10 POINTS
The given table of values represents a linear equation. What is the slope?


x 3 4 5 6

y 1 5 9 13


Responses


2,

3,

5,

4

Answer:

The distance of the line would be 10 units.

AS ACD and ACBare congruent triangles, we have that

so the answer is y=7

Answer:

9.5 liters

Explanation:

The volume of each drink that Ally bought is:

• Lemonade: 4 liters

• Iced tea: 3,000 milliliters

• Fruit Punch: 2,500 milliliters

Since we are required to find the total in liters, convert the volumes given in milliliters to liters.

Therefore:

Therefore, the total volume in liters will be:

Ally bought 9.5 liters of drinks in total.

To find the angle we will use the sine theorem, but first we will find the measure of the missing side:

measure of angle B must be:

Finally convert B to degrees and minutes:

Answer:

Domain: A, [tex](-\infty, \infty)[/tex]

Range: A, [tex][4, \infty)[/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Using a calculator, we calculate the following

Based on these calculations, the square root of 2 is between 1 and 2.

Answer:

Natural:G

Whole number: B

Integer: H,D,J

Rational: A,F,E,I

Irrational: C,K

Step-by-step explanation:

The value of the expression [tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex] is - 98.

The abbreviation BODMAS rule is used to assist kids to recall the proper order of operations when performing mathematics. Operations are essentially the various mathematic operations we can do on numbers. "Brackets, Order, Division, Multiplication, Addition, Subtraction" is what it stands for.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Consider the expression,

[tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex]

Using the BODMAS rule,

We will first solve the parenthesis.

[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-4[35-65-19]}{-2}[/tex]

[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140+260+76}{-2}[/tex]

Now, the next step is to divide the expression.

[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140}{-2}+\frac{260}{-2}+\frac{76}{-2}[/tex]

[tex]\frac{-4[5(7-13)-19]}{2(-1)}=70-130-38[/tex]

Subtracting the expression,

[tex]\frac{-4[5(7-13)-19]}{2(-1)}=-98[/tex]

Hence, the value of the expression is - 98.

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The given triangle is shown below

From the triangle

Using the law of Cosines

Substitute the values of a, b, c into the formula

This gives

Simplifying the expression

Collect like terms

Divide both sides by -880

Find the value of C

Let X be the normally distributed random variable representing the time hiker takes to walk the trail.

Given that mean and standard deviation are 30.1 and 3.6 minutes, respectively,

The sample size is 4,

The z-score corresponding to any value of 'x' is given by,

So the probability that the mean time for the sample is less than 28 minutes is calculated as,

Substitute the value,

Thus, there is approximately 28.1% probability that the mean time for the sample is less than 28 minutes.

we will use here pythagoras theorem here,

5^2 + 12^2 = C^2

25 + 144 = C^2

C = root 169

c = 13

Answer:

b

Step-by-step explanation:

Here,

The length of a rectangle is 4ft less than 3 times the width

Then,

length=3w-4ft

Now,

2(l+w)=P
2(3w-4+w)=54

6w-8+2w=54

2(3w-4)+2w=54

Equation b can be used to find the width of the rectangle

Concept

What is a direct variation? A direct variation is a direct relationship between two variables in which increase in one variable lead to increase in the other variable and decrease in one variable lead to decrease in the other variable.

Hence, the relationship fron the graph between Height and Width of the rectangle is not a direct variation.

Therefore,

The relationship is not a direct variation.

Final answer

Option B = False

The solution to the system of equations is (-10/29, 71/29).

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The possibility of the other two numbers in the given data set is 3.

So, by observing the data, we can simply conclude that:

Therefore, the possibility of the other two numbers in the given data set is 3.

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Answer:4x(y+2)

Step-by-step explanation:

Answer:

A polynomial's degree is the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients)

Step-by-step explanation:

The degree of a polynomial is the exponent of the leading term. For example, (x + 1) is a first-degree polynomial because x has an exponent of 1. (x^5 + 2y^4 - 3y^3 + y^2 - x + 3) is a fifth-degree polynomial because x has an exponent of 5.

We are given the following information about a hexagonal prism.

Base area = 25.6 cm²

Height = 8.9 cm

Recall that the volume is given by

Where B is the area of the base and h is the height of the hexagonal prism.

Let us substitute the given values into the above formula

Therefore, the volume of the given hexagonal prism is 227.84 cubic centimeters.

SOLUTION:

Case: Logarithms

A logarithm is the opposite of power. In other words, if we take a logarithm of a number, we undo exponentiation.

We consider the log of power law below:

Given:

Required: Without using calculators, use log laws to answer

Method:

Applying the law above,

Final answer:

66

Answer:

g(x) = | x - 2 | + 10

Step-by-step explanation:

given g(x) then g(x± h ) is a horizontal translation of g(x)

• if h > 0 then a move to the left of h units

• if h < 0 then a move to the right of h units

here the move is 2 units to the right, then

g(x) = | x - 2 |

given g(x) then g(x) + c is a vertical translation of g(x)

• if c > 0 then a move up

• if c < 0 then a move down

here the move is 10 units up , then

g(x) = | x - 2 | + 10

We first need to

Answer:

y = 7x + 1/2

Step-by-step explanation:

0 = 1 - 2y + 14x
+2y    +2y

2y = 1 + 14x
/2   /2   /2

y = 1/2 + 7x

y = 7x + 1/2

Given:

Nolan wraps 36 presents in 12 hours on Saturday

And wraps 42 presents in 14 hours on Friday

If y = number of gifts, and x = number of hours

So, the proportional equation will be as follows:

Where k is the constant of proportionality

Total gifts = y = 36 + 42 = 78

Total hours = x = 12 + 14 = 26

So, subtitute into the euation to find k

So, the answer will be the constant = 3

The domain of function f(x) is the set of all real numbers.

the range of function f(x) is, f ≤ 14.9225

And the peak height of the flaming stone would be, 14.9 meters

In this question, we have been given a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory. Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function f(x) = -0.25x² + 3.15x + 5, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.

We need to determine the contextual domain and range and justify your answers.

The domain of function f(x) is the set of all real numbers.

The range of function f(x) is, f ≤ 14.9225

From the range of the function, the peak height of the flaming stone would be, 14.9 meters

Therefore, the domain of function f(x) is the set of all real numbers.

the range of function f(x) is, f ≤ 14.9225

And the peak height of the flaming stone would be, 14.9 meters

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Amount of water = 260 gallons

Amount of antifreeze = 60 gallons

let the amount of water = w

amount of water + amount of antifreeze will give 320 gallons of mixture

w + amount of antifreeze = 320

amount of antifreeze = 320 - w ...(1)

The concentration for the antifreeze = 80% = 0.8

The concentration of the mixture = 15% = 0.15

From our question, we are mixing antifreeze with pure water (two different things). In our calculation, we can write the concentration in terms of water or in terms of antifreeze.

Writing the concentration in terms of amount of antifreeze

0.8(amount of antifreeze) + percent of antifreeze (amount of water) = concentraton of the mixture

The mixture contains 15% antifreeze

water contains no antifreeze, percent = 0

0.8(320 - w) + 0(w) = 0.15(amount of mixture)

0.8(320 - w) + 0 = 0.15(320)

256 - 0.8w + 0 = 48

256 - 0.8w = 48

collect like terms:

256 - 48 = 0.8w

208 = 0.8w

divide both sides by 0.8:

208/0.8 = w

w = 260

substitute for w in equation (1)

amount of antifreeze = 320 - 260 = 60

Amount of water = 260 gallons

Amount of antifreeze = 60 gallons

From the statement, we know that we have a right triangle that:

0. has an angle ∠C = 90°,

1. is also an isosceles triangle,

2. has a side AC = 3.

1) From points 2 and 3, we know that:

Because we have a right triangle, we can use Pitagoras Theorem, which states that:

Where:

• c = AB = hypotenuse,

• a = BC = 3,

• b = AC = 3.

Replacing these data in the equation above, we get:

2) From point 2 we know that angles A and B must be equal:

From geometry, we know that the inner angles of a triangle sum up to 180°, so we have:

Where we have used point 1.

The sides of the triangle are:

• AB = √18,,

• AC = 3,

• BC = 3.

The angles of the triangle are:

• ∠A = 45°,,

• ∠B = 45°,,

• ∠C = 90°.

we get that the decrease percentage is

so the percentage of decrease is 50%

Let x represent the number of days

Let f(x) represent water depth

We can see that the water depth is a function of the number of days.

Water depth, f(x) is the dependent variable and number of days, x is the independent variable.

As the days go by, the water depth changes.

The function is therefore:

The domain is the set of values (number of days) for which the pond will have a valid depth, i.e. between 54'' and 0.

Because at 0 days,

And at 108 days,

Answer

Explanation

We are given that

f(x) = (2 - x)/(x + 1)

g(x) = 18 - 3x

We are then asked to find (f o g)(x)

(f o g) (x) is the same as writing the expression for f(x) but instead of x, we will write g(x) in the expression.

Recall that

g(x) = 18 - 3x

So,

Hope this Helps!!!

Area of triangle shape

Area A = BxH/2 = [ 8 x (5+1/2) ]/2

. = 4 x 5.5

. = 22

Then answer is

Area of logo = 22 inches2

OPTION B)