FIND THE GCF. Mathematics

Answer:

6 trust me

Step-by-step explanation:

The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6

What is perimeter of the rectangle?

The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x+ 6

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2( l + w)

Given the following parameters

length l = 8x - 1

width w = 2x + 4

Substitute the expressions for the length and width into the formula;

P = 2(8x - 1 + 2x + 4)

P = 2(10x + 3)

Distribute 2 over each term in the parenthesis

P = 2(10x) + 2(3)

P = 20x + 6

Hence the perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6.

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The complete question is -

The perimeter formula for a rectangle is 2l + 2w, where l is the length and w is the width. Complete the steps to find an expression that represents the perimeter of the rectangle. Substitute the expressions for length and width into the formula 2l + 2w. Distribute 2 to each term in the parentheses. Combine like terms. inches

f(x) + k will shift the graph up k units.

For example, the notation f(x) + 5 will shift the curve up by 5

If k is negative, then the curve shifts down that amount

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

f(x-h) shifts the graph to the right h units

Example: f(x-2) shifts to the right 2 units

Another example: f(x+7) shifts left 7 units. In this case, h = -7

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

y = -f(x) is a reflection over the x axis

This is because we're multiplying each y coordinate by -1

A point like (1,2) reflects to (1,-2)

[tex]- 4 - 9 = - 13[/tex]

Answer:

Hey!

Since we know that both expressions lay on a straight line, we know that when both lines add up it should be 180°

We can write the expression as (7x - 1) + (6x - 1) = 180

Simplify

→ (7x + −1) + (6x + −1) = 180

Combine Like Terms

→ (7x + 6x) + (-1 + -1) = 180 → 13 + -2 = 180

Add 2 To Both Sides

→ 13x - 2 + 2 = 180 + 2 → 13x = 182

Divide 13 To Both Sides

13x/13 = 182/13 → x = 14

Hence, the value of x is 14!

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Hope This Helped! Good Luck!

Answer:

x = -5

Step-by-step explanation:

add 14 to both sides:

x = -19 + 14

x = -5

Answer:

no

Step-by-step explanation:

x=5

5(5+2)=35

8(5)-3=37

37 does not equal 35

[tex]Answer: Q\ is\ not\ midpoint\ of\ \overline {PR}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\\overline {PQ}+\overline {QR}=\overline {PR}\\5(x+2)+(8x-3)=72[/tex]

Expand the parentheses on the left side of the equation:

x(5)+2*(5)+8x-3=72

5x+10+8x-3=72

13x+7=72

13x+7-7=72-7

13x=65

Divide both parts of the equation by 13:

x=5

Hence,

5(5+2)=

5(5)+2(5)=

25+10=

35

8(5)-3=

40-3=

37

35≠37

Answer:

a) 512cm³    b) 2 × 2 ×2

Step-by-step explanation:

A CUBE'S LENGTH WIDTH AND HEIGHT ARE EQUAL

a) Volume of a cube = length × width × height

as the length width and height are equal so it will be

8 × 8 × 8 = 512

b) Volume of a cube = length × width × height

as length, width and height are equal lets suppose the value of each of them will be = x

volume = x × x × x

vol = x³

8 = x³

∛8 = x

x = 2

Answer:

[tex]\textsf{1.} \quad s=\dfrac{8r}{9}[/tex]

[tex]\textsf{2.} \quad s=4[/tex]

[tex]\textsf{1.} \quad x=y(w+z)[/tex]

[tex]\textsf{2.} \quad x=10[/tex]

Step-by-step explanation:

Question 1

1.  Solve for s:

[tex]\implies 2r = \dfrac{5s}{2}-\dfrac{s}{4}[/tex]

[tex]\implies 2r = s\left(\dfrac{5}{2}-\dfrac{1}{4}\right)[/tex]

[tex]\implies 2r = s\left(\dfrac{10}{4}-\dfrac{1}{4}\right)[/tex]

[tex]\implies 2r = s\left(\dfrac{9}{4}\right)[/tex]

[tex]\implies 4(2r) = 9s[/tex]

[tex]\implies 8r = 9s[/tex]

[tex]\implies s=\dfrac{8r}{9}[/tex]

2.  When r = ⁹/₂ :

[tex]\implies s=\dfrac{8\left(\frac{9}{2}\right)}{9}[/tex]

[tex]\implies \dfrac{8}{9} \times \dfrac{9}{2}[/tex]

[tex]\implies \dfrac{8 \times9}{9 \times2}[/tex]

[tex]\implies s=\dfrac{72}{18}[/tex]

[tex]\implies s=4[/tex]

Question 2

1.  Solve for x:

[tex]\implies w=\dfrac{x}{y}-z[/tex]

[tex]\implies w+z=\dfrac{x}{y}[/tex]

[tex]\implies y(w+z)=x[/tex]

[tex]\implies x=y(w+z)[/tex]

2.  When x = -8,  y = -5,  z = 6:

[tex]\implies x=-5(6+(-8))[/tex]

[tex]\implies x=-5(6-8)[/tex]

[tex]\implies x=-5(-2)[/tex]

[tex]\implies x=10[/tex]

Small, random genetic changes that occur over generations is known as genetic drift.

Genetic drift is an evolutionary process in which the frequency of a given gene allele varies randomly across a population. The impacts of genetic drift can be severe, often causing traits to become excessively common or to vanish from a community, even though it predominantly affects small, isolated populations.

Some people might merely by coincidence leave behind a few more offspring (and genes, of course!) than others in each generation. The next generation's DNA and other genetic components will come from the "fortunate" people, not necessarily the healthier or "better" people.

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Using linear functions, we have that:

a. For 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.

b. For any number of games, the cost at alley B will be less.

A linear function is modeled by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence they are given as follows:

The cost for A will be less when:

A(x) < B(x).

Hence:

4x + 7.5 < 4.5x + 5

-0.5x < -2.5

0.5x > 2.5

x > 2.5/0.5

x > 5.

Hence for 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.

For item b, with the increase of $0.5 per game, we have that:

A(x) = 4.5x + 7.5.

Then the costs per game will be the same, while alley B has the lower intercept, meaning that for any number of games, the cost at alley B will be less.

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Answer:

x<44

Step-by-step explanation:

Weight of pet & age of pet  are   the two categories that would yield quantitative data.

What foundation does qualitative data have?

Which two sorts of quantitative data are there?

Weight of pet & age of pet  are   the two categories that would yield quantitative data because both quantity can measured or counted.

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Answer:

M&M's for =Rs.8 per bag

Both team sells a total 240 of a total of Rs.1614

Now

The total of both =1614-240=1374

The basketball team sold 102 packages of licorice and 138 bags of M&M's.

Given that the packages of licorice sold for $5 per package and that of the bags of M&M's for $8 per bag.

The total selling was total of 240 of both for a total of $1614.

We need to find the number of packages of licorice and bags of M&M's were sold.

Let's assume that the number of packages of licorice sold is represented by the variable "L" and the number of bags of M&M's sold is represented by the variable "M."

From the given information, we have two pieces of information to form equations:

The total number of packages and bags sold: L + M = 240

The total revenue from selling these items: 5L + 8M = 1614

Now, we can solve these two equations simultaneously to find the values of L and M.

First, let's solve the first equation for one of the variables (let's solve for L):

L = 240 - M

Now, substitute this expression for L in the second equation:

5(240 - M) + 8M = 1614

Now, distribute the 5:

1200 - 5M + 8M = 1614

Combine the M terms:

3M = 1614 - 1200

3M = 414

Now, solve for M:

M = 414 / 3

M = 138

Now that we know the value of M, we can find the value of L using the first equation:

L = 240 - M

L = 240 - 138

L = 102

So, the basketball team sold 102 packages of licorice and 138 bags of M&M's.

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Answer:

16π m²

Step-by-step explanation:

area of circle = πr²

area = π × (4 m)²

area = 16π m²

Answer:

4725

Step-by-step explanation:

105 students

think of 100 students

100 × 45 = 4500

now the remaining 5 students

cost for 10 students will be

45 × 10 = 450

divide 450 by 2 to find out for 5 students

it is 225

4500 + 225 = 4725

An equation having variables on both sides can be solved by bringing all variables to one side.

An equation with all variables on one side can be solved by simply keeping the variables on the left and simplifying the value on the right. For example,

5x = 6 + 2x;

3x = 6;

x = 2.

For an equation with variables on both sides, just bring all variables on one side. After that, the same process like above is to be followed. For example,

5y - 3 - 3y = 3y + 5 - 3y;

5y - 3y - 3y + 3y = 5 + 3;

2y = 8;

y = 4;

Thus, methods for solving both kinds of equations is similar.

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An equation having variables on both sides can be solved by bringing all variables to one side.

An equation with all variables on one side can be solved by simply keeping the variables on the left and simplifying the value on the right. For example,

5x = 6 + 2x;

3x = 6;

x = 2.

For an equation with variables on both sides, just bring all variables on one side. After that, the same process like above is to be followed. For example,

5y - 3 - 3y = 3y + 5 - 3y;

5y - 3y - 3y + 3y = 5 + 3;

2y = 8;

y = 4;

Thus, methods for solving both kinds of equations is similar.

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(rand() % 6) + 1 is the expression randomly rolls one dice, directly yielding one of those values.

Small objects (polyhedrons) used as playing pieces for dice games and other gambling-related activities. The cube, the most popular type of die, has one to six tiny dots on each side (spots). The spots are positioned in the following traditional patterns: 1 and 6, 2 and 5, 3 and 4, so that spots on opposite sides always sum up to 7. The poker and crown and anchor dice, as well as many other types of dice with 4, 5, 7, 8, 10, 12, 16, and 20 sides, are examples of dice with different configurations of spots or other face designs. The majority of the time, dice are employed to generate a random outcome (usually a number or a mixture of numbers), and the mathematical probabilities depend on the physical characteristics and quantity of dice thrown.

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The conditional operator creates a compound statement that sets up a condition for something to be true. Therefore, if the condition is met, the statement is true. The parts of the conditional statements are two, the first simple statement in a conditional is called the antecedent  and the second simple statement is called the consequent. So, for two statements A (antecedent) and B (consequent) we will have that:

A → B that means: If A then B

In this problem:

A:  A number is even.

B: The number is divisible by 2.

Thus:

A → B: If a number is even, then the number is divisible by 2.

So, the conclusion of this conditional statement is the consequent, that is,  the number is divisible by 2.

Accordingly, the right answer is D. The number is divisible by 2.

the complete question is

What is the conclusion of the following conditional? A number is divisible by 2 if even.

A. The sum of the digits of the number is divisible by 2.

B. If a number is even, then the number is divisible by 2.

C. The number is even.

D. The number is divisible by 2.

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The function rules for each of the given tables are;

11) f(x) = 4x

12) f(x) = x - 3

13) f(x) = x + 12

14) f(x) = x/10

15) This doesn't have a function rule.

16) Function rule here is non existent

11) In this table, we can observe that the output values are all four times the input value. Thus, the function rule here is;

f(x) = 4x

12) In this table, we can observe that the output values are all 3 units less than the input value. Thus, the function rule here is;

f(x) = x - 3

13) In this table, we can observe that the output values are all 12 units more than the input value. Thus, the function rule here is;

f(x) = x + 12

14) In this table, we can observe that the output values are equal to the input value divided by 10. Thus, the function rule here is;

f(x) = x/10

15) This doesn't have a function rule as the values don't match a pattern

16) Function rule here is non existent

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quotient = the answer to a division problem

To divide by a fraction, multiply by the reciprocal of the fraction

reciprocal of a fraction = the numerator and denominator are reversed

First, convert "three and two thirds" into an improper fraction:

[tex]3\dfrac{2}{3}[/tex]

⇒ Multiply the whole number by the denominator and add the numerator:

[tex]\dfrac{11}{3}[/tex]

Now, we want to divide this number by three fifths:

[tex]\dfrac{11}{3}\div\dfrac{3}{5}[/tex]

⇒ Dividing by a fraction is the same as multiplying by its reciprocal:

[tex]= \dfrac{11}{3}\times\dfrac{5}{3}\\\\=\dfrac{55}{9}[/tex]

[tex]\dfrac{55}{9}[/tex]

theannswer wold be 100 .33 .87

The statement is sometimes true.

Points that are located along a single or shared straight line are referred to as collinear points. If two or more points on a line are situated either close to or far from one another, they are said to be collinear in Euclidean geometry.

Three points are automatically coplanar if they are collinear.

What was just said is sometimes true.

This is because three points along a line are typically recognized to be collinear, however it is not always the case.

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Answer:

[tex]{ \tt{f(n) = 7n - 5}} \\ { \tt{f( - 2) = 7( - 2) - 5}} \\ { \tt{f( - 2) = - 14 - 5}} \\ { \tt{f( - 2) = - 19}}[/tex]

Answer:

Step-by-step explanation: Well €550 Euros is equal to $547.42 US dollars in currency. But since this is approximately, (D) should be correct.

Answer:

Step-by-step explanation:

1035x-992/840

======================================================

Explanation:

To find the inverse, we swap x and y, then solve for y.

y = 2x-3

x = 2y-3

x+3 = 2y

2y = x+3

y = (x+3)/2

y = x/2 + 3/2

y = (1/2)x + 3/2

This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.

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

Another approach:

Since we're given a list of multiple choice answers, we can rule out the non-answers.

Plug x = 0 into the first equation of choice A. It leads to y = 2

That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.

This allows us to rule out choice A. Choices B and C are similar stories.

Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.

Answer:

Step-by-step explanation:

Algorithm for deriving the formula of the inverse function

Step 1. In the formula for the original function, replace the notation of the argument and the value:

Step 2. From the resulting formula, express y(x).

Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.

[tex]\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no[/tex]

[tex]y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes[/tex]