There are 32 females cast in the school play. The ratio of male roles to female roles is 3:8. How many males are cast in
the school play?

4x - 6 = x + 9

4x - x = 9 + 6

3x = 15

[tex]x = \frac{15}{3} \\ [/tex]

x = 5 ...

Answer:

[tex]x =5[/tex]

Step-by-step explanation:

[tex]4x - 6=x+9[/tex]

Subtract x from both sides

[tex]4x -6-x=x+9-x[/tex]

[tex]3x-6=9[/tex]

Add 6 to both sides

[tex]3x-6+6=9+6[/tex]

[tex]3x=15[/tex]

Divide both sides by 3

[tex]\frac{3x}{3} = \frac{15}{3}[/tex]

[tex]x = 5[/tex]

When the two lines makes angle of 90 degree , then the lines are known as Perpendicular Lines .

What are Perpendicular Lines ?

Two lines are said to be perpendicular to each other if the straight line  makes an angle of 90 degree with another line. 90 degree is also called a Right Angle and is represented by a little square between two perpendicular lines .

when the two lines intersect at a right angle, they are said to be perpendicular to each other.

For Example : In a football field all the four corners of a football field are perpendicular to each other.

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Step-by-step explanation:

Find angle W first:

37 + 93 + W = 180 ---> W = 50°

Use sine law to find the length w:

w/(sin 50) = 31/(sin 37)

w = 31(sin 50/sin 37)

= 39.5

The opposite of number 27 is -27

We know that the opposite of a number is nothing but the number which is at the same distance from 0 but in the opposite direction on a number line.

Here we have been givena number 27

Let a number 'p' be the opposite of number 27

If we plot 27 on the number line then we can observe that it is  located to the right of 0 on the number line.

So, from the definition of opposite of a number p would be at the same distance from 0  i.e., 27 units but in the opposite direction on a number line.

so, the number p would be -27

Therefore, -27 is opposite of 27

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The original number is 25.

We know that,

The sum of the original number is 7 --(i)

When reversed, the value of the number is increased by 45 --(ii)

Therefore, adding (i) and (ii), we get:

7 + 45 = 52

Also, 5 + 2 = 7

Since 52 is the reversed number,

Therefore, the original number is 25.

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Short term memory is a response variable as it is dependent. Hence Option C is the answer.

A dependent variable is the response variable. It is reliant on the independent variable, which serves as the explanatory variable.

Explanations for the findings revealed by the response variables are provided by the explanatory or independent variables. Explanatory response is qualitative since it is classified based on a category.

The response variable is what the researcher often measures in research studies. The response variable in the example presented above is short-term memory, which is influenced by exercise.

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Answer:

21 meters

Step-by-step explanation:

First find the circumference of the tire:

c = πd

c = 3.14(670)

c = 2103.8

Multiply by 10 to find the distance the bike has travelled:

2103.8*10 = 21,038

Convert millimeters to meters:

21,038 millimeters ≈ 21 meters

Answer:

NEEEEEEGAARRRRR

Step-by-step explanation:

The height of an isosceles triangle can be found by using the Pythagorean Theorem to calculate the length of the hypotenuse, subtracting the lengths of the other two sides, and taking the square root of the difference.

To find the height of an isosceles triangle given three sides, you can use the Pythagorean Theorem. Begin by calculating the length of the hypotenuse (the longest side of the triangle). To do this, square the lengths of the two other sides and add them together. Then, take the square root of that sum. This is the length of the hypotenuse. Next, subtract the lengths of the other two sides from the hypotenuse and take the square root of the difference. The result is the length of the altitude, which is also the height of the triangle.

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Using multiplication we know that the product of 3 * - 4 is -12.

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.

A product is the output of a multiplication operation.

The addition method, lengthy multiplication, grid method, and drawing lines are four different ways to multiply.

So, we have:

3 * -4

Here, we know that 3 is a positive number and -4 is a negative number.

And so the product will be a negative number.

Now, calculate the product as follows:

3 * -4

-12

Therefore, using multiplication we know that the product of 3 * - 4 is -12.

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8/10 liters of water she spilled. This can be solved using the concept of fraction.

A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.

Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.

Given that,

There were 57/10 liters of water in a bucket than she spilled some so she added another 15/10, now she get:

(57/10) + (15/10) = 72/10

After that, there was 64/10 liters of water in the bucket, now she spilled:

(72/10) - (64/10) = 8/10

So, 8/10 liters of water she spilled.

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Answer:

The answere is C

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

0.2(x+50)-6=0.4(3x+20) multiply both sides by 10 to clear the decimals

2(x + 50) = 4(3x + 20) distribute across the terms in the parentheses

2x + 100 = 12x + 80 subtract 80, 2x from both sides

20 = 10x divide both sides by 10

x=2

Answer:

610,000

Step-by-step explanation:

Answer:

610,000

Step-by-step explanation:

614,952 rounded to the nearest ten thousand place is 610,000.

hope this helps and is right :) p.s. i rlly need brainliest.

The answer will start with 500 USD. For every hour, 75 USD is charged. We can multiply 'x' to 75 USD which will represent the amount of hours. The equation will now become, 'y = 75x + 500'. In most cases, like this one, y will represent the total cost. Here are the answers.

a. 75USD

b. x (amount of hours)

c. y (total cost)

d. y = 75x + 500

Hope I understood what you were asking and if not I'm really sorry <3

Answer:

(-4, -8)

Step-by-step explanation:

Note that x in terms of y is x = 2y + 12.  Substitute 2y + 12 for x in the second equation:

5(2y + 12) + 3y = -44

or

10y + 60 + 3y = -44

Then 13y= -104, and y = -8

From the first equation we find x = 2(-8) + 12, or x = -16 + 12, or x = -4

Then the solution is (-4, -8)

x = 448, which is the greatest of these integers.

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.

According to our question-

added together =1341

x +  x-1 + x-2 =1341

3x-3  = 1341

3x = 1344

x = 448

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The value of x in the triangle LMO is 38°

An equation shows how two or more numbers and variables are related to each other.

∠KLO + ∠OLM = 180° (sum of angle in straight line)

134 + ∠OLM = 180°

∠OLM = 46°

∠OML + ∠OMN = 180° (sum of angle in straight line)

∠OML + 84 = 180°

∠OML = 96°

∠OLM + ∠OML + ∠LOM = 180° (angle in a triangle)

46 + 96 + x = 180

x = 38°

The value of x is 38°

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Answer:

$6.51

Step-by-step explanation:

To make a percent a decimal, divide by 100

62% = .62

.62 x 10.50 = 6.51

We know that half of 10.50 is 5.25 and 625 would be a little higher and 6.51 is a little higher.

2x2+4x5=0 is a quadratic equation that can be solved. 2 x 2 + 4 x - 5 = 0. To find the answers, start with the quadratic formula.

Using the quadratic formula, determine the roots of the quadratic equations 2x2-3x-5= 0. The equation's roots must be located. As a result, the equation's roots are 5/2 and -1. Which equation with 2 as a root must be identified. As a result, 2 is not a root of x2-4x + 5= 0.

Since 2 is not a root, x2 + 3x-12= 0 cannot be solved. Thus, 2 is the root of the equation 2x2-7x + 6= 0. The roots of the quadratic equation ax2 + bx + c= 0 are real and equivalent if the discriminant is equal to zero (b2-4ac=0), a, b, and c are real values, and a0. The roots in this situation arex= -b/2a.

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Answer:

➜ ∠4 = ∠2

➜ ∠2 + ∠3 = 180°

➜ ∠1 = ∠3

Step-by-step explanation:

     We can use vertical angles to prove the first statement true, ∠4 = ∠2.

     Next, ∠2 and ∠3 are supplementary angles, so if you add them together you will get 180 degrees. This statement is also true.

       Then, ∠1 and ∠2 are not complimentary angles. This statement is false.

       Lastly, we can use the same reasoning of the first one to prove this statement true as well. They are vertical angles, ∠1 = ∠3.

The solution of the equation is x = 6, y = 0.

1. Subtract the two equations:

   x3y6 - 2x3y12 = 0

2. Simplify both sides of the equation:

   x3y - 2x3y = 0

3. Simplify further calculations:

   x3(y - 2y) = 0

4. Factorize the expression:

   x(y - 2y) = 0

5. Solve for x:

   x = 0

6. Substitute x = 0 into either equation:

   3y = 6

7. Solve for y:

   y = 2

8. Substitute y = 2 into either equation given above:

   x = 6

The solution of the equation is x = 6, y = 2.

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Answer:

dude... I have fallen in love with your profile picture

Answer:

I'm pretty sure it's 97

Step-by-step explanation:

I made three shapes 2 rectangle and 1 triangle

Answer:

4

Step-by-step explanation:

Hypotenuse, on a 30 60 90 triangle, is equal to 2a. A being the shortest side.

That means 2(2) = 4

Answer: Are you talking about Circumference?

If it is then the Formula is 2πr or the easy way ... πd

1st use of formula: you would multiply 7.5 twice then multiplying by Pi or 3.14

2nd use of formula: You would get the diameter then multiply it by Pi or 3.14

Hope this helps :)

The Volume of largest Right Circular Cylinder that can be inscribed in Sphere of radius 3 cm is 65.3 cm³  .

Let the half height of of the cylinder be = h ;

we use h instead of [tex]\frac{h}{2}[/tex] for easier simplification ,

In order to find the Volume of cylinder , we multiply the area of  top with the total height of cylinder .

So , Volume = [tex]\pi \times (Radius Of Cylinder)^{2}\times (Height Of Cylinder)[/tex]

Volume = [tex]\pi \times (\sqrt{r^{2} -h^{2} } )^{2}\times (2h)[/tex];

Volume [tex]= 2\pi h(r^{2} -h^{2} )[/tex]

Now ,  we need the derivative of volume function and equate to 0. If we move the h inside parenthesis, we only need to use power rule to get  derivative.

So , we get , V = [tex]2\pi (r^{2} h-h^{3} )[/tex] ,

On simplifying further ,

we have ,

Volume of Largest Right Circular Cylinder  ⇒ [tex]\frac{4\sqrt{3} \pi r^{3} }{9}[/tex] ;

it is given that radius of sphere is = 3 cm ,

Substituting value of radius in Volume formula ,

we get ,

V =  [tex]\frac{4\sqrt{3} \times 3.14\times 3^{3} }{9}[/tex] ;

V = 65.2636 cm³

V ≈ 65.3 cm³.

Therefore , the volume of the largest right circular cylinder is 65.3 cm³.

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The four types of problem solving can be named as Trial and Error , Algorithms , Inductive Reasoning and Deductive Reasoning .

What is Problem Solving ?

The Problem solving can be defined as the act of defining a problem , finding cause of problem, identifying, prioritizing and selecting the alternatives for solution and implementing it .

The four types of problem solving are :

(i) Trial and Error : It is defined as trying the different ways of doing something until we find the best solution .

(ii) Algorithms : The algorithm can be defined as a  set of step by step procedures which provides correct answer to a particular problem.

(iii) Inductive Reasoning : It is defined as a process where we come to a conclusion where a general statement is reached from specific result.

(iv) Deductive Reasoning : It is defined as a process where we get specific results from general statements .

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Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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Reasonable algorithms expand at polynomial rates or less quickly. Unreasonable algorithms expand exponentially. Even for relatively small problem sizes, the time to solve an unreasonable algorithm increases very quickly.

When the algorithm takes an excessively long time, we say that the number of steps is an exponential function of the size of the input (or some other function that is larger than any polynomial). Simply increasing the input size (n) by 1 doubles the number of steps for an algorithm that runs in 2n time.

Depending on the polynomial, polynomial time can be further decomposed. Algorithms with a runtime of approximately n2 operate in quadratic time. (If the input size is doubled, the number of steps is quadrupled.) In practise, polynomial time algorithms that take longer than cubic (n³) time are uncommon.

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If a train travels 283. 8km in 4. 4 hours, the train travels 71km in 1 hour and the train travels 114.5km in 2.5 hours.

Based on the assumption that the train is traveling at a constant speed throughout its journey.

To find the speed the train travels , we divide the total distance by the total time:

speed = 283.8km/ 4.4 hours

speed = 64.5 km/h

To find the distance the train travels , we multiply the speed of the train by the total time:

Distance travelled in 1 hour = 64.5 km/ hour × 1 hour

Distance travelled in 1 hour = 64.5 km

Distance travelled in 2.5 hours = 64.5 km/hour x 2.5 hours

Distance travelled in 2.5 hours = 161.25km

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