A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one- quarter of the second number and 5. The situation can be represented by using the graph below, where x represents the second number. 16 NO 8 K 3₂ 5 2 4 st 6 8 10 12 14 16 Which equations represent the situation? Hurry ​

The slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

A linear function contains the following points: (0,-3) and (6,15)

The slope:

[tex]\rm m =\dfrac{15-(-3)}{6-0}[/tex]

m = 18/6

m = 3

The equation of a line:

y = mx + c

Plug x = 0, y = -3

-3 = c

Thus, the slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)

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y=2x+3

to find inverse swap x and y

x=2y+3

x-3=2y

y=(x-3)/2

y=(x/2)-(3/2)

The inverse is f^-1(x)=(x/2)-(3/2)

Hope it helps!

Answer:

it's 5 degrees celsius I think you must have entered a 4-32 instead of a 41-32 is what threw you off

Step-by-step explanation:

Answer:

X=∑fX ∑f , where ¯X is the mean.

Mean = 115/4 = 28.75

Standard deviation = [tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]     n = the number of items = 4

Standard deviation = √28.37/4 = √7.0925 = 2.66317

Step-by-step explanation:

Mean is the number which is obtained by adding the values of all the items of a series and dividing the total by the number of items.

Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values

So, Class intervals are given here.

We have to find the middle point of the class interval.

So,

Class interval= 25- 34

Middle point= [tex]\frac{34-25}{2}[/tex]= [tex]\frac{9}{2}= 4.5[/tex]

Let's add 4.5 to the lower interval,

=> 25 + 4.5= 29.5

This is the median point and do the same for the other intervals too

i.e 39.5,49.5 and then 59.5 then multiply the number with the middle point.

So midpoint times the number. So, we get

29.5 * 21.7 = 640.15 & so on we get 129,...

Then add these numbers together. So that becomes 5375.75. And what about the total number here, that is

=>21.7 + 32.8 + 36.8 + 21.7= 118.5

So here,

Mean value, that should be equal to the sum of mean times the number divided by the total number here,

Mean= [tex]\frac{5375.75}{118.5}[/tex] = 45.36

So, this is the mean value.

Standard deviation:

Standard deviation =  [tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]

[tex]\sigma[/tex] = population standard deviation

N = the size of the population

[tex]x_{i}[/tex] = each value from the population

[tex]\mu[/tex] = the population mean

So here is what we have to do,

We have to subtract the mean value from the middle point that is,

=>45.36- 21.5 and squared plus 45.36 -39.5 Squared. And plus this is 45.36 -49.5 Squared plus 45.36 -59.5 squared. And then, this is 45.

Let me just inside the apprentices Inside the practices, this is 45 .36 29.5 and take the square of this one And then add another one Which is 45.36 39.5 and then take the square this one too. And plus inside parentheses, this is 45.36 minus Which is 490.5 And then squared. That is 45.36 And -59 0.5 so And then take the square, there's 12 if you just add all of them, so we will get five 47.1184.

So the standard deviation is the square of 547, divided by The total frequency here.

Standard deviation = √28.37/4 = √7.0925 = 2.66317

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[5, +∞) ∪ (-∞,7] is the notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7​.

We need to use interval notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7​.

A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Let x belong to the set of real numbers (R)

Now, x≥5 and x≤7.

So, x≥5⇒[5, +∞) and x≤7⇒(-∞,7]

Therefore, the notation will be [5, +∞) ∪ (-∞,7].

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Using the cosine ratio, the value of cos(45) in the diagram is: B. 1/√2.

Cosine ratio is, cos ∅ = adjacent length/hypotenuse length of a right triangle.

The triangle is a 45-45-90 triangle, thus, the two legs will be the same length, which is: 9 units each.

Hypotenuse = √(9² + 9²) = √162 = 9√2 units

∅ = 45°

Adjacent = 9 units

cos 45 = 9/9√2 = 1/√2

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Answer:

hope it helps.good day

in case you don't understand anywhere feel free to ask

The point which lies on the graph of the given function is; Choice D; (0, 2).

The point which lies on the graph of the given function; y = 2*3^x is it's y-intercept. The y-intercept which corresponds to the value of y when variable X is set to zero.

Hence, y = 2*3^0;

y = 2 ×1 = 2.

Hence, the point is; (0,2).

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Answer:

7x+y

7(7)+1

49+1

50

Step-by-step explanation:

please mark me as brainlest

Answer:

7x + y

x=7 y=1

7(7) + 1

49 + 1

= 50

Answer:

m∠BAC = 40°

Step-by-step explanation:

Note that line BD passes through A, so ∠BAC and ∠CAD form a linear pair.  By the Linear Pair Postulate, ∠BAC and ∠CAD are supplementary angles, and by definition their measures add to 180°:

m∠BAC + m∠CAD = 180°

Since the diagram gives us that m∠CAD = 140°, we can substitute and solve:

Starting supplementary angles definition equation ...

m∠BAC + m∠CAD = 180°

Substituting the known value of m∠CAD ...

m∠BAC + (140°) = 180°

Subtracting 140° from both sides of the equation...

(m∠BAC + 140°) - 140° = (180°) - 140°

Simplifying/evaluating...

m∠BAC = 40°

The correct representations of this solution are

The inequality is given as:

6 + 2n > 12

The solution is given as:

n > 3

When the above inequality is represented as an interval, we have:

(3, ∞)

Also, the inequality symbol > is represented using an open circle.

This means that the number line would use an open circle and the arrow would point right

Hence, the correct representations of this solution are (d) and (e)

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On a coordinate plane, a line goes through (negative 3, 0) and (0, negative 6).

The graph for the first equation of a system is shown in orange. The second equation is: 3y+30=6x

What is the solution to the system?

A. (2, –10)

B. (1, –8)

C. (–2, –14)

D. (2, –6)

Answer: 4.9/5

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Answer:

B. (1,-8)

Step-by-step explanation:

Slope of the first one:

(-6-0)/(0--3) = -6/3 = -2

y = -2x - 6

3y + 30 = 6x

y + 10 = 2x

-2x - 6 + 10 = 2x

4 = 4x

x = 1

y = -2(1) - 6

y = -8

Answer:

2nd one

as the y is both 4, the points are on the same plane. As such, we care about the distance of x which is between 3 and 7

Answer:

a = 127 kg

b = 55 kg

Step-by-step explanation:

a + b = 182

a - 36 = b + 36

   + 36      + 36

a = b + 72

(a) + b = 182

(b + 72) + b = 182

2b + 72 = 182

      -72    -72

2b = 110

÷2    ÷2

b = 55

a + (b) = 182

a + (55) = 182

   - 55      - 55

a = 127

{127 - 36 = 91}

{55 + 36 = 91}

{91 + 91 = 182}

The most misleading graph is graph B because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale

From the graph, we have the median weekly earnings to be:

So, the ratio is:

Ratio = $750 : $1250

Simplify

Ratio = 3 : 5

Hence, the ratio of the median weekly earnings is 3 : 5

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

Both rectangles have a width of 1 unit.

So, we have:

Ratio = 3 * 1: 5 * 1

Simplify

Ratio = 3 : 5

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

The red rectangle has a width of 3 units, while the blue has 5 units as its width

So, we have:

Ratio = 3 * 3 : 5 * 5

Simplify

Ratio = 9 : 25

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

The red rectangle has a width of 3 units, while the blue has 5 units as its width.

Since the base are squares, we have:

Ratio = 3 * 3  * 3 : 5 * 5 * 5

Simplify

Ratio = 27 : 125

Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125

The most misleading graph is graph B.

This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale

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Answer:

0 m/s

Step-by-step explanation:

Answer:

25/36

Step-by-step explanation:

put 2500 over 3600 and remove the 0's to simplify it

Answer:

- In 45 days = 4,5mm  ;    In 90 days = 9mm

Step-by-step explanation:

in 45 days = 0,1 * 45 = 4,5 mm  ; in 90 days = 0,1 * 90 = 9mm

Answer:

87.92

Step-by-step explanation:

We are given this expression:

3.14(a² + ab)

And we want to evaluate it if a is 4 and b is 3.

To solve this, we need to follow the order of operations, usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have their own variations on the acronym.

Despite this, let's start with P, which would be parentheses.

Because we have the a² + ab in parentheses, we should evaluate this first.

We should substitute the values  of a and b with 4 and 3 respectively, to get this (we can ignore the 3.14 for now):
(4)² + 4 * 3

First, let's go on to exponents.

We do have one exponent, which is the 4 being raised to the second power.

So let's evaluate that.

Raise 4 to the second power (multiply it by itself).

4 * 4 = 16

We can replace (4)² with 16.

16 + 4 * 3

Now, let's move on to multiplication.

We do have one multiplication operation, which is the 4 * 3, so let's evaluate that.

4 * 3 = 12

Replace 4 * 3 with 12.

16 + 12

We don't have any division in this, so we can skip that.

Moving on to addition:

We can add these two numbers together.

16 + 12 = 28

28 is the value of a² + ab.

We now multiply this by 3.14 to get the answer.

3.14 * 28 = 87.92

Topic: substituting values into an expression

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The value of expression 3.14([tex]a^{2}[/tex]+ab) when a =4 and b=3 is 87.92.

Given Expression :3.14([tex]a^{2}[/tex]+ab) and we have to find the value at a=4 and b=3

we know expressions are the combinations of numbers, symbols and coefficients and in the expression given the variable are a and b .Expression shows the relationship between the variables which are present in the expression. When we have to find the value of expression at a=4 and b=3 we have to just put the values of a and b in the expression .

[tex]a^{2}[/tex]=16 and ab=4*3=12

=3.14[tex]((4)^{2}+4*3)[/tex]

=3.14(16+12)

=3.14*28

=87.92

Hence the value of the expression 3.14(a2 + ab) at a=4 and b=3 is 87.92.

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Answer:

  (b)  0.5431

Step-by-step explanation:

The proportion of adult tickets sold is the ratio of the total number of adult tickets sold to the total number of tickets sold. Those totals are found on the bottom line of the table.

__

  proportion = (adult tickets)/(total tickets) = 126/232 ≈ 0.5431

Approximately 0.5431 of the tickets sold were adult tickets.

Answer:

B) 0.5431

Step-by-step explanation:

edge 2023

Answer:

3

Step-by-step explanation:

we can think of the slope of a graph as [tex]\frac{rise}{run}[/tex]

the "rise" is the difference in y-values between two points (the change in y)

the "run" is the difference in x-values between two points (the change in x)

when we divide these (rise/run), we find the slope

you can choose any two well-defined points (with clear x and y values), here are the two we will be using:

(remember, points are written as (x, y)  )  

(0 , 2)

(-1 , -1)

for the "rise", we have risen 3 (difference between 2 and -1 = 3 [2- -1 = 3] )

for the "run" we have ran 1 (difference between 0 and -1 = 1) (0 - - 1 = 1)

so, the slope for this graph is: 3/1 ; which simplifies to 3

So, the slope of our graph is 3

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

technical layout:

[tex]m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]               (note: slope is called "m" in the format of y=mx + b)

[tex]y_{1}[/tex] means one y-value, [tex]y_{2}[/tex] means other y-value

[tex]x_{1}[/tex] means one y-value, [tex]x_{2}[/tex] means other x-value

{note: it is important to keep the y1 and x1 from the same point, and the y2 and x2 from a shared point}

our equation in this layout:

[tex]m=\frac{2 -(-1)}{0-(-1)}[/tex] = [tex]m=\frac{3}{1}[/tex]

                     m = 3

Step-by-step explanation:

option 2 is correct

here the question ask for value of X

to find it we multiple the matrix X with the given matrix in question and equate the answer.

Answer:

75%

Step-by-step explanation:

48x=36

x=36/48

x=3/4

x=0.75=75%

Based on the data given on the number pattern, 4 + 5 = 180

7 + 9 = 254016

3 + 7 = 7779240

5 + 8 = 2496000

7 + 9 = (7 × 9)^|7-9| × (7 + 9) × |7 - 9)

= 69² × 16 × 2

= 4761 × 16 × 2

= 254,016

3 + 7 = (3×7)^|3-7| × (3+7) × |3-7|

= 21⁴ × 10 × 4

= 194,481 × 10 × 4

= 7,779,240

So,

4 + 5 = (4×5)^|4-5| × (4+5) × |4-5|

= 20¹ × 9 × 1

4 + 5 = 180

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The correct statements are:

Function g has a y-intercept of (0,4)

The range of the function g is (3, ∞).

The function g is positive over the interval (-∞ , ∞ ).

The parent function i.e. exponential function is defined by:

y=f(x)=aˣ

From the graph given below,

1. The graph of the function g is 3 units above the graph of the parent exponential function. as the parent exponential function aˣ cuts the y-axis at (0,1) and the child transformed function cut at (0,4) for which g is 4-1=3 units above the parent function  

2. The domain of the function is set of all the inputs for which function is defined. From the graph of function g, it is clear tha the domain of the function is (-∞ , ∞ ) as the domain of the parent exponential function is also (-∞ , ∞ ).

3. The y-intercept is the point at which function cut the y-axis. Graph of function g cut the y-axis at (0, 4). Therefore, Function g has the y-intercept at (0,4).

4. From the graph it is clear that Function g increases over the interval (-∞, 0) .

5. The range of the function is the output values of the function. From the graph, it is observed that the range of function g is (3, ∞). as its minimum value is 3 then the maximum value is ∞.

6. As, the graph of function g is drawn above the x-axis. Therefore, Function g lies completely on +ve y-axis, so function g is positive over the interval (-∞ , ∞ ).

Therefore The correct statements are:

Function g has a y-intercept of (0,4)

The range of the function g is (3, ∞).

The function g is positive over the interval (-∞ , ∞ ).

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11/36 would be the probability of getting 4 , when two dice are thrown simultaneously.

As there are 6 faces of die,
So Probability of Not getting four in one dice = [tex]5/6[/tex]

As both events are mutually exclusive, the probability of not getting four in two dice = [tex](5/6) * (5/6) = 25/36[/tex]

So probability of getting at least one four is = [tex]1-(25/36) = 11/36[/tex]

So probability = [tex]11/36[/tex]

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Answer:

Step-by-step explanation:

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