Here is a regular hexagon and a regular pentagon work out the size of the angle marked x.

Answers

Answer 1

The angle marked x in the regular hexagon is 120 degrees, and in the regular pentagon is 108 degrees.

The angle marked x in the regular hexagon is 120 degrees, because the sum of all the angles in a hexagon is 720 degrees (360 x 2). Each of the angles in a regular hexagon is 120 degrees, so the angle marked x must also be 120 degrees. The angle marked x in the regular pentagon is 108 degrees, because the sum of all the angles in a pentagon is 540 degrees (360 x 1.5). Each of the angles in a regular pentagon is 108 degrees, so the angle marked x must also be 108 degrees.

Regular Hexagon:

Sum of angles = 720 degrees

Number of angles = 6

Angle x = 720 ÷ 6 = 120 degrees

Regular Pentagon:

Sum of angles = 540 degrees

Number of angles = 5

Angle x = 540 ÷ 5 = 108 degrees

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Related Questions

Which of the following is divisible by 3?A. 1432B. 2132C. 2331D. 1453

Answers

The correct option for this question is: Option (C) 2331

Any number that can be divided by three will have digits that add up to three.

For Option (A): 1432
⇒ 1 + 4 + 3 + 2 = 10

For Option (B): 2132
⇒2 + 1 + 3 + 2 = 8

For Option (C): 2331
⇒2 + 3 + 3 + 1 = 9

For Option (D): 1453
⇒ 1 + 4 + 5 + 3 = 13

Here, only 9 is divisible by 3.
∴ 2331 is divisible by 3.

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PLEASE HELP WILL GIVE BRAINLIEST TO THE ANSWER THAT MAKES THE MOST SENSE

Answers

Answer:

go right 2 up 1 starting at (0,0)

Step-by-step explanation:

complete the problems using synthetic division

Answers

Answer:

Step-by-step explanation:

Write k for the divisor.

Write the coefficients of the dividend.

Bring the leading coefficient down.

Multiply the leading coefficient by k.

Add the terms of the second column.

Multiply the result by k.

Repeat steps 5 and 6 for the remaining columns.

factorise x^2 + 3x - 54

Answers

The factorization of the quadratic equation:

x^2 + 3x - 54

Is (x + 9)*(x - 6).

How to factorize the expression?

To factorize the quadratic equation we first need to find the roots:

x^2 + 3x - 54 = 0

Using the quadratic formula we will get:

[tex]x = \frac{-3 \pm \sqrt{3^2 - 4*1*(-54)} }{2} \\\\x = \frac{-3 \pm15 }{2}[/tex]

So the two roots are:

x = (-3 - 15)/2 = -18/2 = -9x = (-3 + 15)/2 = 12/2 = 6

Then the factorized form of the quadratic equation is:

(x - (-9))*(x - 6)

(x + 9)*(x - 6)

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The slope of the line that passes through the points \left( 2 , 3 \right) {and} \ \left( 5 , 9 \right)(2,3) and (5,9) is

Answers

Answer:

so here you'll get the formula

Slope (m) = y2 - y1 / x2 -x1

answer will be 2

correct if I'm wrong

The sum of 9 consecutive positive integers is 99. What is the largest of these Intigers?

Answers

Answer: 15

Step-by-step explanation:

Let x be the first of the consecutive integers.

So, the consecutive integer after x would be x+1. The one after this one would be x+2. Continue this until there are nine consecutive integers.

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) = 99

Simplify:

9x + 36 = 99

9x = 63

x = 7

The largest of these consecutive integers is the last one, x+8. Plug in x to this expression:

(7) + 8 = 15

The largest of these consecutive integers is 15.

can someone answer all that's question....I really² need the answer ​

Answers

1.
In the triangle that contains x (call the other 2 angles as a and b, where a is the angle that is supplemetary to the center angle.)

a = 180 - 110 = 70 (supplemetary angles add up to 180)

b = 30 (b and the angle measures 30 are in the same segment.)

-> x = 180 - 70 - 30 = 80.

2. In triangle PRT, v = 180 - 40 - 70 = 70.

Since P,Q,S,T all lies on the circumference, PQST is a cyclic quadrilateral.

-> w = 180 - PQS = 180 - (180 - 70) = 70.

3.
i) A 1:2 scale means that all sides of P must be shortened by twice the lengths.

Since D is the only shape with the sides shortened from P, it's the correct option.

ii) A 1:1/2 scale means that all sides of P must be enlarged by twice the lengths.

Therefore, the measures of the sides become sqrt(20),6,4,6 (clockwise from diagonal), which is B.

4. Using the Pythagoras' theorem, we can find the hypotenuse PR : [tex]\sqrt{12^{2} + 5^{2} } = 13[/tex]

sin(x) = QP/PR = 5/13 = 0.385 (rounded to 3 d.p)
tan(y) = QP/QR = 5/12 = 0.417 (rounded to 3 d.p)

Question 7 Translate into a mathematical expression: 15 more than the sum of 5 and a number a. 15+(5-n) b. (5+n)+15 c. (5-n) + 15 d. 15+5n

Answers

15 more than the sum of 5 and a number a, when translated into a mathematical expression will become b. (5 + n) + 15.

An algebraic expression is a mathematical expression that can contain numbers, variables, and operations.

An algebraic expression can represent a specific value for a given value of the variable, and can be used to describe mathematical relationships and solve equations.

Algebraic expressions can be simplified, added, subtracted, multiplied and divided.

Algebraic expressions can also be represented in different forms, such as polynomials, rational expressions, exponential expressions and logarithmic expressions.

"15 more than the sum of 5 and a number a" can be represented algebraically as:

15 + (5 + a)

or

(5 + a) + 15

which can also be simplified as

a + 20

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Please help
Really stuck

Answers

Statement                                     Reason

∠1 = ∠2, WX = ZY                            Given

WP = ZP                                         converse of isosceles triangle  theorem

△WXP ≅ △ZYP                              SAS

XP = YP                                           CPCT

∠3 = ∠4                                          Isosceles triangle  teorem

What is the isosceles triangle?

A triangle's corresponding angles are congruent if its two sides are.

Given that ∠1 = ∠2, WX = ZY.

Statement 1 is given.

According to the converse of the isosceles triangle theorem:

WP = ZP  

SAS rule: If the two sides and an included angle of one triangle match the two sides and an included angle of the other, then two triangles are said to be congruent. This is referred to as SAS congruency.

In triangles △WXP and △ZYP:

∠1 = ∠2

WX = ZY.

WP = ZP

According to SAS rule,  △WXP ≅ △ZYP

By CPCT, XP = YP

Again the isosceles triangle theorem ∠3 = ∠4.

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If x = 14 and y = 4, what is the value of the following expression? x - 7+ 5y St​

Answers

Step-by-step explanation:

fill the data in the expression

(14)-7+5(4)

27

Either draw a full m-ary tree with 76 leaves and height 3, where m is a positive integer, or show that no such tree exists.

Answers

If and only if m is a divisor of 76, then there exists a full m-ary tree with 76 leaves and height 3. 1, 2, 4, 19, 38, and 76 are the divisors of the number 76.

One node at the root, 76 child nodes at the second level, and [tex]76^{2}[/tex] = 5776 child nodes at the third level make up the 5776 + 76 = 5852 nodes of a full 1-ary tree with 76 leaves and height 3. As a result, there is no whole 1-ary tree with 76 leaves and a height of 3.

 There would be one node at the root, 38 child nodes at the second level, and [tex]38^{2}[/tex] = 1444 child nodes at the third level, making a total of 1444 + 38 = 1482 nodes in a full 2-ary tree with 76 leaves and height 3. As a result, there is a full 2-ary tree that is 3 in height and has 76 leaves.

 There would be one node at the root, 19 child nodes at the second level, and [tex]19^{2}[/tex] = 361 child nodes at the third level, for a total of 361 + 19 = 380 nodes in a full 4-ary tree with 76 leaves and height 3. As a result, there is a full 4-ary tree that is 3 in height and has 76 leaves.

A full 19-ary tree with 76 leaves and height 3 would have a single node at the root, four children at the second level, and four and a half children, or 16 at the third level, for a total of 16 + four and a half and twenty nodes. As a result, there is a full 19-ary tree that is 3 in height and has 76 leaves.

 A full 38-ary tree would contain a single node at the root, two child nodes at the second level, and two and a half child nodes at the third level, for a total of four + two + six nodes. Consequently, there is a complete 38-ary tree that is 3 in height and has 76 leaves.

 There would be one node at the root, one child node at the second level, and [tex]1^{2}[/tex]= one child node at the third level, for a total of 1 + 1 = 2 nodes in a full 76-ary tree with 76 leaves and height 3. Consequently, there is a full 76-ary tree with 76 leaves and a height of 3.

  As a result, for m = 2, 4, 19, 38, and 76, a full m-ary tree with 76 leaves and height 3 exists.

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Elias is adding and. He finds the lcd to be 10t2 and uses multiplication to find equivalent expressions. Which is the sum of ?.

Answers

The LCD (Least Common Denominator) of 10t2 is 10t2. To determine the equivalent expression is the sum of the fractions is 8t2.

A/B = C/D

Where A and B are the two fractions, and C and D are the equivalent fractions.

We will use this formula to determine the equivalent expression of the given fractions:

3t/20 = C/10t2

We can solve for C by multiplying both sides by 10t2, yielding:

30t2/20 = C/10t2

We can solve for C by multiplying both sides by 10t2, yielding:

30t2/20 = C/10t2

We can then simplify by cancelling out the 10t2 on the denominator, yielding:

C = 30t2/20

The equivalent expression for the given fractions is therefore 30t2/20.

To find the sum of the fractions, we first need to convert all fractions to equivalent fractions with a common denominator. In this case, the LCD is 10t2.

The equivalent expressions for the fractions are therefore:

3t/20 + 5/10t2 = 30t2/20 + 50/10t2

The sum of the fractions is then the sum of the numerators divided by the denominator, or:

30t2/20 + 50/10t2 = 80t2/10t2

We can simplify this expression by cancelling out the 10t2 on the denominator, yielding:

80t2/10t2 = 8t2

Therefore, the sum of the fractions is 8t2.

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The sum of 14t/10t^2 +  (5t^2 + 40t)/10t^2 is (5t^2 + 54t)/10t^2

In this question we have been given that Elias is adding 7t/5t^2 and (t + 8)/2t

He finds the least common divisor (LCD) of 7t/5t^2 and (t + 8)/2t which 10t^2

He uses multiplication to find an equivalent expression.

7t/5t^2 = 7t/5t^2 * 2/2

            = 14t/10t^2

and (t + 8)/2t = ((t + 8) * 5t)/(2t * 5t)

                     = (5t^2 + 40t)/10t^2

We need to find the sum 14t/10t^2 +  (5t^2 + 40t)/10t^2

We know that if the base of two rational expressions a/b and c/b then the denominator of the result is same and we just add numerators i.e., a/b + c/b = (a + c)/b

So, 14t/10t^2 +  (5t^2 + 40t)/10t^2

= [14t + (5t^2 + 40t)]/10t^2

= (5t^2 + 54t)/10t^2

Hence, 14t/10t^2 +  (5t^2 + 40t)/10t^2 = (5t^2 + 54t)/10t^2

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What is 19,992 rounded to the nearest ten

Answers

Answer: 19990

Step-by-step explanation: :)

Answer:

19.990

Explanation:
You can find this by rounding 19.992 on a number line to the nearest tenth. Tens is the first 2 numbers in a number.

Example: 2.535.783
Eighty-Three would be the tenth number.

Given right triangles efg and hjk. find the value of a that satisfies the congruency of the triangles. in two or more complete sentences, explain the relevance between the congruency of the triangles and the calculations made in finding the value of a.

Answers

The given triangles GEF and HKJ are congruent by the AAA test of congruency and the value of a = √2.

The two triangles are proved to be congruent and the value of a is to be determined.

Both triangles are right-angled triangles.

We know that similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

In triangle GEF,

since the sum of the angles in a triangle is 180

∠ G + ∠ F + ∠ E =180

90 + 45 + E = 180

∠ E = 45

similarly, ∠ J = 45

In Triangle GEF and Triangle HKJ,

∠ G = ∠ K (both are 90)

∠  F = ∠ H  (both are 45)

∠ E = ∠ J  (both are 45)

So, Triangle GEF and Triangle HKJ are congruent triangles by AAA congruency.

Now in triangle GEF,

cos 45 = 3a/6

1/√2 = a/2

a = √2

Thus, the given triangles are congruent by AAA . and the value of a = √2.

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The complete question is -

Given right triangles EFG and HJK. find the value of a that satisfies the congruency of the triangles. in two or more complete sentences, explain the relevance between the congruency of the triangles and the calculations made in finding the value of a.

a) Can a 3 × 4 matrix have independent columns? Independent rows? Explain.

b) If A is 4 × 3 and rank A = 2, can A have independent columns? Independent rows? Explain.

c) If A is an m × n matrix and rank A = m, show that m ≤ n.

d) Can a nonsquare matrix have its rows independent and its columns independent? Explain.

e) Can the null space of a 3 × 6 matrix have dimension 2? Explain.

f) Suppose that A is 5 × 4 and null(A) = x for some column x ≠ 0. Can dim(im A) = 2?

Answers

A) A 3 × 4 matrix can have independent columns but not independent rows.

B) A 3 × 4 matrix can have independent columns but not independent rows.

C) If A is an mxn matrix and rank A = m, it follows that m ≤ n.

D) A nonsquare matrix can have its rows independent.

E) The null space of a 3 × 6 matrix cannot have dimension 2.

F) If A is 5x4 and null(A) = x for some column x ≠ 0, dim(im A) cannot be 2.

Matrix Linear Independence Rules

A) A 3 × 4 matrix can have independent columns but not independent rows. This is because a column vector can be linearly independent, meaning no linear combination of other columns in the matrix can create it, but a row vector can't be linearly independent because it can always be written as a linear combination of the columns.

B) If A is 4 × 3 and rank A = 2, it cannot have independent columns but it can have independent rows. This is because if rank A = 2, the number of linearly independent columns is 2, which is less than the number of columns, meaning that not all columns can be linearly independent. However, since rank A = 2, the number of linearly independent rows is also 2, which is less than the number of rows, meaning that some rows can be linearly independent.

C) If A is an mxn matrix and rank A = m, it follows that m ≤ n. This is because the rank of a matrix is the maximum number of linearly independent columns, which cannot be greater than the number of columns.

D) A nonsquare matrix can have its rows independent and its columns independent, as long as the number of rows is not equal to the number of columns.

E) The null space of a 3 × 6 matrix cannot have dimension 2. This is because the dimension of the null space is always less than or equal to the number of columns of the matrix, which is 6 in this case.

F) If A is 5x4 and null(A) = x for some column x ≠ 0, dim(im A) cannot be 2. This is because the dimension of the image of A is equal to the rank of A, which cannot be less than the dimension of the null space. Therefore, dim(im A) must be greater than or equal to the dimension of the null space, which is at least 1.

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Next Finding the Reciprocal: Mastery Test Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Find the reciprocal of 4/5

Answers

The numerator is 3 and the denominator is 5. IN order to determine the reciprocal 4 becomes the denominator and 5 becomes the numerator. The reciprocal is 5/4.

What is Reciprocal?The definition of reciprocal in mathematics is the inverse of a value or a number. If n is a real number, then 1/n will be n's reciprocal. Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9. The result of multiplying a number by its reciprocal now equals one. Inverse multiplicative is another name for it. The Latin word "reciprocus," which means "returning," is where the word "reciprocal" originated. Therefore, if we take the reciprocal of an inverted number, it returns its original value. This article will teach you how to find the reciprocal of numbers, fractions, and decimals with multiple factors.

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PLSSS HELP IF YOU TURLY KNOW THISS

Answers

Answer:

9

Step-by-step explanation:

the square of 3 is 9

3 + 3 + 3 = 9

Find the length of the missing side in simplest radical form.

Answers

Answer: The best I could come up with is √65, −√65 or, 1, you pick!

(Decimal: 8.06225774…, −8.06225774…)

Step-by-step explanation:

Rewrite the equation as

x^2 = 8^2 + 1^2.

One to any power is one.

x^2 = 8^2 + 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x = ± √8^2 + 1

x = ± √64 + 1

Add 64 and 1.

x = ± √65

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

x = √65

Next, use the negative value of the ± to find the second solution.

x = −√65

The complete solution is the result of both the positive and negative portions of the solution.

x = √65, −√65

The result can be shown in multiple forms.

Exact Form:

x = √65, −√65

Decimal Form:

x = 8.06225774..., −8.06225774…

Answer:

[tex]x=\sqrt{65}[/tex]

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

Given a right triangle with the missing hypotenuse.

Use Pythagorean to find the missing side:

[tex]x = \sqrt{8^2+1^2}=\sqrt{64+1} =\sqrt{65}[/tex]

7 x 3/14 as a fraction in simplest form ​

Answers

Answer:

3/2

Step-by-step explanation:

7 x 3/14 can be simplified to 21/14, which is written in simplest form as 3/2.

Hope can help :)

The simplest form of the fraction of the expression is 3/2.

We have,

The expression:

7 x 3/14

Now,

14 is a multiple of 7.

i.e

7 x 2 = 14

So,

7 x 3/(7 x 2)

7 gets canceled.

= 3/2

Thus,

The simplest form of the fraction of the expression is 3/2.

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The table shows the portion of gold medals that were won by the United States in five summer Olympic games. In what year did the United States win the least portion of gold medals? the greatest portion?

Answers

Answer:

2004 to 2012

Step-by-step explanation:

The radius of a basketball hoop is 9 inches. Which expression can be used to find the
hoop's circumference in inches?

Answers

Answer:

C = 2πr, where C is the circumference, π is the mathematical constant pi (approx. 3.14), and r is the radius (9 inches). Therefore, the circumference of the basketball hoop is 2π(9) = 18π inches.

Step-by-step explanation:

In other words use C=2*pi*radius to find the circumference, here you are given the radius is 9 so when you plug that in it gives you a circumfrence of 18pi inches. Hope this helps!

f(x) = 2x² + 4x - 5
g(x) = 6x³2x² + 3
Find (f + g)(x).
O A. (f+g)(x) = -6x³+4x² + 4x - 8
O B. (f+g)(x) = 6x² + 4x - 2
O C. (f+g)(x) = 6x³ - x² + 4x - 2
OD. (f+g)(x) = 8x³ + 2x - 2

Answers

If functions f(x) = 2x² + 4x - 5, g(x) = - 6x³+2x² - 3 then (f + g)(x)=6x³+ 4x² +4x-8

What is a function?

A relation is a function if it has only One y-value for each x-value.

The given two functions are f(x) = 2x² + 4x - 5

and g(x) = - 6x³+2x² - 3

We need to find  (f + g)(x).

(f + g)(x)=f(x)+g(x)

=2x² + 4x - 5 - 6x³+ 2x² -3

Now add the like terms

= 6x³+ 4x² +4x-8

(f + g)(x)=6x³+ 4x² +4x-8

Hence, if functions f(x) = 2x² + 4x - 5, g(x) = - 6x³+2x² - 3 then (f + g)(x)=6x³+ 4x² +4x-8

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Please help asap please I will make you the brainliest

Answers

Answer:

d= Deondre's age

d + 3

c = the number of people in the class

1/2c

w = wildcat's score

a = away team's score

w = 2a + 7

c = cost of the sweater

s = the regular cost of the sweater

c = 1/2s

y = total in the bank

x = number of weeks

y = 75x + 300

y = altitude

x = number of minutes

y = 200x + 1000

Step-by-step explanation:

PLEASE HELP

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8100 ​ft, the liquid boils at 197.04°F. At an altitude of 4500 ​ft, the liquid boils at 202.8°F. Write an equation giving the boiling point b of the​ liquid, in degrees​ Fahrenheit, in terms of altitude​ a, in feet. What is the boiling point of the liquid at 2300 ​ft?

Write an equation.
b= ??

Answers

The equation giving the boiling point b of the​ liquid, in degrees​ Fahrenheit, in terms of altitude​ a, in feet is b = -0.0016a + 210

The boiling point of the liquid at 2300 ​ft is 206.32°F

How to determine the equation giving the boiling point b of the​ liquid

From the question, we have the following parameters that can be used in our computation:

At an altitude of 8100 ​ft, the liquid boils at 197.04°F. At an altitude of 4500 ​ft, the liquid boils at 202.8°F

These parameters mean that

(a, b) = (8100, 197.04) and (4500, 202.8)

The relationship is a linear equation

So, we have

slope = (b2 - b1)/(a2 - a1)

Substitute the known values in the above equation, so, we have the following representation

slope = (202.8 - 197.04)/(4500 - 8100)

Evaluate

slope = -0.0016

The equation is then represented as

b = slope * a + c

Using one of the points, we have

197.04 = -0.0016 * 8100 + c

So, we have

197.04 = -12.96 + c

Evaluate

c = 210

This gives

b = -0.0016a + 210

What is the boiling point of the liquid at 2300 ​ft?

This means that

a = 2300

So, we have

b = -0.0016 *  2300 + 210

Evaluate

b = 206.32

Hence, the boiling point is 206.32°F

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quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (4, -4)(4,−4). What is the vertex of the function defined as g(x)=f(x-2)g(x)=f(x−2)?

Answers

The vertex of the translated quadratic equation is:

(6, -4)

What is the vertex of the translated function?

We know that we have a quadratic function f(x), such that the vertex is at (4, -4).

Here we have the translated function:

g(x) = f(x - 2)

Notice that this is a translation of 2 units to the right

Now, remember that the vertex of f(x) is at f(4), then the vertex of g(x) is at the value of x such that:

x - 2 = 4

x = 4 + 2

x = 6

So the vertex of g(x) is (6, -4)

(the y-value of the vertex does not change).

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Find the area of the isosceles

trapezoid.

Answers

Answer:

See answer below

Step-by-step explanation:

See drawing I made:

How do you dilate a line segment by 1 2?

Answers

In order to dilate a line segment by 1/ 2, every coordinate point of the end point of the line segment is multiplied by the scale factor ½.

Dilation refers to a process of changing the size of an object or shape by either increasing or decreasing its dimensions by some scaling factors. It is a type of transformation, which is used to resize the object, making the objects larger or smaller. This transformation produces an image that is the same in shape as the original but there is a difference in the size. A dilation should either stretch or shrink the original shape and is expressed by the term “scale factor.”

When a dilation creates a larger image, it is called enlargement and when a dilation creates a smaller image, it is called reduction. If the scale factor is 1/2, every coordinate point of the original segment line is multiplied by the scale factor 1/2.

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in a lottery drawing, tickets will be drawn randomly out of a hat. if 1/10 of the tickets in the hat are green. 1/2 of them are white, 1/4 of them are blue, and the remaining 30 tickets are pink, what is the number of blue tickets in the hat

Answers

The number of blue tickets is 50 tickets. The result is obtained by using the concept of operation with fractions.

How to add or subtract fractions?Find the least common denominator.Write the equivalent fraction with the least common denominator.Add or subtract the nominator without changing the denominator.

In a hat, we have:

1/10 of the tickets are green.1/2 of the tickets are white.1/4 of the tickets are blue.The remaining, 30 tickets are pink.

Find the number of blue tickets!

Let's say all tickets is a. Then,

Green tickets = 1/10 aWhite tickets = 1/2 aBlue tickets = 1/4 a

The remaining section (pink tickets) is

= 1 - (green + white + blue) tickets

= 1 - (1/10 + 1/2 + 1/4)

= 1 - (2/20 + 10/20 + 5/20)

= 20/20 - 17/20

= 3/20

All tickets are

3/20 = 30/a

a = (20 × 30)/3

a = 20 × 10

a = 200 tickets

The blue tickets are

= 1/4 a

= 1/4 (200)

= 50 tickets

Hence, the blue tickets in the hat are 50 tickets.

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[tex](4x^{2}-9y^{2})^3+(9y^{2} -16y^{2} )^3+(16z^{2} -4x^{2})^3/(2x-3y)^3+(3y-4z)^3+(4z-2x)^3[/tex]

Answers

The algebraic expression -

{ (4x² - 9y²)³ + (9y² - 16y²)³ + (16z² - 4x²)³ } / { (2x - 3y)³ + (3y - 4z)³ + (4z - 2x)³ } is simplified to give

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How to simplify the given expression

The given algebraic expression is in fraction and we solve by breaking the fraction in to two: numerator and denominator and solve separately then bring them together.

The numerator

= (4x² - 9y²)³ + (9y² - 16y²)³ + (16z² - 4x²)³

bringing the powers together

= (4x² - 9y² + 9y² - 16y² + 16z² - 4x²)³

collecting like terms together

= (4x² - 4x² - 9y² + 9y² - 16y² + 16z² )³

= (0x² - 16y² + 16z² )³

= (16y² + 16z² )³

The denominator

= (2x - 3y)³ + (3y - 4z)³ + (4z - 2x)³

bringing the powers together

= (2x - 3y + 3y - 4z + 4z - 2x)³

collecting like terms

= (2x - 2x - 3y + 3y - 4z + 4z )³

= (0x - 0y - 0z )³

= 0

with a denominator of zero the solution is undefined, this may mean infinite many solutions

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can someone answer this question really quick

The expression 2.4x−3.9y−1.2x+ay is equivalent to 1.2x+1.2y.
What is the value of a?
Enter your answer as a decimal, like this: 42.5

Answers

Answer:

[tex]a=5.1[/tex]

Step-by-step explanation:

[tex]2.4x-1.2x-3.9y+ay=1.2x+y(a-3.9) \\ \\ \implies 1.2=a-3.9 \implies a=5.1[/tex]

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