Which of the following relations is a function?
A. (2,4), (-5, 6), (2, 3), (-6, 2)
B. (8, 1), (-5, 4), (2, 1), (8, 2)
C. (2,4), (-5, 2), (8, 1), (-6, 2)
D.
(2,0).(-5, 3), (8, 1), (-5,5)

Answer:

parenthesis

Step-by-step explanation:

A common technique that is being used in solving with several arithmetic operations is the PEMDAS. It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". It is the order to be followed when calculating involving more than one arithmetic operation.

The correct first operation to perform in a calculation involving multiple arithmetic operations is parentheses, as per the order of operations, known as PEMDAS or BEDMAS.

The correct operation that should be performed first for calculations involving more than one arithmetic operation is parentheses. According to order of operations, the sequence you would follow is: Parentheses (or grouping symbols), Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). This is also commonly remembered by the acronym PEMDAS in the American system or BEDMAS in the Canadian system, indicating the sequence: Parentheses/Brackets, Exponents, Multiplication/Division, and Addition/Subtraction.

Answer:

The answer is 5 people.

Step-by-step explanation:

.25 * 20 people surveyed = 5.

7x + 12 = 3(5x - 12)

Step 1: Distribute the 3 to the numbers in the parentheses (5x and -12)

7x + 12 = (3 × 5x) + (3 × (-12))

7x + 12 = 15x + (-36)

Step 2: Combine like terms

x's go with x's (7x and 15x)

Subtract 7x to both sides

(7x - 7x) + 12 = (15x - 7x) + (-36)

(0) + 12 = 8x - 36

12 = 8x - 36

Normal numbers go with normal numbers

Add 36 to both sides

12 + 36 = 8x + (-36 + 36)

48 = 8x

Step 3: Isolate x by dividing 8 to both sides

48/8 = 8x/8

6 = x

Hope this helped!

Answer:

x = 6

Step-by-step explanation:

Eliminate parentheses using the distributive property.

7x +12 = 15x -36

You have x-terms and constants on both sides of the equal sign. One way to approach this is to find the x-term with the least coefficient (it is 7x) and subtract everything on that side of the equation.

(7x +12) -(7x +12) = (15x -36) -(7x +12)

Simplify, also known as "collect terms."

0 = 8x -48

Now, divide by the coefficient of x: 8.

0 = x -6

Add the opposite of the constant: 6.

6 = x

__

Alternate solution

By looking for the x-term with the smallest coefficient, we get a positive result when we subtract that term. If we were to subtract 15x from both sides of the equation, it would be ...

-8x +12 = -36 . . . . . . . with a negative x-coefficient

You can still work the problem this way, but it can introduce errors if you're not careful with signs. To finish this, we would subtract 12 to get the x-term by itself:

-8x = -48

Then we would divide by the x-coefficient, -8.

x = -48/-8 = 6 . . . . . same solution; same number of steps

_____

Whenever you add, subtract, multiply, divide, you do the same thing to both sides of the equation.

After 6 days, 20 grams will be left from the original 80 grams.

The half-life is the time it takes for half of the radioactive substance to decay. In this case, the half-life of ruthenium is given as 3 days. Starting with an initial quantity of 80 grams, we can calculate the remaining quantity after each half-life period.

After the first 3 days, one half-life will have passed, and half of the 80 grams will have decayed:
80 g / 2 = 40 g remaining.

After the second 3 days, another half-life will have passed, so another half of the remaining 40 grams will have decayed:
40 g / 2 = 20 g remaining.

Therefore, after 6 days, which corresponds to two half-life periods, 20 grams of the radioactive isotope of ruthenium will be left.

Step 1: Distribute the 2 to numbers and variables inside parentheses

(2 × x) + (2 × 3) = 4 (x - 1)

2x + 6 = 4 (x - 1)

Step 2:  Distribute the 4 to numbers and variables inside parentheses

2x + 6 = (4 × x) + ( 4 × - 1)

2x + 6 = 4x+ (-4)

2x + 6 = 4x- 4

Step 3: Combine like terms (x's go with x's) by subtracting 2x to both sides

(2x - 2x) + 6 = (4x - 2x) - 4

6 = 2x - 4

Step 4: Combine like terms by adding 4 to both sides

6 + 4 = 2x - 4 + 4

10 = 2x

Step 5: Isolate x by dividing 2 to both sides

10 ÷ 2 = 2x ÷2

5 = x

x = 5

To check: plug 5 into all the x's of the equation

2(x+3)=4(x-1)

2(5+3)=4(5-1)

2(8) = 4(4)

16 = 16

Hope this helped!

Answer:5

Step-by-step explanation:

Answer:

The coordinates of the vertex are (-5, 41)

Step-by-step explanation:

For a quadratic function of the form

[tex]f(x) = ax ^ 2 + bx + c[/tex]

Where a, b and c are constants and represent the coefficients of the function, then the symmetry of the parabola always passes through its vertex.

In this case we have the following parabola

[tex]f (x) = -x2 - 10x + 16[/tex]

And we know that its axis of symmetry is the line [tex]x = -5[/tex]

Then we know that this axis of symmetry passes through the vertex of the parabola.

Therefore, the x coordinate of the vertex is -5.

To find the coordinate in y of the vertex, we substitute x = -5 in the function.

[tex]f (-5) = -(- 5) ^ 2 -10 (-5) +16\\\\f (-5) = 41[/tex]

Finally, the vertices are in the point (-5, 41).

[tex]A=5m^4\times6m^2=\boxed{30m^6}[/tex]

The result of the calculation (6 * 10^2) / (3 x 10^-5) is 2 x 10^7, when written in standard form.

To solve the equation (6 * 10^2) / (3 * 10^-5), we first simplify both sides. 6 * 10^2 equates to 600, and 3 x 10^-5 equates to 0.00003. Therefore, we are left with the simple division: 600 / 0.00003.

To divide these two numbers, you would get a result of 20000000. However, the problem asks for the answer in standard form. Standard form is a way of writing numbers that are too large or too small to be conveniently written in decimal form. In standard form, 20000000 is represented as 2 x 10^7.

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Find the Least Common Multiple (LCM) of the denominator in order to find the Least Common Denominator (LCD).

LCM = 6/5 * (x^2y^2)

Answer = B. 10x^2y^2

Answer:

Your answer is option B. 10x^2y^2

Step-by-step explanation:

Firstly, Find the Least Common Multiple of the denominator.

Then you'll get your Least Common Denominator.

You'll get LCM as :

LCM = 6/5 * ( x^ 2y ^2 )

Your answer you'll get is 10x^2y^2

Answer:

The domain is all real numbers.

The range is y ≥ −25

Step-by-step explanation:

The equation has no domain restrictions.

Answer:

13/6

Step-by-step explanation:

volume=length*width*height

so

325m^3=10*15*x

325=150x

x=2.16666666 or 325/150

Answer:

the answer is 15 to the nearest tenth

Answer:

add all the points together like

1+3+4+6+6+7+7+7+8+8+8+8+9+9+9+15= 115

the divide by the total number of elements we have. as so

115÷16= 7.18

rounding that to the nearest tenth is going to 7.2

Step-by-step explanation:

hope this helps

correct me if I'm wrong

Answer:

518.4 in³

Step-by-step explanation:

The ratio of the sides of the prisms = 5 : 6, hence

the ratio of their volumes = 5³ : 6³ = 125 : 216

let x be the volume of the larger prism then by proportion

[tex]\frac{125}{300}[/tex] = [tex]\frac{216}{x}[/tex] ( cross- multiply )

125x = 216 × 300 ( divide both sides by 125 )

x = [tex]\frac{216(300)}{125}[/tex] = 518.4

The volume of the larger prism is 518.4 in³

Answer:

x=-2

Step-by-step explanation:

Answer:

x = - 2

y = 7

Step-by-step explanation:

4x - 2y = - 20

Now substitute - 3x for y.

4x - 2(-3x) = -20           combine the xs in the brackets

4x + 6x = - 20               Make the addition      

10x = - 20                      Divide by 10

x = - 20/10                     Do the division

x = - 2                            

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

3x - 2y = - 20                 Put - 2 in for x  

3(-2) - 2y = - 20              remove the brackets              

- 6 - 2y = - 20                 Add 6 to both sides

-2y = - 20 + 6                 Combine

-2y = - 14                         Divide by - 2

y = - 14/-2                        

y = 7

in short, we simply graph her countertpart of y = 7, and then we test a point for "true" or "false" for that region.

say for example the point ( 3, 5 ), meaning x = 3, y = 5

y < 7

5 < 7  

is that really true?  5 smaller than 7?  yeap, so that region is the "true" region, and is the region we shade.

the line in the graph is a dashed one, because it does NOT include the points at the border, y < 7, "y" is less, not equals to, but less than 7.

Check the picture below.

I'm sorry but there is no graph, If you could put up the graph I can answer. Thank You!

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-6}{4-(-1)}\implies \cfrac{1-6}{4+1}\implies \cfrac{-5}{5}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=-1[x-(-1)]\implies y-6=-1(x+1) \\\\\\ y-6=-x-1\implies y=-x+5[/tex]

Answer:

B. Irrational.

Step-by-step explanation:

√99 is irrational.

Its value  just below 10 as √100 = 10.

The scenarios provided represent different types of sampling methods, such as stratified, cluster, simple random, and systematic, based on how the samples are selected from the population.

The type of sampling can be determined based on how the samples are chosen from the population. Here, we discuss different sampling methods using the provided scenarios.

For this case we have to:

Let "w" be the variable that represents the number of savings weeks.

We have that Landon's initial amount is $ 70.

We want to know how much money you have after 5 weeks, knowing that you save $ 7 each week, so be "y" the amount of money after "W" weeks:

[tex]y = 70 + 7w[/tex]

After 5 weeks:

[tex]y = 70 + 7 (5)\\y = 70 + 35\\y = 105\[/tex]

Answer[tex]y = 70 + 7w\\y = 105[/tex]

Hello!

Answer:

The answer is 6 schools.

In a box and whisker plot, every piece of whisker or box represents 25% of the whole number of schools.

The schools participated 1 year or less are represented by the left part of the whisker. Which stands for 25%.

BOOM

Step-by-step explanation:

On analyzing the boxplot, we find that 6 schools have participated for 1 year or less.

A boxplot is a standardized way of displaying the distribution of data based on a five number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum).

The box extends from 1 to 6 on the number line. This implies first quartile (Q1) = 1 and third quartile (Q3) = 6.

There is a vertical line at 3.5, median = 3.5.

The whiskers end at 0 and 8, i.e., minimum = 0 and maximum = 8.

Since, Q1 = 1, this implies 25% of the schools participated for 1 year or less.

(First quartile (Q1) is the value under which 25% of data points are found when they are arranged in increasing order.)

Number of schools that have participated for 1 year or less = 25% of 24 = [tex]\frac{25}{100} * 24 = 6[/tex]

Learn more about boxplot here

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Answer:

Mean:79

Median:81

Standard deviation:15

Interquartile range:22

Mean (aka average)-79.8928

add all the numbers together and divide by how many numbers there are

sum of terms-2237

number of terms-28

Median- 81

I do it this way-

order the numbers from least to greatest

cross off the front number and back number until you are left with a middle

in this case there were 2

80 and 82

the average of those two is 81

Standard Deviation-15.37237

Interquartile Range-22.5

25th percentile-71

50th percentile-81

75th percentile-93

Answer:

4 4/2

Step-by-step explanation:

What you do is you have to do 8-4=4 5-1=4 6-4=2 so there for the answer is 4 4/2

Hello There!

We are given the problem 8 5/6 - 4 1/4

Your answer would be 4 7/12

First, we subtract 4 from 8 and get a difference of 4.

Then we have to subtract 1/4 from 5/6.

We have to find a common denominator.

We can get 10/12-3/12=7/12

Then, we add 4+7/12 and we get 4 7/12.

Answer: 24-11=a

Step-by-step explanation:

Answer:

[tex]\boxed{\text{A.  The y-intercept of function f is greater than the y-intercept of function g}}[/tex]

Step-by-step explanation:

A. y-Intercept of ƒ(x)

ƒ(x) = x² - 4x + 3

f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3

The y-intercept of ƒ(x) is (0, 3).

If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).

Statement A is TRUE.

B. y-Intercept of g(x)

Statement B is FALSE.

C. Minimum of ƒ(x)

ƒ(x) = x² - 4x + 3

a = 1; b = -4; c = 3

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

h = -b/2a = -(-4)/(2×1 = 2

k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1

The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).

Statement C is FALSE.

D. Minimum of g(x)

g(x) is a downward-opening parabola. It has no minimum.

Statement D is FALSE

the set of 6 consecutive integers starting with -3:

{ -3,-2,-1,0,1,2 }

Answer:

Step-by-step explanation:

let :

x , x+1 , x +2 , x + 3 , x+4 , x+5 ....... ( 6  consecutive integers )

x +( x+1 ) + (x +2) + (x + 3)+ (x+4) + ( x+5) = - 3

6x+16 = - 3

6x = - 3 - 16

6x = - 18

x v= -18/6

x = - 3

6  consecutive integers  are : -3  ; - 2 ; - 1 ; 0 ; 1 ; 2

ANSWER

[tex] \frac{15x - 328}{40} [/tex]

EXPLANATION

The given expression is

[tex] \frac{3}{4} ( \frac{1}{2} x - 12) + \frac{4}{5} [/tex]

We expand to obtain;

[tex] \frac{3}{8} x - 9+ \frac{4}{5}[/tex]

The least common denominator is 40

[tex] \frac{15x - 360 + 32}{40} [/tex]

This simplifies to:

[tex] \frac{15x - 328}{40} [/tex]

Answer:

That’s wrong

Step-by-step explanation:

[tex]\bf \cfrac{4}{~~\frac{1}{4}-\frac{5}{2}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{1}{4}-\frac{5}{2}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{(1)1-(2)5}{4}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{1-10}{4}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{-9}{4}~~} \\\\\\ \cfrac{4}{1}\cdot \cfrac{4}{-9}\implies \cfrac{-16}{9}[/tex]

For this case we have the following function:

[tex]c (f) = \frac {5} {9} (f-32)[/tex]

We must find the inverse function. For this we follow the steps below:

Replace c (f) with y:

[tex]y = \frac {5} {9} (f-32)[/tex]

We exchange variables:

[tex]\frac {5} {9} (y-32) = f[/tex]f = \frac {5} {9} (y-32)

We solve for "y":

[tex]\frac {5} {9} (y-32) = f[/tex]

We multiply by[tex]\frac {9} {5}[/tex]on both sides of the equation:

[tex]y-32 = \frac {9} {5} f[/tex]

We add 32 to both sides of the equation:

[tex]y = \frac {9} {5} f + 32[/tex]

We change y by[tex]c^{ -1} (f):[/tex]

[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]

Answer:

[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]

Answer:

[tex]f(c)=\frac{9}{5}c+32[/tex]

Step-by-step explanation:

Given function that is used to convert degrees to Fahrenheit to degrees Celsius,

[tex]c(f)=\frac{5}{9}(f-32)[/tex]

Let y represents the output value of the function and x represents the input value,

[tex]y=\frac{5}{9}(x-32)[/tex]

Switch x and y,

[tex]x=\frac{5}{9}(y-32)[/tex]

Isolate y,

[tex]9x=5(y-32)[/tex]

[tex]\frac{9}{5}x=y-32[/tex]

[tex]\implies y = \frac{9}{5}x+32[/tex]

[tex]\implies f(c)=\frac{9}{5}c+32[/tex]

Which is the required function.

General vertex formula is

(X-h)^2 +k=y

where (h,k) is the vertex

X^2 +6X+14=y

X^2 +6x +9 +14-9=y

Answer is :

(X+3)^2 +5=y