Carlos took a total of 8 quizzes over the curse of 4 weeks. What is his unit rate?

The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.

A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.

A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.

In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.

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Explanation:

x = number of weeks

y = height of the plant (inches)

The first sentence of "plant is 4 inches tall on week 8" gives us the point (x,y) = (8,4)

The second sentence gives us the point (32,16)

To find the growth rate, compute the slope.

[tex](x_1,y_1) = (8,4) \text{ and } (x_2,y_2) = (32,16)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{16 - 4}{32 - 8}\\\\m = \frac{12}{24}\\\\m = \frac{1}{2}\\\\m = 0.5\\\\[/tex]

The slope of 0.5 means the plant grows 0.5 inches per week.

Put another way, the plant grows 1 inch per every 2 weeks.

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Another approach:

The plant goes from 4 inches to 16 inches. It has grown 16-4 = 12 inches over the timespan of 24 weeks (since 32-8 = 24).

So its growth rate is 12/24 = 0.5 inches per week.

Notice how these values and calculations were mentioned in the previous section.

The solution for the given polynomial are x = -9, 9 and -10.

What is polynomial?

Polynomials are algebraic expressions that contain coefficients and variables. Variables are sometimes known as indeterminates. Mathematical operations like addition, subtraction, multiplication, and positive integer exponents can be performed on polynomial equations but division by variables cannot.

Given polynomial:

(x+9)(x-9)(x+10)

Equating it wit zero,

we get solutions as:

x = -9, 9, -10

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Answer:

When you round the number to 5

Step-by-step explanation:

Answer: Your answer is $7.30

Step-by-step explanation:

Finding the amount for a tip is simple!

all that's required is multiplying the bill (36.50) by the amount you want to tip (.20, because 20% is equal to .20)

36.50×.2= $7.30

The velocity of the sign are given as follows:

a) Relative to the car: 60 kilometers an hour.

b) Relative to the ground: 0 kilometers an hour.

The relative speed of one object towards another is given by the rate of change in the position of each these objects relative to each other in regard to time.

Relative to the car, the sign gets 60 kilometers closer every hour, hence the relative speed of the sign will be of 60 kilometers. an hour.

Now, for the ground, the distance between the sign and the ground will always be the same, that is, there is no change in the distance. Hence, the velocity of the sign relative to the ground is of 0 kilometers and hour.

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2(-x - 5) = 12

Step 1 : Expand the bracket.

=> -2x - 10 = 12

Step 2 :Add both side by 10.

=> -2x - 10 + 10 = 12 + 10
=> -2x = 22

Step 3 : Divide both side by -2.

=> -2x : (-2) = 22 : (-2)
=> x = -11

Therefore, x = -11.

Answer:

x = - 11

Step-by-step explanation:

2(- x - 5) = 12 ( divide both sides by 2 )

- x - 5 = 6 ( add 5 to both sides )

- x = 11 ( multiply both sides by - 1 )

x = - 11

The curve is laid out from point to point, the last deflection angle of circular curve is 26.5°

In the given question we have,

Radius of circular curve (R) = 225 ft

intersection or central angle in circular curve (I or delta) = 55°

separtion between stakes alaong arc = 50 ft

Angle of deflection is measured from tangent at PC or PT to any point .

deflection angle formula

deflection angle = (Lc /L)(I/2)

where, Lc is long chord and L is lenth of arc , I is central angle

first we find out the value of Lc and L

using formula , R = Lc / 2sin(I/2)

Lc = 225× 2 sin(55°/2) = 208 ft

L = R × I ×π/180°

L = 225 × 3.14 ×55/180 = 215.8 ~ 216 ft

put all the vales in deflection angle formula we get ,

deflection angle= (208/216)(55°/2) = 26.48° ~ 26.5°

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The measure of the side MK of the triangle is 109.6.

The scale factor is defined as the proportion of the new image's size to that of the previous image. The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.

For the triangles, the scale factor will be calculated as,

Scale factor = 57 /13

The measure of the side MK will be calculated as,

57 / 13 = MK / 25

MK = ( 57 x 25 ) / 13

MK = 1425 / 13

MK = 109.61

Therefore, the measure of the side MK of the triangle is 109.6.

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Answer:

Step-by-step explanation:

Answer:

I don't know if this what you want but...

Step-by-step explanation:

2x+y=17

2x= 17-y

x= 17-y

     2

7 i do not feel like explaining tbh

Answer:

Option D

Step-by-step explanation:

This is because it contains the sum of the same variable to different powers.

Answer:

[tex]9x = 3x - 36 \\ 6x = - 36 \\ x = - 6[/tex]

hopefully this will u...^⁠_⁠^

Answer: 64.95

Step-by-step explanation: The formula is (3√3 s2)/2 so using that we can find the answer which is, 64.95

Step-by-step explanation:

15t + 30 = 20t | -15t

30 = 5t

t = 30/5 = 6

20 + 5t = -6t + 86 | + 6t

20 + 11t = 86 | -20

11t = 66

t = 6

18t + 20 = 24t + 50 | -18t

20 = 6t + 50 | -50

-30 = 6t

t = -30/6 = -5

18t - 2 = 10t + 54 | -10t

8t - 2 = 54 | +2

8t = 56

t = 56/8 = 7

7t - 5 = 15t + 91 | -7t

-5 = 8t + 91 | -91

-96 = 8t

t = -96/8 = -12

The domain of the function f(x) = 3x is (b) All positive integers less than or equal to 4

From the question, we have the following equation of the function that can be used in our computation:

f(x) = 3x

In this case, the notations are given as

x = Number of splits

f(x) = number of new roots in each split

From the question, we have

Splits = 4

This means that the maximum value of x is 4

The other values of x would be

x = 1, 2, 3, 4

This can be represented as

0 ≤ x ≤ 4

The interpretation of the above notation is all positive values less than or equal to 4

Hence, the domain value is option (b)

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The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

The quadratic function is

f(x) = [tex]-3x^2[/tex] + 18x + 3

The general form of the quadratic function is

y = [tex]ax^2[/tex] + bx + c

If a < 0, the quadratic function has maximum value

Here the value of a = -3

Therefore the function has maximum value.

Maximum value will be at x = -b / 2a

= -18 / 2(-3)

= -18 / -6

= 3

The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a

Substitute the value in the equation

(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3

= (-36 - 324 / -12

= -360 / -12

= 30

Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

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The domain of y equals two divided by the quantity x minus three squared all minus one [y = (2)/(x - 3)² - 1] is: all real numbers.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values which are located on the x-coordinate.

Translating the word problem into an algebraic equation, we have;

y = (2)/(x - 3)² - 1

When x = 3, we have:

y = (2)/(3 - 3)² - 1

y = 2/-1 = -2

When x = 1, we have:

y = (2)/(1 - 3)² - 1

y = 2/3

In conclusion, the domain of this function is all real numbers.

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The value of the given expression is 9/2 when substituting the values of m = -3, n = 2, and p = -1 in the expression.

The value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.

Given that m = -3, n = 2, and p = -1

The expression is given in the question

⇒ m(p -n)²/ 3p +m

Substitute the values of m = -3, n = 2, and p = -1 in the expression

⇒ -3(-1 -2)²/( 3(-1) +(-3))

⇒ -3(-3)²/(-3-3)

⇒ -3(9)/(-6)

⇒ 27/6

⇒ 9/2

Given that x = 3, y = 2, and z = 4

The expression is given in the question

⇒ (3z + 2x + y)/(4y - 2x + z)

Substitute the values of x = 3, y = 2, and z = 4 in the expression

⇒ (3×4 + 2×3 + 2)/(4×2 - 2×3 + 4)

⇒ (12 + 6 + 2)/(8 - 6 + 4)

⇒ 20/6

⇒ 10/3

Thus, the value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.

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When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

So, the equations are graphs are:

Now, graph both equations as follows:

Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

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Answer:

324 cm²

Step-by-step explanation:

area of a square = L x L = L²

L = 18cm

(18cm)² = 18cm x 18cm = 324 cm²

Answer: 2a+5

5a-2-3a+7

First gather together the like terms

5a-3a  and  -2+7

then solve

5-3=2   and -2+7=5

answer = 2a+5

Based on the calculations, the unknown number (x) is equal to 7.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the unknown number. Therefore, translating the word problem into an algebraic equation, we have the following;

Multiply a number (x) by 5 = 5x

The product is equal to the sum of 20 and 15 = 20 + 15 = 35.

Combining the above information, we have:

5x = 20 + 15

5x = 35

Dividing both sides by 5, we have:

x = 35/5

x = 7.

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Friday hope that this helps

Answer:

h(8) = 2

Step-by-step explanation:

substitute x = 8 into h(x) , that is

h(8) = 2(8 - 7) = 2(1) = 2