The width of a rectangle is 3 units less than the length. The area of the rectangle is 18 units. What is the length, in units, of the rectangle?

Step-by-step explanation:

We only combine like terms when the like terms are alike

To combine like terms, we have to add the coefficients and keep the variables the same. We add like terms to make one term. Example: 7x+3x both are like terms we can combine together and write 10x.

The answers are subtraction, subtraction, and addition property of equality

There are 9 properties of equality, which are addition, subtraction, multiplication, division, distributive, substitution, reflexive, symmetric, and transitive. In this case, we are using the first 2. In algebra, whatever you do to one side has to be done to the other, in the case of the first problem x is being subtracted on both sides, which represents the definition of the subtraction property (If a = b, then a – c = b – c, a is the one side of the equation, b is the other side, and c is the subtraction done on both sides). The first one is the subtraction property of equality, then, and if we look at problem 2, the same thing is done (apart from that it is done with a number, which doesn't affect the property), so it is also the subtraction property.

Now the last problem seems to do the opposite, it seems to be adding instead, in this case, adding 1 on both sides. This follows the definition of the addition property of equality (If a = b, then a + c = b + c) since it is adding c (1) on both sides. So the last problem is the addition property of equality.

The mass of ingredient is given by 66g, 45g, 100g, 150g.

What is mass?

Mass is a parameter of measurement that calculates how much matter is contained in a body.

Mass is a physical quantity. Mass is measured in terms of the weight of a body. Gram, kilogram, and pounds are some standard mass units to measure it. The SI unit of mass is the kilogram; however, smaller objects are measured in grams.

Given, the ratio of the ingredients by mass as 2:2:1.

Let x be the mass of the ingredients.

A) total mass is given by 330g

therefore, 2x+2x+1x = 330

5x = 330

x = 330/5

x = 66

Hence the mass of oat = 2(66) = 132g

mass of cereal = 2(66) = 132 g

mass of nuts = 66g

B) 2x+2x+1x = 210

5x = 210

x = 210/5

x = 42g

Hence,  the mass of oat = 2(42) = 84g

mass of cereal = 2(42) = 84 g

mass of nuts = 84

C) 2x+2x+1 = 500

5x = 500

x = 100

hence,  the mass of oat = 2(100) = 200g

mass of cereal = 2(100) = 200 g

mass of nuts = 100g

D) 2x+2x+1 = 750g

5x = 750

x = 750/5

x = 150

Hence, the mass of oat = 2(150) = 300g

mass of cereal = 2(150) = 300 g

mass of nuts = 150g

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Equation represents a line which is parallel to the line

y = 1/2x +3 with (2,5)

Since you are looking for an equation that is parallel to a line, the slope is the same: m = 1/2

Use Point-Slope equation [y-y1 = m(x-x1)]

with the given point (2,5): y-

5=1/2(x-2)

Distribute the 1/2: y-5=1/2x-1

Move the 5 to the other side to put it in y=mx+b form: y=1/2x-1+5

Answer:

y=1/2x+4

A parallel equation can be located in what way?

In the absence of an intersection, two lines are said to be parallel. Each line has the same slope. In the event that m1=m2, f(x)=m1x+b1 and g(x)=m2x+b2 are parallel. If m 1 = m 2, then f (x) = m 1 x + b1 and g (x) = m 2 x + b2 are parallel.

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The factored expression of the expression given as (a + b)^2 = 4 is (a + b + 2)(a + b - 2) = 0

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(a + b)^2 = 4

Express 4 as 2^2

So, we have

(a + b)^2 = 2^2

Rewrite as

(a + b)^2 - 2^2 = 0

Apply the difference of two squares

So, we have

(a + b + 2)(a + b - 2) = 0

Hence, the equivalent expression of the expression given as (a + b)^2 = 4 when it is factored is (a + b + 2)(a + b - 2) = 0

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Answer:4/3-2

Step-by-step explanation:

Answer: 68.75

Step-by-step explanation: I did the math myself so it may not be correct, but it's at least very close.

Answer:

the correct answer is D:68.75

Answer:

4 x 10^7 i.e. 40000000

Step-by-step explanation:

(4x10^7) is obtained by multiplying (5x10^2) by (8x10^4).

The equation can be solved by multiplying the coefficients (5 and 8) first, adding the exponents (2 and 4), and writing the result in scientific notation:

(5 x 8) x 10^(2 + 4) = 40 x 10^6 = 4 x 10^7.

C x -300 is the expression that represents the price of the television set after the instant rebate is applied and before the tax is applied

We are given that an expression  models the final price of television set with an instant rebate in a state that charges a sales tax.

0.07x+(x-300)

The sale tax in on the original price .

We have to find an expression that represents the price of the television set after the instant rebate is applied but before the tax is applied.

Let x be the original price of television.

Instant rebate is subtracted from original price x.

Then , the cost of the television set=x-300

In the given expression 0.07 x is sales tax. where  tax is 7 %  on the original price x.

Sales  tax is  added to the  price of television set.

Hence, option C is true and answer is C x -300

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Answer:

m<2= 2x+6

Step-by-step explanation:

so you have +6 or six more than 2x or twice than m<1 so therefore m<2= 2x+6

The value of the expression is [tex]-2x^2[/tex]-8x + 6.

Given expression:-

[tex](2x^2-5x+4)-(4x^2+3x-2)[/tex]

We have to find the value of the given expression.

We know that, while subtracting quadrating equations, we subtract like terms from like terms.

Like terms

Like terms are those that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only we can combine like terms.

For example : While adding (5x + 3) and (4x - 5), we will add 5x to 4x and 3 to -4 to get the answer that is 9x - 1.

Hence, we can write,

([tex]2x^2-4x^2[/tex]) + (-5x -3x) + (4 -(-2)) = [tex]-2x^2[/tex] -8x + 6.

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In this Triangle, ΔUVW, UW is extended through point w to point x

∠ WUV = (3x - 4)°

∠ VWX = (6x + 6)°

∠ UVW = (x + 20)°,  

the value of x is 5

According to the question, given that

∠ WUV = (3x - 4)°

∠ VWX = (6x + 6)°

∠ UVW = (x + 20)°

because ∠ VWX = ∠ WUV + ∠ UVW

             ⇒  (6x + 6) = (3x - 4) + (x + 20)

             ⇒  (6x + 6) = 4x + 16

             ⇒ 2x = 10

             ⇒ x = 5

{The sum of triangle's interior angles is 100°}

{The sum of supplementary angles is 180°}

Therefore, In ΔUVW, UW is extended through point w to point x, then the value of x is 5.

The interior angles of a triangle always add up to 180° while the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.

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The distance between the two men is 7.2 ft. That is, they are 7.2 ft apart

From the question, we are to determine the distance between the two men

Let the distance between the men be x

From the given information,

The man of the diving board is 6 ft tall

and

The angle of elevation from the man in the water to the man on the diving board is 40°

Considering the triangle formed, we can write that

Opposite = 6 ft

Adjacent = x

Angle = 40°

From SOH CAH TOA, we have that

tan (angle) = opposite / adjacent

∴ tan 40° = 6 / x

x = 6 / tan 40°

x ≈ 7.2 ft

Thus,

The men are 7.2 ft apart

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Answer:

22x + 4y + 13xy

Step-by-step explanation:

First, you add the like terms

(the terms that contain the same variable which is raised to the same power)

6x + 5x + 11x= 22x

2y + 2y = 4y

13xy

Then since nothing else shares the like terms you leave it as 22x + 4y + 13xy

Answer and Explanation:

y = 5x is a line with a constant of proportionality of 5 (it goes through the origin). It goes through quadrants I and III.

See the attached image for a graph.

Using the binomial distribution, it is found that:

The probability of no correct answers is 0.1678 = 16.78%.

For each question, there are only two possible outcomes, either it is answered correctly, or it is not. The answer of a question is independent of any other question, thus the binomial distribution is used to solve this question.

The formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

In the context of this problem, considering the number of questions and the probability of each being answered correctly, the parameters are given as follows:

n = 8, p = 0.2.

The probability of no correct answers is P(X = 0), hence:

P(X = 0) = (0.8)^8 = 0.1678.

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Answer: Heres your answer! I hope we can be friends!

Step-by-step explanation: The answer for A is the specified rate fro 70+66, which would be 126x2 is 166. B as derivative would be your preference! I hope this helped have a good day!

When a family's ratio of income to poverty measurement is 1.05 , then the family is considered by the census bureau as rich.

The "economy food plan," which is based on the U.S. Department of Agriculture, is used as the basis for an absolute poverty indicator in the country. The World Bank also uses an absolute definition of poverty. Extreme poverty is defined as surviving on less than $1.90 USD a day.

A ratio of less than 1 generally indicates that the income is below the poverty line. When the ratio is 1, income and poverty level are equal, and when the ratio is larger than 1, income is greater than poverty level. In this case, the family is rich.

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The length of the segment indicated to the nearest tenth are as follows:

The length of the segment can be found as follows:

Therefore, the segment indicated in question 5 is the radius of the circle.

The radius of a circle is the distance from the centre of the circle to any point on it's circumference.

The radius is half of diameter.

The radius from the second to one end of the circumference is given as 7. Therefore, the radius from the centre to another end of the circumference will be as follows:

The second circle, the line from the centre bisect the chord into equal halves. Since the other half is 8, that means the second half will be as follows:

Therefore, the length of the segment indicated are 7 and 8 respectively.

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With the two solutions, the quadratic equation is x^2 - 11x + 10 = 0

From the question, we have:

Number of solutions = 2

Variable = x

Where the solutions are

1 and 10

This means that

x = 1 and x = 10

Rewrite the above solutions as

x - 1 = 0 and x - 10 = 0

Multiply the above equations

(x - 1) * (x - 10) = 0

This gives

x^2 - 11x + 10 = 0

Hence, the quadratic equation in standard form is x^2 - 11x + 10 = 0

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Owing 175 dollars is more than owing 150 dollars.

Thereby, the correct answer is A) -175 dollars

Answer:

11.1x²

Step-by-step explanation:

Answer:

1. given

2. corresponding angle theorem

3. vertical angle theorem

4. transitive

Step-by-step explanation:

1. it is given because the question supplies the fact at the top above the diagram called "Given:"

2. corresponding angle theorem: "when a line intersects 2 parallel lines, then the corresponding angles in the 2 regions of intersection are congruent" (also look at correspond_screenshot, the first image)

3. vertical angle theorem: "when two straight lines intersect, they form two sets of linear pairs with congruent angles" (also look at vertical_screenshot, the second image)

4. transitive: since we now know <2 ~= <1 ~= <3, we can say <2 ~= <3

("If any segments or angles are congruent to the same angle, then they are congruent to each other")

The interval of x-values over which the function is increasing is (-3 , -1)

A law that connects two variables—the dependent and the independent variables—is known as a function.

A function's range and domain are always specified.

The x and y values are:

-6      -34

-5       3

-4      -10

-3      -11

-2      -6

-1        -1

0        -2

1        -15

It is necessary to identify the range of x-values across which the function increases.

The function is not rising in this interval, hence the first option is (-6, -3).

The function is rising in this range, hence the second alternative is (-3, -1).

The function is not rising in this interval, hence the third alternative is (-3, 0).

The function is not rising in this period, hence the fourth alternative is (-6, -5).

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By means of vector sum and Pythagorean theorem, the line segment BC has a length of 5 units.

We find a line segment whose endpoints are known and set on Cartesian plane, the length of the line segment must be found by means of vector sum and Pythagorean theorem. First, determine the vector associated to the line segment:

[tex]\overrightarrow {BC}[/tex] = C(x, y) - B(x, y) = (0, 2) - (- 3, - 2) = (3, 4)

Second, determine the magnitude of the vector derived in the previous step:

BC = √(3² + 4²)

BC = 5

The length of the line segment BC is equal to 5 units.

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Answer: linear equation

Step-by-step explanation:

because x is not squared

The expression after applying the distributive property is: (-3.6)(-2) + (-3.6)(-7).

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

The distributive property states that when the sum of two (2) or more addends are multiplied by a specific number, the same output would be produced as when each addend is multiplied respectively by the number, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

x(y + z) = xy + xz.

By applying the distributive property of multiplication to the given expression, we have the following expression:

-3.6(-2 + (-7)) = (-3.6)(-2) + (-3.6)(-7).

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