Find the value of x and y. Show all of your work or explain how you get your answer.

The solution of the inequality expression given as 12 + 4y < 32 is y < 5

An inequality expression is an expression where both sides of the expression have unequal values and they make use of any of the symbols <, >, <=, >= and !=

The inequality expression is given as

12 + 4y < 32

Subtract 12 from both sides of the inequality

So, we have the following expression

12 - 12 + 4y < 32 - 12

Evaluate the like terms in the above inequality

So, we have the following expression

4y < 20

Divide both sides of the inequality by 4

So, we have the following expression

4y/4 < 20/4

Evaluate the quotient

y < 5

Hence, the solution is y < 5

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Answer: 12 is the answer. Hope this helps Have a good day mark me brainlist

Step-by-step explanation:

4•(5-8)

Calculate the difference

4•(-3)

The absolute value of any number is always positive is always positive.
4•3

Multiply the numbers

=12

We can say that the graph of 4x+5y = 3/7 is a line because it can be represented by the straight line equation.

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.

Given equation :   4x+5y = 3/7

The given equation can be written as

5y = -4x + 3/7

y = (-4/5)x + 3/35

This is a form of y = mx + c

It is a the equation of the straight line.

Therefore, we can say that the graph of 4x+5y = 3/7 is a line as it can be represented as the equation of the straight line.

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Answer:h

Step-by-step explanation:

Answer:

2a

Step-by-step explanation:

when you have two of the same variable you can combine them. We know that all variables that do not have a coefficient by default have the constant 1 so 1a+1a equals 2a

If a given point, P, exists on a great circle on the surface of a sphere, no line can be drawn on the sphere that is parallel to the great circle because each pair of great circles(parallel lines) will always intersect, regardless of how they are drawn.

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The product of the HCF and LCM of 12 ,18,30 can be written as 1080.

The H.C.F.  can be described as the greatest factor  that can be found when expressing given two or more numbers, on the other hand the LCM can be described as the least factor that exist between a two given number.

factors of 12 are: 3, 4, 2, 6, 12.

factors of 18 are: 2, 3 , 6 9 , 18

factors of 30 are ; 2, 3, 6, 5, 10

HCF; The factor that is greatest among the factors of the numbers = 6

To calculate the LCM, we need to find to find the prime factor of the three numbers as:

Prime factor of 12 are ;  2*2*3

Prime factor of 18 are ; 2*3*3

Prime factor of 12 are ; 2*3*5

LCM is now the multiplication of the prime factors which is the highest occurrence of them in either numbers as ; 2*2*3*3*5 =180

From the given numbers we can see that the HCF = 6 and LCM = 180, then if we find the product as (6*180)=1080 which is the number of the product of the lowest common factor as well as the highest common factor.

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Area of Rectangles of the given values are 5/3inches², 20/3inches², 10/3inches² and 1 inches²

What is Area of Rectangle?

The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle called its area.

Since we know that,

Area of Rectangle = length x width

So, by the given values we can find the area of the following:

a) 5inch and 1/3inch

Let,

Length = 5inch

Width = 1/3inch

Since,

Area of Rectangle = length x width

                               = 5 x 1/3

                               = 5/3inches²

b) 5inch and 4/3 inch

Let,

Length = 5inch

Width = 4/3inch

Since,

Area of Rectangle = length x width

                               = 5 x 4/3

                               = 20/3inches²

c) 5/2inch and 4/3 inch

Let,

Length = 5/2inch

Width = 4/3inch

Since,

Area of Rectangle = length x width

                               = 5/2 x 4/3

                               = 5 x 2/3

                               = 10/3inches²

d) 7/6 inch and 6/7inch

Let,

Length = 7/6inch

Width = 6/7inch

Since,

Area of Rectangle = length x width

                               = 7/6 x 6/7

                               = 1 inches²

Hence, The following area of rectangles are 5/3inches², 20/3inches², 10/3inches² and 1 inches²

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10 is a natural number, whole number and an integer.

Natural numbers may be defined as the numbers which include all the positive integers that is non-negative integers, and the numbers will be from 1 to infinity. 10 is a natural number as it lies in the range from 1 to infinity. Whole numbers may be defined as the numbers which include all the positive integers as well as zero. So, the range of whole numbers is from zero to infinity and 10 is a whole number as it lies in this range. Integers may be defined as the collection of positive and negative numbers along with zero but no fractions. 10 lies in this range so 10 is an integer.

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The table can be given as for 3 hours we have 18 km and for 4 hours we have 24km, founded by using average.

So, we are given that Callan hikes at a rate of 6 km an hour.

In this way, he will hike 18 km in 3 hours.

(Refer to the graph attached below)

Hence, using averages, we know that the table can be given as for 3 hours we have 18 km and for 4 hours we have 24km.

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The value of the [tex]\lim_{x\to \ 0} h(x)[/tex] cannot be determined based on the given information.

Squeeze Theorem :

When standard algebraic techniques like factorization, conjugation, algebraic manipulation, etc. fail to solve a limit problem, the squeeze principle is utilized. It does, however, demand that you can "squeeze" your issue between two other, "simpler" functions whose bounds are quickly computed and equal.

It states that if [tex]g(x),f(x) and h(x)[/tex] are three functions such that,

[tex]g(x)\leq h(x)\leq f(x)[/tex]

and [tex]\lim_{x\to \ 0} f(x) = \lim_{x \to \ 0} g(x) =L[/tex] , Then

[tex]\lim_{x\to \ 0} h(x) = L[/tex]

Given Data :

[tex]g(x)=\frac{x^{2} }{3} +\frac{2}{5}[/tex]

Now, [tex]\lim_{x\to \ 0} g(x) =\frac{2}{5}[/tex]

and [tex]f(x) = x^{2} -2x+4\\[/tex]

and [tex]\lim_{x \to \ 0} f(x)=4[/tex]

Since,[tex]\lim_{x \to0} f(x) \neq \lim_{x\to \ 0} g(x)[/tex]

Thus, we cannot employ the Squeeze Theorem, Hence the data is insufficient to calculate the limit of h(x).

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The area is 28.26 in²

Because we have a closed dot at (4, 17), we conclude that when x = 4 the value of the function is 17, so the correct option is the third one.

Here we have the graph of a piecewise function, and we want to see which value the function takes when x = 4.

To do so, we need to find x = 4 on the horizontal axis, and then move until we hit the graph.

For x = 4 we can see two points on the graph.

One open point at y = 7, where the open dot means that this value does not belong to the function.

A closed point at y = 17, where the closed dot means that this value belongs to the function.

From this, we conclude that when x = 4, the value of the function is 17.

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Answer:2.10971436E14

Step-by-step explanation:

Answer:

Step-by-step explanation:

1,747,544,165,078,382 is the answer.

19x/3+2/9 is the quotient and 50 is the remainder for the given equation (6x³+13x²-12x-6)÷(3x+2).

The result of dividing two numbers is known as the quotient. Six divided by two results in the number three. Latin's "how many times" is the meaning of the word "quotient." That makes perfect sense: by dividing two numbers, you can determine "how many times" the second number enters the first.

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remainder is the name for this amount.

On dividing the equation,

The quotient will be 19x/3+2/9 and the remainder will be 50.

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The radical form  ∛ is 1/3.

The radical form of the expression [tex]15^{\frac{1}{3}[/tex] is ∛15.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. 

Example: 3 + x, 3x, √4, ∛27 are all expressions.

We have,

[tex]15^{\frac{1}{3} }[/tex]

We need to write it in radical form.

This means we must remove the power 1/3 in the given expression.

Some of the expressions in the radical form are:

∛ = 1/3

√ = 1/2

We know that,

∛ = [tex]\frac{1}{3}[/tex]

So,
Since ∛ is 1/3 we can write the expression as ∛15.

[tex]15^{\frac{1}{3} }[/tex] = ∛15.

Thus,

The radical form of the expression [tex]15^{\frac{1}{3}[/tex] is ∛15.

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The distance between the two boats is found as 21.60 m.

For the given question,

Let the distance of ship c from the bottom of the cliff is 'a'.

Let the distance between both ships is 'b' m.

The height of the cliff is 110 m.

The angle of depression by both the ship with the top of the cliff is 48° and  57°.

Data from the figure shown,

Consider right triangle ABD,

tan 48° = AB/BD

tan 48° = 110/(a+b)

a + b = 110/tan 48°

a + b = 99.04   .......eq 1

Now in  right triangle ACD,

tan 57° = 110/a

a = 110/tan 57°

a = 71.43 m

Put the value of in eq 1.

a + b = 99.04

b = 99.04 - 71.43

b = 21.60 m

Thus, the distance between the two boats is found as 21.60 m.

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IN THE PLACE OF Y PLUG IN 0

[tex] = \frac{( {0})^{2}}{5} \\ = \frac{0}{5} \\ = 0[/tex]

The answer is 0

Answer:

Jos is 14 years

Step-by-step explanation:

Let Father's age be x

[tex]{ \tt{father = x}} \\ { \tt{jos = x - 33}}[/tex]

- The question says, product of their ages is 658

[tex]{ \tt{x(x - 33) = 658}}[/tex]

- Open the brackets following distributive property;

-

[tex]{ \tt{ {x}^{2} - 33x = 658 }} \\ { \tt{ {x}^{2} - 33x - 658 = 0 }}[/tex]

- Using bulldozer method;

[tex]{ \tt{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }} \\ [/tex]

- A general quadratic equation has a format ax² + bx + c = 0

[tex]{ \tt{x = \frac{ - ( - 33) \pm \sqrt{ {( - 33)}^{2} - (4 \times 1 \times - 658)} }{2 \times 1} }} \\ \\ { \tt{x = \frac{33 \pm \sqrt{3721} }{2} }} \\ \\ { \tt{x = \frac{33 \pm61}{2} }} \\ \\ { \tt{x = \frac{33 + 61}{2} \: \: or \: \: \frac{33 - 61}{2} }} \\ \\ { \tt{x = 47 \: \: \: or \: \: \: - 14}}[/tex]

- Father's age = 47 years

- Jos's age = (47 - 33) = 14 years

Answer: Jos is 14 years old

Step-by-step explanation:

Let Jos is x years old

Hence, father is (x+33) years old

[tex]x(x+33)=658\\\\x^2+33x=658\\\\x^2+33x-658=658-658\\\\x^2+33x-658=0\\\\a=1 \ \ \ \ \ b=33\ \ \ \ \ c=-658[/tex]

[tex]\displaystyle\\x=\frac{-bб\sqrt{D^} }{2a} \\\\D=b^2-4ac\\\\D=33^2-4(1)(-658)\\\\D=1089+2632\\\\D=3721\\\\\sqrt{D}=\\\\ \sqrt{3721}=\\\\61\\\\ x=\frac{-33б61}{2(1)}\\\\ x=\frac{-33-61}{2}\\\\x=-47\notin\\\\x=\frac{-33+61}{2} \\x=\frac{28}{2} \\\\x=14[/tex]

Answer:

6/4

Step-by-step explanation:

For a RIGHT triangle, Tan = opposite leg / adjacent leg  =  6/4 for angle F in this example

we have the equation

2x^2-11x=1​

2x^2-11x-1=0

where

a=2

b=-11

c=-1

substitute in the quadratic formula

the solutions are

Answer:

G(0) = 5

Step-by-step explanation:

substitute x = 0 into G(x) , then

G(0) = - 3(0) + 5 = 0 + 5 = 5

If a caterer needs 21 pounds of pasta and a local store sells 8 pounds of pasta for $12, then the caterer has to pay a total amount of $31.5 at the store for their 21 pounds of pasta, calculated using the unitary method.

As per the question statement, a caterer needs 21 pounds of pasta to cater a wedding, while a local store sells 8 pounds of pasta for $12.

We are required to calculate the total amount which the caterer will have to pay at the store for their 21 pounds of pasta.

To solve this question, first we will need to calculate the price of 1 pound of pasta at the local store, from their rate provided in the question statement, and then multiply the cost of unit pound of pasta with the number of pounds the caterer needs, to obtain our desired answer, that is,

Using the unitary method, we get,

The local store sells 8 pounds of pasta for $12,

Or, it then sells 1 pound of pasta for $(12/8)

Or, the cost of 21 pounds of pasta at this store will $[(12/8) * 21] = $31.5

Hence,  the caterer has to pay a total amount of $31.5 at the store for their 21 pounds of pasta.

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Answer:

Your answer is 1649 miles.

Step-by-step explanation:

[tex]5^{4} + 4^{5} = 1649[/tex]

The bridge is 895.79 feet above the river.

The length of the section of the bridge above the arch is 179.58 feet.

The underside of the bridge is in the shape of an arc.

The height of the bridge is represented by the function,

y = - 0.000475x² + 0.851x

Now, when the height will be maximum, dy/dx = 0

Therefore,

dy/dx = (d/dx)( - 0.000475x² + 0.851x )

dy/dx = - 0.00095x + 0.851 = 0

- 0.00095x + 0.851 = 0

Subtracting 0.851 from each side,

- 0.00095x = - 0.851

Dividing each side of the equation by 0.00095

x = 895.7895 feet ≈ 895.79 feet

Therefore, the maximum height of the bridge is h = 895.79 feet.

The length of the section is represented by x,

y = - 0.000475x² + 0.851x

To obtain the x-intercept, we put y = 0:

- 0.000475x² + 0.851x = 0

x ( - 0.000475x + 0.851) = 0

Therefore,

x = 0 and,

- 0.000475x + 0.851 = 0

- 0.000475x = - 0.851

x = 1791.58 feet

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Answer: no clue sonny boi but good luck

The number of arrangements of the word DARWIN beginning and ending with a vowel = 48 ways

The number of letters in DARWIN = 6

The vowels are "A" and "I"

Number of vowels = 2

Number of ways of arranging the two vowels that will be at the beginning and end = 2! = 2 x 1 = 2 ways

There are 4 remaining letters after excluding the vowels

Number of ways of arranging the 4 remaining letters = 4!

Number of ways of arranging the 4 remaining letters = 4 x 3 x 2 x 1

Number of ways of arranging the 4 remaining letters = 24 ways

Therefore, the number of arrangements of the word DARWIN beginning and ending with a vowel = 2 x 24

The number of arrangements of the word DARWIN beginning and ending with a vowel = 48 ways

The polynomial factors are (x -2)(x+ i)(x - i)

In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

To find the factors of the given polynomial, we can proceed as

[tex]x^3 -2x^2 + x - 2[/tex]

Let's factor out a common term

[tex]x^3 - 2x^2 + x - 2 = x^2(x-2) + (x-2)\\x^2(x-2)+(x-2)\\(x-2)(x^2+1) = (x-2)(x+i)(x-i)[/tex]

The factors of the given polynomial is (x-2)(x+ i)(x- i)

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