QUESTION 5
REVIEW: Find the slope that passes through (2, 4) and (4,7)

Answer:

x = -5/6

Step-by-step explanation:

First, set the equation (6x + 5) * 86 equal to 0. The equation is now (6x + 5) * 86 = 0. Next, simplify (6x + 5) * 86 by multplying 86 to 6x and 5. This will turn the equation into 516x + 430 = 0. Next, subtract 430 from both sides, cancelling out the 430 on the left side. After that, get the x value by itself by dividing 516 on both sides, cancelling out the 516 on the left side. Now, x = -430/516. From here, find the common factor of both the numerator and denominator; this turns out to be 86. Since 86 is the common factor, divide the numerator and denominator by 86 and you get x = -5/6.

Work will be=\(386.4\) kilowatt-hours

Work is the action of a force over a distance. Lifting a weight off the ground and placing it on a shelf is a good example of work. The force is equal to the weight of the object and the distance is equal to the height of the shelf.

Power is work done per unit of time. The unit of power is Watt = 1 Joule/1 second.

If we use one kW of energy, a kWh of energy lasts for one hour.

Calculation of work, energy, and power

\(WORK = W=Fd\)

Since energy is the ability to do work, we measure energy and work in the same units (N*m or joules).

POWER (P) is the rate of generation (or absorption) of energy over time: \(P = E/t\)

The SI unit of power is the watt, which represents the generation or absorption of energy at a rate of \(1\) Joule/s. The unit of measurement of power in the English system is horsepower, which is equivalent to \(735.7\)watts.

Given:

Power=\(230\)w

Time= \(12\) hours a week for \(5\) months

To find:

Energy in kilowatt-hours

Solution:

Using the relation between power, work, and time which is \(P=W/t\)

We can find out the energy in kilowatt-hours

Firstly change power into kilowatts which is 230/1000=0.23kW

Now convert time into hours which is 4*7*5*12=1680 hours

Now use the formula which is \(P=W/t\)

\(0.23=W/1680\) kilowatt-hours

Hence work will be=\(386.4\) kilowatt-hours

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The largest integer less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13. is 1440

Given, a number less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13.

On using the Chinese remainder theorem. As, the numbers 7, 11, 13 are pairwise coprime.

Firstly, an integer  m  such that  m−5  is divisible by 7 and  m−10  is divisible by 11 .

The Chinese remainder theorem says that all integers that work will be of the form  54+7⋅11⋅k=54+77k  for any integer  k .

Next an integer  n  such that  n−10  is divisible by 13 and  n−54  is divisible by 77.

Then, by the Chinese remainder theorem, all the integers that also work are of the form  439+13⋅77⋅k=439+1001k .

Hence, the positive integers satisfying the condition are: 439, 439 + 1001 = 1440, 1440 + 1001 = 2441, and so on.

The largest integer less than 2010 is 1440.

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Answer:

Step-by-step explanation:

1. Since we know that Lila wants to use 1 cup of pretzels, we can multiply 1/2 x 1/2, which is 1.

2. Now that we multiplied 1/2 by 1/2, we have to multiply 1 1/4 by 1/2.

So 5/4 x 1/2 is 5/8.

3. Lila will need 5/8 cups of raisins.

Step-by-step explanation:

bodmas

7-4/4+12-10

7-4/16-10

3/4

0.75

Step-by-step explanation:

Here,

y= 2x

and x € (1,2,3)

now,

when x=1 , when x=2 , when x= 3

y=2x y= 2x y=2x

= 2×1 = 2×2 = 2×3

= 2 = 4 = 6

Therefore, y = (2,3,6)

If I were to choose a Bradford pool table for my home, I would choose the standard size table (50 inches by 100 inches). This is because I have a large home and I like to play pool with a group of friends. I also like to play tournament-style pool, so I need a table that is the same size as the tables used in tournaments.

The standard size Bradford pool table is also the most common size of pool table, so it would be easy to find replacement parts and accessories for it. Additionally, the standard size table is the most affordable of the three sizes offered by Brunswick Billiards.

Of course, there are some factors that might lead me to choose a different size table. For example, if I had a small home, I might choose the 7-foot table. And if I were only interested in playing pool casually with my family, I might choose the 6-foot table.

Ultimately, the best way to choose a Bradford pool table is to consider your own needs and preferences. If you are serious about playing pool, I recommend choosing the standard size table. But if you are just looking for a table to play with your family and friends, you might be happy with a smaller size table.

Here are some additional factors to consider when choosing a Bradford pool table:

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Complete question :

Pool Tables. The Bradford pool table made by Brunswick Billiards comes in three sizes of playing area, 50 in. by 100 in., 44 in. by 88 in., and 38 in. by 76in. Source: Brunswick Billiards

Which size Bradford pool table would you choose for your home, and why?

the equation of the conic section in standard form is:
7(x + 8)² - 3(y - 5)² = 543To write the equation of the conic section in standard form, we need to complete the square for both the x and y terms.

Starting with the given equation:
7x² - 3y² + 56x + 30y + 16 = 0

Let's focus on the x-terms first:
7x² + 56x

To complete the square, we need to add and subtract half of the coefficient of x (56/2)^2 = 784:
7(x² + 8x + 784/7) - 784 = 0

Now let's work on the y-terms:
-3y² + 30y

Completing the square, we add and subtract half of the coefficient of y (30/2)^2 = 225:
-3(y² - 10y + 225/3) + 225 = 0

Simplifying further:
7(x + 8)² - 784 - 3(y - 5)² + 225 + 16 = 0
7(x + 8)² - 3(y - 5)² - 543 = 0

Thus, the equation of the conic section in standard form is:
7(x + 8)² - 3(y - 5)² = 543

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The factor of the expression becomes:

π(R² - r²) = π(R + r) (R - r)

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It is possible to multiply, divide, add, or subtract in math. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, 10m + 5 is an expression including the terms 10m and 5 as well as m, the variable of the supplied expression, all separated by the arithmetic sign "+".

An annulus is the region between two concentric circles. The area of the annulus shown in the figure is πR² - πr²

= πR² - πr²

= π(R² - r²)

(R² - r²)  is of the form (a² - b²)

where, a = R and b = r

As we know, (a² - b²) = a² - 2ab + b² = (a + b) (a - b)

so, (R² - r²) = (R + r) (R - r)

The polynomial factored completely is then:

π(R² - r²) = π(R + r) (R - r)

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Answer:

\(x = - 1.9 \)

The answer of this equation is:

1.9

Answer:

1/10

Step-by-step explanation:

SInce there are a total of 10 cards and only one card with the number 2, then out of the ten cards you only have a 1/10 chance of grabbing the number 2 card! Hope this helps :)

Answer:2×3=6

or Add 2 three times

in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.

The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
Thus, in this case, correct option is:b

in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf

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B. {3,4}⊆A and D. {1,2}⊆A.

You provided the following statements:

A. {1,2}∈A
B. {3,4}⊆A
C. {3}∈A
D. {1,2}⊆A

Let's analyze each statement:

A. {1,2}∈A: This means {1,2} is an element of A. This is false, as 1 and 2 are individual elements, not a set.
B. {3,4}⊆A: This means {3,4} is a subset of A. This is true, as {3, 4} is an element of A.
C. {3}∈A: This means {3} is an element of A. This is false, as the set {3} is not present in A.
D. {1,2}⊆A: This means {1,2} is a subset of A. This is true, as both 1 and 2 are individual elements of A.

Therefore, your answer is: Select the statement that is true: B. {3,4}⊆A and D. {1,2}⊆A.

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The method of variation of parameters or the method of undetermined coefficients to find the solution.

a. True

The method of solving a second-order linear homogeneous ODE using the characteristic polynomial and the quadratic formula applies only to equations with constant coefficients. The general form of such an equation is:

a(d^2y/dt^2) + b(dy/dt) + cy = 0

where a, b, and c are constants.

However, the given ODE has a non-constant coefficient in the term (7t^3+cost)dy/dt. Therefore, we cannot use the same method to solve it as we use for equations with constant coefficients.

Instead, we need to use other methods like the method of variation of parameters or the method of undetermined coefficients to find the solution to this ODE.

The method of variation of parameters involves assuming that the solution to the ODE can be written as a linear combination of two functions u(t) and v(t), where:

y(t) = u(t)y1(t) + v(t)y2(t)

where y1(t) and y2(t) are two linearly independent solutions to the corresponding homogeneous ODE. The functions u(t) and v(t) are found by substituting this form of the solution into the ODE and solving for the coefficients.

The method of undetermined coefficients involves assuming a particular form of the solution that depends on the form of the non-homogeneous term. For example, if the non-homogeneous term is a polynomial of degree n, then the particular solution can be assumed to be a polynomial of degree n with undetermined coefficients. The coefficients are then determined by substituting the particular solution into the ODE and solving for them.

In summary, the method of solving a second-order linear homogeneous ODE using the characteristic polynomial and the quadratic formula is only applicable to equations with constant coefficients. For ODEs with non-constant coefficients, we need to use other methods like the method of variation of parameters or the method of undetermined coefficients to find the solution.

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Answer:

A

Step-by-step explanation:

most plausible answer.. because answer B.. teachers do not have offices and C isn't a logial answer at all .. ask yourself who is the who and in there.. in where?

Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

An instrument for comparing the sizes of two or more quantities in proportion to one another is called a ratio. A list of the structured equivalent ratios of every given ratio is called a ratio table. By multiplying as well as dividing the 2 terms of such a ratio by an identical number, equivalent ratios can be created.

Given data:

Area of triangle = 1/2* base * height

Ratios:

area of larger triangle / area of smaller triangle = (1/2*B*H) / (1/2*b*h)

area of larger triangle / area of smaller triangle = B*H / b*h

area of larger triangle / area of smaller triangle = 10*5 / 5*2

area of larger triangle / area of smaller triangle = 50 / 10

area of larger triangle / area of smaller triangle = 5/ 1 = 5:1

Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

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Complete question:

what is the ratio of the area of larger triangle to the area of smaller triangle ? express your answer as a common fraction.

Dimension of  larger triangle: base B = 10 cm, Height H = 5 cm.

Dimension of  smaller triangle : base b = 5 cm, Height H = 2 cm.

Answer:

8

Step-by-step explanation:

Answer:

18 and 1 Over 6 meters squared

Step-by-step explanation:

Hello There!

We can find the area of a square by multiplying its side by itself ( more specifically squaring it)

So the area of the square is equal to

\(4.25^2\\4.25*4.25=18.06\)

so the area of the square is 18.06

This statement is false.

DeMorgan's laws are fundamental laws in propositional logic that show the relationship between negation, conjunction, and disjunction. Specifically, DeMorgan's laws state:

The negation of a conjunction is the disjunction of the negations: ¬(p ∧ q) ≡ ¬p ∨ ¬q

The negation of a disjunction is the conjunction of the negations: ¬(p ∨ q) ≡ ¬p ∧ ¬q

If the negation operator distributes over the conjunction and disjunction operators, then DeMorgan's laws are still valid. In fact, the distributive law of negation over conjunction and disjunction is sometimes called one of DeMorgan's laws. The distributive law states:

The negation of a conjunction is equivalent to the disjunction of the negations: ¬(p ∧ q) ≡ ¬p ∨ ¬q

The negation of a disjunction is equivalent to the conjunction negations: ¬(p ∨ q) ≡ ¬p ∧ ¬q

So, the distributive law of negation over conjunction and disjunction is a valid form of DeMorgan's laws.

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Answer:

19.3 cm

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle B = 71°

Adjacent = 6.3 cm

Hypothenus = BC =?

The length BC can be obtained by using cosine ratio. This is illustrated below:

Cos B = Adjacent / Hypothenus

Cos 71 = 6.3 / BC

0.3256 = 6.3 / BC

Cross multiply

0.3256 × BC = 6.3

Divide both side by 0.3256

BC = 6.3 / 0.3256

BC = 19.3 cm

Thus, Lenght of side BC is 19.3 cm

Answer:

Horizontal

Step-by-step explanation:

Answer:

y = 9 is a horizontal line :)

Step-by-step explanation:

y=9 is the equation of a horizontal line. The slope is 0. This means that for any value of x that is chosen, the y-value is always 9 Hence y=9 .

Answer:

-3, 1

Step-by-step explanation:

There are actually 2 x-intercepts of the parabola. You can find them simply by looking along the x-axis and seeing where the lines of the parabola touch the axis, so -3 and 1.

Hope this helps :)

Answer:

1 and  -3

Step-by-step explanation:

At x-intercept y = 0

So, parabola intersect x-axis at two places (1 , 0) and (-3 , 0)

X-intercepts are 1 and -3

Answer:

You would save $53.50

Step-by-step explanation:

2,500*0.0849=212.25

For New York: $2712.25

2500*0.0635=158.75

For CT:$2658.75

The type of interference is this :

Comparing proportions from 2 independent samples

Given,

In the question:

Complete question is this:

Do upperclassmen (Seniors and Juniors) spend more money on alcoholic beverages then underclassmen (Freshman and Sophomores)? What type of inference is this?

a. Comparing proportions from 2 independent samples

b. One proportion

c. Comparing means from dependent samples

d. Comparing means from 2 independent samples

e. Comparing proportions from dependent samples

f. One mean

Now, According to the question:

Hence, The type of interference is this :

a. Comparing proportions from 2 independent samples

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Answer:

Slope - 21 Intercept - 15

The equation of the function h(x) is h(x) = 21x + 15, slope = 21, and y-intercept = 15.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The equation of the function f(x) is:

f(x) = -7x + 9

add 2 to the input off to create a new function g:

f(x + 2) = g(x) = -7(x + 2) + 9 = -7x - 5

g(x) = -7x - 5

Multiply the output of function g by -3 to create function h:

h(x) = -3g(x)

h(x) = -3(-7x - 5)

h(x) = 21x + 15

The slope = 21 and

y-intercept = 15

Thus, the equation of the function h(x) is h(x) = 21x + 15, slope = 21, and y-intercept = 15.

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Shelly ordered the 16 candy bags.

The operation or process of finding the difference between two numbers or quantities, denoted by a minus sign (−).

We have the information from the question:

Shelly paid a total of $15 for bags of candy she ordered on-line.

The cost of each bag was $0.75

Shipping charge was a flat rate $3.00

We have to find the how many bags of candy did shelly order.

Now, According to the question:

We have to subtract shipping charge from total paid charges, we get:

Total paid - shipping charge

=> 15 - 3

= 12

Number of bags = 12/ 0.75

Number of bags = 16

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