Determine the solution for 0.4(3y + -18) = 1.2y + 7.2.
No solution
Infinite solutions
y = 10
y=6

The simplified expression is 8

To find the simplified form of the mentioned expression, we will first simplify the value in bracket. Then, multiply the powers to solve it.

As per the known fact, 4² and 2⁴ result to give the number 16.

Expression = (2⁴)³/₄

Now, again as per the known fact, the exponents can be multiplied.

Exponents = 4×(3/4)

Cancelling 4 as it is common in both numerator and denominator

Exponents = 3

Putting the resultant exponent back to the expression -

Expression = 2³

Taking cube -

Expression = 2×2×2

Performing multiplication

Expression = 8

Hence, the simplified form of expression is 8

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Answer:

[tex] \sf \: x ≤ \frac{11}{6} \: or \: x> \frac{11}{3} [/tex]

Step-by-step explanation:

First question

6x-2≤9

Step 1: Add 2 to both sides.

6x−2+2≤9+2

6x≤11

Step 2: Divide both sides by 6.

6x/6 ≤ 11/6

x≤11/6

Second question

4+3x>15

Step 1: Simplify both sides of the inequality.

3x+4>15

Step 2: Subtract 4 from both sides.

3x+4−4>15−4

3x>11

Step 3: Divide both sides by 3.

3x/3 > 11/3

x> 11/3

The factoring of the expression x² = 5 x + 14 is (x+2)(x-7)

By ordering the values, we get:

x²- 5x - 14 = 0

To solve this exercise, we have to follow the rules of factoring:

1. Looking for the a and b number that state the following equations:

Analyzing that (a*b) is a negative number, it means that (a) and (b) have different signs, and due to the results of (a+b) is negative the higher number has to be the negative one.  

The number could be:

a = 2

b = -7

Confirming:

a + b = 2 + (-7) = -5

a * b = 2 * (-7) = -14

2. Rewriting the factored expression (x+a)(x+b) with the obtained values, we get:

(x+2)(x-7)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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Answer:

63/2

Step-by-step explanation:

Multiply the fraction.

[tex]\frac{9}{4}\cdot \:14\\=\frac{9}{4}\cdot \frac{14}{1}\\=\frac{9\cdot \:14}{4\cdot \:1}\\=\frac{9\cdot \:14}{4}\\=\frac{9\cdot \:2\cdot \:7}{4}\\=\frac{9\cdot \:2\cdot \:7}{2\cdot \:2}\\=\frac{9\cdot \:7}{2}\\=\frac{63}{2}[/tex]

Answer:

63/2

Step-by-step explanation:

[tex]\frac{9}{4}[/tex] [tex](\frac{14}{1})[/tex]  You can write 14 as a fraction by putting it over 1.

Now, multiple across

[tex]\frac{126}{4}[/tex]

Now divide the top and the bottom by 2

[tex]\frac{63}{2}[/tex]

The integer fraction of the expression 14x⁻², for x = 7 is 2 / 7.

The expression is expressed as follows:

14x⁻², for x = 7

This simply implies we have to simplify the expression when x = 7.

Therefore, we have to substitute the value of x in the expression. The value of x is 7.

Hence,

using indices law,

x⁻¹ = 1 / x

Therefore,

14x⁻² = 14 / x²

Hence,

14 / x² = 14 / 7²

14 / 7² = 14 / 49

14 / 49 ÷ 7 / 7 = 2 / 7

Therefore, the integer fraction of the expression 14x⁻², for x = 7 is 2 / 7.

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The answer to the question is 3√10.

The concept used here is radical expressions

Radicals, like fractions, are often simplified till you have got the littlest attainable elements. 

Be conscious of what numbers square measurewithin the unconventional sign and that square measure not! Unless you'll be able to take the rootof the individual prime numbers, they have to stay beneath the unconventional.The same methodworks for variables beneath the unconventional.

On multiplying  5 and 18 we get expression as -√90

90 can be rewritten as 9×10

9 can further be written as 3²

On simplifying we get √9×10

Since 9 is the square root of 3 we can take 3 outside the square root sign.

So the final answer is 3√10.

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Your question was incomplete. Please refer below to find the table in the image.

We need to know about powers and indices to solve the problem. The value of nonzero number raised to the power of 0 is 1.

When a number is raised to a certain power, it can be simplified as the number is multiplied to itself the number of times as the power. For example if we write [tex]2^{3}[/tex] we mean 2x2x2 which is 8. Similarly in this question we have to find the various powers of 9, the answer to [tex]9^{4}[/tex] is given, we need to find for the powers 3,2,1, and finally 0.

[tex]9^{3}[/tex]=9x9x9=729

[tex]9^{2}[/tex]=9x9=81

[tex]9^{1}[/tex]=9

[tex]9^{0}[/tex]=1

When any nonzero number is raised to the power of zero the result is one.

Therefore we found out using the concept of powers and indices that the value of a nonzero number raised to the power of 0 is 1.

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The value of the term 9w using the slope of the line is found as 54.

As per the given question;

The slope of the line is given as;

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = m = -1/9

The two coordinates from where the line is passing is (w, -2) and (3, -3).

Thus,

(x₁, y₁) = (w, -2)

(x₂, y₂) = (3, -3)

Put the values in the slope equation;

m = (y₂ - y₁)/(x₂ - x₁) = -1/9

(-3 + 2)/(3 - w) = -1/9

Cross- multiplying the terms;

9(-3 + 2) = -(3 - w)

Simplifying;

-9 = -3 + w

w = 6

The value of 9w = 9×6

9w = 54.

Therefore, the value of 9w is found as 54.

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√6 is greater than √2+1.

Suppose that √6 is greater than √2+1. Then we check if our assumption is correct.

So √6 > √2+1

Squaring both sides and using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex],

⇒ 6 > 3 + 2√2

Subtracting 3 from both sides,

⇒ 3 > 2√2

Again squaring on both sides,

⇒ 9 > 8

This is true. So our assumption is right.

Therefore,  √6 > √2+1

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Answer: 3/5

Step-by-step explanation:

First prime factor to get GCF:

36= 2 x 2 x 3 x 3

60= 2 x 2 x 3 x 5

GCF= 2 x 2 x 3 = 12

Therefore u divide each number by 12 to get your answer.

36/12=3     60/12=5

Fraction in lowest terms= 3/5

Using the Segment Addition Postulate, considering the congruent segments and the trisection, the missing lengths of the segments are given by the following items:

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For this problem, two other concepts are important, given by the bullet points below:

CD = 12, hence, considering the trisection: (12/3) = 4.

CD is also congruent to CB, hence:

CB = 12.

CE = 6, and AE = 2CE, hence:

Due to the postulate, since DG = 8 and GE = 12, and the entire lengths are of 12, and considering the congruence:

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The situation is a function; the independent variable is the number of lines and the dependent variables is the total cost

The domain is 0 <= x <= 4 and the range is 0 <= y <= 120

The statement is given as

A cell phone plan costs $30 for each line

Let the number of lines be x and the total cost be y

So, we have

y = cost per line * x

This gives

y = 30x

The above equation represents a linear function

This means that the situation is a function; the independent variable is the number of lines and the dependent variables is the total cost

From the question, we have

You can have a maximum of four lines on a plan.

This means that the possible values of x are

x = 0, 1, ... 4

When these values are substituted in y = 30x, we have

y = 30 * 0 = 0

y = 30 * 4 = 120

Hence, the domain is 0 <= x <= 4 and the range is 0 <= y <= 120

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Answer: 72 degrees

Step-by-step explanation:

ok, so the interior angles of a pentagon are 108 degrees, and the line that the two angles are on is equal to 180 degrees, so 180-108 is 72 degrees

Answer:

Step-by-step explanation:

11. Areas as Sum: 7d+28

   Areas as Product: 7(d+4)

12. Areas as Sum: [tex]y^{2}[/tex]+3y

    Areas as Product: y (y+3)

Answer:

Step-by-step explanation:

Using the distributive property, you would multiply 7(d+4) for the question after the example. The side length is your root, and you are multiplying the numbers after it by that root.

The form of the linear equation y = -5x/4 + 5/4 is 0 = 5x + 4y - 5

The linear equation is given as

y = -5x/4 + 5/4

Multiply through the equation by 4

So, we have

4 * y = -5x/4 * 4 + 5/4 * 4

Evaluate the product in the above equation

So, we have

4y = -5x + 5

Collect the like terms in the above equation

So, we have

5x + 4y - 5 = 0

Rewrite as

0 = 5x + 4y - 5

Hence, the form of the linear equation y = -5x/4 + 5/4 is 0 = 5x + 4y - 5

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36 students will be in each buses for the trip.

The total number of empty seat in the buses is 32

The school ordered 16 buses that each have 40 seats for a school trip.

There are 32 teachers and 576 students.

Each bus must have 2 teachers and the rest students.

The students were distributed evenly amongst the buses.

Therefore,

number of student in each buses = total number of student / number of buses

number of student in each buses =  576 / 16

number of student in each buses = 36

Therefore, 36 students will be in each buses for the trip.

Each buses has 40 seats.

Recall, 2 teachers are even distributed in each buses.

Therefore

number of empty seat in total = 16 × (40 - 36 - 2)

number of empty seat in total = 16 × 2

number of empty seat in total = 32

Therefore, the total number of empty seats in the buses is 32.

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A classmate writes the matrix at the right to represent a system and says that the solution is x = 2, y = 0. Classmate's error and how to describe it is mentioned as follows:

Given:

x = 2

y = 0

From this we can say that The second row of the matrix doesn't have a coefficient in the y column. The equation represented by second row is 0 = 0 and not y = 0.

Thus it is concluded that the equation represented by second row  is 0 = 0 not y = 0.

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Answer:

The slope is 2.

Step-by-step explanation:

You can use the slope formula or pick two points, count up from one point then to the right. Use rise/run if you use the counting method.

The slope formula is y2-y1/x2-x1

Use the points (20, 20) and (30, 40)

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Hope this helps!

Please mark as brainliest if correct!

We'll use 3/8 cup of macadamia nuts.

Describe ratios.

A ratio is defined as a/b where b is not equal to 0. Since a and b are separate portions of the two values, the total combined amount is expressed as (a + b).

Given:

3/4 cup of macadamia nuts are used in a banana macadamia nut bread recipe that Vincent created. We are aware of this based on the information provided.

The quantity of nuts needed if he decides to make only half the recipe is:

used macadamia nuts = 1/2 * 3/4

used macadamia nuts =3/8

Therefore, there will be 3/8cup of Macadamia nuts utilized.

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The correct question is given below

"Vincent found a recipe for banana macadamia nut bread that uses 3/4 cup of macadamia nuts. If he only wants to make half the recipe, how many cups of macadamia nuts should be use?"

The multiplication equations are :

a. 10 ÷ 5 =  2 × 5 = 10 and  5 × 2 = 10

b. 4.5 ÷ 3 = 3 × 1.5 = 4.5 and1.5 × 3 = 4.5

A complete multiplication equation will have the numbers that are being multiplied together on one side of the equal sign, and what they are equal to on the other side of the equal sign.

a. 10 ÷ 5 = ?

First we will solve the given equation

so, 10 ÷ 5 = 2

In simple way we can write the multiplication equation of above equation in two ways :

First we can write it as 2 × 5 = 10

And second is as         5 × 2 = 10

These two don't have different conclusion but they have just different written pattern.

Same as we will do the other equations.

b. 4.5 ÷ 3 = ?

Let's solve the equation first

4.5 ÷ 3 = 1.5

Multiplication equation :

3 × 1.5 = 4.5

1.5 × 3 = 4.5

c. 1/2 + 4 = ?

Solution of the above equation is :

1/2 + 4 = 9/2 = 4.5

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Carolyn will win the contest as the money raised by her is more than the money raised by Gershon.

We are given that:

For Carolyn:

Money given by parents = $ 100

Money she raises every day = $ 15

For Gershon:

Money given by parents = $ 50

Money he raises every day = $ 15

Let the number of days a contest lasts be x.

So, the equations for both will be:

For Carolyn:

100 + 15 x

For Gershon:

50 + 15 x

By comparing, we get that:

Money raised by Carolyn > Money raised by Gershon.

Therefore, we get that, Carolyn will win the contest as the money raised by her is more than the money raised by Gershon.

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The area of the whole figure includes the areas of the rectangle and the two triangles and the value is 60 square units

The area of a shape is the amount of space on the shape.

For most regular shapes, the area is the product of their width and the length

Rectangle A

The dimensions of this rectangle are

Length = 8

Width = 10 - 5 = 5

The area of the rectangle is

Area = Length * Width

This gives

Area = 8 * 5

Evaluate the product

Area = 40

Triangle B

The dimensions of this rectangle are

Base = 6

Height = 10 - 5 = 5

The area of the triangle is

Area = 0.5 * Base * Height

This gives

Area = 0.5 * 6 * 5

Evaluate the product

Area = 15

Whole figure

The area of the whole figure is

Area = Rectangle A + Triangle B + Triangle C

This gives

Area =

Evaluate the product

Area = 40 + 15 + 5

Evaluate

Area = 60

Hence, the area of the whole figure is 60 square units

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Answer:

7(n+8)

Step-by-step explanation:

It says 7 times the SUM of a number, n, and 8. According to the order of operations or PEMDAS, you would find the sum first, which would be in parenthesis, and then multiply by the 7.

Hope this helps! :)

Answer:

r = 2

Step-by-step explanation:

-12r + 16 = -8

Subtract 16 from both sides to isolate the r term.

-12r + 16 - 16 = -8 - 16

-12r = -24

Divide both sides by negative twelve.

-12r/-12 = -24/-12

Solve.

r = 2

Answer:

r=2

Step-by-step explanation:

sub 16 frome each side: -12r=-24

divide both sides by -12: r=2

would have made it more detailed but im lazy rn, have a good day

The binomial expansion for ( X + Y )⁴ is X⁴ + 4 X³(Y) + 6 X²(Y²) + 4 XY³ + Y⁴.

Use the binomial expansion theorem to find each term. The binomial theorem states ( a + b )ⁿ = ⁿ∑ _{k = 0} n C k ⋅ ( a^(n - k) × b^{k} ) .

⁴∑ _{k = 0} = ( 4 ! / [ ( 4 − k ) ! k ! ] ) × ( X )^{4 - k} × ( Y )^{k}

Expanding the summation.

( X + Y )⁴ = ( 4! / ( 4 − 0 )! 0! ) × ( X )⁴⁻⁰ × ( Y )⁰ + ( 4! /( 4 − 1 )! 1! ) × ( X )⁴⁻¹ × ( Y )¹ + ( 4! / ( 4 − 2 )! 2! ) × ( X )⁴ ⁻ ² × ( Y )² + ( 4! /( 4 − 3 )! 3! ) × ( X )⁴ ⁻ ³ × ( Y )³ + 4! / ( 4 − 4 )! 4! × ( X )⁴ ⁻ ⁴ × ( Y )⁴

Simplify the exponents for each term of the expansion.

( X + Y )⁴ = 1 × ( X )⁴ × ( Y )⁰ + 4 × ( X )³ × ( Y )¹ + 6 × ( X )² × ( Y )² + 4 × ( X )¹ × ( Y )³ + 1 × ( X )⁰ × ( Y )⁴

Therefore,

( X + Y )⁴ = X⁴ + 4 X³ (Y) + 6 X² (Y²) + 4 X Y³ + Y⁴

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Based on the fraction of their books that they have sold, the number of books that Alexander is left with is 30 books and the number of books that Sophia is left with is 11 books.

Alexander has sold 3/8 of the 48 books and so to find the number of books left, the formula is:

= 48 - (3/8 x 48 books)

= 48 - 18

= 30 books

The number of books that Sophia is left with is:
= 38 - (5/7 x 38)

= 38 - 27

= 11 books

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