Express the given statement in the form of expression.



5 less than three times a number x .



The expression to represent the above statement is

Answer:

What figure lol

Step-by-step explanation:

When you multiply two odd numbers together, the result is always an odd number.

This is because odd numbers are defined as integers that cannot be evenly divided by two. Therefore, when you multiply two odd numbers, there is no way to divide the resulting product evenly by two, which means it remains an odd number.

For example, let's consider two odd numbers, 3 and 5. When we multiply them together, we get 3 x 5 = 15, which is also an odd number.

Similarly, let's consider two other odd numbers, 7 and 9. When we multiply them together, we get 7 x 9 = 63, which is also an odd number.

Therefore, it can be concluded that the product of any two odd numbers is always an odd number. This is a mathematical property that is always true, regardless of the specific odd numbers used in the multiplication.

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Answer:6,8,10

Step-by-step explanation:

The value of \(n = 3m\) after solving the equation.

In mathematics, an equatiοn is a fοrmula that expresses the equality οf twο expressiοns, by cοnnecting them with the equals sign = The wοrd equatiοn and its cοgnates in οther languages may have subtly different meanings; fοr example, in French an équatiοn is defined as cοntaining οne οr mοre variables, while in English, any well-fοrmed fοrmula cοnsisting οf twο expressiοns related with an equals sign is an equatiοn.

Sοlving an equatiοn cοntaining variables cοnsists οf determining which values οf the variables make the equality true. The variables fοr which the equatiοn has tο be sοlved are alsο called unknοwns, and the values οf the unknοwns that satisfy the equality are called sοlutiοns οf the equatiοn. There are twο kinds οf equatiοns: identities and cοnditiοnal equatiοns. An identity is true fοr all values οf the variables. A cοnditiοnal equatiοn is οnly true fοr particular values οf the variables.

A equatiοn is a term in which twο quantity are equate with each οther by using variοus algebraic fοrmulas.

As per the questiοn

\(\frac{n}{m}+7=10\\ \frac{n}{m}=3\\ n=3m\)

Hence,  the value of n = 3m.

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Answer:

I think the answer is D

Step-by-step explanation:

The last figure is representing an undefined term "line".

A ray is a segment of a line where one point is fixed and the other has no defined end. It denotes that a ray has one terminating end and an indefinitely long other end.

The first illustration depicts a ray with an end point at X, which is a phrase that is described as "a ray is a line with one end point."

The second graphic depicts a line segment with endpoints at X and Y. This phrase is described as "A line segment is a line with 2 end points."

The joint of two rays in the third illustration creates an angle, which is once again a defined phrase.

The final illustration depicts a line that is not defined and has no endpoints.

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Answer:

Step-by-step explanation:

6x10 to the power of 21 the answer is too long for my calculator sadly

Answer:

It means 6 multiplied by 10 raised to the power of 21

We are given three set of system of equations

3x + 2y + z = 8

x + y + 2z = 4

4x + y + z = 7

We have three equations with three unknowns (x, y, and z)

Firstly, we need to eliminate of the variables, so that we can solve the remaining equation simultaneously.

Firstly., we will be eliminating z

Let us combine equation 1 and 2 together

3x + 2y + z = 8 ------ equation 1

x + y + 2z = 4 --------- equation 2

To eliminate z, multiply equation 1 by 2 and equation 2 by 1

3x * 2 + 2y*2 + 2*z = 2 * 8

x *1 + y * 1 + 1 * 2z = 1 * 4

6x + 4y + 2z = 16 ------ equation 4

x + y + 2z = 4 ----------- equation 5

Substract equation 5 from 4

6x - x + 4y - y + 2z - 2z = 16 - 4

5x + 3y + 0 = 12

5x + 3y = 12 -------------- equation 6

Secondly, combine equation 2 and 3 together

x + y + 2z = 4

4x + y + z = 7

To eliminate z, multiply equation 1 by 1 and equation 2 by 2

x * 1 + y * 1 + 2z * 1= 4*1

4x *2 + 2 * y + 2*z = 2 * 7

x + y + 2z = 4 ----------- equation 7

8x + 2y + 2z = 14 -------- equation 8

Substract equation 8 from 7

x - 8x + y - 2y + 2z - 2z = 4 - 14

-7x - y + 0 = -10

-7x - y = -10 -------------- equation 9

Solve equation 6 and equation 9 simultaneously to get the values of x and y

5x + 3y = 12

-7x - y = -10

Let us eliminate y

To eliminate y, multiply equation 6 by 1 and equation 9 by 3

5x * 1 + 3y*1 = 12*1

-7x * 3 - y*3 = -10*3

5x + 3y = 12 ------ equation 10

-21x - 3y = -30----- equation 11

Add equation 11 and 10 together

5x + (-21x) + 3y + (-3y) = 12 + (-30)

5x - 21x + 3y - 3y = 12 -30

-16x + 0 = -18

-16x = -18

Divide both sides by -16

-16x/-16 = -18/-16

x = 18/16

x = 8/9

To find y, put the value of x in equation 9

-7x - y = -10

-7(8/9) - y = -10

-72/9 - y = -10

Collect the like terms

-y = -10 + 72/9

-y = -10 *9 / 1 + 72 x 9 / 9 / 9

-y = -90 + 72 / 9

-y = -18/9

-y = -2

Divide both sides by -1

-y/-1 =- -2/-1

y = 2

To find the value of z, substitute the values of x and y into equation 2

x + y + 2z = 4

Make 2z the subject of the formula

2z= 4 - x - y

2z = 4 -8/9 - 2

2z = 4 x 9 - 8 - 2*9 /9

2z = 36 - 8 - 18 / 9

2z = 10/9

Divide both sides by 2

2z / 2 = 10/9 / 2

z = 10/18

z = 5/9

The solutions are x = 8/9, y = 2 and z = 5/9

Answer: x=2, y=4

Step-by-step explanation:

Use the elimination method to find x and y.

3x-y=2

2x+y=8

5x=10

x=2

Using the value of x, plug it in the equation to get the value of y.

4+y=8

y=4

Therefore , the solution of the given problem of domain comes out to be range of f-1(x) is the scope of f(x).

The range of potential values that a function can take is known as its domain. These numbers serve as a representation for the cross of an equation like f. (x). The range of potential numbers on which a function can be used is known as its domain. The value which the function gives following the insertion of a x value is this set. A formula with x as the predictor variables and y as even the dependent variable is defined as

Y = f. (x).

Here,

Given :

To find domain and range of inverse function :

=> Inverse Functions' Subject and Scope .

The scope of an inverse function, f1, is the spectrum of a function, f(x).

The range of f-1(x) is the scope of f(x).

Therefore , the solution of the given problem of domain  comes out to be range of f-1(x) is the scope of f(x).

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The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.

The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Each element of X receives exactly one element of Y when a function from one set to the other is used.

According to the question,

f (x) = 1/3x - 2

now to find inverse ,

Add 2 to x term  and then divide by 1/3 so, we get,

f⁻¹(x) = (x + 2) / 1/3

f⁻¹(x) = 3(x + 2)

now, compare with f⁻¹(x) = a (x + 2)

a = 3

Calculate the x-intercept by putting f(x) = 0

0 = x + 2

x = -2

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Answer:

x=6   x=3

Step-by-step explanation:

x^2-9x+18=0

Factor

What 2 numbers multiply to 18 and add to -9

-6*-3 = 18

-6-3 = -9

(x-6) (x-3) =0

Using the zero product property

x-6 =0  x-3 =0

x=6   x=3

Answer:

c) -2y = 10x + 6

Step-by-step explanation:

The equation of a line in slope-intercept form is:

\(y=mx+b\)

The variables stand for:

\(y:$ y-coordinate of any point on the line\\$x:$ x-coordinate of any point on the lien\\$m: $ Slope of the line\\$b: $ y-intercept of the line; where the line meets the y-axis\)

Plugging in the given information into the equation:

\(y=-5x+(-3)\\y=-5x-3\)

Go through the answer choices:

a)  2y = -5x - 3

Divide both sides of the equation by 2

\(y=-\frac{5}{2}x-\frac{3}{2}\rightarrow\text{Incorrect!}\)

b) -2y = 10x - 6

Divide both sides of the equation by -2

\(y=\frac{10}{-2}x-\frac{6}{-2}\\y=-5x-(-3)\\y=-5x+3\rightarrow\text{Incorrect!}\)

c) -2y = 10x + 6

Divide both sides of the equation by -2

\(y=\frac{10}{-2}x+\frac{6}{-2}\\y=-5x+(-3)\\y=-5x-3\rightarrow\text{Correct!}\)

d) 2y = 10x - 6

Divide both sides of the equation by 2

\(y=\frac{10}{2}x-\frac{6}{2}\\y=5x-3\rightarrow\text{Incorrect!}\)

Therefore the answer is c) -2y = 10x + 6

Additional Comments:

We can only divide both sides of the equation by 2 and/or -2 because of the Division Property of Equality. This property states that if we divide one side of the equation by a certain quantity, we must divide the other side by the same quantity so that the equation remains equal.

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The equation given as 2/(7 - m) = 4/(m - 5) - m/(7 -m) has no real solution for m

The equation is given as

2/(7 - m) = 4/(m - 5) - m/(7 -m)

Take the like terms of the above equation

So, we have

m/(7 -m) + 2/(7 - m) = 4/(m - 5)

Evaluate the like terms in the above equation

So, we have

(m + 2)/(7 -m) = 4/(m - 5)

Cross multiply the above equation

So, we have

m^2 + 2m - 5m - 10 = 28 - 4m

Evaluate the like terms

m^2 + m + 18 = 0

Using a graphing tool, we have no solution for m

Hence, the equation given as 2/(7 - m) = 4/(m - 5) - m/(7 -m) has no real solution for m

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Answer:

7. 6y+84+3 = 151-2y

y=8

measure of angle m is 51 degrees

8. 90 + 5x = 20x - 15

x=7

measure of angle ABC is 125 degrees

Mean= 5.1 (Sum of all the terms/number of terms)

‭( 6   +   7   +   2   +   4   +   6   +   6   +   9   +   5   +   3   +   3 )   ÷   10 =‬  5.1

Median= 5.5 (The middle term when you order them from lowest to highest)

2 3 3 4 5 6 6 6 7 9

Step-by-step explanation: The mean of a data set is equal tot he sum of the set of numbers divided by however many numbers are in the set.

So to find the mean of the data set shown here,

let's begin by adding the numbers.

So we have 6 + 7 + 2 + 4 + 6 + 6 + 9 + 5 + 3 + 3.

Adding the numbers, we get 51.

Now, 51 will be divided by the number

of numbers in the set which is 10.

So 51 divided by 10 gives us 5.1.

So the mean of the data set is 5.1.

Now, the median is the middle number in the data set

when the data set is written from least to greatest.

So let's write our data set from least to greatest.

So we have 2, 3, 3, 4, 5, 6, 6, 6, 7, 9.

Notice that there are two numbers in the middle, 5 and 6.

In this situation, add the numbers and divide by 2.

So 5 + 6 is 11 and 11 divided by 2 is 5.5.

So the median is 5.5.

Answer:

0.2

Step-by-step explanation:

Answer:

0.2

Step-by-step explanation:

Mark the first decimal place

Examine the second decimal place and if it is lower than five we round down and vice versa

A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:

f(x) = 20x + 100

g(x) = 10x + 500

B. When f(x) = g(x), x = 40.

A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.

Part A:

Equation for Lyle:

y-intercept / initial value (b) = $100

Slope / unit rate (m) = $20

To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:

f(x) = 20x + 100.

Equation for Lyle:

y-intercept / initial value (b) = $500

Slope / unit rate (m) = $10

To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:

g(x) = 10x + 500.

Part B: To solve the system, we would do the following:

20x + 100 = 10x + 500

20x - 10x = -100 + 500

10x = 400

x = 400/10

x = 40

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The growth rate of the bacterial colony after 3 hours is 32%, the population of a slowly growing bacterial colony after t hours is given by the function p(t) = 100 + 24t + 2t²

The growth rate of the colony is the rate of change of the population, which is given by the derivative of the function. The derivative of p(t) is p'(t) = 24 + 4t

The growth rate after 3 hours is p'(3) = 24 + 4 * 3 = 32. This means that the population of the colony is increasing by 32% after 3 hours.

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Answer:

28 students

Step-by-step explanation:

If 20% were at a sports meet, then 80% were in class. 80% of 35 is 28

The variable represented in the statement "record the percentage change in the price of a stock for 100 stocks publicly traded on wall street." is a Quantitative Variable .

The Quantitative variables are defined as numerical which represent a measurement or a count.

In the statement :  the percentage change in the price of a stock is a numerical representation of the amount of change in the price of a stock, expressed as a ratio or a percentage.

Therefore ,  the variable "percentage change in the price of a stock" is a quantitative variable because it is numerical and represents a measurement of change in the price of a stock.

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My age is 2 years from the given condition.

Given that, if you square my age and subtract 28 times my age, the result is 60.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x be my age.

Now, square my age is x²

28 times my age =28x

The square of my age and subtract 28 times my age, the result is 60.

x²-28x=60

⇒ x²-28x-60=0

⇒ x²+30-2x-60=0

⇒ x(x+30)-2(x+30)=0

⇒ (x+30)(x-2)=0

⇒ x=2

Hence, my age is 2 years from the given condition.

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Diversified Citrus Industries will sell Zap to wholesalers at a price of $0.035 per 8-ounce can. The contribution per unit for Zap is -$0.205, indicating potential profitability issues.

a. To determine the price at which Diversified Citrus Industries will be selling its product to wholesalers, we need to consider the suggested retail price, the unit variable costs, and the desired margins for retailers and wholesalers. The suggested retail price to the consumer for the 8-ounce can is $0.05. The unit variable costs for the product are $0.18 for materials and $0.06 for labor. The company intends to give retailers a margin of 20% off the suggested retail price and wholesalers a margin of 10% of the retailer's cost.

Price to Wholesalers = Suggested Retail Price - Retailer's Margin - Wholesaler's Margin

Price to Wholesalers = $0.05 - ($0.05 * 20%) - ($0.05 * 10%)

Price to Wholesalers = $0.05 - $0.01 - $0.005

Price to Wholesalers = $0.035

Therefore, Diversified Citrus Industries will be selling its product to wholesalers at a price of $0.035 per 8-ounce can.

The contribution per unit for Zap can be calculated by subtracting the unit variable costs from the selling price to wholesalers:

Contribution per Unit = Price to Wholesalers - Unit Variable Costs

Contribution per Unit = $0.035 - ($0.18 + $0.06)

Contribution per Unit = $0.035 - $0.24

Contribution per Unit = -$0.205

Since the contribution per unit is negative, it means that the variable costs exceed the price to wholesalers. This suggests that the product may not be profitable in its current pricing and cost structure.

The break-even unit volume in the first year can be calculated by dividing the fixed overhead costs by the contribution per unit:

Break-even Unit Volume = Fixed Overhead Costs / Contribution per Unit

Break-even Unit Volume = $90,000 / (-$0.205)

However, since the contribution per unit is negative, the break-even unit volume cannot be determined using this approach.

The first-year break-even share of the market cannot be determined based on the information provided. The total market size and the expected sales volume of Zap are not specified, making it impossible to calculate the market share at the break-even point.

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The estimated area of the unshaded rectangle is 5625 square inches.

The formula for calculating the area of a rectangle. Rectangle surface area. A = l × b.

Once the length and breadth of a rectangle are determined, the area is computed.

The area of a rectangle may be calculated by multiplying its length and width.

The estimated value of the length of the shaded square is: 11 inches

The estimated value of the area of the unshaded rectangle is: 5625 square inches.

To find the estimated length of the shaded square,

We can use the square root of the area:

√(125) = 11

To find the estimated area of the unshaded rectangle,

We can multiply the length by the width:

75 * 11 = 825

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The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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Answer:

x = 27°

Step-by-step explanation:

Because of the two parallel lines, we can conclude that

corner DAB = corner FDE = 2x

In ∆DAB

Corner DAB = 2x

Corner BDA = 2x (given)

Corner ABD = 72 (given)

The sum of three corners in any trianle, adds up to 180°.

So if one corner is 72° and the other two corners are the same, then the two corners together, must be 180-72 = 108°.

For each corner that is 108/2= 54

so corner BDA = 54° and also corner DAB = 54°.

Given was BDA = 2x and BDA = 54°

so 2x = 54°

then x = 27°

The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

The summation notation is a way to represent the sum of a series of terms. In the summation notation, the series of terms is represented by an expression that is followed by a summation symbol (∑). The summation symbol is usually followed by an index of the summation (k in this case), an equal sign (=), the starting value of the index, and a colon (:). The series of terms is then written below the summation symbol, with the index replacing the variable in each term.

To rewrite the given expression using the summation notation, we can use the following steps:

Identify the series of terms: 1 + 2 + 3 + ... + n.

Write the series of terms below the summation symbol: ∑ k = 1

Replace the variable in each term with the index: 1! + 2! + 3! + ... + (n+1)!

The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

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