please help look at picture

Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

to find k use any ordered pair from the table

using (2, 4 ) , then

4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

16 = k

y = [tex]\frac{16}{x^2}[/tex] ← equation of variation

(b)

when y = 25 , that is

25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )

25x² = 16 ( divide both sides by 25 )

x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]

the positive value of x is then [tex]\frac{4}{5}[/tex]

Answer:

10

Step-by-step explanation:

(2w + 4) - (2w - 6)

2w + 4 - 2w + 6

2w - 2w + 4 + 6

10

I hope this helps!

From the properties of a right triangle is found that the missing length x= [tex]5\sqrt{3}[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) .

The sum of the internal angles of a right triangle also is equal to 180°.

The question gives a figure which is compound for two right triangles.

For each triangle is informed two angles, then:

       45+90+ x = 180

       135 + x =180

        x=180-135

        x=45°

       60+90+ y = 180

       150+ y =180

        y=180-150

        y=30°

Thus, the angles for the given triangle are:

From the trigonometric ratio sinФ, you can find the hypotenuse the triangle 2. See below.

[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 45 =\frac{hypotenuse \ triangle 2 }{hypotenuse \ triangle 1} \\ \\ \frac{\sqrt{2} }{2}=\frac{hypotenuse \ triangle 2 }{10\sqrt{2} }\\ \\ 2*hypotenuse \ triangle 2 = 10*2\\ \\ hypotenuse \ triangle 2 = \frac{10*2}{2} \\ \\ hypotenuse \ triangle 2 =10[/tex]

If the hypotenuse of triangle 2 is 10, you can apply again the trigonometric ratio sinФ for finding x

[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 60=\frac{x }{hypotenuse \ triangle 2} \\ \\ \frac{\sqrt{3} }{2}=\frac{x }{10}\\ \\2x=10 \sqrt3\\ \\ x=5\sqrt3[/tex]

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

Answer: C. (2, 1)

Step-by-step explanation:

The numbers labeled are

(-5, -8)

(-2, 1)

(4, 0)

(2, 9)

Find coordinates by looking at each line. (x, y)

The x-axis is the horizontal line in the middle.

The y-axis is the vertical line going across.

The x-axis always goes first when plotting down coordinates, and y goes second.

So, the one NOT labeled is C (2, 1)

Answer:717 calories

Step-by-step explanation:

first you need to find what one ounce would be:

430/12=35.83...

then you multiply the answer by 20

35.83*20=716.6...=717

The equation that could be used to solve for the time t in hours that she drove before her stop is 80t + 100(8/3 - t) = 250.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let t = time she drove before her stop

If the total trip time is 3 hours including the stop, which took 20 minutes, then the time she drove after the stop is 3 - t - 1/3 or 8/3 - t.

If altogether she drove a distance of 250 km, then the sum of the products of the rate of speed and time each drive is equal to 250.

(80 km/h)(t) + (100 km/h)(8/3 - t) = 250

Simplify the equation.

80t + 100(8/3 - t) = 250

Learn more about equation here: brainly.com/question/3927786

#SPJ4

Answer:

Step-by-step explanation:

Ok;

1. Area is base times height.

Here shown, the base is 18cm and the height is 11cm. Don't be fooled by the 14cm for it is just the leg of a triangle not full height!!

18*11=198cm^2

2. Divide by two. We just caculated the area of the rectangle. Now we know a triangle is half of a rectangle's area so divide by 2!

198/2= 98cm^2

A 12-ounce can of beer contains the same amount of alcohol as a five-ounce glass of wine.

In a five-ounce glass of wine, the percentage of alcohol is 12%, which is the same in the 12-ounce can or bottle of beer, and 1.5 ounces of 86-proof liquor. Although a person under the influence of alcohol will have impaired judgment and therefore must avoid driving, doesn't matter what kind of alcoholic beverage they drink. Digestion of alcohol doesn't take place as soon as you drink it, it is absorbed in your bloodstream which reaches the brain and thus creates impaired judgment.

To learn more about fluids and their concentrations,

https://brainly.com/question/19961339

#SPJ4

Answer:

Step-by-step explanation:

     I am going to transform this equation into slope-intercept form, as it is usually easier to graph it that way.

  Given:

-8 + x = 4y - 16

  Add 16 to both sides of the equation:

-8 + x + 16 = 4y

  Divide both sides of the equation by 4:

-2 + [tex]\frac{1}{4}[/tex]x + 4 = y

  Reflexive property and combine like terms:

y = [tex]\frac{1}{4}[/tex]x + 2

  Now, we will graph. The 2 is our y-intercept and the  [tex]\frac{1}{4}[/tex] is our slope, graphed as "rise over run." This means we will rise one unit up and run four units right.

      See attached.

The triangle does not exist, as the property, the sum of two sides of a triangle is greater than the third side length of the triangle does not hold true.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric forms is represented by the symbol △ and consists of three connected vertices. Triangles may be categorized into a number of different varieties according to their sides and angles.

It is a triangle's property that the sum of any two sides of a triangle is greater than the third side.

Here sides given are 3 m, 5 m, 9 m.

Let us add the sides length 3 m and 5 m

3 m + 5 m = 8 m

Compare this with the third-side length of the triangle

8 m < 9 m

So, the property does not hold true.

So, the triangle does not exist.

To know more about triangles, visit:

https://brainly.com/question/2773823

#SPJ1

The expression that is equivalent is y(x + 2) and xy + 2y and x(x + y + 2) and  x² + xy + 2x

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

y(x + 2) and xy + 2y

xy + 2y and xy + 2y

Therefore, the expressions are equivalent.

x(x + y + 2) and  x² + xy + 2x

x² + xy + 2x and x² + xy + 2x

They are equivalent expression.

learn more on equivalent expression here: https://brainly.com/question/27911936

#SPJ1

The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.

What is least common denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Given fractions are

2/3 and 8/11

L.C.M of 3 and 11 is 33.

We get,

2/3 ×11/11 = 22/33

and

8/11×3/3 = 24/33

To know more about least common denominator, visit:

https://brainly.com/question/4911096

#SPJ13

8.08 percent of babies are born prematurely .

We have following information,

lengths of pregnancy of humans are Normally distributed.

mean of distribution ( μ ) = 268 days

standard deviations of distribution = 15 days

We shall find out the pecent of babies are born. prematurely.

Using the Normal distribution formula ,

Z = ( X - μ ) /σ

where X---> sample mean

μ --> poplution mean

putting the possble values of variables we get,

if a baby born three weaks early then he is considered as premature.

X = 21 , μ = 268 , r =

Z = ( 21-268)/ 15 = - 247/15 = - 16.4

Now, p-value corresponding to Z-value= -16.4 is

8.08..

thus for z= -16.4 , p-value will be 8.08 .. So, 8.08 percent of babies are born prematurely.

To learn more about Normal distribution, refer :

https://brainly.com/question/28059926

#SPJ4

The measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

According to the question,

We have the following information:

We have a figure where angle MCJ is 130°.

Now, we can extend the two given lines as imaginary lines. After extending the lines, we will find that these lines are parallel and the lines are being cut by another line.

We know that in this case the alternate interior opposite angles are equal and the sum of consecutive alternate interior angles is 180°.

Now, ∠MCJ and ∠CMB are alternate interior opposite angles and thus they are equal.

Hence, the measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

To know more about alternate interior opposite angles here

https://brainly.com/question/17679982

#SPJ1

The value of the algebraic expression 2/5g + 3h - 6 if evaluated when g = 10 and h = 6 is 16.

2/5g + 3h - 6

When g = 10 and h = 6

2/5g + 3h - 6

2/5(10) + 3(6) - 6

20/5 + 18 - 6

4 + 18 - 6

16

In conclusion, the value of the expression 2/5g + 3h - 6 when evaluated is given by 16

Complete question:

Evaluate 2/5g + 2h - 6 start fraction, 2, divided by, 5, end fraction, g, plus, 3, h, minus, 6 when g=10 g, equals, 10 and h=6 h, equals, 6

Read more on algebraic expression:

https://brainly.com/question/15280356

#SPJ1

Answer:

1200

Step-by-step explanation:

1,500-300=1200

The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

a)

The given condition makes a right-angle triangle as shown below,

The tan function,

tanθ = 6/25

θ = 14.50°

b)

When a player is 5 feet closer means (20 feet far)

tanθ = 6/20

θ = 16.70°

c)

As the player gets closer the angle becomes more and more.

Hence "The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases".

For more information about the trigonometric function,

https://brainly.com/question/14746686

#SPJ1

It will take 6 days for the sister to earn as much as the brother.

Two or more expressions with an equal sign are defined as an equation.

Given that, the sister earns $30 per day and pays a $60 license fee and the brother earns$20 per day.

The income of the sister in x days is:

30x - 60

The income of the brother in x days is:

20x

The income of the sister and the brother is equal when:

30x - 60 = 20x

30x - 20x = 60

10x = 60

x = 6

Hence, It will take 6 days for the sister to earn as much as the brother.

Learn more about equations here:

https://brainly.com/question/10413253

#SPJ1

An example of experiment is B. Researchers working for a company test their new sneaker design to see if it helps athletes run faster.

An experiment simply means a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. It should be noted that experiments provide insight into cause-and-effect as they demonstrate what outcome occurs when a particular factor is manipulated

Experiments have a vital place in the development of science because experiments are used to test the reality of a thought, an axiom, or a phenomenon with a theoretical basis and to turn it into a law or a theorem.

In this case, testing the new sneakers is an experiment.

Learn more about experiments on:

https://brainly.com/question/17274244

#SPJ1

Answer:

11.6666666 (infinitely)

Answer:

c = 11.46 yd

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ c² = (8.1)² + (8.1)²

→ c² = 65.61 + 65.61

→ c² = 131.22

→ c = √131.22

→ [ c = 11.46 yd ]

Hence, value of c is 11.46 yd.

The answer is 6 groups of 0.7 tenths is 4.2. in the decimal form.

What is Decimals?

Decimals are a form of a number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

6 groups of ____ tenths is 4.2

4.2 ÷ 6 = 0.7

Hence,  6 groups of 0.7 tenths is 4.2

Learn more about Decimals, by the following link.

https://brainly.com/question/1827193

#SPJ1

432 ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a different color from each of its proper divisors.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It claims that if there are n ways to do something and m ways to do something else after that, then there are n m n*m methods to do both of these acts.

Here,

(1) All prime number can take any of three colors, except one of 2 or 3 as both are connected via 6..

so 2, 5, 7 can have 3 ways each - 3*3*3 = 27 ways

(2) Let us take the multiples of 2..

4 can take any of the remaining 2 colors, while 8 would take the remaining colour. As like 4, 6 can also take any of 2 colors other than the colour of integer 2.

Thus 2*2*1=4

3 is restricted because of 6, so it cannot have the same color as 6 and therefore 3 can have any of the remaining 2 colors.

We could also have taken 3 colors for 6, and then 2 and 3 would have 2 colors each and overall 2*2*3.. We are still getting the same

Only integer left is 9, so it will take any of the 2 colors other than that of 3, so 2 ways..

Total 2*2=4

Combined way of  integers = 27∗4∗4=432 ways

There are 432 different methods to paint the numerals 2, 3,..., 9 red, green, or blue so that each number has a different hue from each of its suitable divisors.

To know more about counting principle,

https://brainly.com/question/28384306

#SPJ4

The transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

The given functions are f(x)=-1/4 x-2 and r(x)=4f(x).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

r(x)=4f(x)

So, r(x)=4(-1/4 x-2)

⇒ r(x)=-x-2

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Vertical: stretch

The graph of the functions is given below.

Therefore, the transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ1

The expected value of the sum of these events will be 2 / 3.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that the expected value for getting heads, on 30 coin tosses, is 15. The expected value for rolling a 1, after 30 die rolls is 5.

The probability of the sum will be calculated as,

P = ( 15 / 30 ) + ( 5 / 30 )

P =  ( 20 / 30 )

P = 2 / 3

Therefore, the expected value of the sum of these events will be 2 / 3.

To know more about probability follow

https://brainly.com/question/24756209

#SPJ1

To get the answer go to desmos

Answer:

2.2360679775 or 2.24

Answer:

to find the max number of guests:

25x-400 = 50

25x = 50 + 400

25x + 450

then divide

x = 450/25

x = 18

to find the min number of guests:

25x = 400 - 50

25x = 350

then divide

x = 350/25

x = 14

Minimum number of tables reserved:

is dividing the max/7 per table

x = 18/7

x = 3

Step-by-step explanation: