I didn’t understand when my teacher taught this. Could you help show me how to solve this

Answer:

you mean greatest common factor?

Answer

- The solution of this compound inequality is x < 3 OR x ≥ 4

- The graph of this solution is attached below

- The interval notation is (-∞, 3) OR [4, ∞)

Explanation

The compound inequality to be solved is

6x - 3 < x + 12 OR 5x - 6 ≥ 3x + 2

To solve this, we solve each of the pair one at a time for the two-part solution

6x - 3 < x + 12

6x - x < 12 + 3

5x < 15

Divide both sides by 5

(5x/5) < (15/5)

x < 3

OR

5x - 6 ≥ 3x + 2

5x - 3x ≥ 6 + 2

2x ≥ 8

Divide both sides by 2

(2x/2) ≥ (8/2)

x ≥ 4

So, the solution is

x < 3 OR x ≥ 4

So, this solution says that x is less than 3, but greater than or equal to 4.

For the graph, Note that

In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.

But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.

This solution tells us that the wanted parts are numbers less than 3 and numbers greater than 4.

Also, in writing inequalities as interval, the signs (< or >) indicate an open interval and is written with the bracket () while the signs [≤ or ≥] denote a closed interval which is denoted by the brackets [].

x < 3, that is, x ranges from negative infinity to just before 3.

x < 3 is (-∞, 3)

x ≥ 4, that is, x ranges from 4 to infinity

x ≥ 4 is [4, ∞)

Hope this Helps!!!

(a)

The expression are equivalent to each ohter if both expressions give same value for all assign values of x. From the table it can be observed that both expression do not give same value for all values of x. Thus expression

and 3x + 4 are not eqivalent to each other.

(b)

From the table, it can be observed that values of the expression are equal for x = 4. So equation

holds true for x = 4.

Answer:

D

Step-by-step explanation:

I'll try to be brief

Let's plug in our 'y' variable (2x)

2x + (2x) = 20

4x = 20

x = 5

Now, plug in our 'x' variable to get our 'y' variable:

y = 2(5)

y = 10

So, our answer in (5, 10)

Or, D

By using the concept of factors and multiples, it can be inferred that

Product of a and b i.e. ab has atleast (m + n) trailing zeroes which is greater than both m and n

What are factors and multiples?

Suppose the number is k. Factors of k are those numbers that divide k.

For example: Factors of 6 are 1, 2, 3 and 6

Multiples of k are those numbers which are divided by k.

For example Multiples of 6 are 6, 12, 18, ....

Since the factors are of multiple of 10, then the factors will have atleast one trailing zero. Let the factors be a and b

Suppose a has m trailing zeroes and b has n trailing zeroes.

Product of a and b i.e. ab has (m + n) atleast trailing zeroes which is greater than both m and n

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When we apply the concept of factors and multiples, we concluded that the product of a and b i.e. ab has at least (m + n) trailing zeroes that are greater than both m and n.

What are factors and multiples?

A multiple is a number that, up to a given number of times, can be divided by another number without leaving a leftover.

A factor is a pair of integers or more that divide a given number by itself without leaving a residue.

Here,

the factors are of multiple of 10, then the factors will have at least one trailing zero.

We let the factors be a and b

Suppose a has m trailing zeroes and b has n trailing zeroes then, the Product of a and b i.e. ab has (m + n) at least trailing zeroes which are greater than both m and n.

Hence, we concluded that the product of a and b i.e. ab has at least (m + n) trailing zeroes that are greater than both m and n.

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Answer: I believe it's just custom. Some nations follow the quantity with a currency symbol, such as the dollar sign.

According to one hypothesis I've heard, the currency symbol was added before the quantity to stop individuals from modifying handwritten amounts, like changing 25.00 into 125.00, for example. It might be accurate, however I believe that the amount is always spelled out in words in the majority of situations when such fraud would be conceivable, such as on checks.

Step-by-step explanation:

a. The expression represents the perimeter of a polygon:

n represents the number of sides of the polygon.

b. If we have 60 sides, then n = 60.

We can calculate the approximation given by the expression as:

We can then calculate the difference with π using a calculator as:

The difference is approximately 0.0036.

Data

Rey wrapped 6 presents every 10 hours.

will it take to wrap 18 presents?

Procedure

It will take 30 hours

Answer: it will take 30 hours to wrap 18 gifts

Step-by-step explanation:

I cant really explain it so i will show you.

() = h (hours)

| = g (gifts)

( | | | | | | ) }-6

( | | | | | | ) }-6

( | | | | | | ) }-6

10h + 10h + 10h = 30h

6g + 6g + 6g = 18g

I hope this helped

It order to find f(5) and f ( -6 ) we just replace x on the equation with

x = 5 and x = -6

In the first case, x = 5

In the second case, x = -6

In linear equation, 50x is the total cost of dance classes each month.

What is a linear equation example?

C = 50x + 75, where 75 is the application fee. When they take out the application fee, it will become:

C = 50x +75 (-75)

C = 50x

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Answer:

The word sentence you are looking for is:

n + 4.1 ≤ 7

Step-by-step explanation:

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Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

Answer:

3

Step-by-step explanation:

Since + × - = -

The - sign will change

+7 - 4 = 3

Least common denominator is the lowest number to which all the fractions can be expanded, so it is the Least common multiple of all denominators.

Given that,

We have to find the difference of LCD and LCM.

The least common multiple, or LCM, is the smallest common multiple of any two or more numbers. What does "common" mean? In this context, the word "common" refers to something that is shared by two or more people.

The LCD, or least common denominator, is the least common multiple of two or more denominators. In this instance, the denominator, or bottom number, of a fraction contains the common multiple. When arithmetically adding or subtracting fractions, the LCD must be computed. When dividing or multiplying fractions, the LCD is not required.

For example,

Let's check the following fractions:

(1/2,2/3,5/6)

To find the Least common denominator of the fractions we have to find the Least common multiple of the fractions' denominators:

lcd(1/2,2/3,5/6)=lcm(2,3,6)

To calculate the Least common multiple we have to find the lowest number which can be obtained by multiplying those numbers.

This number is 6 because we can multiply 2×3 and 3×2 to get 6.

Therefore, Least common denominator is the lowest number to which all the fractions can be expanded, so it is the Least common multiple of all denominators.

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Answer:

4x - y = - 19 and x + 4y = 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

8x - 2y = - 5 ( subtract 8 from both sides )

- 2y = - 8x - 5 ( divide through by - 2 )

y = 4x + [tex]\frac{5}{2}[/tex] ← in slope- intercept form

with slope m = 4

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

to find c substitute (- 4, 3 ) into the partial equation

3 = - 16 + c ⇒ c = 3 + 16 = 19

y = 4x + 19 ← equation of parallel line in slope- intercept form

subtract y from both sides

0 = 4x - y + 19 ( subtract 19 from both sides )

- 19 = 4x - y , that is

4x - y = - 19 ← equation in standard form

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

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex] , then

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

to find c substitute (- 4, 3 ) into the partial equation

3 = 1 + c ⇒ c = 3 - 1 = 2

y = - [tex]\frac{1}{4}[/tex] x + 2 ← equation of perpendicular line in slope- intercept form

multiply through by 4 to clear the fraction

4y = - x + 8 ( add x to both sides )

x + 4y = 8 ← equation in standard form

We want to solve the following equation

x² + 16x + 5 = 0

↓

x² + 16x = 5

We want to rewrite the equation so its left side is

(x + a)²

We know that

(x + a)² = x² + 2ax + a²

where a is a number, then, we want that the left side look something like

x² + 2ax + a²

Then we first want to find which must be the number a in this case.

Since 2 · 8 = 16, then the left side is

x² + 16x = x² + 2 · 8x

then, in this case a would be 8

a = 8

We want that the left side of our equation looks like:

x² + 2ax + a²

Since it has the first two terms

x² + 16x = 5

we have to add a² = 8² = 64

We add it both sides of the equation:

x² + 16x + 8² = 5 + 64

x² + 2 · 8x + 8² = 69

Now, we can write it as (x + a)²

x² + 2 · 8x + 8² = 69

↓ since (x + a)² = x² + 2ax + a²

(x + 8)² = 69

In order to solve the equation, we want to "leave x alone" on the left side:

(x + 8)² = 69

↓ squaring root both sides

(x + 8) = ±√69

x + 8 = ±√69

↓ taking 8 to the right side

x = - 8 ±√69

We have two solutions:

x₁ = - 8 -√69

x₂ = - 8 + √69

Since

A straight line can be written in the form of a two variable linear equation.

The equation of line passing through point (4,0) is  y = -1 / 17 x + 4.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

Given that,

The line is passing through the point (4,0).

It is parallel to the line passing through (7, -3) and (-10. -2).

The slope of the line passing through (7, -3) and (-10. -2) is

m₁ = (-2-(-3)) / (-10 - 7)

m₁ = - 1 / 17

Since the slope of two lines parallel to each other is equal, the slope of the line passing through point (4,0) is - 1 / 17.

Thus, the equation of line passing through point (4,0) can be written as,

(y - 4) / (x - 0) =  - 1 / 17

=> y = -1 / 17 x + 4

Hence, the equation of the given line is y = -1 / 17 x + 4.

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Explanation:

Let x be the number of people and y be the amount of meat.

They have a proportional relationship:

To find the constant of proportionality k we use the initial information that for 10 people she uses 4 pounds of meat.

x=10 and y=4:

The relationship is:

Now we just have to replace x by 20, 30, 40, 50 and 75 in this relationship and find y

Answer:

Number of people Amount of meat

20 8

30 12

40 16

50 20

75 30

We can use the quadratic formula to solve this question. The quadratic formula is given below.

In our case,

Then, the solutions are

The solutions are 1/2+sqrt(3)/2 and 1/2-sqrt(3)/2

Answer:

There would be 88 fluid ounces in 4 prints and 3 cups.

Step-by-step explanation:

So, if 1 print is equal to two cups, and we have 4 prints, that would mean we can multiply 4 x 2, which equals 8 cups. Now that the prints are out of the way, we add the 3 cups still remaining, to get 11 cups. Now, it wants us to find the fluid ounces, which 16 fluid ounces are in 2 cups, so, 11 divided by 2 = 5.5. So, 5.5 x 16 = 88 fluid ounces.

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Answer:

88

Step-by-step explanation:

16x4=64

8x3=24

64+24=88

To understand the question, let us draw the graphs of each one

The red graph represents A

The blue graph represents B

The green graph represents C

The purple graph represents D

Let us find the narrowest

The blue graph is the narrowest because it is closed to the y-axis more than the other graphs

The correct answer is B

The linear inequality that represented by the graph is given as follows:

y < -4x/3 + 5.

The inequality is represented by a line, which has the following format:

y = mx + b.

In which the coefficients of the equation of the line are listed as follows:

The two points of the line are given as follows:

(0,5) and (3,1).

Hence the intercept is:

b = 5.

The slope is given by the change in y divided by the change in x, hence it is of:

m = (1 - 5)/(3 - 0) = -4/3.

Hence the line is:

y = -4x/3 + 5.

The inequality is below the shaded line, hence it is:

y < -4x/3 + 5.

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Answer:

y < -4/3x + 5.

Step-by-step explanation:

The required equation for line M will be 4x+72=y as in the form of y=ax+b because line L is perpendicular to line M.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign. A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here,

If x-intercept=B and y-intercept=E

Point B=(16,0)

Point E=(0,4)

point A=(-16,4+4)

=(-16,8)

line M is perpendicular to line L,

slope of L=-4/16

=-1/4

slope of M=-1/-1/4=4

The equation of line M will be,

point=(-16,8)

slope=4

y-8=4(x+16)

y-8=4x+64

4x-y+72=0

Line L is perpendicular to line M, so the required equation for line M will be 4x+72=y in the form of y=ax+b.

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Answer:

x+1/x-1 + 1-x/x+1 + 4x/1+x^2

Answer:

A. Subtract the distance between each point and the x-axis.

Step-by-step explanation:

The points shown are horizontally distanced. Because of this, you need to subtract their x values. In coordinate planes, the variable "x" represents how far a point is or is not from the origin. Given this information, you need to subtract the x values to get the distance they are apart. Note: Distance on a number line or graph is always given in absolute value. Absolute value is the term for when a number is converted to its positive form. For instance, |-1| has these brackets around it representing absolute value. Whenever a number in absolute value is a negative number or is greater than 0, it will become its positive form. |-1| = 1

Hope this helps!

Option A is correct, By subtracting the distance between each point and the x axis we  find the distance between the points shown

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The given two points in the given graph are A(-8, -4) and B(2,-4)

Now let us plug in these points in the formula.

x₂= 2, x₁ = -8, y₂=-4, y₁=-4

Distance=√(x₂-x₁)²+(y₂-y₁)²

=√(2+8)²+(-4+4)²

=√(10)²

=10 units.

By subtracting the distance between each point and the x axis we can find the distance.

Hence, Option A is correct, By subtracting the distance between each point and the x axis we  find the distance between the points shown

​

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Answer:-53/4

Step-by-step explanation:

Answer: -53/4

Step-by-step explanation:

[tex]\displaystyle\\-13.25=\\\\-13\frac{25}{100}=\\\\-13\frac{25(1)}{25(4)}=\\\\-13\frac{1}{4} =\\\\-\frac{13(4)+1}{4} =\\\\-\frac{52+1}{4}=\\\\-\frac{53}{4}[/tex]

Answer:

-3

Explanation:

To calculate the rate of change of the function, we pick two pairs of points.

(8, -40) and (17,-67)

We use the formula below:

The rate of change of the function is -3.

Answer:

6. 24

Step-by-step explanation:

A) Use pythogaras theoram

8x8 - 5x5 = axa - bxb = c

64-25= 39

39 square root =6.24

Area: (4 * 2) + (4 *2) = 16cm^2

Perimeter: (4 + 2 )+ 6 + (2 + 2 + 4) = 20

The equation of the line that is passing through the point (4,−17) and is perpendicular to y=x/7−3 is 7x -y = -30.

The line is passing through the point (4,-17) and is perpendicular to the line y = x/7-3

Now, the slope of the given line y = x/7-3 is,

M = 1/7

If the other line is perpendicular to it and has slope m, then the, we can write,

Mm = -1

So, putting values,

(1/7)m = -1

m = -7

Now, we have the slope m = -7 of the line and the point (4,-17) of the line,

So, the equation of the line will be,

m = [y-(-17)]/[x-4]

-7 = y+17/x-4

7x+47 = y+17

7x -y = -30

So, the equation of line is 7x -y = -30.

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