Select the correct proportion to solve for the missing measurement.




Question 3 options:


10/Z=6/15


10/15=z/6


z/10=15/6


10/15=6/z


What is the answer to the proportion you set up in the last problem? Type ONLY the number in the box.

The given statement "a structure chart should be more horizontal and less vertical because the main function should make a majority of the user- defined function calls" is FALSE because it should not necessarily be more horizontal and less vertical.

The orientation and structure of a structure chart depends on the specific requirements and characteristics of the system being modeled.

The purpose of a structure chart is to visually represent the components of a system and the relationships between them, not to follow a specific format or layout. The most important consideration when creating a structure chart is to accurately depict the system's functionality and structure in a clear and understandable way.

Therefore, the orientation of a structure chart should be chosen based on the system's needs rather than any arbitrary rules or guidelines.

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Answer:

The expression is:

\((5*6.50)+(3*24)-12=t\)

The total Bella paid is:

$92.50

Step-by-step explanation:

5 shirts at $6.50 each

3 pairs of pants at $24.00 each

12 dollar discount

Let "t" be the total Bella paid.

\((5*6.50)+(3*24)-12=t\)

\((32.50)+(3*24)-12=t\)

\((32.50)+(72)-12=t\)

\(32.50+72-12=t\)

\(104.5-12=t\)

\(92.5=t\)

Answer:

60 degrees

Step-by-step explanation:

Since the two lines are intersecting, the angles formed by them are vertical angles. Therefore:

2x+24=144

2x=144-24=120

x=120/2=60

Hope this helps!

Step-by-step explanation:

Therefore,

2x+24= 144° [ Vertically positive angles]

Or, 2x= 144-24

Or, 2x= 120

Or, x= 120/2

Therefore, x= 60°

Answer:

the cist of entry for x adults

Answer:

i think it would be d)

Step-by-step explanation:

cuz like, it says to write an expression. for an expression, most of the time you need more than one like number and variable

hope this helped :)

Answer:

Step-by-step explanation:

x = 5

The value of x in the given angle is 5.

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge.

Labelling the figure,

We have,

Measure of complete angle of circle = 360 degree

∠ABC = 360 - (81 + 74)

          =  205 degree

Now from figure,

∠APE = (205 - 81 )/2

          = 62 degree

Since we know that,

∠APE = 17x - 23

Therefore,

17x - 23 = 62

17x = 85

  x = 5 degree,

Hence,

Required value is 5.

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Answer:

21.1

Step-by-step explanation:

sin 49 = x / 28

0.75470958 = x/28

x = 21.1

Answer:

x=18.4

y=35

Step-by-step explanation:

So to solve for x, you're going to use one of the six trigonometric functions (you really only need to use the three main ones, sin, cos, and tan, to solve these problems). In this case you know the adjacent of the angle 49 degrees, and the hypotenuse. There is a trigonometric function which is defined as: \(\frac{adjacent}{hypotenuse}=cos(\theta)\). So let's plug in the known values:

\(cos(49) = \frac{x}{28}\)

Multiply both sides by 28

\(cos(49) * 28 = x\\\)

Calculate cos(49) using a calculator (make sure it's in degree mode):

\(0.656 * 28 \approx x\)

\(18.4 \approx x\)

So the second problem, you need to use the inverse of one of the trigonometric function, which essentially takes what f(x) is, and returns x. So in this case we're looking for a trigonometric function that is defined using the opposite and adjacent side, which tan is. \(tan(\theta)=\frac{opposite}{adajcent}\). In this case opposite=19, and adjacent=27. So plug in the known values:

\(tan(y)=\frac{19}{27}\)

Apply the inverse of tan to both sides

\(y=tan^{-1}(\frac{19}{27})\)

Calculate inverse of tan of 19/27 using a calculator:

\(y\approx35\)

Answer:

25%

Step-by-step explanation:

Answer:

Total Cost (p) = 90 + 14p

For 70 people = $1070

Step-by-step explanation:

Let p stand for the number of people attending the banquet

Fixed cost = $90

Variable cost = $14p

Total Cost (p) = 90 + 14p

=================

Cost for 70 people (p=70)

Total Cost = $90 + $14(70)

Total = $1070

Answer:

Angle covered by the hour  hand = 60°

Step-by-step explanation:

Numbers mentioned on an analogue clock = 12

Number of sectors between two numbers = 1

Angle between two numbers or 1 sector = \(\frac{360^0}{\text{Total numbers on the clock}}\)

                                                                    = \(\frac{360^0}{12}\)

                                                                    = \(30^0\)

If the hour hand moves clockwise from 3 to 5, sectors covered = 2

Therefore, angle between two sectors = 2 × 30°

                                                                = 60°

Angle covered by the hour  hand = 60°

Answer:

??

Step-by-step explanation:

well according to G it's x=4±5i lol

Step-by-step explanation:

I couldn't figure it out on my own had to G it. sorry if this doesn't help

1. The value of x in the triangle is B. 22.5°.

2. The value of x in the triangle is B. 22.5°.

3. The value of the limit illustrated is D. 32

1. It should be noted that the total angle in a triangle is 180°. The three angles given are illustrated as:

Angle 1 = 3x

Angle 2 = x + 30°

Angle 3 = 180° - 120° = 60°

The value of x will be:.

3x + x + 30 + 60 = 180

4x + 90 = 180

4x = 180° - 90°

4x = 90°

x = 90/4.

x = 22.5°

2. Note that the question was repeated. Therefore, the answer is illustrated above The value of x is 22.5°.

3. x³ + 7x² - 4

when x = 2

x³ + 7x² - 4

= 2³ + 7(2)² - 4

= 8 + 28 - 4

= 32

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Answer:

Divide 360 by the difference of the angle and 180 degrees. For example, 360 divided by 15 equals 24, which is the number of sides of the polygon. Divide 360 by the amount of the exterior angle to also find the number of sides of the polygon.

The slope of the line that passes through the points (-5, 8)and (−5,4) is undefined.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A line that passes through the points (-5, 8)and (−5,4).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂),

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = (4-8) / (-5 + 5)

m = -4/0

The slope is undefined.

Therefore, the slope is undefined.

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The answer Is B. In 7-9, There is a large cluster of students.

Answer:

b

Step-by-step explanation:

Therefore, if the input is angle_elev = 3.8 and shadow_len = 17.5, the estimated height of the tree would be approximately 1.166 meters.

To calculate the height of a tree given the angle of elevation (angle_elev) and the shadow length (shadow_len), you can use trigonometry.

Let's assume that the tree height is represented by the variable "tree_height". Here's how you can calculate it:

Convert the angle of elevation from degrees to radians. Most trigonometric functions expect angles to be in radians.

angle_elev_radians = angle_elev * (pi/180)

Use the tangent function to calculate the tree height.

tree_height = shadow_len * tan(angle_elev_radians)

Now, if the input is angle_elev = 3.8 and shadow_len = 17.5, we can plug these values into the formula:

angle_elev_radians = 3.8 * (pi/180)

tree_height = 17.5 * tan(angle_elev_radians)

Evaluating this expression:

angle_elev_radians ≈ 0.066322511

tree_height ≈ 17.5 * tan(0.066322511)

tree_height ≈ 1.166270222

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Answer:

cos (\(\frac{7\pi}{8}\)) = \(-\frac{\sqrt{2+\sqrt{2}}}{2}\)

Decimal value: −0.9238795325...

Step-by-step explanation:

Write,

cos \(\frac{7\pi}{8}\) = cos \((\pi-\frac{\pi}{8})\) = −cos \(\frac{\pi }{8}\)

Now using half angle formula, cos(x) = 2 cos²(\(\frac{\pi }{2}\)) − 1, we can write cos \(\frac{\pi }{4}\) = 2

cos²(\(\frac{\pi }{8}\)) − 1

This means \(\frac{1}{\sqrt{2}}\) + 1 = 2 cos²(\(\frac{\pi }{8}\))

2 cos²(\(\frac{\pi }{8}\)) = \(\frac{\sqrt{2}+1}{\sqrt{2}}\)

cos²(\(\frac{\pi }{8}\)) = \(\frac{\sqrt{2}+1}{2\sqrt{2}}\)

cos(\(\frac{\pi }{8}\)) = \(\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}\)

Simplify,

\(\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}\) = \(\sqrt{\frac{2+\sqrt{2}}{4}\) = \(\frac{\sqrt{2+\sqrt{2}}}{2}\)

Hence,

cos (\(\frac{7\pi}{8}\)) = −cos (\(\frac{\pi }{8}\)) = \(-\frac{\sqrt{2+\sqrt{2}}}{2}\)

The exact value of cos(7pi/8) is \(\rm -\dfrac{\sqrt{2+\sqrt{2}} }{2 }\) and this can be determined by using the trigonometric properties.

Given :

Expression  -- \(\rm cos(\dfrac{7\pi}{8})\)

The following steps can be used to determine the exact value of the given expression:

Step 1 - Write the given expression.

\(=\rm cos(\dfrac{7\pi}{8})\)

Step 2 - Rewrite the above expression.

\(= \rm cos(\dfrac{8\pi - \pi}{8})\)

Step 3 - The above expression is reduced to:

\(= \rm -cos(\dfrac{ \pi}{8})\)    --- (1)

Step 4 - According to the trigonometric properties:

\(\rm cos(x) = 2 cos^2(\frac{x}{2})-1\)

Step 5 - Substitute the value of x = \(\pi\)/4 in the above expression.

\(\rm cos(\frac{\pi}{4}) = 2 cos^2(\frac{\pi}{8})-1\)

Step 6 - Simplify the above expression.

\(\rm cos(\frac{\pi}{8})=\sqrt{\dfrac{\dfrac{1}{\sqrt{2}} +1}{2}}\)

\(\rm cos(\frac{\pi}{8})=\sqrt{\dfrac{1+\sqrt{2} }{2\sqrt{2} }\)

\(\rm cos(\frac{\pi}{8})=\dfrac{\sqrt{2+\sqrt{2}} }{2 }\)

Step 7 - Substitute the value of cos(\(\pi\)/8) in the expression (1).

\(\rm -cos(\frac{\pi}{8})=-\dfrac{\sqrt{2+\sqrt{2}} }{2 }\)

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Step-by-step explanation:

You want to solve for x:

First, distribute -2 into the parenthesis, you will end up with 44 - 6x - 8 = -18x

Next, combine like terms, you will end up with 36 - 6x = -18x

Next, add 6x to both sides, you will end up with 36 = -12x

Finally, divide both sides by -12, you will end up with x = -3

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

it is suggested that students allocate around 2-3 hours of study time per credit hour per week for a college-level course. However, the actual study time required may vary based on individual learning styles, prior knowledge, and the specific requirements set by professors or institutions.

Let's apply this general guideline to your scenario:

One three-credit class that is less demanding:

Assuming 2-3 hours of study per credit hour, for a three-credit class, you would ideally spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Two three-credit classes that are typically demanding:

Similarly, for each of the two three-credit classes, you would spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Since you have two such classes, the total time would be:

2 * (6-9) hours = 12-18 hours per week.

One four-credit class that is very challenging:

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

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Answer:

12

Step-by-step explanation:

Tree diagram

Heads - 1

           - 2

           - 3

           - 4

           - 5

           - 6

Tails    - 1

           - 2

           - 3

           - 4

           - 5

           - 6

Count all the possibilities, and boom- 12 :)

Sorry if its wrong tho-

Answer:

x = 68°

Step-by-step explanation:

This is an isosceles triangle, which means the two base angles will be the same. (56° and 56°)

All triangles angles must add up to 180, so if we take 180-56-56 we will find the missing angle (x).

180-56-56 = 68

x = 68°

Explanation

Step 1

let n represents the number

so,

Five times a number

hence

Five times a number, minus three

"is" can written as equal (=),so

Five times a number, minus three, is twelve.

I hope this helps you

Answer:

Step-by-step explanation:

8x² + 7x - 1 = 0

Rewrite 7x as a difference

That's

8x² + 8x - x - 1 = 0

Factorize

8x( x + 1) - ( x + 1) = 0

(8x - 1)( x + 1) = 0

8x - 1 = 0 x + 1 =0

8x = 1 x = - 1

x = 1/8

The solutions are

Hope this helps you

The equation part of the given word problem is x+y=52 and y=x+16.

a) Let x = number of green eyed dolls

And let y = number of blue-eyed dolls

Now we are told the following:

x+y=52 → eq1

and

y=x+16 → eq2

b) substitute y = x+16 from eq2 into eq1:

x+x+16 = 52 subtract 16 from each side

x+x+16-16 = 52-16 collect like terms

2x = 36 divide each side by 2

x = 18 → number of green-eyed dolls

substitute x = 18 into equation2

y = 18+16 =34 → number of blue-eyed dolls

18+34=52

52=52

and

18+16=34

34=34

THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:

Let x = Number of green-eyed dolls

Then 52-x = Number of blue-eyed dolls

Now we are told that:

x+16 = 52-x add x to and subtract 16 from each side

x+x+16-16 = 52-16-x+x collect like terms

2x=36 → same as before

x = 18.

Hence, the equation part of the given word problem is x+y=52 and

y=x+16.

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Answer: speed of train = 94.53 km/h

Speed of car = 59.98 km/h

Step-by-step explanation:

Let x = speed of the train

Let y = speed of the car

The total distance travelled by the man is 600 km. It takes 8 hours 40 min if he travels 320km by train and rest by car. This means that the distance travelled by car is 600 - 320 = 280km

60 minutes = 1 hour

The total time of travel = 8 + (40/60) = 8.67 hours

Total time = total distance/total speed

8.67 = 320/x + 280/y

320/x = 8.67 - 280/y

320/x = (8.67y - 280)/y

Cross multiplying, it becomes

320y = x(8.67y - 280)

y = x(8.67y - 280)/320- - - - - - - - - - -1

it would take 30min more if he travels 200km by train and rest by car. The total time would be 8.67 + 0.5 = 9.17 hours

Distance covered by the car is 600 - 200 = 400 km

Therefore,

9.17 = 200/x + 400/y

200/x = 9.17 - 400/y

200/x = (9.17y - 400)/y

Cross multiplying, it becomes

200y = x(9.17y - 400)

y = x(9.17y - 400)/200 - - - - - - - 2

Equating equation 1 to equation 2, it becomes

x(8.67y - 280)/320 = x(9.17y - 400)/200

Dividing both sides by x, it becomes

(8.67y - 280)/320 = (9.17y - 400)/200

Cross multiplying, it becomes

200(8.67y - 280) = 320(9.17y - 400)

1734y - 56000 = 2934.4y - 128000

2934.4y - 1734y = - 56000 + 128000

1200.4y = 72000

y = 72000/1200.4

y = 59.98 km/h

Substituting y = 59.98 into equation 1, it becomes

59.98 = x(8.67 × 52.98 - 280)/320

52.98 × 320 = x(459.3366 - 280)

16953.36 = 179.3366x

x = 16953.36/179.3366

x = 94.53 km/h