How to solve 2-step equations

Answer:

1:2

Step-by-step explanation:

The total number of marbles is

3+5+8 = 16

blue : total

8 : 16

Divide each side by 8

8/8 : 16/8

1:2

Answer:

1:2

Step-by-step explanation:

There are 16 marbles in total. 3+5+8=16

8 of them are blue so it is 8:16 simplify 1:2

Answer:

A and B: slope = 0

S and T: slope = undefined    

Step-by-step explanation:

To find the slope of the line that passes between a pair of points, use the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\). Substitute the x and y values of two points into that formula and simplify.

1) Let's try this with the first problem. Substitute the x and y values of (4,5) and (-3,5) into the formula, then solve:

\(m = \frac{(5)-(5)}{(-3)-(4)}\\m = \frac{5-5}{-3-4} \\m = \frac{0}{-7} \\m = 0\)

So, the slope of the line between A and B is 0.

2) Do the same with the second problem, substituting the x and y values of (3,-6) and (3,-9):

\(m = \frac{(-9)-(-6)}{(3)-(3)} \\m = \frac{-9+6}{3-3} \\m = \frac{-3}{0} \\\)

However, we can't divide by zero. So, the slope between points S and T must be undefined.

The optimal solution to the LP is x1 = 0, x2 = 2, with an optimal objective function value of 2.

To use the formulas from section 6.2 of the textbook to find the optimal tableau, we need to start with the initial feasible tableau, which has the following form:

Basis x1 x2 s1 s2 RHS

s1 2 1 1 0 4

s2 1 1 0 1 2

z -1 1 0 0 0

The first step is to identify the pivot element, which is the smallest positive ratio of the right-hand side (RHS) to the coefficient of the basic variable in each row. In this case, the ratios are:

s1: 4/2 = 2

s2: 2/1 = 2

Since both ratios are equal, we choose the variable with the smallest coefficient in the objective function as the entering variable. In this case, that is x1.

The second step is to perform the pivot operation, which involves dividing the pivot row by the pivot element and subtracting a suitable multiple of the pivot row from each of the other rows to eliminate the x1 variable from them. The result is a new tableau:

Basis x1 x2 s1 s2 RHS

s1 1 0 1/2 -1 2

x1 1 1 0 1 2

z 0 2 1 1 2

The new tableau shows that x2 and s1 are the basic variables in the optimal solution, with values of 2 and 2, respectively. The optimal value of the objective function is also shown in the tableau, which is 2.

Therefore, the optimal solution to the LP is x1 = 0, x2 = 2, with an optimal objective function value of 2.

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Answer:

The distance from Jerusalem to Galilee is approximately 150 km depending on the route you take. You can get a bus from Jerusalem's central bus station to Tiberias, on the edge of the Sea of Galilee. The journey takes about 2-3 hours.Sep 4, 2019

Answer:

The club has 56 members

Step-by-step explanation:

We can set up a ratio problem to find the total number of kids in the club. There are two ways to do this, and I will show you both. The first way is to immediately set up a ratio between the number of boys and the number of total members in the club. Since the ratio of girls to boys is 6:2, the ratio of boys to members is 2:8 (add the number of girls and boys in the ratio to get the total number of people). Now, we can set up an equation, letting x equal the number of members total, and solve using cross multiplication:

\(\frac{2}{8}=\frac{14}{x}\\\\ 112=2x\\\\ x=56\)

The other way to solve this problem would be to figure out the number of girls in the club if there are 14 boys and then add the two quantities together. If we let y be the number of girls in the club, we get the following solution:

\(\frac{6}{2}=\frac{y}{14}\\\\ 2y=84\\\\ y=42\\\\x+y=56\)

Either way, we get that the total number of members is 56

Answer:

SACAN MÃ QR VÀ NHẬN CÂU TRẢ LỜI

VUI LÒNG ĐƯA TÔI Ở BRAINLIEST

Step-by-step explanation:

Answer:

Part A: Assuming the pattern continues, the next four terms in the sequence can be calculated as follows:

5/8, -6/9, 7/10, -8/11

To find the pattern, we observe that the numerator starts with 1 and increases by 1 each time, while the denominator starts with 4 and increases by 1 each time. The sign alternates between positive and negative.

Part B: To write the explicit equation for f(n) to represent the sequence, we can express the numerator and denominator in terms of n.

The numerator follows the pattern: n, -(n+1), (n+2), -(n+3), ...

The denominator follows the pattern: n+3, (n+4), -(n+5), (n+6), ...

Therefore, the explicit equation for f(n) is:

f(n) = (-1)^(n+1) * (n / (n+3))

Part C: To determine the sign of 7^(59) without calculating its value, we can consider the parity of the exponent (59).

Since 59 is an odd number, (-1)^(59) will be negative. This is because any odd exponent of -1 will result in a negative value.

Answer:

Step-by-step explanation:

Given:

Pattern:

\(-\frac{1}{4}, \frac{2}{5} , -\frac{3}{6}, \frac{4}{7}\)

Solution:

A) Your answer is correct.  The pattern is where the top is increasing by 1 each time and the bottom is increasing by 1 as well but starting at 4 and it switches from negative to positive so the next numbers will be:

\(-\frac{5}{8}, \frac{6}{9} , -\frac{7}{10} , \frac{8}{11}\)

B) Equation for f(n)

n is the number you are on.  

So for the first number \(-\frac{1}{4}\)   n=1 because that is the first number in the pattern.

For \(\frac{2}{5}\) ,  n=2    so on and so forth.

The top part of the equation is easier you can see that whatever n is the top is the same.

For the bottom part, add 3 because it's starts off 3 higher than n

So far we have:

\(\frac{n}{n+3}\)

Now we need to deal with the negative positive.  you can't just put a - in front  or multiply by a -1 because it would make it negative every time.

You would need to multiply by something that changes from neg to pos each time and we need to use exponents for that  \((-1)^{n}\)    See when n is odd, 1, 3, 5 it will produce a negative, but when n is even it will be positive.

Put it together:

\(f(n) = (-1)^{n}(\frac{n}{n+3} )\)

C) As discussed at the end of B F(59) = negative   because 59 is odd.

(-1)⁵⁹      will produce a negative answer so F(59 is negative

Answer:

x = 9

Step-by-step explanation:

first step, multiply both sides by 6. This is going to get rid of that fraction-looking situation on the left.

3x+9 / 6 = x - 3

6• 3x+9 /6 = 6(x-3)

On the left the 6s cancel (cancel is not a technical math term, but 6/6 is 1, so you are left with only the 3x+9)

3x + 9 = 6(x - 3)

Next, use distributive property on the right side.

3x + 9 = 6x - 18

Subtract 3x from both sides.

9 = 3x - 18

Add 18 to both sides.

27 = 3x

Divide both sides by 3.

27/3 = x

9 = x

x = 9

Answer:

3 yards

Step-by-step explanation:

12 divided by 4 equals 3.

The average rate of change of f is less than the average rate of change of g.

The symmetry axis for the functions f and g is either the same or different.The line that passes through the vertex's x value is known as an axis of symmetry. It is the line of symmetry, but for a quadratic equation, and it divides the equation in half.

By examining function f, we can determine the vertex's location by either the lowest point, or (-3, -10). This is so that the numbers before and after (-3, -10), which increase by the same amount, have the same interval as the x values. (For instance, the symmetric pairs x = -5 and x = -1 have y values of -2 and x = -4 and x = -2, respectively, have y values of -8.)

Consequently, x = -3 is the axis of symmetry for function F.because the vertex's x value is -3.The graph demonstrates that x = -3 is also the axis of symmetry for function g because an illustrative vertical line drawn through this value bisects the quadratic.As a result, the symmetry axis for the functions f and g is the same.

The relationship between f's and g's y-intercepts is (less than, equal to, greater than) Where an equation crosses the y axis is known as the y intercept. As x = 0 is the y axis, it always has a value of 0.Looking at function f, the y-intercept of the function is equal to 8 when x = 0.We can observe the y value of when the function g returns aOn the graph, the quadratic intercepts the y axis. It is y = -2.As a result, f's y-intercept is larger than g's y-intercept.The average rate of change of f is (equal to, less than, or greater than) the average rate of change of g across the range [-6, -3].The amount that the y value rises for each unit of x that passes is the rate of change.

For function f, we can see that the function declines by 18 between x = -6 and x = -3. The sum of the rate of change (the amount the y changed / difference between the x values of points) is therefore -18 / 3 = -6.For function g, we can see that the function grows between x = -6 and x = -3. In this instance y value, but we may calculate that it rises by around 9. 9 / 3 = 3.

The average rate of change of f is therefore lower than the average rate of change of g.

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Answer:

The value of x is 11 degrees

Step-by-step explanation:

Here, given that two angles are vertical angles, we are interested in calculating the value of x. We simply want to use an important property of vertical angles to get the value of x as given in the question.

When we talk of vertical angles, they are angles which lies on opposite side to each other when we have two intersecting line.

By property, vertically opposite angles are equal.

Thus, in this case, we are to equate the angles we are having since they are both vertical angles;

Thus,

Mathematically;

angle A = angle B

3x + 3 = 4x -8

Collect like terms;

4x-3x = 3 + 8

x = 11 degrees

Answer:

Xsquared +3x -28

Step-by-step explanation:

Use foil so first to the 3rs then first to the 4th then 2nd to the 3rd then 2nd to the 4th.

x squared minus 4x plus 7x minus 28

The derivative of y = 2^(3x^3-4) * log(2x + 1) is:

dy/dx = ln(2) * 9x^2 * log(2x + 1) + (2^(3x^3-4) * 2) / (2x + 1)

To differentiate the given function, we will use the chain rule and the power rule of differentiation. Let's start by differentiating each part separately.

1. Differentiating 2^(3x^3-4):

Using the power rule, we differentiate each term with respect to x and multiply by the derivative of the exponent.

d/dx [2^(3x^3-4)] = (d/dx [3x^3-4]) * (d/dx [2^(3x^3-4)])

Differentiating the exponent:

d/dx [3x^3-4] = 9x^2

The derivative of 2^(3x^3-4) with respect to the exponent is just the natural logarithm of the base 2, which is ln(2).

So, the derivative of 2^(3x^3-4) is:

d/dx [2^(3x^3-4)] = ln(2) * 9x^2

2. Differentiating log(2x + 1):

Using the chain rule, we differentiate the outer function and multiply by the derivative of the inner function.

d/dx [log(2x + 1)] = (1 / (2x + 1)) * (d/dx [2x + 1])

The derivative of 2x + 1 is just 2.

So, the derivative of log(2x + 1) is:

d/dx [log(2x + 1)] = (1 / (2x + 1)) * 2 = 2 / (2x + 1)

Now, using the product rule, we can differentiate the entire function y = 2^(3x^3-4) * log(2x + 1):

dy/dx = (d/dx [2^(3x^3-4)]) * log(2x + 1) + 2^(3x^3-4) * (d/dx [log(2x + 1)])

dy/dx = ln(2) * 9x^2 * log(2x + 1) + 2^(3x^3-4) * (2 / (2x + 1))

Therefore, the derivative of y = 2^(3x^3-4) * log(2x + 1) is:

dy/dx = ln(2) * 9x^2 * log(2x + 1) + (2^(3x^3-4) * 2) / (2x + 1)

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Answer:

100-(12+28+12+15)

100-(67)

100-67=33

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

2e-3c

=10-9

=1

2x5 - 3x3

10-6=4

replace the letter with the numbers

With 95% confidence, there is a statistically significant difference in the proportion of patients who developed polyps. Taking an aspirin a day appears to be effective in reducing the chance of developing subsequent polyps.

According to the study done by the Ohio State University Medical Center, a 95% confidence interval on the difference in proportions of the two groups [aspirin group (p1) minus non-aspirin group (p2)] was found to be -0.164 < p1 - p2 < -0.036. This means that the probability of the difference in the proportions of polyp development in the aspirin group and the non-aspirin group is between -0.164 and -0.036 with 95% confidence level. Since the interval doesn't contain zero, it indicates that there is a statistically significant difference in the proportion of patients who developed polyps between the two groups. Therefore, taking an aspirin a day appears to be effective in reducing the chance of developing subsequent polyps.

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This is the quarterly interest rate on the account. Rounded to four decimal places, the base of the exponential expression is 1.032.

To rewrite the function representing account C to reveal the quarterly interest rate on the account, we can rewrite the function in the form:

C(t) = C0\((1 + r)^{(nt)}\)

Where C0 is the initial amount of money in the account, r is the periodic interest rate, and nt is the number of periods over which the interest is compounded.

Substituting the values in the function,

3,000\((1.032)^{2t}\) = C0\((1 + r)^{(2t)}\)

Dividing both sides by C0, we get:

\((1.032)^{2t}\) = \((1 + r)^{(2t)}\)

Applying logarithms on both sides,:

2tln(1.032) = 2tln(1 + r)

Solving for r, we get:

r = ln(1.032)/2 = 0.0159/2 = 0.00795

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There are probability of total of 5 x 6 = 30 ways to roll 4 dice with the same number and 1 die with a different number in this case.

To calculate the number of ways to roll 4 dice with the same number and 1 die with a different number, we need to consider two cases: the die with the different number can either be the first die or one of the other four.

If the die with the different number is the first die, then there are 6 choices for its value. The remaining 4 dice must all have the same value, which means there is only 1 choice for their value. Therefore, there is a total of 6 ways to roll 4 dice with the same number and 1 die with a different number in this case.

If one of the other four dice has a different number, then there are 5 choices for which die will have the different number. There are also 6 choices for the value of that die.  

The remaining 3 dice must all have the same value, which means there is only 1 choice for their value. Therefore, there are a total of 5 x 6 = 30 ways to roll 4 dice with the same number and 1 die with a different number in this case.

Adding up the two cases, we get a total of 6 + 30 = 36 ways to roll 5 dice with 4 dice having the same number and 1 die having a different number.

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The function that has a horizontal asymptote at y = 1 include the following: D. graph of function D.

In Mathematics and Geometry, a horizontal asymptote is a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the horizontal line passing through the ordered pair (1, 8) on the graph of this rational function represents a horizontal asymptote and it has an equation of y = 1, as shown in the image attached above.

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Answer:

Step-by-step explain

3n - 2 = n + 10.    add 2

3n = n + 12           subtract n from both sides

2n = 12.                divide by 2

N = 6

Answer:

Both pass there all higher the 50%

Step-by-step explanation:

Slope , m , betwen the two points

(y1-y2) / (x1-x2) =  (-2 -2) /(5-7) = -4/-2 = 2

SO  y = mx + b form would be

        y = 2x + b

              sub in one of the points to calculate 'b'

           -2 = 2(5) + b    shows b = -12

  so equation is   y =  2x -12  

Answer:

  the rule for repeated denominator factors applies

Step-by-step explanation:

You want to know why is there not a separate rule in the partial fraction decomposition key idea for what to do if you have a cubic function in the denominator of a rational function.

The rule for repeated denominator factors is that there is a fraction in the partial fraction sum for each power of the denominator factor up to its greatest power.

  A(x)/B(x)^n = a1(x)/B(x) + a2(x)/B(x)^2 + a3(x)/B(x)^3 + ... +an(x)/B(x)^n

This rule applies to cubic factors as well as factors of any other power.

__

Additional comment

The attached calculator display shows an example of a repeated factor.

<95141404393>

There is no separate rule in the partial fraction decomposition key idea for what to do if you have a cubic function in the denominator of a rational function because the general method can be applied to any rational function regardless of the degree of the denominator.

Partial fraction decomposition is the process of decomposing a rational function to a sum of simpler fractions. It is a technique used in the integration and simplification of algebraic expressions. The partial fraction decomposition key idea is a method for separating a rational function into its parts so that it can be more easily manipulated.

1: Factorize the denominator of the rational function into linear factors.

2: Write the partial fraction decomposition of the function as a sum of simpler fractions, with each term having a denominator that matches the factors.

3: Determine the unknown coefficients by equating the coefficients of like terms in the original function and its partial fraction decomposition.

The degree of the denominator does not affect the general method of partial fraction decomposition.

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Answer:

I think it's 4 and why do I have to write 20 letters?

Answer: QR = 6 units

Step-by-step explanation:

QR + RS = QS

2x + x + 7 = 16

3x = 9

x = 3

QR = 2x = 2*3 = 6

First, let's list all the possible arrangements of the digits 2, 4, and 6 with a decimal point between two digits: - 2.4.6
- 2.6.4
- 4.2.6
- 4.6.2
- 6.2.4
- 6.4.2

Now, we need to find the sum of every number less than 4.4 than grogg writes. This means we need to add up all the numbers that are less than 4.4 and are also less than each of the six numbers on our list.

Let's start with the first number on our list, 2.4.6. The numbers that are less than 4.4 and less than 2.4.6 are:

- 2.4
- 2.6

So we add those two numbers together:  2.4 + 2.6 = 5, That's the sum for the first number on our list. Now we can repeat this process for each of the other five numbers on our list, and add up all the sums at the end. For 2.6.4, the numbers less than 4.4 and less than 2.6.4 are: - 2.6 .

So the sum for 2.6.4 is:  2.6, For 4.2.6, the numbers less than 4.4 and less than 4.2.6 are:
- 4.2
- 4.6, So the sum for 4.2.6 is: 4.2 + 4.6 = 8.8, For 4.6.2, the numbers less than 4.4 and less than 4.6.2 are:
- 4.2
- 4.6

So the sum for 4.6.2 is:
4.2 + 4.6 = 8.8

For 6.2.4, the numbers less than 4.4 and less than 6.2.4 are:

- None

There are no numbers less than 4.4 and less than 6.2.4, so the sum for 6.2.4 is 0.
Finally, for 6.4.2, the numbers less than 4.4 and less than 6.4.2 are:
- None

Again, there are no numbers less than 4.4 and less than 6.4.2, so the sum for 6.4.2 is 0.
Now we can add up all the sums:  5 + 2.6 + 8.8 + 8.8 + 0 + 0 = 25.2

So the sum of every number less than 4.4 than grogg writes is 25.2.

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Step-by-step explanation:

Uh, uh, uh, uh

Day and night (what, what)

I toss and turn, I keep stressing my mind, mind (what, what)

I look for peace but see I don't attain (what, what)

What I need for keeps this silly game we play, play

Now look at this (what, what)

Madness to magnet keeps attracting me, me (what, what)

I try to run but see I'm not that fast (what, what)

I think I'm first but surely finish last, last

'Cause day and night

The lonely stoner seems to free his mind at night

He's all alone somethings will never change

The lonely loner seems to free his mind at night (at, at, at night)

At, at, at, at, at, at night

At, at, at, at, at, at night

Hold the phone (what, what)

The lonely stoner, Mr. Solo Dolo (what, what)

He's on the move can't seem to shake the shade (what, what)

Within his dreams he see's the life he made, made

The pain is deep (what, what)

A silent sleeper you won't hear a peep, peep (what, what)

The girl he wants don't seem to want him to (what, what)

It seems the feelings that she had are through, through

'Cause day and night

The lonely stoner seems to free his mind at night

He's all alone through the day and night

The lonely loner seems to free his mind at night (at, at, at night)

Day and night

The lonely stoner seems to free his mind at night

He's all alone, some things will never change (never change)

The lonely loner seems to free his mind at night (at, at, at night)

Day and night

The lonely stoner seems to free his mind at night

He's all alone somethings will never change

The lonely loner seems to free his mind at night (at, at, at night)

At, at, at, at, at, at night

At, at, at, at, at, at night

At, at, at, at, at, at night

At, at, at, at, at, at night

Explanation:

We follow PEMDAS in reverse to undo every operation that is applied to variable x

Doing so will lead to the following

t = 0.4x + c

t - c = 0.4x

0.4x = t - c

x = (t - c)/(0.4)

The last equation is the same as writing \(x = \frac{t-c}{0.4}\) which is what choice B shows.

Confounding may invalidate the conclusions of the study as it can cause a bias that can make the effect of the explanatory variable look larger or smaller than it actually is.

This means that the relationship between alcohol drinking status and incidence of lung cancer is influenced by  After the classification of smokers and non-smokers, a separate analysis can be done to find the effect of alcohol drinking on lung cancer in both groups.

Explanatory and Confounding Variable in the study :In the given study, the explanatory variable is obesity and the response variable is coronary disease. Whereas, the confounding variable is hypertension and diabetes because these diseases are associated with obesity. The confounding variable can invalidate the conclusions of the study as it can affect the relationship between obesity and coronary disease .To eliminate the effect of the confounding variable, the study can be changed in the following ways.

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