In the following exercises, multiply the binomials. Use any method.
256. (r + s)(3r + 2s)

Answer:

all calculators are not the same!

Answer:

Hence the positive numbers are 246, and 41

(246, 41)

Step-by-step explanation:

From the question,

Let the first positve number be \(x\)

and the other number be \(y\)

Hence,

\(x = 6y\) ....... (1)

Also,

That is,

\(x - y =205\) ........(2).

To solve for the two unknowns, substitute the value of \(x\) in equation (1) into equation (2).

Since,

\(x = 6y\)

Then

\(x - y =205\) becomes

\((6y) - y =205\\\)

Then,

\(6y - y = 205\\5y = 205\\\)

Divide both sides by 5

\(\frac{5y}{5} = \frac{205}{5} \\ y = 41\\\)

∴ the value of \(y\) is 41

Now, substitute the value of y into equation (1) to find \(x\)

Then,

\(x = 6y\) becomes

\(x = 6(41)\\x = 246\\\)

∴ the value of \(x\) is 246

Hence the positive numbers are 246, and 41

(246, 41)

Answer:

60

Step-by-step explanation:

Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

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The values of x and y in the functions are

Function 1

This is given as

y = 6x + 8

When x = -6, we have

y = 6 x -6 + 8

Evaluate

y = -28

When the equation y = 20, we have

20 = 6x + 8

Evaluate the like terms in the above function

6x = 12

Divide by 6

x = 2

Function 2

This is given as

y = 2/3x

When x = -6, we have

y = 2/3 x -6

Evaluate

y = -4

When the equation y = 20, we have

20 = 2/3x

Evaluate the like terms in the above function

20 = 2/3x

Divide by 2/3

x = 30

Function 3

This is given as

y = -x + 5

When x = -6, we have

y = -6 + 5

Evaluate

y = -1

When the equation y = 20, we have

20 = -x + 5

Evaluate the like terms in the above function

x = -15

Function 4

This is given as

y = 6.5x + 7

When x = -6, we have

y = 6.5 x -6 + 7

Evaluate

y = -32

When the equation y = 20, we have

20 = 6.5x + 7

Evaluate the like terms in the above function

6.5x = 13

Divide by 6.5

x = 2

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If the medium drink cost $1. 50, the inequality that represents the cost of a popcorn is x ≤ 3.5. Hence, the most he can pay for each popcorn is $3.5.

To translate a word problem into an inequality:

In this problem, let:

x = the cost of 1 popcorn

Three popcorns means = 3x

The cost of a medium drink = 1.5

The amount he need to pay for a medium drink and 3 popcorn:

amount = 1.5 + 3x

However, he only has 12 dollars. Hence,

1.5 + 3x ≤ 12

Subtract both sides by 1.5

3x ≤ 12 - 1.5

3x ≤ 10.5

Divide both sides by 3

x  ≤ 10.5/3

x ≤ 3.5

Hence, the maximum price of a popcorn is $3.5

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Answer:

I believe its (-6, 7)

The image of D surely lies on the ray BA ,as ray BA is antiparallel to the ray BD.

Consider D’ to be the image of point D obtained ,when D is rotated 180 degrees anti-clockwise(or counter-clockwise),with B as center of rotation.

From the image above,it is clear that the rays BA and BD are antiparallel.

A ray is a segment of a line with a starting point and an infinite length in one direction.

Antiparallel rays are the rays which are parallel but oppositely directed.The angle between such rays is 180 degrees.

Hence,D’ must lie on the ray BA, as ray BA is antiparallel to BD(i.e the angle between the rays is also 180 degrees).

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Answer:The value of 147 + (-43) + (-16) is 88.

Step-by-step explanation:

88

its basically 147 - 43 - 16=88

CaTansposing The modeled function is given as,

For w = 72 kg and B.S.A = 1.9, height is calculated as follows,

Disposing root in L.H.S,

Calculating the value of h,

Thus the required value of height is 180.5 cm.

The solution set for the equation \(e^x\) = 15.49, expressed in terms of logarithms, is x ≈ ln(15.49).

To express the solution in terms of logarithms, we can take the natural logarithm (ln) of both sides of the equation. The natural logarithm of \(e^x\)is simply x, so we have ln(\(e^x\)) = ln(15.49). Applying the logarithmic property, we get x ln(e) = ln(15.49). Since ln(e) equals 1, the equation simplifies to x = ln(15.49).

Using a calculator to obtain a decimal approximation, we can find the value of ln(15.49) to be approximately 2.735. Therefore, the solution set for the equation \(e^x\)= 15.49, expressed in terms of logarithms, is x ≈ 2.735.

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Answer:

659x

Step-by-step explanation:

I think you mean 2x but here's how to do it.

So you have to remember an important phrase. Combine like terms. All that means is that terms that are alike go together.

Ex. 2 goes with 4, 83y goes with 26y

So basically you are adding it like it's a normal addition equation.

So, 2x + 657x=659x.

Hope you get an A! <3

Answer: 659x.

Step-by-step explanation:I think you mean 2x but here's how to do it.

So you have to remember an important phrase. Combine like terms. All that means is that terms that are alike go together.

Ex. 2 goes with 4, 83y goes with 26y

So basically you are adding it like it's a normal addition equation.

So, 2x + 657x=659x.

Answer:

I am

Step-by-step explanation:

I’m stuck on points

The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

What is the discriminant of a polynomial?

The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.

It is represented as ‘D’

D = b² - 4ac

Where,

a is the coefficient of x²

b is the coefficient of x

c is a constant term

x² + 5x + 4 = 0

We have given:

x² + 5x + 4 = 0

Comparing the equation with the standard form.

a = 1, b = 5 and c = 4

Substituting it in the formula

D = 5² - 4 × 1 + 4

By further calculation

D = 25 - 16

D = 9,

The quadratic roots are real and distinct

Therefore, the value of b² - 4ac is 9.

Hence, The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

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Answer: 25.6

Step-by-step explanation: Have an Amazing Day :)

Answer:

25.6 this will be the answer

Step-by-step explanation:

Hope it helps

The probability that there will be two long-furred dogs and three long-furred cats will be 0.2728.

Number of animals = 30

Number of dogs with long fur = 12/15 = 0.8

Number of cats with long fur = 11/15 = 0.73

The probability that there will be two long-furred dogs and three long-furred cats will be:

= (0.8)³ × (0.73)²

= 0.512 × 0.5339

= 0.2728

Therefore, the probability that there will be two long-furred dogs and three long-furred cats will be 0.2728.

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Answer:3/2

Step-by-step explanation: just did the test

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

In its simplest form, a scale factor is the proportion between the model measurement and the actual measurement. The scale factor, as opposed to a scale ratio, does not contrast various measurement units. A model car that is scaled at one-twentieth of its real-world counterpart is said to be that size. The car is also 20 times bigger than the model, according to this statement.

16 feet is the length of a fence. The fence is depicted as being 4 inches tall on a map. Write a ratio comparing the two quantities before attempting to calculate the scale factor of the drawing to the actual fence.

Given triangle side are 6, 6, 8 and scaled triangle is 9,9,12

The corresponding sides are

6/9, 6/9, 8/12

When you simply, we get

2/3, 2/3, 2/3

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

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Answer:

The APR reflects the interest rate plus the fees you paid directly to the lender or broker or both: origination charges, discount points and any other costs. Those fees add to the cost of the loan, and APR takes them into account. That's why APR is higher than the interest rate.

Step-by-step explanation:

Have a good day

Answer:

x = 2y

Step-by-step explanation:

we don't need to do complicated trigonometric conversions. just try to express x by a term of y (or vice versa) and look.

so, starting with x = 2y.

if that is the case, then what is our equation looking like ? is it true ?

sin(2y - y)/sin(y) + cos(y - 2y)/cos(y) = 2

sin(y)/sin(y) + cos(-y)/cos(y) = 2

1 + cos(-y)/cos(y) = 2

cos(-y)/cos(y) = 1

cos(-y) = cos(y)

and yes, this is indeed true for all y. cos decreases from 1 to -1 with the increase of the absolute value of the angle from 0 to 180 degrees (meaning we could go up or down the same angle from 0, and cos would be the same), and then increases again to +1 for the increase of the absolute value of the angle from 180 to 360 degrees. and then it all starts again. and again, and again, ...

so, since the original equation is true under the assumption x=2y, this must be the correct option.

The p-value for this z test statistic is equal to 0.0287.

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

The z test statistic can be calculated by using this formula:

\(t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }\)

Where:

In this scenario, the z test statistic for a one-tailed hypothesis test (lower tail) is equal to -1.9. Therefore, by using a t-distribution and z-score calculator for a normal distribution, the p-value for this test is given by:

P-value = P(t > -1.9)

P-value = 0.0287.

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Answer:

B. 180 degrees

Step-by-step explanation:

The straight angle represents 180°. Hence, option (B) is the correct answer.

The total number of red marbles in the vase are 10.

A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.

The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.

Now, according to the question;

Let 'x' be the red marbles in the vase.

Let 'y' be the orange marbles in the vase.

The total number of marbles in the vase are 60

x  + y = 60 (equation 1)

The ratio of red marbles to orange ones is 1:5.

Thus, x/y = 1/5

cross multiplying;

5x = y

or y = 5x

substitute the value of y in equation 1;

x  + y = 60 (equation 1)

x  + 5x = 60

6x = 60

x = 10  (red marbles)

Thus, the number of red marbles in the vase are 10.

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Answer:

12 and (-12)

Step-by-step explanation:

Solve for x.

x^2= 144

square root both sides and get,

x= 12

and

x= (-12)

remember to put your negative and 12 into parenthesis because you are multiplying the negative as well.

Answer:

x = 12

x = -12

Step-by-step explanation:

Step 1: Take the square root of both sides.

Therefore, x = 12 and x = -12 are the answers.

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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Based on the information, the person traveled 117.8 feet by the Ferris wheel.

Circumference = π×diameter

Keep the values in formula and perform multiplication to find the circumference of the wheel

Circumference = 50π

On 1 complete revolution of 360 degrees, the distance covered = 50π

So, revolution of 270 degrees, the distance covered will be = (50π/360) × 270

Performing multiplication and division on Right Hand Side of the equation

The distance traveled = 117.8 feet

Hence, the person travelled 117.8 feet.

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On solving the provided question, we can say that he probability there are women in positions thru and a woman in position  = 0.028

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Choose one woman from the list of 15 and place her in position 17. Then, take seven of the remaining fourteen, and nine of the males; permute them in positions one through sixteen. Next, swap the remaining individuals in positions 18 through 25.

(15/1)(14/7)(10/9)16!8! / 25! = 0.028

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Substituting the value of x and solving the function we get the value of y as y = 1

To evaluate the co-ordinate point (x, y) for the function

y = f(x) = -1.25x -0.25,

you need to substitute the value of x into the function and solve for y.

If x = -1,

then y = f(-1) = -1.25×(-1) - 0.25 = 1.25 - 0.25 = 1.

Therefore, the coordinate point (x, y) for the function:

y = f(x) = -1.25x - 0.25 when x = -1 is (-1, 1).

A function in mathematics is a collection of values connected by a predetermined rule or formula. The output value (also known as the dependent variable) is represented by a letter or a symbol that depends on the input value, whereas the input value (also known as the independent variable) is represented by a letter (such as x or y). Functions are frequently used to represent relationships between several numbers or to simulate real-world occurrences.

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Answer:

the answer is A. 0.48 $

Step-by-step explanation:

the price of ounce of the watermelon is :

\( \frac{5.76}{12} = 0.48 \: \)

The correct answer is option 2. Yes, the mean of the sample proportions is 0.6, which is the same as the population proportion.

To determine if the sample proportion is an unbiased estimator, we need to check if the mean of the sample proportions equals the population proportion. In this case, the population proportion of officers who are younger than 18 is given as 0.6. The sample proportions for all possible samples of size 2 are calculated and given in the table.
To calculate the mean of the sample proportions, we add up all the proportions in the table and divide by the total number of samples, which is 9.
Mean of sample proportions = (0 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 1 + 1 + 1) / 9 = 0.6
Since the mean of the sample proportions equals the population proportion, we can say that the sample proportion is an unbiased estimator.

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