = 14

x2 = (294 - 238)/38 = 56/38 = 28/19 = 1.473684211...

I assume, we are looking for a whole number solution.

so, x = 14 is the solution.

Using the Fundamental Counting Theorem, the sample size of these outcomes is of 12.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering the number of options for Entree, Side and Drink, the parameters are:

n1 = 3, n2 = 2, n3 = 2.

Hence the sample size of outcomes is:

N = 3 x 2 x 2 = 12.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

#SPJ1

The equation that runs through the location (4,-6) has the slope-intercept form,  [tex]y=-\frac{3}{4}x-3[/tex] .

A line's equation written in the slope-intercept form:

y=mx+b

where m= slope & b= y-intercept

The slope of two parallel lines is equal.

Currently, we know the line's equation:

[tex]y=-\frac{3}{4} x-5[/tex]

here, slope, m= [tex]-\frac{3}{4}[/tex]

A line equation is created by adding the slope's value and the point's coordinates (4, -6):

[tex]-6=-\frac{3}{4}(4)+b[/tex]

⇒ -6=-3 +b [adding 3 to both sides]

⇒-3=b

⇒b= -3

Hence the solution is  [tex]y=-\frac{3}{4}x-3[/tex] .

Learn more about slope-intercept form here:

https://brainly.com/question/9682526

#SPJ4

Answer:

D. {-2, -3, 12, 8, 4, −5}

Step-by-step explanation:

The domain is the set of x coordinates, so the answer is {-2, -3, 12, 8, 4, −5}.

Answer:

C

Step-by-step explanation:

There are 6 outcomes and you are seeking 2 of them.  

2/6 or 1/3 1:3

Answer:

2nd, 3rd, and 6th option are correct

Step-by-step explanation:

using a²+b²=c² those are the obly that meet the criteria (im pretty sure)

In the given triangle equations AC² = AB² + BC², AB² = AD² + BD² and BC² = CD² + BD² are true.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.

Given that,

ABC is a right angle triangle.

And BD is perpendicular to AC.

To show the equations which are true,

Use Pythagorean theorem,

(Hypotenuse)² = (base)² + (height)²

In triangle ABC,

AC² = AB² + BC²

In triangle ABD,

(AB)² = AD² + BD²

And in triangle BCD,

BC² = CD² + BD²

Therefore, option (2), (3) and (6) are correct.

To know more about Triangle on :

https://brainly.com/question/2773823

#SPJ2

i. Line BD = 6√2 cm

ii. Perimeter = 3 (π + 4) cm

iii. Area = 18 ( π - 2) cm

Let the length of BD = x

Since B is the midpoint of the arc AC, then ∠BOC = 15°

In ΔBDB

Let's use the trigonometric ration, tan

[tex]Tan 45 = \frac{BD}{CD}[/tex]

CD = x

Then, using the Pythagorean theorem

[tex]x^2 + x^2 = 12^2[/tex]

[tex]2x^2 = 144[/tex]

[tex]x^2 = \frac{144}{2}[/tex]

[tex]x = \sqrt{72}[/tex]

[tex]x = \sqrt{36 *2}[/tex]

[tex]x = 6\sqrt{2}[/tex]

Thus, line BD is [tex]6\sqrt{2}[/tex] cm

ii. Perimeter = BC + BD + CD

= 2πr/8 + x + r -  x

= π(12)/4 + r

= 3π + 12

= 3 ( π + 4) cm

iii. Area of shaded area = Area of BOC + Area of BOD

⇒ πr^2/8 × 1/2x^2

= π144/8 × 1/2(72)

= 18π - 36

= 18 ( π - 2) cm²

Learn more about quadrant of a circle here:

https://brainly.in/question/1591300

#SPJ1

The algebraic expression for: the sum of a number and 5 decreased by twice the number is (n + 5) - 2n

let

sum of a number and 5

= n + 5

decreased by twice the number

= -2(n)

= - 2n

sum of a number and 5 decreased by twice the number

= (n + 5) - 2n

= n + 5 - 2n

= 5 - n

Therefore, the algebraic expression which can be used to represent; the sum of a number and 5 decreased by twice the number is (n + 5) - 2n

Learn more about algebra:

https://brainly.com/question/4344214

#SPJ1

The system of equations that can be used to find the lengths of the legs of the sun shade is given as follows:

y = 0.5x², y = 64.

The system of equations is obtained considering the equation for the area of a right triangle, which is given by half the multiplication of the legs.

In this problem, we have an isosceles right triangle, meaning that both legs have the same measure.

The area of the right triangle is of 64 feet, hence the area is calculated as follows:

0.5x² = 64.

Thus the equations that compose the system are:

Meaning that the second option is correct.

The options are given by the image shown at the end of the answer.

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Assuming all the fishes caught by Bridget and her dad have the same total weight, then the first fish Bridget caught would weigh 5 ounces while the first fish caught by her dad weighed 17 ounces.

Weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Also, the weight of a physical object (body) is typically measured in Newton or ounces.

First of all, we would determine the weight of all of the fishes caught by both Bridget and her father (dad) while translating the word problem into an algebraic equation as follows:

For Bridget, we have:

Bridget's fish = f + 2f + 3f + 2 + ½f + ⅗f

Bridget's fish = 7 f/10 + 2      ......equation 1.

For her dad, we have:

Dad's fish = 3f + 2 + ⅘f + 2f + 4 + ½f

Dad's fish = 6 3f/10 + 6            ......equation 2.

Equating eqn. 1 and eqn. 2, we have:

7 f/10 + 2 = 6 3f/10 + 6

7 f/10 - 6 3f/10 = 6 - 2

8f/10 = 4

8f = 40

f = 40/8

Bridget, f = 5 fishes.

Since her dad's fish weighed 2 more than 3 times, we have:

Dad = 3f + 2

Dad = 3(5) + 2

Dad = 15 +2

Dad = 17 ounces.

In conclusion, the first fish Bridget caught would weigh 5 ounces while the first fish caught by her dad weighed 17 ounces assuming all the fishes caught by Bridget and her dad have the same total weight.

Read more on word problems here: brainly.com/question/13170908

#SPJ1

Complete Question:

Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was 2 times the weight of the first fish, another was 2 more than 3 times the weight of the first fish, the next was 1/2 the weight of the first fish, and the last was 3/5 the weight of the first fish. Bridget’s dad caught four fish. The first fish he caught weighed 2 more than 3 times the weight of the first fish caught that day. One fish weighed 4/5 the weight of the first fish caught that day, one weighed 4 more than 2 times the weight of the first fish caught that day, and the last weighed 1/2 the weight of the first fish caught that day.

If all the fish Bridget caught have the same total weight as all the fish her dad caught, then the first fish Bridget caught weighed___ ounces and the first fish her dad caught___ weighed ounces.

Expression which is equivalent to [tex]$\sqrt{8 x^{7} y^{8}}[/tex] is [tex]$=2 \sqrt{2} x^{3} y^{4} \sqrt{x}$[/tex].

What are equivalent expressions?

Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

Solution of the given equation [tex]$\sqrt{8 x^{7} y^{8}}[/tex].

      [tex]$\sqrt{8 x^{7} y^{8}}=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]

                    [tex]$=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]

Simplify [tex]$\sqrt{x^{7}}: x^{3} \sqrt{x}$[/tex]

                     [tex]$=\sqrt{8} x^{3} \sqrt{x} \sqrt{y^{8}}$[/tex]

Simplify [tex]$\sqrt{y^{8}}: y^{4}$[/tex]

                     [tex]$=\sqrt{8} x^{3} \sqrt{x} y^{4}$[/tex]

                [tex]$\sqrt{8}=2 \sqrt{2}$[/tex]

                     [tex]$=2 \sqrt{2} x^{3} \sqrt{x} y^{4}$[/tex]

To know more about equivalent expressions visit:

https://brainly.com/question/17102319

#SPJ4

The complete question is :

Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0. x y squared StartRoot 8 x cubed EndRoot 2 x cubed y cubed StartRoot x y squared EndRoot 2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot 4 x cubed y Superscript 4 Baseline StartRoot x EndRoot

The solution and extraneous solution of the equation as given are; x=7 and x=-2 respectively.

It follows that the equation given is;

(3/(x²+5x+6)) + ((x-1)/(x+2)) = 7/(x+3)

Hence, by multiplying both sides by (x²+5x+6); we have;

3 + x² +2x -3 = 7x + 14.

x²-5x -14 = 0

On this note, the solutions of the quadratic equation are; x =7 and x=-2.

It therefore follows that x= 7 is a solution while x=-2 is an extraneous solution because it renders (x-1)/(x+2) undefined.

Read more on extraneous solution;

https://brainly.com/question/26218294

#SPJ1

Answer:

x=7  

x=-2

Step-by-step explanation:

If Aaron is designing a party game in which he needs exactly 24 possible outcomes, then he can use the following sets of actions to have a statistically fair game from the Statistics point  of view,

Toss a coin twice, and then then roll a 6-sided number cube.

How can he play a statistically fair game to get exactly 24 outcomes?

The game has 24 alternative outcomes, as far as we know. The next step is to identify a series of activities that produces 24 distinct outcomes with equal probabilities.

The first of the alternatives is the only one with a sample space of 24 elements.

Flip two coins, then roll a D6.

The results of each coin toss are 2:  (tails and heads).

There are 6 outcomes for the D6: (1, 2, 3, 4, 5, 6)

The combined outcomes of the two throws and rolling the number are then given by the product between the numbers of outcomes for each individual part, as solved below:

C = 2 × 2 × 6

C = 24

Thus, by tossing a coin twice, and then then rolling a 6-sided number cube, Aron can play a statistically fair game if h needs exactly 24 outcomes.

Learn more about outcomes here:

https://brainly.com/question/9222927

#SPJ1

Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

In this problem:

Her initial balance is of $300, hence . A(0)=300

The growth rate is of 15%, hence R =0.15

Then,

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\[/tex]

It will reach $450 after t years, for which A(t) = 450, hence:

[tex]A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9[/tex]

It will take about 2.9 years for Emma's balance to reach $450

Learn more about logarithm here

https://brainly.com/question/247340

#SPJ4 .

Answer:

53.7

Step-by-step explanation:

The area of the rectangular base is 7(2.3)=16.1.

So, the total volume is (1/3)(16.1)(10), which is about 53.7

$1799.10

Each year, the amount of money in the account is increased by 8%. This is the same as multiplying by 1.08 each year.

For 10 years, you multiply the original $100,000 by 1.08 a total of 10 times.

This tends to be simplified to:

[tex]100,000 * 1.08^{10}[/tex]

This gives $215892.4997.

This is paid back over 10 years, which is 10 x 12 months, or 120 months.

Divide the $215892.4997 by 120 to get the monthly payment of:

$1799.10 (round to 2 decimal places as it is a currency)

The rational function represented in the given graph is; f(x) = 1/(x - 4)

From the given graph , the vertical asymptote is at x = 4

Let's find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator = 0

A) x + 4 = 0

x = -4

This is not correct

B) 4x = 0

x = 0

Not correct

C) Denominator does not have a variable and so is also incorrect

D) x - 4 = 0

x = 4

Thus, this is correct

Read more about Asymptotes Function at; https://brainly.com/question/16995471

#SPJ1

One accurate statement amount Arab Americans is that b. Arab Americans include both Muslims and Christians.

Arab Muslims are known to include both Muslims and Christians and indeed it is estimated that more Arab Americans are Christians as opposed to Muslims.

They are also quite urbanized and have very high rates of education which has given then access to more income.

Options for this question include:

a. Arab Americans are not urbanized.

b. Arab Americans include both Muslims and Christians.

c. Arab Americans rank relatively low in terms of income and occupation

d. Arab Americans tend to have low levels of education and skills.

Find out more on Arab Americans at https://brainly.com/question/27190720

#SPJ1

The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

According to the statement

we have to give the terms which explain the sin (pi/3) perfectly.

And we have choose these terms from the these below written conditions like From Right Triangle, Hypotenuse, and unit circle.

And Now we explain all terms below

So,

"Right Triangle is a triangle whose one of the angle measures 90° "

And "The hypotenuse is a longest side of the right triangle.

And"Unit Circle is a circle with radius 1."

For given question,

We have been  given a unit circle.

So, We need to find the sin (pi/3)

We know, in a right triangle for any angle , θ

Sinθ = Opposite side of angle / Hypotenuse

So, for , Sin(pi/3) = Opposite side of angle / 1

Sin(pi/3) = Opposite side of angle

Therefore, The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

Learn more about Trigonometry here https://brainly.com/question/8120556

#SPJ4

The value of the given expression (a + b/2)/a - bx² = 219.5/(76 - 287x²).

An expression is the combination of variables, coefficients, and constants that are separated by an arithmetic operator(+, -, ...).

The given expression is

(a + b/2)/a - bx²

It is given that a = 76 and b = 287

On substituting,

(a + b/2)/a - bx² = (76 + 287/2)/76 - 287x²

⇒ (76 + 143.5)/76 - 287x²

⇒ 219.5/(76 - 287x²)

Therefore, the given expression for the values a = 76 and b = 287 is 219.5/(76 - 287x²).

Learn more about an expression here:

https://brainly.com/question/723406

#SPJ1

Answer:

Step-by-step explanation:

Factors

(b)/(7.8)=-2.15

Multiply each term in the equation by 7.8.

(b)/(7.8)*7.8=-2.15*7.8

Cancel the common factor of (1)/(7.8).

1b=-2.15*7.8

Multiply -2.15 by 7.8 to get -16.77.

1b=-16.77

Divide each term in the equation by 1.

(1b)/(1)=-(16.77)/(1)

Cancel the common factor of 1.

b=-(16.77)/(1)

Divide -16.77 by 1 to get -16.77.

b=-16.77

#SPJ10

Answer:

((24+13)/28.5

Step-by-step explanation:

The expression that shows the amount of money in dollars that Maggie has d - 3

An equation is an expression that shows the relationship between two or more numbers and variables.

Let d represent the amount of money Ron has on Tuesday. Hence:

Money Maggie has = d - 9 + 6 = d - 3

The expression that shows the amount of money in dollars that Maggie has d - 3

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

Find lower quartile first: 1/4 (61)th term which equals to 15.25th term. Use your graph to estimate where 15.25 is and draw a line till it meets tne curve. As soon as it touch the curve, continue the line downward and you'll get LQ in kg. Secondly, find upper quartile: 3/4(61)th term which equals to 45.75th term. Proceed the same thing I mentioned above for lower quartile. Then the formula for interquartile range is upper quartile minus lower quartile and you'll get the answer in kg.

The second bus is traveling at a speed of 33.3 miles per hour.

Given that the speed of first bus is 60 miles per hour , distance between both the buses is 700 miles after 8 hour.

We are required to find the speed of second car which is heading towards south.

If first car is travelling at a speed of 60 miles per hour then the distance of first car after 8 hours is 60*8=480 miles.

We have been given that the distance between both the cars after 8 hours is 700 miles,So,

Distance of second car after 8 hours=700-480=220 miles.

We know that the speed is equal to distance divided by time.

We know that we have calculated distance after 8 hours so the speed of second car will be =20/6

=33.3 miles per hour

Hence the speed of second car which is heading towards south is 33.3 miles per hour.

Learn more about speed at https://brainly.com/question/4931057

#SPJ1

The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

Read more about tree diagram at:

brainly.com/question/13311154

#SPJ1

The joint relative frequency is 21%.

Joint relative frequency can be described as the ratio of the frequency of data in a certain category to the total number of data points in that category.

The joint relative frequency for teachers who teach math and not English = number of teachers who teach maths and not English / total number of teachers

(22 / 104) x 100 = 21%

Please find attached the full question. To learn more about joint relative frequency, please check: https://brainly.com/question/9565792

#SPJ1

The expression that is not a rational expression is:

[tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex]

A rational expression is an expression that has a variable in the denominator.

For expression [tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex], x + 3 is a common term to the numerator and denominator, hence it is simplified to 2x - 1 and is not a rational expression.

More can be learned about rational expressions at https://brainly.com/question/2264785

#SPJ1

The option that is not a rational expression is [tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]

Rational expression are fraction whose numerator and denominator are polynomials.

In other words, rational expression is the ratio of two polynomials.

Therefore, an example of a ration expression is as follows:

[tex]\frac{x^{2}+9 }{x + 1}[/tex]

Therefore, the option that is not a rational expression is as follows;

[tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]

learn more on rational expression here: https://brainly.com/question/17134322

#SPJ1

Answer:

-3

Step-by-step explanation:

So just like the picture provides, the slope can be defined as: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex]. So this means we can take any two points and find the change in x and y to define the slope, since the slope is constant throughout the entire line, since it's a linear line, meaning it's straight.

So you can use the points (0, 15) and (2, 9). So let's look at the x-values, and you want to make sure, you maintain the order at which you look at the  "change in x", for example I can define the change in x through the two points as 0 to 2, or 2 to 0, one case is 2, and the other is -2, but if I look at the change from 0 to 2, then I looked at the first point first then the second, this means when looking at the y-values I have to find the change from 15 to 9, and not 9 to 15, since I did 0 to 2 in the first case. I could look at the change from 9 to 15, but only if I looked at the changed from 2 to 0.

Anyways let's find the change from 0 to 2, it's 2. Now let's look at the change from 15 to 9, it's -6 (since the value went down). So this gives us equation: -6 / 2 = -3

The slope is -3