Solve for x. Show each step of the solution.

5(2-x)-10=25-2(3x+40)

Integer Numbers

It can be defined as the number that can be written without a fractional (decimal) component.

Integers can be positive, negative, or 0.

From the numbers on the list only -4, 0, and 2 are integers. The rest of the numbers cannot be written without a decimal component.

For example:

-2/3 = -0.666

π = 3.14

The square root of 6 is 2.45

4.111... has an evident decimal component.

Answer: -4, 0, and 2

In the first graph, we have that the whole figure is 1

it is divided in 4 parts:

Then, we want to divide 1 into 4 parts. That is

Then, we have that:

It is the same for the second figure:

Each 1/4 corresponds to each part. Then if we add them:

The length of the line segment will be 10 units.

What is Distance?

The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √( y₂ - y₁)² + (x₂ - x₁)²

Given that;

Two endpoints of the line segment are (6, -5) and (0, 3).

Now,

The length of the line segment is distance between two endpoints (6, -5) and (0, 3).

So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √(0 - 6)² + (3 - (-5))²

D = √36 + 64

D = √100

D = 10 units

Thus, The length of the line segment will be 10 units.

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The value of x = -12.

Define Function.

A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/2 ("f of x equals x divided by 2")

The given expression is

H(x)=-5/6 x

also, H(x) = 10

so, put H(x) value in given expression,

10 = -5/6 x

Now, solve for 'x'

-5x = 60

x = 60/(-5)

x = -12

Therefore, the value of x = -12

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Answer: Relation

Step-by-step explanation: it is a relation because if you take any number on the x axis and look at its points there are two points on multiple parts

As per the concept of Simple interest, the value of x that refers the time is 0.000057.

Simple interest:

Simple interest is obtained by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Give,

Here we have the expression like the following:

p*r*t=I

4350 * 4 * x =1

Here we need to find the value of x.

While we looking into the expression, we have identified that the value of

Principal amount (p) = 4350

rate of interest (r) = 4

Time = x

Interest amount (I) = 1

So, while we execute this expression then we get the value of times as,

=> 4350 x 4 x x = 1

Here we need the value of x so, we have to move the other to the right hand side, then we get,

=> x = 1/(4350 x4)

=> x = 1/17400

=> x = 0.000057

Therefore, the value of x is 0.000057.

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The number of sheets of toilet paper that have not been used is 193473.

Multiplication simply has to do with the product of numbers.

From the information, the roll had 969696 sheets when it was new and the person used 999 sheets of toilet paper each day for 777 days.

Therefore, the sheet left will be:

= Number in the new roll - Sheets used

= 969696 - (777 × 999)

= 969696 - 776223

= 193473

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We have that:

then, in this case, we have:

therefore, the velocity of the cart is 0.9 meters per second.

Hello,

Two parallel lines have the same slope, which means that our line's slope, will also be 1.2.

So now we have a point and a slope, so we can use the following formula to find the equation of the line:

y-y1 = m (x-x1)

Where:

y1 - y coordinate of a point on the line

x1 - x coordinate of the same point on the line

m - slope

Plugging in we get:

y+3 = 1.2 (x-0)

y = 1.2x - 3 (slope intercept form)

or

5y-6x = -15 (standard form)

Cheers

Remember that the formula to calculate the total amount in an account with compoud interest is:

Where:

• P, is the principal (amount incially invested)

• r ,is the rate of interest

• n, is the times that the interest is compounded

Using this and the data given we'll get:

Thereby, we can conclude that the accounts balance after 9 years is $3,049.87

The number that you can square to give an answer bigger than 500 but bigger than 600 = 25.

The square of a number is defined as the ability to multiple the given number by itself to give a perfect whole number.

For example the square of 2, which is written as 2² = 2×2 = 4

From the given scenario, the number that would be squared to give an answer bigger than 500 but bigger than 600 = 25

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The volume of blocks = 27n³cm3.

volume of the cube box = 216n⁹ cm3.

Here given,

6n³cm is the length of the cube-shaped box's side.

3n cm is the side length of the cube-shaped blocks.

We must calculate the volume of the box and the blocks.

The formula for cube volume is,

S³ = V

where s is the cube's side length

by substituting the values,

(6n³)³ cm3 box volume

= 216 n⁹ cm³

(3n)³ cm3 is the volume of the blocks.

= 27n³ cm³

As a result, the volume of the blocks is 27n³cm3 and the volume of the box is 216 n⁹ cm³.

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Answer:

A)  Volume of one block = 27n³  cm³

     Volume of the box = 216n⁹  cm³

B)  8n⁶ blocks will fit in one box.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cube}\\\\$V=s^3$\\\\where:\\ \phantom{ww}$\bullet$ $V$ is the volume. \\\phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]

The side length of the cube-shaped block is 3n cm.

Substitute the given side length into the formula to find the volume of the block:

[tex]\begin{aligned}\implies \textsf{Volume of one block}&=(3n)^3\\&=3^3 \cdot n^3\\&=27n^3\;\sf cm^3\end{aligned}[/tex]

The side length of the cube-shaped box is 6n³ cm.

Substitute the given side length into the formula to find the volume of the box:

[tex]\begin{aligned}\implies \textsf{Volume of one box}&=(6n^3)^3\\&=6^3 \cdot (n^3)^3\\&=216n^9\; \sf cm^3\end{aligned}[/tex]

To find the number of blocks that will fit in the box, divide the volume of the box by the volume of one block:

[tex]\begin{aligned}\implies \textsf{Number of blocks}&=\dfrac{\textsf{Volume of box}}{\textsf{Volume of block}}\\\\& = \dfrac{216n^9}{27n^3}\\\\&=\dfrac{216}{27} \cdot \dfrac{n^9}{n^3}\\\\&=8 \cdot n^{9-3}\\\\&=8n^6\end{aligned}[/tex]

The number of two pt problems are 30 and 5 pt problems are 8.

Two or more expressions with an Equal sign is called as Equation.

Let x= one type of question

Let x-22= the other type of questions

100=2x+5(x-22) Distribute

100=2x+5x-110

100=7x-110

100+110=7x

210=7x

Divide both sides by 7

one type 30=x

second type 30-22=8

Hence the number of two pt problems are 30 and 5 pt problems are 8.

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letter D is the answer

Answer:

Inconsistent: parallel lines.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=4x+4\\-12x+3y=3\end{cases}[/tex]

Use arithmetic operations to isolate y in the second equation:

[tex]\implies -12x+3y+12x=3+12x[/tex]

[tex]\implies 3y=12x+3[/tex]

[tex]\implies\dfrac{3y}{3}=\dfrac{12x}{3}+\dfrac{3}{3}[/tex]

[tex]\implies y=4x+1[/tex]

Therefore, we can see that both equations have the same slope and so the graphs of these equations are parallel.

The solution to a system of linear equations is the point of intersection.

As parallel lines never intersect, there are no solutions to this system and the system is said to be inconsistent.

Answer:

The perimeter is 12 units.

Step-by-step explanation:

The answer would be 12 units because each side is 1 unit. If you count all the sides together, you get 12 units.

Answer: 12 units

Step-by-step explanation:

       The perimeter is the length around a 2D shape. We will count the units that make up this shape's outline. See attached. Please note that as long as you count every side for this shape, it doesn't matter the order you count.

       The perimeter is 12 units, the last option.

For the point 13. we have that the line passes through the points (-1,-2) and (0,1) then the slope is

and the line equation will be:

For the point 14: we have that the line passes through the points (-1,0) and (0,-1) then the sslope is:

and the line equation will be:

For the point 15: the line equation is y=-3 because the y coordinate will be always the same (-3) and the slope of the line will be equal to zero

Answer:

The equations that have infinitely many solutions are;

Explanation:

For an equation to have infinitely many solutions, the left-hand side of the equation and the right side of the equation must be equivalent/equal.

That means that the expression before the equal sign must be equivalent to the expression after the decimal.

such as;

From the given equation, the equations that have their left and right sides equivalent are;

Therefore, the equations that have infinitely many solutions are;

The greatest common factor of a polynomial is the largest expression that divides all of the terms of the polynomial. In this case, we have:

First, find the GCF of the coefficients of the terms. The coefficients are 2, 14 and 6, their GCF is 2.

On the other hand, notice that the factor (c+y) is a common factor for all three terms. Find the greatest power of (c+y) that divides all the terms. Since the lowest power of (c+y) in the expression is 2, then, the greatest power of (c+y) that divides all the terms is (c+y)^2.

The GCF of the expression is the product of the GCF of the coefficients and the GCF of the factors with variables.

Then, the GCF of the expression is:

Factor out 2(c+y)^2 from the expression:

Therefore, the answer is option A and the expression inside the box should be:

Answer: He is not correct because when simplifying an expression, you can only add like terms together.  

Step-by-step explanation:

you are given the expression: x^2 + 4x - 2x

when simplifying an expression, you can only add/subtract like terms (terms that have the same variable which are raised to the same power).

in the expression, you can only subtract 4x - 2x because they have like terms/the same variable.

you cannot add x^2 to 4x because x^2 and x are NOT like terms/the same variable. (If 4x was 4x^2, then you would be able to add them together.

meaning the simplified expression should be: x^2 + 2x and not 3x^2

Using ratio and proportion, Louie is correct.

Ratio is defined as the relationship between two quantities. On the other hand, proportion is defined as the equality between two or more ratios.

From the given graph (see attached photo), the coordinates of Point F and Point G is (4, 8) and (-6, -7).

If the ratio of FP to PG is 4 to 1, then the ratio of the horizontal distance and vertical distance between the two endpoints is also 4 to 1.

FP : PG = 4 : 1

FP/PG = 4/1 = 4

x-coordinate of P

(4 - x)/(x - -6) = 4

(4 - x) = 4(x + 6)

4 - x = 4x + 24

-5x = 20

x = -4

y-coordinate of P

(8 - y)/(y - -7) = 4

(8 - y) = 4(y + 7)

8 - y = 4y + 28

-5y = 20

y = -4

Hence, the coordinates of Point P is (-4, -4).

Therefore, Louie is correct, while Nicky is mistaken probably while setting up the proportion and solving for the coordinates.

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A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position.

n/37=236n=1111 /37 =0.2972972972972972972972972972972972972972

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The value of x in the triangle is 3.

The exterior angle of the triangle is VBC.

Using the exterior angle theorem, the value of x can be found in the triangle.

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

In other words,  an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Therefore,

m∠D = 9x - 2

m∠C = 40°

m∠VBC = 20x + 5

Hence,

20x + 5 = 9x - 2 + 40

20x + 5 = 9x + 38

20x - 9x = 38 - 5

11x = 33

x = 33 / 11

x = 3

Therefore,

x = 3

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The ∛35 will be plotted between 3 and 4, but closer to 3 on the number line.

In basic mathematics, real numbers are shown as a fine graphic of a graduated straight line which is called a number line.

We know that 35 lies between 27 and 64 , and 27 = 3³ and 64 = 4³.

Hence the ∛35 will be plotted between 3 and 4 and since 35 is closer to 27 than 64 , therefore it will be closer to 3.

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We are given a graph and we are asked to determine if it is a function or not. To do that we will use the vertical line test. We will draw a vertical line and if the line touches the graph in more than two places in any given value of "x" then it is not a function. Therefore, the vertical line we get is:

Since the vertical line touches the graph in two axes this means that the given graph is not a function.

Hey there!

2v - 7 - 12v + 15
COMBINE the LIKE TERMS

= (2v - 12v) + (-7 + 15)

= 2v - 12v - 7 + 15

= -10v + 8

Therefore, your answer should be:

-10v + 8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

126

Step-by-step explanation:

90 ÷ 10 = 9

9 × 4 = 36

90 + 36 = 126

According to Euler's Theorem, if gcd(a,n) = 1, then a(n) 1. (mod n). The number of relatively prime integers in the range of 1, 2,..., n-1 is represented by the Euler totient function.

The probability that mn has a units digit of 1 = 2/5

By Euler's Theorem, we have that [tex]$a^{4} \equiv 1 \pmod {10}$[/tex] if [tex]$\gcd(a,10)=1$[/tex] Hence[tex]$m=11,13,17,19$,[/tex][tex]$n=2000,2004,2008,2012,2016$[/tex] work.

Also note that [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex] because [tex]$11^b=(10+1)^b=10^b+10^{b-1}1+...+10(1)+1$[/tex], and the latter[tex]$\pmod {10}$[/tex]is clearly [tex]$m=11$[/tex],  [tex]$n=1999,2001,2002,2003,2005,...,2018$[/tex] work (not counting multiples of 4 as we would be double counting if we did).

We can also note that [tex]$19^{2a}\equiv 1 \pmod {10}$[/tex] because[tex]$19^{2a}=361^{a}$[/tex], and by the same logic as why [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex]we are done. Hence [tex]$n=2002, 2006, 2010, 2014, 2018$[/tex] and [tex]$m=19$[/tex] work (not counting any of the aforementioned cases as that would be double counting).

We cannot make any more observations that add more[tex]$m^n$[/tex] with unit digit [tex]$1$[/tex], hence the number of [tex]$m^n$[/tex] that have units digit one is [tex]$4\cdot 5+1\cdot 15+1\cdot 5=40$.[/tex] And the total number of combinations of an element of the set of all [tex]$m$[/tex]and an element of the set of all n is  [tex]$5\cdot 20=100$[/tex]. Hence the desired probability is [tex]$\frac{40}{100}=\frac{2}{5}$[/tex].

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