what is the slope of the line?​

Answer:

b

Step-by-step explanation:

because 2/8 + 1 7/8 is 2 1/8

Answer:

\(2\frac{1}{8}\) inches

Step-by-step explanation:

\(\frac{2}{8} + 1\frac{7}{8}\)

Answer:

418/(g + 15) = 22

Step-by-step explanation:

He had an unknown amount of gas in the tank.

Call the original unknown amount g.

He added 15 gallons.

The full tank has g + 15 gallons.

He drove 418 miles with g + 15 gallons, so his gas mileage is

418/(g + 15).

We are told his mileage is 22 mpg.

Equation:

418/(g + 15) = 22

Answer:

4g in his tank previously.

Step-by-step explanation:

418/22=19, and 19-15=5.

Answer:

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

Find the third and tenth terms using the nth term equation, then add them up.

The sum is:

The sum of the third and tenth terms is 20

Since an arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence:

The third and tenth terms use the nth term equation, then add;

a(3) = 2(3) - 3 = 6 - 3 = 3

a(10) = 2(10) - 3 = 20 - 3 = 17

Therefore the nth term of such sequence would be  \(T_n = ar^{n-1}\) (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).

The sum is:

3 + 17 = 20

Learn more about arithmetic sequence here:

https://brainly.com/question/3702506

#SPJ1

Answer:

y =0

Step-by-step explanation:

If we are on the x axis, the x value can change, but the y value is zero

Answer:

y=0

Step-by-step explanation:

The correct term for a sample obtained in such a way that every element in the population has an equal chance of being selected is a "random sample."

In a random sample, each member of the population has an equal probability of being chosen, providing a representative subset of the population. This sampling method helps to reduce bias and ensures that the sample is more likely to accurately reflect the characteristics of the entire population.

Random sampling is a fundamental principle in statistics and research, allowing for generalizations and inferences to be made about the population based on the characteristics observed in the sample. It is widely used in various fields, such as social sciences, market research, and opinion polls, to draw meaningful conclusions about a larger population.

 To learn more about population click here:brainly.com/question/15889243

#SPJ11

As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

To know more about angle,

https://brainly.com/question/14569348

#SPJ1

Let's try to understand how we can solve this equation

Given equation,4f+2=6f-12

Now we will take the terms on one side and constants on the other.

=> 2+12=6f-4f

=> 14=2f

=>7=f

So, the value of f would be 7. Remember that while bringing value to another side, the sign of that value changes. If it is a positive sign then it is going to be transformed into a negative one and vice versa.

The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

Learn more about simple interest here:

brainly.com/question/30964674

#SPJ11

Answer:

rational function is the correct answer

Answer:

Step-by-step explanation:

Givens

Time = 6.25 hours

distance = 13.6 cm - 11.1 cm = 2.5 cm

Formula

rate = distance / time

Solution

rate = 2.5 / 6.25

rate = 0.4 cm/hour

Answer:

\(x = \frac{c}{a + b} a = - b\)

The amount of inventory that Baryla can hold is **$16.1 million**.

The inventory turnover ratio is calculated as sales / inventory. To maintain an inventory turnover ratio of at least 5.6, Baryla's inventory must be no more than $90 million / 5.6 = $16.1 million.

Calculation:

```

sales = $90 million

gross profit margin = 35%

inventory turnover ratio = 5.6

inventory = sales / inventory turnover ratio = $90 million / 5.6 = $16.1 million

```

**b. Currently, some of Baryla's inventory includes $1.5 million of outdated and damaged goods that simply remain in inventory and are not salable. What inventory turnover ratio must the good inventory maintain in order to achieve an overall turnover ratio of at least 5.6 (including the unsalable items)?**

The good inventory must maintain an inventory turnover ratio of **9.4 times** in order to achieve an overall turnover ratio of at least 5.6.

The overall inventory turnover ratio is 5.6, and the unsalable inventory is $1.5 million. This means that the good inventory is $90 million - $1.5 million = $88.5 million.

The good inventory must maintain an inventory turnover ratio of $88.5 million / 5.6 = **9.4 times** in order to achieve an overall turnover ratio of at least 5.6.

overall inventory turnover ratio = 5.6

unsalable inventory = $1.5 million

good inventory = $90 million - $1.5 million = $88.5 million

good inventory turnover ratio = $88.5 million / 5.6 = 9.4 times

to learn more about ratio click here:

brainly.com/question/28851311

#SPJ11

The answers to the questions about this orbit system are as follows:

We have the following equation

\(16x^{2} + 192x + 576 + 25y^{2} = 1600\)

we can factorize as:

= \(16(x^{2} + 12x + 36) + 25y^{2} = 1600\)

\(= 16(x + 6) (x + 6) + 25y^{2} = 1600\)

\(= 16(x+6) ^{2} + 25(y-0)^{2} = 1600\)

\(= \frac{(x+6) ^{2}}{10^{2} } + \frac{(y-0)^{2}}{8^{2} } = 1\)

The equation that we have above is the standard ellipse equation.

2.

\(16x^{2} -96x+144+ 25y^{2} = 400\)

\(= 16(x^{2} -6x+9)+ 25y^{2} = 400\)

\(= 16(x^{2} -3x-3x+9)+ 25y^{2} = 400\)

\(= 16(x -3)(x-3))+ 25y^{2} = 400\)

\(= 4^{2} (x-3)^{2} + 5^{2} (y-0)^{2} = 400\)

\(= \frac{(x-3)^{2}}{5^{2}} + \frac{4^{2} }{4^{2}} = 1\)

The equation that we have above is the standard ellipse equation.

We can see that the semi major axis of the first equation gives us 10 units while that of the second gives us 5 units. The first equation has the larger orbit than the second.

3. (x + 6)²/100 + y²/64

= x-3²/25 + y²/16

\(16x^{2} +192x+576+25y^{2} = 1600\)

\(16x^{2} -96x+144+ 25y^{2} = 400\)

solve both equations using the simultaneous linear equation

the values for x and y are

2.667 and -3.99

Complete question

4. Gravity holds objects in space together. It makes the moon orbit our planet, and it makes the planets in our solar system orbit the sun. In some parts of space, gravity can make two s All changes saved orbit each other, and when this happens, we call the pair "binary stars." In reality, both stars orbit a center of mass outside of their individual masses, as shown below:

orbit of less

orbit of more

For the above system, we place the center of mass at the origin. The equations for the two stars' orbits are:

16x2+192x+576+25y² = 1600

16296x+144+ 25y² = 400

a) Determine whether the equations represent parabolas, hyperbolas, or ellipses.

b) Write both equations in standard form, and show how you arrived at your answers. Which equation matches with each orbit? How do you know? c) Although these two stars are unlikely to crash, at how many points on their orbits would such an event be possible? Explain how you would find those

Read more on standard ellipse equation here: https://brainly.com/question/10259559

#SPJ1

Answer:

1/10

Step-by-step explanation:

For multiplying fractions, just multiply the numerators by eachother and the denominators by eachother.  (The number on top being the numerator and the number on bottom being the denominator.)  

3 × 4 = 12 and 8 × 15 = 120, so your answer so far is 12/120.  

Divide 12 and 120 by something that goes into both of them, I'll do 6, and you get 2/20.  2/20 is equal to 1/10, which is the lowest you can go, therefore being the final answer.  (If you are allowed to simplify, just put 12/120 as your answer.)

I hope this helps!  Don't worry, your not bad, I hard a hard time with fractions too.  :)

Answer:

\(\frac{1}{10}\)

Step-by-step explanation:

1) \(\frac{3}{8}\)×\(\frac{4}{15}\)

Reduce the numbers with the greatest common factor: 3

2) \(\frac{1}{8}\)×\(\frac{4}{5}\)

Reduce the numbers with the greatest common factor: 4

3) \(\frac{1}{2}\)×\(\frac{1}{5}\)

Multiply the fractions

4) \(\frac{1}{10}\)

On December 13, 2007, 56.65 dollars is worth 27.77 pounds.

On December 13, 2007, 163.23 pounds is worth  332.99 dollars.

The exchange rate of a currency is the rate at which one currency is exchanged for another currency. There are usually two pairs of currency in an exchange rate. The exchange rate given in these question is: 1 pound = 2.04 dollars. This means that 1 pound would buy 2.04 dollars.

In order to determine the value of pounds given the value of the dollars, this formula would be used:

Value in pounds = value of dollars / exchange rate

56.65 / 2.04 = 27.77 pounds

In order to determine the value of dollars given the value of pounds, multiply the given value of dollars by the exchange rate.

Value in dollars = value of pounds x exchange rate

163.23 x 2.04 = 332.99 dollars

A similar question was answered here: https://brainly.com/question/19437632?referrer=searchResults

Matrix-vector multiplication is a linear operation because it satisfies the properties of scalar multiplication and vector addition, which are a(u+v) = au + av and a(cu) = cau, where a is a scalar and u and v are vectors.

Matrix-vector multiplication is a fundamental operation in linear algebra, where a matrix is multiplied by a vector to produce another vector. This operation is considered linear because it adheres to certain properties.

The first property is scalar multiplication, which states that multiplying a vector u by a scalar a and adding it to another vector v (a(u+v)) is equivalent to multiplying u by a (au) and v by a (av) separately and then adding the results (au + av). In other words, the operation distributes over vector addition.

The second property is the distributive property of scalar multiplication, which states that multiplying a vector u by a scalar c and then multiplying the resulting vector (cu) by another scalar a is equivalent to multiplying u by the product of the two scalars (cau). This property allows the scalar multiplication to be distributed over scalar multiplication.

These properties ensure that matrix-vector multiplication preserves the linearity of the underlying vector space. They enable the manipulation and analysis of systems of linear equations, transformations, and other mathematical operations involving matrices and vectors.

Learn more about distributive property here: https://brainly.com/question/30321732

#SPJ11

Answer:

See below.

Step-by-step explanation:

A)

The end behavior is basically how the function behaves as it approaches negative or positive infinity.

As the function approaches negative infinity, we can see that the graph is going up. In other words:

\(f(x)\rightarrow\infty\text{ as }x\rightarrow-\infty\)

As the function approaches positive infinity, we can see that the graph is going down. In other words:

\(f(x)\rightarrow-\infty\text{ as }x\rightarrow\infty\)

B)

In even-degree polynomials, both ends of the graph will be going the same way. In this graph, the two ends are going opposite ways so this is an odd-degree function.

C)

The number of real zeros is simply the amount of times the graph crosses the x-axis. In the graph, the function does this three times. Thus, the number of real zeros is 3.

When making a joint probability table, the type of probabilities is contained in the cells except those cells on the margin of the table joint probabilities, while those on the margins are marginal probabilities.

A joint probability refers to the probability that two independent events will both occur. two or more random variables. It is a statistical measure that calculates the probability of two events occurring together and at the same point in time i.e., joint probability is the probability of event Y occurring at the same time that event X occurs. A joint probability table represents a joint probability distribution for two or more random variables illustrating the relationship between variables (it uses variables or conditions instead of events). In the joint probability table, the type of probabilities that are contained in the cells are joint probabilities, while those on the margins are marginal probabilities (probabilities of values of the variables in the subset without reference to the values of the other variables.).

Learn more about Joint probability:

https://brainly.com/question/29563436

#SPJ4

The correct answer is OD. Although the word "then" appears in the statement, it is not used as a logical connective. So the statement is not compound.

The statement "If Laura sells her quota, then Marie will be happy" is a single declarative sentence. It consists of a conditional clause ("If Laura sells her quota") and a consequent clause ("then Marie will be happy"). However, these two clauses are not independent statements that can stand alone. Instead, they are connected in a cause-and-effect relationship. The word "then" in this context is not functioning as a logical connective, but rather as an indicator of the consequent clause.

A compound statement is formed by combining two or more independent statements using logical connectives such as "and," "or," or "if...then." In the given statement, there is no logical connective joining two independent statements.

Therefore, the statement is not compound.

Learn more about compound statement click;

https://brainly.com/question/5429065

#SPJ4

Answer:

12 for length, 6 for width

Step-by-step explanation:

Trust me its right

Answer:

12 for length 6 for width (:

Step-by-step explanation:

The need for capital by the Sport Bat Corporation will spread through the financial system as it interacts with banks, investors, and the broader financial markets.

When the Sport Bat Corporation needs to borrow $2 million to upgrade their equipment, they will likely seek a loan from a financial institution, such as a bank. The bank will evaluate the creditworthiness of the company and may require collateral or a personal guarantee before approving the loan.

Once the loan is approved, the bank will add the Sport Bat Corporation's loan to their portfolio of assets. The bank may choose to sell the loan to other investors, such as insurance companies or pension funds, to diversify their portfolio and manage risk.

These investors will then receive the interest payments on the loan as a source of income. The loan may be bundled together with other loans and sold as a package, called a securitization, to other investors in the financial markets, thus representing the spread of the loan throughout the financial system.

More can be learned about loans at https://brainly.com/question/11686424

#SPJ1

Answer:

2.3%

Step-by-step explanation:

jdbxjdjebdudbbdjdbdbd

Answer:

Give Brainliest please! BRAINLIEST

Step-by-step explanation:

Using the rational root theorem, the possible rational roots of f(x) = 4x^3 + 10x^2 + 14x + 6 can be expressed as follows:

Factors of 6 (constant term): ±1, ±2, ±3, ±6

Factors of 4 (leading coefficient): ±1, ±2, ±4

So the possible rational roots are:

±1, ±2, ±3, ±6, ±1/2, ±3/4, ±1/4, ±3/2

Therefore, the list of all possible/candidate rational roots of f(x) is:

-6, -3, -2, -1, -3/2, -1/2, -3/4, -1/4, 1/4, 3/4, 1/2, 3/2, 1, 2, 3, 6

These roots can be expressed as integers or as fractions in simplest form.

Answer:

W (3 , 4) or W (3 . -4)

Step-by-step explanation:

W (3 , y), origin (0 ,0)

WO = √(3-0)²+(y-0)² = √9+y²

WO = 5

√9+y² = 5

9+y² = 25

y² = 16

y = ± 4

W (3 , 4) or W (3 . -4)

Answer:

-4

Step-by-step explanation:

A=4\(\pi -8\)

that is your answer :-)

Answer:

\(A = 4\pi - 8\)

Step-by-step explanation:

ody

Answer:

(5 - 7i)(8 + i)

F) 40 - 561

H) 37 - 371

K) -16 - 2i

G) -33 - 61i

J) 47 - 51i

- 9 below

Step-by-step explanation:

Answer:

Step-by-step explanation: I think you have to add all the numbers together then divide by all the numbers i think

Answer:

54%

Step-by-step explanation:

129/240 =  0.5375  (divided to find the % change)

0.5375 * 100 (to convert decimal to percent form)

53.7 which is rounded to 54 percent (I needed to round it to the nearest whole percent number)

a² + b² = c² is true for the first triangle but false for the second triangle.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

a² + b² = c²

Where:

a, b, and c represents the length of sides or side lengths of any right-angled triangle.

By substituting the given parameters into the formula for Pythagorean's theorem, we have the following;

a² + b² = c²

4² + 2² = c²

c² = 16 + 4

c = √20 or 2√5 units.

a² + b² = c²

5² + 2² = (√45)²

45 = 25 + 9

45 = 34 (False).

Read more on Pythagorean theorem here: brainly.com/question/15430861

#SPJ1